SPH4UMotion Diagnostic

Match the quantity to its symbol, definition, expression and example. Then write whether it is a vector or scalar. (Not all of them have expressions)

Name Symbol Definition Expression Example Vector or Scalar

Time

Time interval

Distance

Position

Displacement

Speed

Velocity

Definitions: How fast you are moving Distance from a reference

point, with direction Amount of time that has

passed How much ground you

covered Change in position Change in position over

time, with direction A value read from a clock

Symbols:

∆t, , v, , t, ∆, d

Expressions:

, , ,

,

Examples: 356 km 4:06 am 56 mm/min [W] 12 cm [East of Toronto] 2 min, 38 s 42 miles [N] 12 m/s

Name that Quantity (and write the symbol)

(time, time interval, distance, position, displacement, speed, velocity)(t, ∆t, d, , ∆ , v, )

Quantity: Name: Quantity: Name:

35 miles Distance (d)_ 4.5 ms _________________

4:05 pm __________________ 36 km/h _________________

22 m [N] __________________ 15 cm _________________

24.5 m/s [up] __________________ 182 km [NE] _________________

12 miles __________________ 3600 km [East] _________________below ground of Paris

3.62 hours __________________ 18 cm / min _________________

36.72 feet/s __________________ 12 knots [SW] _________________[diagonal]

58 min [up] __________________ 34 m out from the _________________shore

12.4 km __________________ 18 cm [right] _________________

Midnight EST __________________ 36 m/s [W] _________________

12 h 15 m 32 s __________________ 13.2 km/min [back] _________________

5 feet 9 inches __________________ 12 miles [N] of here _________________

Match the position-time graphs to the descriptions

Not moving, positive position

Not moving, negative position

Slow, forward motion

Fast, forward motion

Slow, backwards motion

Fast, backwards motion

A B C

D E F

Speeding up in the negative direction

Slowing down in the negative direction

Speeding up in the positive direction

Slowing down in the positive direction

G H I

J

Match the velocity-time graphs to the descriptions

Negative constant motion

Slow, positive acceleration High, positive acceleration

Slow, positive constant motion

A B C

D E F

Fast, positive constant motion

Negative acceleration

High, negative acceleration

Slowing down to a stop then speeding up the other way

G H

SPH4U – Measuring the acceleration of gravity with a LabQuest

1. Plug the photogate into the “DIG-1” input on the right side of the LabQuest2. Turn the LabQuest on3. Click “sensors” and “sensor setup”4. Go down to “DIG-1”. Click on the dropdown menu arrow and select “photogate”5. Click “OK”6. The LabQuest is ready to begin. Drop the Fence through the photogate and it will

begin recording automatically (it will also stop automatically). You will now have a position-time graph and a velocity-time graph

7. Click on “analyze” and then “curve fit”a. First fit your “distance”-time graph

i. What do you expect the relationship to be between d and t? Use your kinematic equations to get an expression for d in terms of t (this is what we did in class and will also be part of your write-up)

ii. You can try all of the fits, but you will notice that one fits best. Which one is it? Explain why.

b. Now fit your “velocity”-time graphi. What do you expect the relationship to be between v and t? Use

your kinematic equations to get an expression of v2 in terms of tii. Which model fits best? Explain why.

iii. Write down the slope of the line you get and compare it to the accepted value of g = 9.81 m/s2.

8. Repeat the experiment 4 times, but only fit your velocity graph. Write down all values of ‘g’ from the slope of your v-t graph and fill in the table below.

Trial Slope of v-t graph

1

2

3

4

5

Average Slope: ______________ m/s2

DELIVERABLES – mini lab write-up1. PROCEDURE: [C] Explain the steps of performing the experiment (not analyzing

the information in LabQuest, just the steps involved in setting up the photogate on a retort stand, dropping the picket fence through, catching it, etc.) Number the steps, “1. …”, “2. …”. No personal pronouns “I” or “we”. Write in past tense. You shouldn’t need more than 5 steps – just enough so someone else could repeat the experiment.

2. THEORY: [C] Use your kinematic equations (as we did at the start of the lesson) to derive an expression of (a) d in terms of t and (b) v in terms of t. Summarize the information with a couple of sentences. E.g. “It is expected that there will be a squared relationship between … as seen from the expressions derived above.”

3. RESULTS: Copy the table of slopes from the 5 trials you did. Find the average value for ‘g’ and compare it to the accepted value of 9.81 using a % difference. Show your work.

% difference = 100 x (measured value – accepted value) / accepted valueWrite “The experimental average differs from the accepted value of 9.81 m/s2 by ____ % “.

4. DISCUSSION / ERROR ANALYSIS: [C, A]

Write down at least two sources of experimental error. Comment on magnitude of the errors. Estimate how large the error might have been. Something like this:“Sources of experimental error:

1. Very slight air resistance would have caused a ___________ second difference.

2. ………… “

Also write down and explain one additional reason why your value is different from the accepted value (HINT: it’s related to your latitude on Earth).

How does your answer to the previous question affect Athletes competing for records in different locations on Earth?

Entire Lab Write-up: LESS than 2 pages

Projectile Motion Applet Questions:

http://www.ngsir.netfirms.com/englishhtm/ThrowABall.htm

Begin with the platform at 100 m. Fire off a shot.1. Describe the shape of the motion [parabola]2. What forces are acting on this projectile in this simulation? [gravity only]. If

they say “air resistance”, ask them what air resistance depends on [surface area] and ask them if the object in the simulation has any surface are.* get them to realize theoretically, a projectile is imagined as a single point in space with no volume, only mass. Therefore, gravity is the only force acting on it. These obviously incorrect assumptions allow us to analyze the motion of many falling things very easily and surprisingly accurate.

3. Describe the motion in the horizontal plane [if only gravity acts on it, what happens to its horizontal velocity?]* add a grid to the simulation so they can see equal spacing

4. Describe the motion in vertical plane* have students see that vertical displacement increases every time

5. Getting back to baseball – show that the simulation does have the largest range for a 45 degree shot by comparing it to 40 degrees and 50 degrees (which should give the exact same range)

6. Bring the platform down to 0 m. Fire it at 45 degrees and note the range and the time. Then fire it at 20 degrees. It will go less than half the distance, but it will take more than less than half the time.

