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Name: ________________________________________________ Assignment Due Date: March 5, 2012
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AP Physics: Potential Energy and Conservative Forces
Problem
1. The force acting on an object is given by Fx = a/x2. Determine the potential energy of the object as a function of x.
2. The potential energy of an object is given by U(x) = 3x2 - 2x3, where U is in joules and x is in meters. (a) Determine the force acting on this object. (b) At what positions is this object in equilibrium? (c) Which of these equilibrium positions are stable and which are unstable?
3. The potential energy of an object is given by U(x) = 8x2 - x4, where U is in joules and x is in meters. (a) Determine the force acting on this object. (b) At what positions is this object in equilibrium? (c) Which of these equilibrium positions are stable and which are unstable?
Name: ________________________
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4. The 3-kg object in the figur below is released from rest at a height of 5 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant k =400 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. (a) Find x. (b) What happens to the object after it comes to rest?
5. The 2-kg block in the figure below slides down a frictionless curved ramp, starting from rest at a height of 3 m. The block then slides 9 m on a rough horizontal surface before coming to rest. (a) What is the speed of the block at the bottom of the ramp? (b) What is the energy dissipated by friction? (c) What is the coefficient of friction between the block and the horizontal surface?
Name: ________________________
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6. In the figure below, the coefficient of kinetic friction between the 4-kg block and the shelf is 0.35. (a) Find the energy dissipated by friction when the 2-kg block falls a distance y. (b) Find the total mechanical energy E of the two-block system after the 2-kg block falls a distance y, assuming that E = 0 initially. (c) Use your result for (b) . to find the speed of either block after the 2-kg block falls 2 m.
Name: ________________________
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An object of mass 0.5 kg experiences a force that is associated with the potential energy function
U(x) = 4.02.0 + x
, where U is in joules and x is in meters.
7. On the axes below, sketch the graph of U(x) versus x.
8. Determine the force associated with the potential energy function given above.
9. Suppose that the object is released from rest at the origin. Determine the speed of the particle at x =2 m.
Name: ________________________
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10. In the laboratory, you are given a glider of mass 0.5 kg on an air track. The glider is acted on by the force determined in question 10. Your goal is to determine experimentally the validity of your theoretical calculation in question 11.
From the list below, select the additional equipment you will need from the laboratory to do your experiment by checking the line next to each item. If you need more than one of an item, place the number you need on the line.
11. Briefly outline the procedure you will use, being explicit about what measurements you need to make in order to determine the speed. You may include a labeled diagram of your setup if it will clarify your procedure.
ID: A
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AP Physics: Potential Energy and Conservative ForcesAnswer Section
PROBLEM
1. ANS:
REF: Tipler 4th ed. p.175 #67 2. ANS:
REF: Tipler 4th ed. p.175 #68 3. ANS:
REF: Tipler 4th ed. p.175 #70 4. ANS:
REF: Tipler 4th ed. p.204 #9 5. ANS:
REF: Tipler 4th ed. p.207 #49
ID: A
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6. ANS:
REF: Tipler 4th ed. p.207 #51 7. ANS:
REF: Free Resp Ques 2002 Mech #3a
ID: A
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8. ANS:
REF: Free Resp Ques 2002 Mech #3b 9. ANS:
REF: Free Resp Ques 2002 Mech #3c 10. ANS:
REF: Free Resp Ques 2002 Mech #3d
ID: A
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11. ANS:
REF: Free Resp Ques 2002 Mech #3e
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