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APP1 – Unit 4: Work and Energy (1)

11 Nov 15

Warm Up

Incorrect: While weight (m x g) is correct – it gives the ball its acceleration downwards - there is no such thing as force “D.” The ball moves independently in the x-direction IAW N1L: a body in motion remains in motion.

1

2

1 – 2D Motion poco Fiesta! 2 – 2D Motion grande Fiesta! 3 – Energy poco Fiesta!

Begin Energy

Unit

3

The prudent student who is not in class will check PlusPortals

Key Theme of this Unit

The amount of energy in the Universe remains constant at all times (closed system)

The conservation of energy is one of the foundation principles of physics

The Laws of Thermodynamics are… well… LAWS!

Work

Work Done by a Constant Force: W = F · d SI unit: newton-meter (N · m) = joule, J

Work

If force applied at an angle: W = F (cos θ) d …. or Fd (cos θ) (that distributive law you learned in math class)

Work

The work done may be positive, zero, or negative, depending on the angle between the force and the displacement:

Defining your frame of reference remains important

Work

The force needed to push the box up the ramp with a constant velocity is equal in magnitude, but opposite in direction, to the component of gravity in the same direction.

Path dependence of work: Do not conflate “work” with “effort.”

A wee bit of practice 1. A farm hand pushes a 23-kg bale of hay 3.4 m across the floor of a barn,

exerting a force of 86N on the hay. Determine how much work she has done.

3. At the pumpkin patch, you pick out your pumpkin. You lift the 3.2-kg

pumpkin to a height of 1.2m, then carry it for 50.0m on level ground. Determine a) work done on the pumpkin as you lift it; b) work done on the pumpkin as you carry it from the field.

9. A 55-kg packing crate is pulled with constant velocity across a rough floor with a rope that is at an angle of 40-degrees above the horizontal; the tension in the rope is 125 N. Determine the work done on the crate to move it 5.0m.

11.A small plane tows a glider at constant speed and altitude. The plane does 2.00 x 105 J of work to tow the glider 145m, with a tension in the rope of 2560 N. Determine the angle between the rope and the horizontal.

(from p. 200)

11/11 Practice For Thursday: Read for comprehension: Section 7-2 (pp. 186 – 190) Conceptual questions (p. 199): 1, 3, 7, 9 Conceptual exercises (p. 199): 3 Problems (p. 200): 15, 17

Goal time: 30 minutes

APP1 – Unit 4: Work and Energy (2)

12 Nov 15

Warm Up

Incorrect

Kinetic Energy

K = ½ mv2

Unlike Work, never negative Scalar You either have it, or you don’t

Work Energy Theorem

The total work done on an object is equal to its change in K

Completely general – applies across the Universe. One of the most useful theorems in physics

Work Energy Theorem

Example 7-6 Pulling a sled. F = 11 N, θ = 29°, m=6.40 kg, vo = 0.5 m/s (a) Work done by boy ? (b) vf after 2 m

https://youtu.be/t8XMeocLflc

11/12 Practice For Thursday: Read for comprehension: Section 7-2 (pp. 186 – 190) Conceptual questions (p. 199): 1, 3, 7, 9 Conceptual exercises (p. 199): 3 Problems (p. 200): 15, 17

Goal time: 30 minutes

APP1 – Unit 4: Work and Energy (3)

13 Nov 15

Session information: The Second High School Science and Technology Program session of the 2015-2016 school year will be held at the Research and Innovation Center (RIC) in Dearborn on Saturday, November 14th , 2015. This session will be held on Saturday morning from 9 a.m. - 11:30 p.m. and the topic is “Powertrain Controls, Calibration, & NVH". During this session, students will have the opportunity to see demonstrations of the in-vehicle hardware that makes up the Powertrain control system and see how the various sensors and actuators are used to deliver the required attributes. Location: This event will take place at the Research and Innovation Center (RIC) in Dearborn

Next Ford HSSTP Event

Saturday Morning Physics is on for

Tomorrow!