Name: _______________________SPH4U – Projectile Motion Quiz

1. A seaplane is carrying water to drop over a forest fire, traveling horizontally at 112 km/h. It releases the water when the fire is 2.45x102 m ahead, horizontally, and the water lands directly on the fire, putting it out. How high is the helicopter above the ground? (HINT: use motion in the horizontal (x) dimension first)

Name: _______________________SPH4U – Projectile Motion Quiz

1. A seaplane is carrying water to drop over a forest fire, traveling horizontally at 112 km/h. It releases the water when the fire is 2.45x102 m ahead, horizontally, and the water lands directly on the fire, putting it out. How high is the helicopter above the ground? (HINT: use motion in the horizontal (x) dimension first)

SPH4U – Lab ActivityChapter 2 – Forces

Using Newton’s 2 nd Law to Measure Mass

[A] Expected Value:

Measure and record the mass of the cart:

M = _________________ kg

[B] Deriving the Theory:

1. Draw a system diagram of the setup and a FBD2. Write FNET = mTa and analyze the forces acting on the total system. Write

all forces in terms of the mass of the cart, M, mass on the pulley, m, a, g and inclination angle, θ

3. Derive your expression for M in terms of m, g, a, and θ.

[C] The Experiment:

1. Stick the picket fence along the top of a dynamics cart2. Set up an inclined ramp with a photogate near the centre, that will

measure the picket fence as the cart goes up the ramp3. Measure the angle of inclination and put it in the top left of table 1 below4. Place 250 g on the pulley and record it in the table5. Release the apparatus so that the LabQuest creates a velocity-time graph

of the picket fence as it passes through. Be careful to catch the falling mass and cart once the fence has passed through

6. Use LabQuest to fit a linear model to your velocity data. The slope of the line represents the acceleration

7. Fill in your table8. Repeat 2 more trials for that mass and fill them in the table9. *** change the mass on the pulley to 350 g and repeat steps 5-7 (3 more

trials with a new mass)10.*** if you have time, increase the angle of inclination and repeat the

experiment, filling in the second table

[D] Results:

1. Use each acceleration from every trial and your theory from part [B] to estimate the mass of the cart, M. Fill them into table 3.

2. Circle any outliers in your data (measurements of M that seem very different from the others)

3. Compare your overall average mass to the measured mass in part [A] using % difference. If you had any outliers from single trials, circle it and don’t include it when you calculate the mean mass, M, for the 3 trials.

[E] Discussion: to be written in paragraph form, including:

1. Describe any sources of error / assumptions in your experiment with detail. You should have at least 3.

2. Explain the benefits of performing 3 trials for each mass, using two different masses and 2 different angles. What errors are reduced by doing this?

3. Estimate the effect a +/- 10 g error in the pulley mass, m, would have on your result for M for any given trial. To do this, use your theory equation, add (and subtract) 10 g to “m” for a few different trials of different masses and angles (choose a good selection), and see the % error effect it has on M. Summarize your results with 1-2 sentences. SHOW how you did this calculation.

4. Repeat step 4, estimating the effect of a +/- 1 g error in the pulley mass.5. Repeat step 4 estimating the effect a +/- 2º error in the measurement of

the angle could cause (a reasonable error in this experiment).6. Using your answers from 1-7 explain any discrepancies between your

measured M and your experimentally determined M. If your answers are extremely close, then comment on the effectiveness of the experiment. If your estimate of M is too high, explain why. If it is too low, explain why. You must justify.

[F] Deliverables: *** refer to lab guidelines posted online1. A cover page2. Purpose: 1 sentence explaining the purpose of the experiment.3. Introduction: a few sentences describing the theory behind the

experiment. You will have to introduce Newton’s second law here briefly, draw a diagram of the setup, and derive the theory you will be using.

4. Procedure: draw a diagram of the setup and a step-by-step list of steps performed, not including your analysis. Write your steps in past tense with no personal pronouns (approx. ½ page)

5. Observations: reproduce the three tables in your report. Remember to include overall % difference

6. Discussion: your answers to the questions in part [E], in full paragraph, with full sentences. You may do your calculations by hand on a separate sheet and refer to it in your discussion, or do it with MS Word equations. NB: If you don’t have MS Word equations built in, you must write them out by hand. Because:

V = √gM/r^2 looks awful and unclear.

Table 1:Angle 1: _____ º Trial 1: Trial 2: Trial 3: Mean:m1 (kg) = m1g = a = a = a = a =

m2 (kg) = m2g= a = a = a = a =

Overall mean acceleration for angle 1: a* =

Table 2:Angle 2: _____ º Trial 1: Trial 2: Trial 3: Mean:m1 (kg) = m1g = a = a = a = a =

m2 (kg) = m2g= a = a = a = a =

Overall mean acceleration for angle 1: a* =

Table 3: Calculating Estimated Mass: Use your theory equation from class to calculate an estimated mass, M of the cart + picket fence.

Angle mpulley Trial 1 Trial 2 Trial 3 Mean

1: ______ m1: ____ M = M = M = M =

1: ______ m2: ____ M = M = M = M =

2: ______ m1: ____ M = M = M = M =

2: ______ m2: ____ M = M = M = M = Overall average mass, M (average the entire last column)

M = _____

SPH4U – Mini-Lab – Friction

Using a Newton-meter and a wood block, answer the following:

What is the relationship between FN and Fk?

[A] Wood on Desk

Note: mass of the test tube rack = 240 g.

Trial m (kg) FN = mg Fk (N) Fk / FN1

2

3

4

5

[B] Wood on Paper Towel

Trial m (kg) FN = mg Fk (N) Fk / FN1

2

3

4

5

Questions:

1) Is there a pattern in the ratio of Fk/FN? If so, what is it?

