Worksheet Problem 5

A kinematic formula derived in Chapter 2 for conditions of constant acceleration relates speed, acceleration, and displacement:

2a (x – x0) = v2 – v02.

a) Multiply both sides of this equation by m/2.

b) Explain the resulting formula in terms of the work-energy theorem.

Worksheet Problem 6

This is a type of question popular on driver’s license exams: If a car initially traveling 30 mi/h skids to a stop in 100 ft, how far will it skid before coming to a stop if its initial speed is 60 mi/h?

a) What force is responsible for the net force on the skidding car?

b) How does the stopping time depend on initial speed?

c) To what quantity is stopping distance proportional?

d) What is the answer to the driver’s license exam question?

e) Explain the result without referring to work or kinetic energy.

Gravitational Potential Energy

Energy of height

§ 7.1

Potential Energy

The energy of relative position of two objects

gravity

springs

electric charges

chemical bonds

Potential Energy

Energy is stored doing work against a potential

Potential energy increases when “the potential” does negative (< 0 ) work

• lifting a weight

• stretching a spring

Gravity Does Negative Work

Source: Young and Freedman, Figure 7.2b.

Work from Potential Energy

When a potential does work on a body:

• The body’s potential energy decreases

• The body’s kinetic energy increases

• Or, more than one potential can operate at once

CPS Question

When a cute furry animal moves downward in free-fall:

A. Its gravitational potential energy increases.

B. Its kinetic energy increases.

C. Both A and B.

D. Neither A nor B.

Gravity Does Positive Work

Source: Young and Freedman, Figure 7.2a.

CPS Question

When a disgusting scaly thing moves upward in free-fall:

A. Its gravitational potential energy increases.

B. Its kinetic energy increases.

C. Both A and B.

D. Neither A nor B.

Worksheet Problem 7

A small rock with a mass of 0.20 kg is released from rest at point A at the top of a hemispherical bowl of radius R = 0.5 m. The rock slides rather than rolls. The work done by friction when it moves from A to B is –0.22 J. What is the speed v of the rock when it reaches point B?

A

B

v

R

CPS Question

As the rock slides down the trough, the normal force on it depends on

A

B

v

R

A. The local slope of the trough.

B. The rock’s speed.

C. Both of these.

Mechanical Energy

The energy available to do work

Kinetic + potential = K + U

Gravitational Potential Energy

Gravitational potential energy =

the work to raise an object to a height

Gravitational U = mgh

Conservation of Mechanical Energy

• If the only force doing work is gravity, mechanical energy does not change.

E1 = E2

K1 + Ug1 = K2 + Ug2

1/2 mv12 + mgy1 = 1/2 mv2

2 + mgy2

Worksheet Problem 8

A 50-g egg released from rest from the roof of a 30-m tall building falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. What values do the students find for:

a) Initial gravitational potential energy Ugrav 0?

b) Final gravitational potential energy Ugrav f?

c) Change in gravitational potential energy Ugrav?

d) Kinetic energy just before impact Kf?

Worksheet Problem 9

Your cousin Throckmorton, m = 20 kg, plays on a R = 1.5-m swing. What is his change in gravitational potential energy as he swings from an angle  = /6 from vertical down to  = 0?

a) If the height of the swing pivot is 0, what is Throckmorton’s height h at = /6? At  = 0?

b) What is his change in height h?

c) What is his change in potential energy DUgrav?d) What is his speed at the bottom?