Name
Period
Date
Energy: Worksheet 8
1. A force acts on a 3.0 kg object in such a way that the position of the object as a


function of time is given by x  3.0t  4.0t 2  1.0t 3 where x is in meters and t in
seconds. Find the work done by the force from t  0 s to t  4.0 s .
2. An 8.00 kg stone rests on a vertical spring. The spring is compressed 10.0 cm by the
stone.
a. What is the spring constant of the vertical spring?
The stone is pushed down an additional 30.0 cm and released.
b. What is the potential energy of the compressed spring just before that release?
c. How high above the release position will the stone rise?
Energy: Worksheet 8
3. A thin rod whose length is L  2.00 m and whose mass is
negligible is pivoted at one end so that it can rotate in a vertical
circle. A heavy ball is attached to the lower end. The rod is
pulled aside through an angle   30. , as shown, and then
released.
a. How far above its
b. How fast is the ball moving
lowest point is the ball
at its lowest point?
when it is at a 30.
angle to the vertical?
page 2

L
4. A 3.5 kg block is released from a compressed
spring whose spring constant is 640 N . After
m
leaving the spring at the spring’s relaxed length,
the block travels over a horizontal surface, with a
No Friction
7.8 m
coefficient of kinetic friction of 0.25 , for a
k  0.25
distance of 7.8 m before coming to rest.
a. How much mechanical energy was dissipated by the frictional force in bringing
the block to rest?
b. What was the maximum kinetic energy of the block?
c. How far was the spring compressed before the block was released?
Energy: Worksheet 8
page 3
P
5. A small block of mass m can slide
along the frictionless loop-the-loop
track as shown. The block is
released from rest at point P .
State all answers in terms of m, g,
and R.
a. How fast is the block moving at
point Q ?
5R
R
Q
R
b. Draw a force
diagram of the
block when it is at
point Q .
c. Calculate the Fg and
the FN acting on the
block at point Q .
d. What is the magnitude
of the net force acting
on the block at point Q ?
Energy: Worksheet 8
page 4
Suppose that the block is now released at a different height so that it is on the verge
of losing contact with the track at the top of the loop.
e. What is the speed of the block when it is on the verge of losing contact with the
track at the top of the loop? Begin by drawing a force diagram of the block when
it is on the verge of losing contact with the track at the top of the loop.
f. At what height above the bottom of the loop must the block be released so that it
is on the verge of losing contact with the track at the top of the loop?