2) How does the ratio of Fk/FN for the paper towel compare to the ratio for the desk? Why is this?

http://www.engineeringtoolbox.com/friction-coefficients-d_778.html

SPH4U – Centripetal Force Activity

For an object undergoing uniform circular motion with a speed v and radius r the following equation holds:

(1.1) Σ F = mac

Where i) ac = v2/r ii) ac = 4πr/T2 iii) ac = 4π2rf2

Choosing expression (iii) we have

(1.2) Σ F = ms(4πr2f2)

In this activity you will verify the above equation for a rubber stopper being swung in a circle of radius r. ms represents the mass of the stopper. See diagram 1 below.

The centripetal force will be supplied by a mass hanging downwards from the hand piece.

(1.3) Σ F = ms(4πr2f2)

(1.4) mag = ms(4πr2f2)

Where ma is the hanging mass.

Diagram 1: Experimental setup to verify Newton’s theory for horizontal circular motion

Theory:

Rearrange the equation (1.4) to solve for frequency, f, and write it below.

Constants:

g = 9.81 m/s2

r = 70 cm = 0.70 mms = 50 g = 0.050 kg

Rubber stopper

Hanging mass

Predictions: Use the equation and the above constants to predict frequencies of motion for the hanging masses given in the table below.

Table 1: Frequencies predicted from Newton’s theoryms (kg) f (Hz – revolutions per second)0.150

0.250

0.350

0.450

Experimental Data:

Now swing the rubber stopper for each given mass at a constant speed such that the radius stays constant at 0.70 m. Time 10 revolutions. Fill out the table below.

Table 2: Frequencies determined through experimentationms (kg) Δt (s) for 10 revolutions

***Perform 3 trialsAverage Δt (s) Frequency,

f = 10 / Δt (Hz)0.150

0.250

0.350

0.450

Comparison:

1) For each hanging mass, compare your experimental data with your theoretical predictions using % difference (include all 5 calculations)

2) Account for differences in your experimental and theoretical data with an error analysis (one one paragraph needed)

Deliverables: (informal lab)

1. One page with:a. The purpose of the lab [1 mark]b. A labeled diagram of the apparatus showing how you will be spinning the

stopper in a horizontal circle (I suggest drawing it bird’s eye view) [3 marks]

c. A derivation of the equation you are testing (similar to what you did on page 1 of this document) [5 marks]

Make sure you explain every step with one statement

2. Hand in these tables (no need to reproduce them unless they are very messy) [3 marks]

3. Answers to your comparison questions [3 marks]

Total marks: 15

SPH4U – Centripetal Force Assignment

1. A Bola, an ancient weapon, consists of a stone sphere attached to a rope, which is swung in a horizontal circle, above the hunter’s head, and released to hit a target near the hunter. A bola of mass 4.5 kg and radius 2.3 m is being used to hunt a dangerous cougar. The rope’s breaking tension is 127 N.

a. What is the maximum speed it can be swung without breaking? [3 marks]b. What is the frequency of the swing? [2 marks]c. If the bola is released horizontally at that maximum speed from your

height (in m), how far away, horizontally, will it land? (yes, this is a projectile motion problem) [5 marks]

2. A car traverses a curve of radius 97 m. Assuming a frictionless surface, determine the required banking angle for the car to make it safely around the turn with a speed of 82 km/h. * Show all of your work: include a system diagram as well as force equations in both dimensions [10 marks]

3. A yo-yo master is swinging a yo-yo in an “around the world”, a vertical circle. The yoyo has a mass of 0.240 kg and the length of the string is 1.7 m. It is swung slow enough such that the tension in the string at the top of the circle just approaches zero.

a. Draw an FBD of the yoyo at the top of the circle. [1 mark]b. Use your FBD to find the speed of the yoyo. [4 marks]c. What is the centripetal acceleration? [2 marks]d. What is the tension in the string at the bottom of the circle? [3 marks]

4. According to astronomers, the moon is not moving in a uniform circle, but rather is getting farther away from the Earth every year, by a few cm. Is the moon moving too fast or too slow to stay in a uniform circle? Explain your answer in 1-2 sentences. [2 marks]

5. A Ferris wheel (the ride that goes in vertical circles) at an amusement park somehow falls off its support and rolls along the ground.

a. If it’s radius is 22 m, how many rotations would the wheel have to make, travelling in a straight line, to make it to Winnipeg? State all assumptions and show all calculations. [5 marks]

b. Imagine that you are sitting on a Ferris wheel undergoing uniform circular motion. Use a centripetal acceleration equation to show how you could determine the radius of the ride using a stopwatch and a vertical accelerometer (the tool that measures acceleration at Canada’s Wonderland using a vertical mass attached to a spring). [5 marks]

Name: ________________________SPH4U – Kinematics Quiz [30 mins]

1. An eagle, chasing a mouse on the ground, flies 271 m [E10N] and then 480 m [N30W]. The entire trip takes 2.4 minutes. Calculate: [8 marks]a) The total displacement (you may use either components or cosine law methods)b) The average velocity* marks are given for correct notation, labeling and equations.

2. A motorboat coasting at speed v1 spots a passing shark and accelerates to catch up with it. The motor has a constant acceleration of 4.3 m/s2 and catches the shark moving at a speed of 42 m/s [6 marks]a) If the boat catches up to the shark in 104 m, what was its initial velocity?b) How long did it take the boat to catch the shark?

Name: ________________________

SPH4U – Test 1Kinematics and Forces

Total Marks: _________ / 33 (27 for extra time students)

Extra time students do not answer questions marked with [X] and shade in this box: [ ]

Formulas:

Fg = mg ΣFx = max ΣFy = may v = ∆d/∆t d = v1∆t + ½ at2

v22 = v1

2 + 2a∆d v2 = v1 + a∆t d = v2∆t - ½ at2 g = 9.81 m/s2 [down]

Part A: True or False – circle either “T” or “F” and if the answer is false, explain why and/or give a counter example with one sentence. [9 marks] [T, A, K]

1. A person moving East cannot be experiencing a net westward force: T / F

[X] 2. The acceleration of gravity is larger in Mexico than it is in Toronto: T / F

[X] 3. Nanometers per hour per decade is a possible unit for acceleration: T / F

4. One possible unit of weight is the kg: T / F

5. An arrow is fired directly upwards. At the top of its path, the magnitude of its acceleration is zero: T / F

Part B: Calculations [20 marks]

