1 chapter 10 newton’s laws class question how do units differ from variables? list 10 clear...
TRANSCRIPT
Class Question
How do units differ from variables?
List 10 clear examples of units and 10 clear examples of variables.
Class Objectives
Learn the relationship between position, velocity, and acceleration
Learn and apply Newton’s First, Second, and Third Laws
Learn some secrets of Calculus
What are the Forces of Nature?
Gravitational Force Electromagnetic Force
– Electrostatic and Magnetic Nuclear Force
– Strong and Weak Friction Spring Tension Push
Newton’s 1st Law
Law of Inertia“Bodies remain at rest or in uniform motion in a straight line unless a net force acts on it.”
Thought QuestionsWhy don’t planets move in straight lines?Would they move it straight lines if there were no gravitational force?
Newton’s Cannon
Newton’s Second Law
F = m a
“The amount of acceleration that a force produces depends on the mass of the object being accelerated.”
Newton’s Second Law
Example Questions:– What happens to acceleration if the force is doubled?
Answer:
– ….if the mass is double? Answer:
Newton’s Third Law
Action-Reaction
“Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.”
Gravity QuestionsGravity Questions
Did the Moon exert a gravitational force on the Apollo astronauts?
What kind of objects can exert a gravitational force on other objects?
The constant G is a rather small number. What kind of objects can exert strong gravitational forces?
Gravity QuestionsGravity Questions
If the distance between two objects in space is doubled, then what happens to the gravitational force between them?
Find the gravitational force between a 90-kg person and the Earth using the inverse square law (Equation 10-37) and Table 10.6. Show your work and include units for your answer.
Definitions
Vector Quantity– a quantity that has both magnitude and direction
Vector– an arrow drawn to scale used to represent a vector
quantity
Scalar Quantity – a quantity that has magnitude but not direction
Vector or Scalar?Vector or Scalar?
Speed……….. Velocity……... Acceleration.. Time…………. Force………… Distance……..
scalar
vector
vector
scalar
scalar
it depends...
Some Definitions
Position - a location usually described by a graphic on a map or by a coordinate system
54321-3 -2 -1
4
3
2
1
00
-1
-2
-3
-4
(-2, -3)
(4, 3)
Some Definitions
Displacement -- change in position,
where 12 rrr
Δ
1r
r
Δ
2r
54321-3 -2 -1
4
3
2
1
00
-1
-2
-3
-4
(-2, -3)
(4, 3)
Example Write an expression for each vector below
and find their magnitudes.
1r
r
Δ
2r
54321-3 -2 -1
4
3
2
1
0
0-1
-2
-3
-4
(-2cm, -3cm)
(4cm, 3cm)
Vector Notation Position Vector
Unit Vectors
Magnitude
kzjyixr ˆˆˆ
k,j,i ˆˆˆ
222 zyxrr
Team Exercise 4.4
Some Definitions
Average velocity
rate of position change with time
scalarTimeElapsed
vectorntDisplaceme
t
rvave
Example
Suppose that your drive around in a circle in a parking lot at 30mph.
Consider the instant that your car is facing north.
What is your speed? What is your instantaneous velocity ? What is average velocity?
Some Definitions
Average Acceleration - rate of velocity change with time
Instantaneous Acceleration
t
v
tt
vva
12ave
12
dt
vd
t
va
0t
lim
Kinematic EquationsWhere did they come from?
tavvo0 xxx
tavoo yyy v
2xxo ta
2
1tvxx
oo
2yyo ta
2
1tvyy
oo
Newton’s Laws
1st – Law of Inertia 2nd – F=ma 3rd – Action Reaction
– Demo Metal ball launcher and dropper Maximum Range and the 90-degree-rule Airplane flare:
http://observe.phy.sfasu.edu/courses/phy101/lectures101/Movies/Plane%20Drops%20Flare.wmv
Example
Assume that r(t)=kt where k is a constant.
Plot r versus t. Plot v versus t. Plot a versus t. Write an equation for v(t) and a(t).
Example
Assume that r(t)=Ct3 where C is a constant.
Plot r versus t. Plot v versus t. Plot a versus t. Write an equation for v(t) and a(t).
Example
Assume that r(t)=rosin(t) where ro and are constants.
Plot r versus t. Plot v versus t. Plot a versus t. Write an equation for v(t) and a(t).
Example 10.1
Assume that you...– walk at 3mph for 15 minutes,– then drive at 40mph for 2 hours, and– then ride a bike at 10pm for 45 minutes.
Plot v versus t. Plot r versus t. Do you differentiate or integrate to get r(t)?
Example
Assume that a(t)=k where k is a constant.
Plot a versus t. Plot v versus t. Plot r versus t. Write an equation for v(t) and r(t).
Newton’s Second Law (A second look)
A non-zero net force will cause a mass to accelerate.
The time-rate-of-change of momentum is proportional to the net force on the object.
amF
dt
Problem 10.2
A motorcycle moves with an initial velocity of 30m/s.
When its brakes are applied, it decelerates at 5.0m/s2 until it stops.
Plot the position, velocity and acceleration as a function of time.
What is the position, velocity and acceleration 2 seconds after the brakes are applied?
2ooo ta
2
1tvxx tavv o
Multiple Directions
The equations of motion can be written for each direction independently.
Velocity
Position
tavvo0 xxx
tavoo yyy v
2xxo ta
2
1tvxx
oo
2yyo ta
2
1tvyy
oo
Problem 10.3
A girl shoots an arrow upward. It strikes the ground 10.0 seconds later. What was its initial velocity and what was the
maximum height?
