Worksheet Problem 5

1
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.

1. Multiply both sides of this equation by m/2.
2. Explain the resulting formula in terms of the
   work-energy theorem.

2
Worksheet Problem 6

• This is a type of question popular on drivers
  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?

1. What force is responsible for the net force on
   the skidding car?
2. How does the stopping time depend on initial
   speed?
3. To what quantity is stopping distance
   proportional?
4. What is the answer to the drivers license exam
   question?
5. Explain the result without referring to work or
   kinetic energy.

3
Gravitational Potential Energy

• Energy of height

7.1
4
Potential Energy

• The energy of relative position of two objects

gravity springs electric charges chemical bonds
5
Potential Energy

• Energy is stored doing work against a potential

Potential energy increases when the potential
does negative (lt 0 ) work

• lifting a weight
• stretching a spring

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Gravity Does Negative Work
Source Young and Freedman, Figure 7.2b.
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Work from Potential Energy

• When a potential does work on a body
• The bodys potential energy decreases
• The bodys kinetic energy increases
• Or, more than one potential can operate at once

8
CPS Question

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

1. Its gravitational potential energy increases.
2. Its kinetic energy increases.
3. Both A and B.
4. Neither A nor B.

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Gravity Does Positive Work
Source Young and Freedman, Figure 7.2a.
10
CPS Question

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

1. Its gravitational potential energy increases.
2. Its kinetic energy increases.
3. Both A and B.
4. Neither A nor B.

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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
R
v
B
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CPS Question

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

1. The local slope of the trough.
2. The rocks speed.
3. Both of these.

A
R
v
B
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Mechanical Energy

• The energy available to do work

Kinetic potential K U
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Gravitational Potential Energy

• Gravitational potential energy
• the work to raise an object to a height
• Gravitational U mgh

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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 mv22 mgy2

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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

1. Initial gravitational potential energy Ugrav 0?
2. Final gravitational potential energy Ugrav f?
3. Change in gravitational potential energy DUgrav?
4. Kinetic energy just before impact Kf?

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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 q  p/6 from vertical down to q  0?

1. If the height of the swing pivot is 0, what is
   Throckmortons height h at q  p/6? At q  0?
2. What is his change in height Dh?
3. What is his change in potential energy DUgrav?
4. What is his speed at the bottom?