1. A boat has to reach an aquatic destination 56 km [E28°S] in 72 minutes. It is moving in a water current of 31 km/h [N]. You will only be setting up this problem, not solving. a) Write a vector equation solving for the velocity of the boat relative to the water. Use only symbols and subscripts, no numerical values.[2 marks]b) Draw a vector diagram for your above equation. Label all angles, magnitudes and vectors appropriately with subscripts. [3 marks, K, C]

2. A mountain climber is using a rope to hang against a vertical cliff, shown below. The tension in the rope is 862 N [31°below the horizontal] and the climber is still. Determine:a) The mass of the climber [4 marks – 2 for a FBD, K, C][X] b) The force of the cliff on the climber’s feet (i.e. the normal force). [2 marks, K]

3.In a football game, a player of mass 96.2 kg dives to catch a pass and slides 4.3 m along the ground coming to a stop in 1.6 s. Determine the force of friction acting on the player [3 marks, K]

4. A movie stuntman, running across a rooftop has to make a jump to an adjacent building’s rooftop, a distance of 6.2 m horizontally and a drop of 4.8 m. He jumps with an initial velocity of 5.5 m/s [40° above the horizontal]. Will he make it, or will he fall into the safety net? Assume no air resistance [6 marks, K]

Part C: Communication [5 marks]

[X] 1. A black mamba, the world’s fastest snake can achieve speeds of 12 mph. It looks like it slides without friction across the ground. Use Newton’s 3rd law to explain how it is able to propel itself forwards. Maximum 3 sentences. [2 marks, C, A]

2. Imagine you are moving North in an open convertible at a high speed, with no seatbelt on. You notice a raccoon on the road and swerve sharply to the left. Doing so seems to cause your body to swing to the right and you end up in the passenger seat. Use Newton’s first law to explain why you *feel like* you are being thrown to the right. It may help to consider a bird’s eye perspective, i.e. you are looking down on the open car from above. Maximum 3 sentences [2 marks, C, A]

END OF TEST

Total Marks: 34 you will be rewarded for showing all equations and work, as well as using

appropriate labels you will be deducted for not showing all work or not using appropriate labels

1. A man is dragging a 190 kg box along the floor shown below. He pulls at an inclination of 48° and there is 670 N of tension in the rope. The box is accelerating horizontally forward at a rate of 0.25 m/s2. a) Draw a FBD for the box showing ALL forces acting on it [2 marks]b) Calculate the force of friction between the box and the floor [4 marks]c) Calculate the normal force acting on the box [4 marks]

2. Two blocks are hung vertically from opposite ends of a pulley, as shown below. There is 23 N of friction inside the pulley’s rotating mechanism. Calculate:

a) The acceleration of the system (include an FBD) [6 marks]

b) The tension in the rope [4 marks]

3. Two blocks, connected by a rope are setup on a frictionless pulley/ramp system shown below.

a) What is the acceleration of the system (include FBD)? [6 marks]b) What is the tension in the rope? [4 marks]c) What mass of block A would keep the system in equilibrium (assuming same

mass of B and zero friction)? [4 marks]

a = 0.25 m/s2

Write a full solution to the following 4 questions

You will be marked on:

Neatness and order of solution:o Diagrams are at least ¼ of a page and drawn with rulers, with accurate

angleso GRASP stepso Vectors notationo Unitso Significant Digitso Indicate positive directions in X and Y dimensions

Correctness Make sure to convert all units (e.g. m, s, m/s, etc.)

1. A car heads 42 km/h [E]. After 1.2 minutes, its final position is 1.3x103 m [W] of a building. What is its initial position from the building? [5 marks] [C, K] (Be careful with directions for this one! Draw a diagram of what is happening)

2. A swimmer attempts to swim across Lake Ontario at 2.5 m/s [N40°E]. The current is moving at 1.2 m/s [N24°W]. Calculate her resultant velocity. Use the triangles/cosine law method. [6 marks] [A, C]

3. A cat, chasing a bird, runs from its house (H) to the mailbox (M) with a displacement of 13 m [N]. It runs from the mailbox (M) to the sidewalk with a displacement of 8.0 m [N34°W]. Finally, the cat runs down the sidewalk with a displacement of 6.2 m [W20°S]. The entire run takes 38 sh. Calculate: [12 marks] [T, K]a) The cat’s total distance traveledb) The cat’s average speedc) The cat’s total displacement (Use components method – and make sure to draw each displacement separately)d) The cat’s average velocity

4. Reaction time is crucial to avoiding a traffic accident. It is the time between when you see a red light, or other obstruction, and when your foot begins to press on the brake. You are driving at 56.0 km/h [E] when you notice a fallen tree 32.0 m in front of you. Applying the brakes, you come to a stop just before the tree. Your brakes provide a constant acceleration of - 5.20 m/s2 [E]. You cover a certain distance while reacting to the obstruction and traveling at a constant speed, and a certain distance while decelerating the car. [7 marks] [A, K]a) How long will it take your car to stop after the brakes are applied?b) How far will you travel in that time?c) How far did your car travel while you were reacting (i.e. before you hit the brakes)?d) What is your reaction time?

SPH4U – MinilabQuantifying the force in a spring, Fx

Purpose: to determine the equation for the force being applied by a spring, Fx in terms of the distance it is being stretched, x.

The setup is shown below:

Adding mass to the spring will cause it to stretch. Once you stop the spring from vibrating (you will have to stop it), it will reach a new equilibrium where the force applied by the spring upwards, Fx, will balance the force of gravity on the hanging mass, mg. The distance the spring has stretched from its initial length is ‘x’.