10am – 12pm Student entrance will be open

Warm Up

a. Less than; b. Equal to; c. Equal to.

a. Will the magnitude of the horizontal velocity of Rock A be (i) greater than; (ii) less than; (iii) equal to the magnitude of the horizontal velocity of Rock B? b. Will the magnitude of the vertical velocity of Rock A be (i) greater than; (ii) less than; (iii) equal to the magnitude of the vertical velocity of Rock B? c. Will the magnitude of the horizontal acceleration of Rock A be (i) greater than; (ii) less than; (iii) equal to the magnitude of the horizontal acceleration of Rock B?

Work done by a variable force

If the force is constant, we can interpret the work done graphically:

Work done by a variable force

We can then approximate a continuously varying force by a succession of constant values.

Work done by a variable force

The force needed to stretch a spring an amount

x is F = kx.

.

The work

done in stretching

the spring is:

W = ½ k x2

Work done by a variable force

Example: A block compresses a spring. mass block = 1.5 kg; v0=2.2m/s; k = 475 N/m. Determine the compression of the spring when the spring comes to rest.

Work done by a variable force

Power

Power is a measure of the rate at which work is done:

P = W / t SI unit: J/s = watt, W 1 horsepower = 1 hp = 746 W

Power

If an object is moving at a constant speed in the face of friction, gravity, air resistance, etc., the power exerted by the driving force can be written: This is a pretty cool derivation; I bring it up here to demonstrate how you can manipulate factors in equations to solve for an unknown.

1. Rocky runs his 79.9-kg mass up the 6.5 m high steps at the Philadelphia Art Museum at a constant speed in 7.15s. Determine the vertical work that Rocky did and his power rating.

https://www.youtube.com/watch?v=NubH5BDOaD8 (1:57)

Practice

2. On a recent adventure, Anita Brake went rock climbing. During one effort, Anita was able to lift her 65-kg body 20m straight up in 100s. Determine Anita’s power rating for this climb.

Practice

3. In one of my less-than-famous ideas, I thought I could generate power using a large family of 23 squirrels. I trained the squirrels to do pushups, and captured the work they did in the “up” direction. The average body mass that each squirrel lifted was 1.1 kg, and they raised their bodies 5 cm. Through proper training, the squirrels were able to do 71 push-ups a minute. Determine the power we could generate by these squirrels.

Practice

Practice 4. An elevator lifts a 715-kg mass straight up from the ground level to the 4th floor (11m) at a constant speed in 9.35s. Determine the power rating of the elevator.

Weekend Practice For Monday: Read for comprehension: Intro, Section 8-1 and 8-1 (pp. 204 – 214) Conceptual questions (p. 231): 1, 3, 5 Conceptual exercises (p. 232): 1, 3 Problems (p. 233-234): 1, 3, 5, 7

Goal time: 1 hour or less

APP1 – Unit 4: Work and Energy (4)

16 Nov 15

Warm Up

Shorter time. Acceleration only in y-direction; A has shorter distance to fall, and will hit the floor first no matter what the Vxo may be.

Conservative force: The work done is stored in the form of energy that can be

released at a later time

The work done by a conservative force moving an object around a closed path is zero

Example: gravity, spring Example of a nonconservative force: friction

Conservative and Nonconservative Forces

Conservative and Nonconservative Forces

Conservative (gravity) Nonconservative (friction)

Work done by a conservative force on any closed path is zero.

Conservative Forces

Potential Energy (U) and WC

Consider U as a “storage” system for energy.

Note: each different conservative force has a different

expression for U.

Defined: WC = Uo – Uf = -(Uo – Uf) = -ΔU

The work done by a conservative force is equal to the

negative change in potential energy.

U is scalar, units are J (like work).

We can only determine the difference in U between two

points, not the actual value of U.

U is a property of the entire system, not its individual parts.

Gravitational Potential Energy

ΔUg = mgΔy (APP1 Equation Sheet Equation)

We can set “0” wherever we want to simplify our process

1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

Check for Understanding

2. If a force of 14.7 N is used to drag the loaded cart (same from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?

Check for Understanding

2. On a recent adventure, Anita Brake went rock climbing. During one effort, Anita was able to lift her 65-kg body 20m straight up in 100s.