2yoyoo ta
2
1tvyy tavv yyoy
Problem 10.4
A bullet is fired vertically into the air and reached a maximum height of 15,000ft.
What was the initial velocity? What assumptions must be made?
2yoyoo ta
2
1tvyy tavv yyoy
Problem 10.5
A man standing on a 200-ft tower throws a ball upward at 40 ft/s.
How long does it take to hit the ground?
Announcements
Homework 12 due on Wednesday.
Remember to get advising.
Project Two is due on December 6th.– That’s next week today.
Project Two
Scoring: – 1 Point for each inch that the projectile travels.
Instructions:– See course home page
Homework 12
http://www.physics.sfasu.edu/astro/OnlineExams/FCI/fci_main.html
Kinematic EquationsWhere did they come from?
tavvo0 xxx
tavoo yyy v
2xxo ta
2
1tvxx
oo
2yyo ta
2
1tvyy
oo
Calculus Basics
Derivative
Indefinite Integral
Definite Integral
1nn nxx dx
d
1n
xx
1nn
1n
a
1n
b
1n
xdxx
1n1nb
a
1nb
a
n
Constant AccelerationEquation of motion is
dt
dva
dvdt a
dtadv
tavv o
The o in v subscript refers to the original or initial value at the beginning of the time interval of interest.
Integrate both sides
where acceleration is constant.
Arranging this equationdt
dxv
dxdtv
dttavdx oo
dttavdx oo
2ooo ta
2
1tvxx
Substituting the velocity equation from the previous page
Integrating both sides
Coil Gun
Final Exam Question– How fast must the projectile be traveling when it
leaves the straw if it is to travel 100 inches horizontally?
Newton’s Laws -- Review
First LawInteria
Second LawF=ma
Third Law– Action/Reaction
Law of Gravity
221
r
mmGF
Team Exercise, 3 min.1. The derivative of velocity with respect to time is:
– position or acceleration
2. By integrating velocity with respect to time we get:– distance traveled or acceleration
3. The derivative of position with respect to time is:– acceleration or velocity
4. Integrating acceleration twice with respect to time is :– velocity squared or distance
5. The derivative is associated with the _________ while the integral is associated with _________
– area under the curve, slope
Homework 12
5. According to Newton’s Second Law, what is the net force on a 2000-lb car if it travels at a constant 60mph for 2 hours?
Homework 12
6. A 1500-kg automobile has a projected frontal area of 1.9 m2 and a drag coefficient of 0.35. It is traveling at 100km/h on a flat road when suddenly both the engine and brakes fail. What is the drag force on the automobile at the moment the brakes fail? The density of air is 1.3 g/liter.
2d AvC
2
1F
Homework 12
Will the drag force increase, decrease or stay the same as time goes by?
What would the drag force be if the medium was water rather than air?
Problem 10.7 (modified)
Assume that a projectile is fired upward at an angle and that air resistance is negligible.
Find y as function of x instead of time using the equations below.
What is the shape of the projectiles path?
2xxo ta
2
1tvxx
oo 2
yyo ta2
1tvyy
oo
Team Exercise (3 minutes)
One dimensional motion– What is the distance traveled in 3 seconds? – What is the acceleration at 1.25 hours?
Sp
eed
, mp
h
3210
010
20
Time, hours
Exercise - Newton’s Laws
A pickup truck is moving with a constant speed of 30 mph along a city street.
You are sitting in the back of the truck and you throw a ball straight upwards at a speed of 20 mph.
Neglecting air resistance:– What will be the path of the ball with respect to the
pickup truck and where will the ball land with respect to the truck? (i.e. what are the x and y values of the peak and final positions)
Solution (cont’d)
The ball follows a parabolic path and remains directly above the truck at all times.
Is a horizontal force acting upon the ball? – Votes for yes?– Votes for no?
Solution
Answer: NO. There is no horizontal force acting on the ball.– The horizontal motion of the ball is the result of its own
inertia. When thrown from the truck, the ball already possessed a horizontal motion, and thus will maintain this state of horizontal motion unless acted upon by a force with a horizontal component (Newton's first law).
Summary: forces do not cause motion (velocity); rather, forces cause accelerations (change in velocity).
Today’s Demos
Inertia– Lead Brick and Hammer– Inertia Bars– Disk and Ring Race– Rotating Platform– Metronome– Balancing A Meter Stick
Rotation Adds Stability– Bicycle Tires– Moving Water– Spin Guns
Center of Mass– State of Texas– Curious George
Next Week– Bed of Nails– Fluid Flasks– And more....
Trebuchet Problem (Modified 10.6)
The projectile is fired at an angle of 35° relative to the ground.
It is fired with a velocity of 100ft/s. Find the following:
– vxo and vyo
– axo and ayo
How long was the projectile in the air? How high did it go? How far did the projectile go?
tavvo0 xxx
tavoo yyy v
2xxo ta
2
1tvxx
oo
2yyo ta
2
1tvyy
oo
Section 10.3 - Forces
Forces are vector quantities.
kFjFiFF zyx
kN5jN10iN10F
What is the magnitude of this force?
Problem 10.1
A car starts from rest and travels northward. It accelerates at a constant rate for 30 seconds
until it reaches a velocity of 55mph. Plot the acceleration, velocity and position as a
function of time.
Final Trebuchet Tweaks
Consider a trough Weight and test your trebuchet Allow for hole and pin adjustments Prepare for rain