Since the forces are balancedFx = mg

OBSERVATIONS

Apply various masses to the spring and measure the stretch. Remember – the stretch distance is not the full length of the stretched spring. Fill out the table below. You must have the (0, 0) data point and 5 additional data points

mass (kg) Fx = mg (N) x (m)0 0 0

Total marks: 14 Value: the value of a HW assignment

GRAPH AND CALCULATIONS

1) On graph paper, plot stretch, x, on the x-axis, vs. Fx on the y-axis. Include all data points, including (0, 0). Make sure the graph is drawn neatly with a ruler and everything is labeled appropriately [5 marks]

2) Draw a line of best fit [1 mark]

3) Determine the slope of the line, with correct units. Show the points you are choosing to do this on the graph, and show your work on the back of the graph paper [3 marks]

4) Write an equation for your line in the form y = mx + b, but using the variable names Fx and x. [1 mark]

5) What is the unit for the slope? In 1-2 sentences, explain, in plain English what the unit means [2 marks]

6) Use LabQuest to determine the slope of your graph (see instructions below). Write down the LabQuest-determined slope and compare it to your hand-determined slope using % difference. [2 marks]

Using LabQuest to determine slope

Click on ‘Table’ Double click on the first cell to enter data:

o The ‘x’ column in the LabQuest table is the stretch of the spring, ‘x’o The ‘y’ column in the LabQuest table is the force, Fx = mg

After you enter each data point, you must hit the enter button After entering all data, click on the graph icon in the top left to plot it Apply a linear fit to the graph and record the slope

SPH4UMomentum in 1-Dimension

p = mv

vAi = 0vBi = 0Therefore, initial momentum pi = 0.

After the “explosion”…

mA mB vAf vBf pAf pBf pfinal

What can we conclude about the momentum of a system before and after a collision?

SPH4U – Ballistics Pendulum - Assignment:

Explain how you would design a ballistics pendulum to measure the firing speed of an air-gun with equipment you could obtain fairly easily in a science lab. You must explain how you are setting up all of the apparatus and how all measurements are taken. You may suggest sophisticated electronics to take measurements (e.g. labquest, motion sensor, digital video camera, etc.), but you must explain exactly how you will use them. E.g. “use the motion sensor to measure how far it goes” is far too vague.

Assessment:1) Sensible apparatus is chosen [T/I]2) Diagram of apparatus [C]3) Explanation is clearly worded and invokes physics principles [K/U, C]4) A derivation of the speed in terms of initial variables (similar to what we

did in class, but include more explanation of the steps) [K/U, T/I, C]

Total Length: 2-3 pages

Name: __________________________

SPH4U Momentum Assignment

1. Superman jumps off of a building and lands on his feet without bending his knees. The ground does not break so the entire force of impact is taken by Superman’s legs. He jumps off of the same building again, but this time bends his knees upon landing. Sketch Force (y) vs. Time (x) graphs for both situations below. Use the graphs, the equation for impulse and 1-2 sentences to explain why bending his knees will make it hurt less. [4 marks] [K, A, C]

2. Continuing question 1, assume Superman (m = 75 kg) falls vertically off of a 315 m tall building and behaves like a projectile, i.e. no air resistance. Compare the force of impact on his legs upon landing if he does NOT bend his knees (duration of impact = 80 ms) to the force if he does bend his knees (duration of impact = 350 ms). [6 marks] [T, A]

3. A pickup truck of mass 5.61x103 kg collides with a stationary car of mass 3.12x103 kg. The two cars mash together and slide a distance of 18.8 m. If the truck was originally moving at 108 km/h, determine:a) The speed of the truck and car just after the collision [3 marks]b) The magnitude of the force of friction acting on the truck and car [4 marks]

4. Two 10-pin bowling balls of the same mass collide. The initial velocity of ball A is 4.85 m/s [N]. After the collision, the velocities of the two balls are 1.60 m/s [E32ºS] and 3.92 m/s [N22ºE]. What is the initial velocity of ball B? [6 marks] [T, K, A]

5. In a physics experiment, a professor performs a controlled explosion on an object of mass m, initially moving at speed v. After the explosion, it has blown into 2 pieces. One piece is three times as massive as the other and flies off in the same direction as the original object, but with ¼ the original speed. What is the speed and direction of the other piece? Express your answer in terms of v [5 marks] [T, A]

Name: _____________________________

SPH4U – Test 2Total Time: 60 min

Total Marks: 41Part A: True or False – 5 marks [T, C, K]

Circle either T or F. If the statement is false, explain why in the space provided.

For the following questions assume you are twirling a small rubber stopper of mass m at a constant speed, v, tied to a string in a vertical circle. Seen face on in the diagram below, the stopper is spinning counterclockwise.

1. At position 3, the direction of the acceleration is west and the direction of the velocity is upwards [ T / F ]

__________________________________________________

__________________________________________________

__________________________________________________

2. The tension in the string at position 1 exceeds the tension at position 4 by an amount equal to mg [ T / F ]

________________________________________________________________________

3. For a constant radius and frequency of revolution, the magnitude of the centripetal acceleration is directly proportional to m [ T / F ]

________________________________________________________________________

Part B: Short Answer [4 x 2 = 8 marks] Answer with ONE small calculation

1. A 9.5 kg box is initially stationary on a horizontal table. The coefficient of kinetic friction between the table and box is 0.49. The coefficient of static friction is 0.65. Calculate the minimum force to get the box moving [K, T]

2. A rocket of mass m is on the surface of the Earth (at a distance of rE from Earth’s centre). Its engines are fired to launch it to a distance of 3rE. Since it has used up fuel, the rocket’s new mass is m/2. How much stronger is the gravitational force on the rocket on Earth than in its second position? [K, A]

3. Calculate the approximate work you do against gravity by climbing a ladder that is your height. [T, A]

4. Three stones are thrown with identical initial speeds from the top of a cliff onto the ground below. Air resistance is negligible. The speeds with which stones 1, 2 and 3 hit the ground are: (circle the correct answer – no calculation necessary) [T, A]

a) v1 = v3 > v2 b) v2 > v1=v3 c) v1 > v2 > v3 d) v3 > v2 > v1e) v1 = v2 = v3

PART C: Calculations [28 marks]

1. A mountain climber of mass 72 kg, tethered to his partner, falls off of a cliff and is hanging vertically. The partner, mass 93 kg, is standing on a hill with a 27° decline. If the coefficient of friction between the partner’s boots and the ground is 0.12 and there is no friction between the rope and the edge of the cliff, find the acceleration of the pair [6 marks] [A, K]

