**AP Conservation of Energy and Power**

1. An
electrical motor lifts a 575 N box 20 m straight up by a rope in 10 s. What
power is developed by the motor? (1.1510W)

2. A block slides down a frictionless inclined
plane of height

*h*= 1 m, making angle θ with the horizontal. At the bottom of the plane, the block continues to move on a flat surface with a coefficient of friction μ = 0.30. How far does the mass move on the flat surface? (3.3m)
3. A cyclist approaches the bottom of a hill at a
speed of 11 m/s. The hill is 6 m high. Ignoring friction, how fast is the
cyclist moving at the top of the hill? Assume that he doesn’t peddle and ignore
air resistance. (1.81m/s).

4. A
100 kg mass traveling with a velocity of 15 m/s on a horizontal surface strikes
a spring with a spring constant k = 5 N/m.

a. Find the compression of
the spring required to stop the mass if the surface is frictionless.(67.1m)

b. Find the compression of the spring if
the surface is rough (0.4

*k*μ=0). (*x*= 25 m)
5. An amusement park roller coaster car
has a mass of 250 kg. During the ride, it is towed to the top of a 30 m hill,
where it is released from rest and allowed to roll. The car plunges down the
hill, then up a 10 m hill and through a loop with a radius of 10 m. Assume that
the tracks are frictionless. (Use

*g*= 10 m/s^{2}.)
a. What is the Potential Energy of the
car at the top of the 30 m hill?(75000 J)

b. What are the Kinetic Energy and the
speed of the car at the bottom of the 30 m hill? (75000
J) (24 m/s)

c. What are the Kinetic Energy and the
speed of the car at the top of the 10 m hill? (50000J) (20m/s)

d. If the hill makes an angle of 60o
with the horizontal and the car takes 15 seconds to be towed up the hill,
determine the length of the hill, the velocity of the car, the force required to
tow the car up the hill, and the power of the motor pulling the car up the
hill.(5KW)