Determine Anita’s ΔUg

Determine Anita’s power rating for this climb.

Practice

Practice 4. An elevator lifts a 715-kg mass straight up from the ground level to the 4th

floor (11m) at a constant speed in 9.35s.

Determine the ΔUg for the elevator.

Determine the power rating of the elevator.

Potential Energy of a Spring

Us = ½ k x2 (APP1 Equation Sheet Equation)

A spring’s U is always increased whenever it is displaced from zero.

Us is always greater than / equal to zero.

Check for Understanding

PMPM 01: I can represent the motion of a projectile using horizontal and vertical

components of motion (velocity and acceleration).

PMPM 02: I can represent the motion of a projectile using position-time, velocity-time,

and acceleration-time graphs.

PMPM 03: I can predict the future behavior of particles in projectile motion.

PMPM 04: I can determine the x- and y-components of velocity for an object

experiencing projectile motion.

PMPM 05: I can solve problems involving objects experiencing projectile motion for

horizontal launch angles.

PMPM 06: I can solve problems involving objects experiencing projectile motion for

general launch angles.

Practice for 11/18 For Wednesday: Read for comprehension: Section 8-3 (pp. 214-222) Conceptual questions (p. 232): 11 Conceptual exercises (p. 232): 5, 9, 11 Problems (p. 233-235): 19, 21, 23

Goal time: 1 hour or less (you have two days to complete)

APP1 – Unit 4: Work and Energy (5)

18 Nov 15

Warm Up

Warm Up

“The Romans are sure of victory, for their drills are battles without bloodshed, and their battles -

bloody drills.” --Flavius Josephus

Definition of mechanical energy:

E = U + K

Using this definition, and considering only conservative forces, we find:

Ef = Ei

Or equivalently:

E = constant

Conservation of Mechanical Energy

We can use energy conservation to solve kinematics problems. Example: A 0.14kg pinecone falls 16m straight to the ground, and impacts with a velocity of 16 m/s. (consider air resistance) a) Determine the velocity with which the pinecone would strike

the ground without air resistance.

b) Determine the work done by air resistance (also – positive or negative work?)

Conservation of Mechanical Energy

Conservation of Mechanical Energy

Δy

Using conservation of mechanical energy, predict the velocity of the Hot Wheels car at the end of the inclined plane

Conservation of Mechanical Energy

A cannon is fired at an elevation of 45-degrees above the horizontal. The projectile has an initial velocity of 50 m/s, and impacts on a target 10m below the point of launch. Ignoring air resistance, determine: a. The highest point above the point of launch that the projectile achieves.

b. The velocity with which the projectile strikes the target.

1) Solve using kinematics only.

2) Solve using conservation of energy only.

450

Practice for 11/19 For Thursday: Read for comprehension: Section 8-4 (pp. 222-227) Conceptual questions : N/A Conceptual exercises (p. 232-33): 15 Problems (p. 233-235): 29, 31

Goal time: 30 minutes

APP1 – Unit 4: Work and Energy (6)

19 Nov 15

Warm Up

B = C > A

Conservation of Mechanical Energy

A cannon is fired at an elevation of 45-degrees above the horizontal. The projectile has an initial velocity of 50 m/s, and impacts on a target 10m below the point of launch. Ignoring air resistance, determine: a. The highest point above the point of launch that the projectile achieves.

b. The velocity with which the projectile strikes the target.

1) Solve using kinematics only.

2) Solve using conservation of energy only.

450

Energy Conversion Histograms

Ball +

Earth

U K Wnc U K Wnc

A

B

C

D

E

F

G

Work by Nonconservative Forces

Work by Nonconservative Forces

In the presence of nonconservative forces, the total mechanical energy is not conserved:

Wtotal = Wc + Wnc

= -ΔU + Wnc = ΔK

Solving for Wnc

Wnc = ΔU + ΔK = ΔE

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Build backbones of steel through grit and resilience!