2. Tarzan is being chased through the forest by an angry rhinoceros. Running at 8.2 m/s towards a vertically-hanging, vine, he plans to grab the vine and swing up to a safe platform. Unfortunately, Tarzan stumbles and his feet slide the final 7.5 m towards the vine. He then grabs the vine, and swings to a maximum height of 1.8 m. Find the coefficient of kinetic friction between Tarzan’s feet and the ground [6 marks] [K, A]

3. Jonathan Goldfish, a grade 12 physics student, is on a ride at Canada’s Wonderland in which participants strap themselves to the inside of a large horizontally circular steel machine, which moves in a uniform horizontal circle. Passengers on the ride feel a centrifugal force, a fictitious force which makes you feel as if you are being pushed against the machine as it spins. Jonathan measures the period of the ride with a stopwatch to be 2.9 s and when he holds up a thread with a mass on the end, the mass hangs from an angle of 26° out from the vertical (i.e. towards the outside of the circle). [A, K]a) Draw an FBD of the mass as seen in Jonathan’s frame of reference. Label all forces [2 marks]

b) Find the radius of the ride [6 marks]

4. A 80 g mass is attached to a vertical spring hanging from a ceiling. Once the mass is attached the spring it is steadied and it reaches an equilibrium 10 cm below the original hang of the spring. [T, K]a) Find the spring constant of the spring [2 marks]

b) The spring is then stretched a further 7.0 cm down, so it is 17 cm below its original equilibrium, and is released. How fast is the mass moving when the spring is 5.0 cm above its release height? Include a diagram [6 marks]

END OF TEST

kFx

Et = ½ kx2

SPH 4U0 - Grade 12 University Physics Name: ____________________________Energy & Momentum Date: _____________________________Determining the Spring Constant (k)Background Information

Potential energy can be stored in a spring in a similar fashion to energy of position, or gravitational potential energy. It takes work in order to stretch or compress a spring. This work is released when the spring returns to its original position (resting position). The amount of energy stored in a spring depends upon two factors: the spring constant and the distance of stretching or compression measured from the resting position. Each spring has a particular spring constant, k.

The spring constant is the force per unit change in spring length. It is generally obtained from a plot of force versus spring length. The slope of the line represents the spring

constant, k.

Once the spring constant is known, the potential energy stored in a spring

(Ee) is obtained from the following equation:

where k is the spring constant (N/m) and x is the stretched/compressed distance (m).

Materials

Hooke’s Law Apparatus (3 different springs, ruler, weight hanger, stand)Various Masses

Procedure

Devise a procedure for determining the spring constant for three particular springs. List a set of procedural steps and follow these.

Results

Make three separate tables of spring length as a function of force applied. Use this table to generate three graphs of force versus distance stretched/compressed. Calculate the spring constant for each (from the graph). Include a sample of any calculations performed. Once the spring constants, k, are determined, calculate the elastic potential energy for each spring at each value for x. Plot a graph of elastic potential energy versus stretched length for each spring.

Discussion Determine the value of k for each spring. Discuss the significance of this k value.

Include sources of experimental error. How would you test the validity of this value of k (HINT: think about the equation for the potential energy of a spring)? Briefly discuss this test in terms of “next steps” in your activity write-up.

SPH4U Name: Date:Assignment # 3 Circular motion

Knowledge/Understanding [3 marks each]17

1. A pilot of mass 75 kg takes her plane into a dive, pulling out of it along a circular arc as she nears the ground. If the plane is flying at 1.5 102 km/h along the arc, what is its radius such that the pilot feels four times heavier than normal? Provide an appropriate free-body diagram.

2. An object of mass 6.0 kg is whirled around in a vertical circle on the end of a 1.0 m long string with a constant speed of 8.0 m/s. Include a free-body diagram for each of the following questions:(a) Determine the maximum tension in the string, indicating the position of the object at the time the maximum tension is achieved.(b) What is the minimum speed the object could be rotated with and maintain a circular path?(c) If the object is rotated with the same speed (8.0 m/s) on a horizontal surface, what is the tension in the string if the string is parallel to the surface?

3. A flea stands on the end of a 1.0 cm long sweep second hand of a clock that rests horizontally on a table. What is the minimum coefficient of static friction which would allow the flea to stay there without slipping? Include an appropriate free-body diagram.

Thinking: [4 marks each]

4. A ball of mass 4.0 kg is attached to the end of a 1.2 m long string and whirled around in a circle that describes a vertical plane.(a) What is the minimum speed that the ball can be moving at and still maintain a circular path? Provide a free-body diagram.(b) At this speed, what is the maximum tension in the string? Provide another free-body diagram.(c) If the ball is rotated in a horizontal circle at the same speed with the end of the string held above the head, what angle does the string make with the horizontal?

6. A satellite orbits Earth at an altitude of 325 km above the planet’s surface. What is its orbital period? Express your answer in minutes. (rE = 6.38 106 m,

SPH4U Name: Date:Assignment # 2 Dynamics

Knowledge/Understanding[4 marks each]

26

1. A 12.0-kg box is pushed along a horizontal surface by a 24-N force as illustrated in the diagram. The frictional force (kinetic) acting on the object is 6.0 N.

(a) What is the acceleration of the object?(b) Calculate the value of the normal force acting on the object.(c) If the 12.0-kg object then runs into a 4.0-kg object that increases the overall friction by 3.0 N, what is the new acceleration?(d) What force does the 4.0-kg object exert on the 12.0-kg object when the two are moving together?

2. A pulley device is used to hurl projectiles from a ramp (k = 0.26) as illustrated in the diagram. The 5.0-kg mass is accelerated from rest at the bottom of the 4.0 m long ramp by a falling 20.0-kg mass suspended over a frictionless pulley. Just as the 5.0-kg mass reaches the top of the ramp, it detaches from the rope (neglect the mass of the rope) and becomes projected from the ramp.

(a) Determine the acceleration of the 5.0-kg mass along the ramp. (Provide free-body diagrams for both masses.)(b) Determine the tension in the rope during the acceleration of the 5.0-kg mass along the ramp.(c) Determine the speed of projection of the 5.0-kg mass from the top of the ramp. (d) Determine the horizontal range of the 5.0-kg mass from the base of the ramp.

