1. A particle of mass 0.30 kg moves along the x-axis with a potential energy whose dependence on x is shown below.

a. What is the force on the particle (in N) at x = 2.0, 5.0, 8.0, and 12 m? (Indicate the direction with the signs of your answers.)

x = 2.0 m F = _____ N

x = 5.0 m F = _____ N

x = 8.0 m F = _____ N

x = 12 m F = _____ N

b. If the total mechanical energy E of the particle is 8.0 J, what are the minimum and maximum positions of the particle (in m)?

minimum: _____ m

maximum: _____ m

c. What are these positions (in m) if E = 4.0 J?

minimum: _____ m

maximum: _____ m

d. If E = 20 J, what are the speeds of the particle (in m/s) at the positions listed in part (a)?

x = 2.0 m v = _____ m/s

x = 5.0 m v = _____ m/s

x = 8.0 m v = _____ m/s

x = 12 m v = _____ m/s

2. A3.30-kg mass starts from rest at point A and moves along thex axis subject to the potential energy shown in the figure below

a. Determine the speed of the mass at points B, C, D.

b. Determine the turning points for the mass. (Select all that apply.)

point A

point B

point C

point D

point E

3. A force of constant magnitude pushes a box up a vertical surface as shown in the figure. The box moves at a constant speed. If the mass of the box is3.30 kg, it is pushed2.30 m vertically upward, the coefficient of friction is 0.350 and the angle is 30.0, determine the following.

a. work done on the box byF

b. work done on the box by the force of gravity

c. work done on the box by the normal force

d. increase in gravitational potential energy of the box as it moves up the wall

4. A1.4 kg ball at the end of a1.9 m string swings in a vertical plane. At its lowest point the ball is moving with a speed of20 m/s.

a. What is its speed (in m/s) at the top of its path?

b. What is the tension (in N) in the string when the ball is at the bottom and at the top of its path?

bottom of its path

top of its path

5. A small bead with a massm =13.0 g slides along the frictionless wire form shown in the figure. The three heightsh_A =7.00 m,h_B =5.70 m, andh_C =2.00 m are all measured from the floor. The bead is released from rest at point A.

a. What is the speed of the bead at points B and C?

vB = _____

vC = _____

b. What is the net work done on the bead by the force of gravity as it moves from point B to C?