Special Saturday Morning Physics on Saturday

1pm – 3pm

Student entrance will be open

Practice for 11/20 For Friday: Read for comprehension: Section 8-5 (pp. 227-230) Conceptual questions (p. 232): 13 Conceptual exercises (p. 233): 13, 15 Problems (p. 233-235): 41, 43

Goal time: 30 minutes Reading quiz tomorrow

APP1 – Unit 4: Work and Energy (7)

20 Nov 15

Special Saturday Morning Physics on Saturday

1pm – 3pm

Student entrance will be open

ETM 02: I identify when the total energy of a system is changing or not changing, and I can identify the reason for the change in the form of a general equation.

ETM 03: I can construct a mathematical expression from, and an energy bar graph to, describe energy changes in a system.

ETM 04: I can use the conservation of energy to solve problems, starting from a general conservation of energy equation.

ETM 05: I can use the relationship between the force applied to an object (or system) and the displacement of the object to calculate the work done on that object (or system).

Standards for Monday’s Fiesta!

Do not fret on springs

Energy Skate Park Lab

Weekend Practice For Monday: Read for comprehension: N/A Conceptual questions: N/A Conceptual exercises: N/A Problems (p. 236-237): 57, 59, 61, 65

Goal time: 30 minutes

Review your material from Chapter 7 and 8 for Monday’s Poco Fiesta

APP1 – Unit 4: Work and Energy (8)

25 Nov 15

The next month in APP1

1

2

3 4

1 – 2D motion reassessment; 2 – Work/Energy assessment; 3 – Impulse/Momentum assessment; 4 – Work/Energy reassessment (?) Saturday Morning Physics

Begin Impulse/

Momentum

Saturday Morning Physics on Saturday

10am – 12pm

Student entrance will be open

Energy Skate Park Lab

Weekend Practice For Monday: Read for comprehension: N/A Conceptual questions: N/A Conceptual exercises: N/A Problems (p. 236-237): 57, 59, 61, 65

Goal time: 30 minutes

Review your material from Chapter 7 and 8 for Monday’s Poco Fiesta

APP1 – Unit 4: Work and Energy (9)

30 Nov 15

B > C > A > D.

Warm Up

The next month in APP1

1

2

3 4

1 – 2D motion reassessment; 2 – Work/Energy assessment; 3 – Impulse/Momentum assessment; 4 – Work/Energy reassessment (?) Saturday Morning Physics Also note: Pacing guide updated for the rest of the school year; posted on PlusPortals

Begin Impulse/

Momentum

Work/Energy: the main structure

Work: F (cos θ) d

Conservation of Mechanical Energy: Ei = Ef

Work-Energy Theorem: WTotal = ΔK = ½ mvf2 - ½ mvo

2

Every situation can be analyzed using this structure

Force-Distance Graphs

A box is pushed to the right with a varying horizontal force. The graph above represents the relationship between the applied force and the distance the box moves. Determine the work done on the box.

Forc

e (N

)

Position (m)

Force-Distance Graphs

3.0

2.0

1.0

0 0 0.030 0.060 0.090

The graph above shows the net force exerted on an object as a function of the position of the object. The object begins at rest at position x = 0m and acquires a velocity of 3.0 m/s after traveling a distance of 0.090m. Determine the mass of the object. (a) 0.015-kg (b) 0.030-kg (c) 0.045-kg (d) 0.060-kg

Equipotential and Bar Graphs

A 3.0-kilogram object is placed on a frictionless track at point A and released from rest. Assume the gravitational potential energy of the system to be zero at point C. a. Create a quantitative energy bar graph for the changes between points A through G (A-B, B-C, C-D, D-E, E-F, F-G). b. Predict the difference in your graphs if friction does – 2J of work between each point. c. Explain what you would have to do to get the object to point H.

Practice For Tuesday: Read for Comprehension: Section 9-3 (pp. 244-248) Review: Intro and Section 9-1 and 9-2 (pp. 240 – 244) Conceptual questions: N/A Conceptual exercises: N/A Problems (p. 237-238): 67, 69, 72, 73 (from Ch 8) – if not already complete.

Goal time: 30 minutes