3. Crates of mass 50.0 kg must be hoisted onto a platform 8.0 m above the ground. A person exerts 600.0 N of force on a rope that goes up and over a pulley suspended from the ceiling. The other end of the rope is attached to the 50.0-kg mass.(a) How long will it take the person to lift a crate from the ground to the platform while exerting maximum force?(b) If a 45.0-kg person grabs the free end of the rope when the crate is next to the platform in its elevated position, what will the acceleration of the crate be as it falls?(c) What is the tension in the rope in this case?

4. A 5.0-kg box accelerates across the floor at 1.2 m/s2 when pulled by a force of 12 N acting horizontally. The same box is then pulled by the same force acting at an elevation of 30.0.(a) Draw the free-body diagrams for both situations.(b) Determine the coefficient of sliding friction.(c) Calculate the acceleration of the block if the force is directed 30.0 above the horizontal.

Thinking:[5 marks each]5. Two blocks of mass 500.0 g and 200.0 g are suspended vertically as shown in the diagram. The

top string is lifted vertically upward exerting a force of 8.48 N on the 500.0-g block.

(a) At what rate do the blocks rise?(b) How much tension must the string connecting the two blocks withstand so it does not break when the blocks accelerate upward?(c) If the string connecting the two blocks can withstand only 6.0 N, what maximum force can be exerted on the upper string without the bottom string breaking?

6. A boy pulls a toy train (consisting of an engine and a caboose) along a rough floor, exerting 2.00 N of force as indicated in the diagram. A frictional force of 0.60 N acts on the engine and a frictional force of 0.40 N acts on the caboose.

(a) Draw free-body diagrams of both the engine and caboose. (b) Determine the acceleration of the entire train.(c) Calculate the tension in the string between the engine and the caboose.

SPH4U Name: Date:

24

Assignment # 1 Projectile Motion

Knowledge/Understanding [4 marks each]1. A shell is fired from a cliff that is 36 m above a horizontal plane. The muzzle speed of the shell is

80.0 m/s and it is fired at an elevation of 25 above the horizontal.(a) Determine the horizontal range of the shell.(b) Determine the velocity of the shell as it strikes the ground.

2. A football quarterback attempts a pass to one of the receivers. As the ball is snapped, the receiver leaves the line of scrimmage and runs directly down field. The quarterback releases the ball 2.0 s later and from a position 3.0 m behind the line of scrimmage. He throws the ball with a speed of 26 m/s at an elevation of 60 above the horizontal. The receiver makes a diving reception, catching the ball just as it reaches the ground. See the diagram below.

(a) What is the time of flight of the football?(b) What is the average speed of the receiver?

3. A circus clown is fired from a cannon into a net that is situated 2.0 m above the cannon and some distance from it. The cannon is elevated at 50.0 to the horizontal and the clown’s speed at launch is 15 m/s. See the diagram below.

(a) Find the horizontal distance from the cannon where the net needs to placed in order for the clown to land in it.(b) Calculate the clown’s velocity as he lands in the net.

Thinking: [6 marks each]

4. A boat is 50.0 m from the base of a cliff, fleeing at 5.0 m/s. A gun, mounted on the edge of the cliff fires a shell at 40.0 m/s and hits the boat when it has fled another 50.0 m. See the diagram below.

(a) At what angle above the horizontal must the gun be aimed so that the shell will hit the target?(b) How high is the cliff?(c) With what velocity does the shell hit the boat?

5. A baseball is hit by a bat and given a velocity of 40.0 m/s at an angle of 30.0 above the horizontal. The height of the ball above the ground upon impact with the bat is 1.0 m.(a) What maximum height above the ground does the ball reach?(b) A fielder is 110.0 m from home plate when the ball is hit and the ball’s trajectory is directly at him. If he begins running at the moment the ball is hit and catches the ball when it is still 3.0 m above the ground, how long does he run before catching the ball?(c) How fast (average speed) does he have to run in order to catch the ball?

SPH4U1 Name: Date:Unit Test :Dynamics

Modified True/FalseIndicate whether the statement is true or false. If false, change the identified word or phrase to make the statement true.

____ 1. A car drives with constant speed around a corner. If it enters the corner travelling west and leaves travelling south, its acceleration through the turn is directed south-west. _________________________

____ 2. A rubber ball changes velocity from 6.5 m/s [down] to 6.5 m/s [up] in a time of 2.0 s. Its average acceleration during this period can be considered to be zero. _________________________

____ 3. The acceleration due to gravity on Earth varies according to both altitude and latitude. _________________________

____ 4. An object is thrown vertically upward. At the top of its flight, when its velocity is momentarily zero, its acceleration is zero. _________________________

____ 5. A plane’s destination is due east of its departure point. If a steady wind is blowing from the north-west, the plane must point south-east to reach its destination. _________________________

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 6. Which of the following forces is NOT associated with the “electromagnetic force”?a. friction d. gravityb. tension e. buoyancyc. air resistance

____ 7. With respect to Newton’s third law, the action and reaction forcesa. being equal, imply a “balanced” force situationb. act on different objectsc. are equal provided the object is at restd. are equal provided the object is moving with uniform motione. are equal provided the object is NOT at rest or moving with uniform motion

____ 8. The diagram below shows a rock on the end of a string being whirled around in a circle in the horizontal plane. The motion is viewed from above and the stone is rotating clockwise. What are the directions associated with its instantaneous velocity and instantaneous acceleration, respectively?

a. south, east d. west, westb. east, west e. south, westc. south, south

____ 9. Two identical masses, A and B, are each tied to the ends of strings A and B, respectively, and whirled around in circles that are both oriented horizontally. The length of string A is twice that of string B. For the tension in the strings to be the same, the ratio of the speeds of the masses (vA:vB) must be

a. 1.4:1 d. 1:2b. 1:1.4 e. 1:1c. 2:1

____ 10. For objects travelling with uniform circular motion, the centrifugal force they experiencea. is radially outwardb. is apparently present in the noninertial frame of referencec. increases with speedd. doesn’t actually existe. all of the above

CompletionComplete each statement.

11. When the net force acting on an object is nonzero, the object is certain to ____________________.

12. For an object travelling with uniform circular motion, the direction of its acceleration at any point is ______________________________.

13. Besides static friction, the force responsible for directing a car around a banked curve is the ____________________ force.

14. For a planet orbiting the Sun, the centripetal force is supplied by ____________________.

15. The physicist ____________________ was responsible for the theory of universal gravitation, but it was ____________________ who determined the value of the universal gravitational constant.

Matching

Match the calculation with the quantity it determines.a. velocity d. displacementb. acceleration e. change in velocityc. jerk

____ 16. the area under a velocity-time graph

Three boats set out to cross a river that has a current. The speed of the three boats relative to the water is the same. Boat A points at an angle of 30 upstream from a point directly across the river. Boat B points directly across and boat C points 20 downstream from a point directly across the river. Match the boat with the relative time it takes to cross.a. Ab. Bc. C

____ 17. moderate time

A plane’s destination is due west of its departure point. Match the direction in which the wind is blowing to heading the plane could have to reach its destination.a. wind blowing south-west c. wind blowing eastb. wind blowing north d. wind blowing south-east

____ 18. plane heading south-west

The diagram below shows an object travelling with uniform circular motion as viewed from above. Match each of the following quantities with its proper direction.

a. north c. eastb. south d. west

____ 19. instantaneous velocity____ 20. centrifugal force

21. Under what condition is an object’s average velocity for a trip zero?

22. Provide a brief description of how the acceleration due to gravity across the surface of Earth varies with both latitude and altitude.

23. Why are curves in roadways often banked?

24. A ball is thrown vertically upward from a window that is 3.6 m above the ground. Its initial speed is 2.8 m/s.(a) With what speed does the ball hit the ground?(b) How long after the first ball is thrown should a second ball be simply dropped from the same window so that both balls hit the ground at the same time?

25. A pilot of mass 75 kg takes her plane into a dive, pulling out of it along a circular arc as she nears the ground. If the plane is flying at 1.5 102 km/h along the arc, what is its radius such that the pilot feels four times heavier than normal? Provide an appropriate free-body diagram.

26. A 1.2-kg mass is tied on the end of a 80.0 cm long rope and whirled around in a vertically-oriented circle at an ever-increasing rate. The rope breaks just as the frequency of rotation reaches 8.4 Hz. What maximum mass could this rope support if it is simply held vertically? Provide an appropriate free-body diagram.

27. An Earth satellite has an orbital period of 3.2 h. What is its orbital radius?(ME = 5.98 1024 kg)

Unit 2 Energy and Momentum Test

True/FalseIndicate whether the sentence or statement is true or false.____ 1. Imagine a hole is drilled straight through to the centre of the Earth and a stone is dropped

from the surface and it falls towards the centre. As it falls, the stone's gravitational potential energy increases and its kinetic energy decreases.

____ 2. Temperature is the total kinetic energy and potential energy of the atoms or molecules of a substance.

____ 3. The formula for power is P = (E )(

____ 4. The doubling time for earth's population of humans can be calculated by dividing 72 by the predicted average yearly percentage rate of growth.

Multiple ChoiceIdentify the letter of the choice that best completes the statement or answers the question.____ 5. Water with 2.5 104 J of total energy is about to fall over a waterfall. Assuming that the

hydroelectric generator at the base of the falls is 90% efficient and uses 30% of the water, the amount of energy produced by the hydroelectric generator will bea. 7.5 103 Jb. 2.2 104 Jc. 6.8 103 Jd. 7.5 104 Je. not possible to calculate given the above information

____ 6. The specific heat capacity of iron is 4.5 102 J/kg·C. The heat energy required to heat 5.0 kg of iron from 10C to 40C isa. 9.0 104 J d. 2.2 104 Jb. 6.8 104 J e. 7.5 101 Jc. 3.0 100 J

____ 7. The amount of work an 118-W electric mower can do in 3.0 min isa. 3.5 102 J d. 2.1 104 Jb. 1.5 100 J e. 3.9 101 Jc. 2.5 10–2 J

____ 8. Assuming the growth rate of energy consumption was 10.5% per year, the doubling time would bea. 6.9 d d. 0.15 db. 15 a e. 6.9 ac. 7.6 a

____ 9. The unit of energy isa. joule d. newtonb. watt e. none of the abovec. kg·m/s2

____ 10. Which of the following is the least energy efficient?a. automotive engine d. wind generatorb. electric motor e. fossil fuel power plantc. incandescent light bulb

____ 11. A 1000-W tennis ball machine releases a 0.028-kg ball at a speed of 100 m/s every 0.20 s. The efficiency of the machine isa. 70% d. 1.4%b. 14% e. 7.0%

c. 28%____ 12. The largest abundance of tar sands in the world are found in which country?

a. Saudi Arabia d. Canadab. Kuwait e. Russiac. United StatesCompletion

Complete each sentence or statement.13. In a conventional power station,

chemical energy ____________________ kinetic energy electrical energy.

14. A ____________________ refrigerator sends sound waves vibrating back and forth through gases in the resonating tube. The vibrating gases carry heat away from the food to a radiator that emits the radiant energy to the air outside the refrigerator.

MatchingMatch each item with the its correct unit below. (Use each item only once.)a. power d. temperatureb. work e. specific heat capacityc. efficiency f. energy

____ 15. percentageMatch each item with the correct answer below.a. principle of heat exchange g. thermal energyb. radiation h. conductionc. temperature i. kineticd. convection j. nuclear potentiale. electrical k. specific heat capacityf. gravitational potential l. elastic potential

____ 16. Amount of energy needed to raise the temperature of 1.0 kg of a substance by 1.0C.

Problem17. A 500 g piece of silver at 150C is submerged in 1000 g of water at 5C to be cooled.

Determine the final temperature of the silver and water givencwater = 4.18 103 J/kg·Ccsilver = 2.4 102 J/kg·C

18. A microwave rated at 1500 W heats a 850-g glass of water from 10C to 35C in 2.5 min. Determine the efficiency of the energy transformation.