Section 7.4 Work
J. Lewis
When a force, F is applied through a distance, D, than the work done is W=FD.
I Springs: Hooke's Law The force required to hold a spring x units beyond its natural
length is a constant, k, times x. k is called the spring constant.
F=kx
If the natural length of the spring is L , then the work done in stretching a spring from
L  a to L  b is W 
b
a
kx dx 
1
k (b
2
2
 a )
.
2
Examples
1. #6 in 7.4 of Stewart. A spring has a natural length of 20 cm. A force of 25N is
required to hold it at a length of 30 cm. Find the work done in stretching it from
20 cm to 25 cm.
2. #8 in 7.4 of Stewart. The work done in stretching a spring 1 ft. beyond its natural
length is 12 ft.-lb. Find the work done in stretching the spring 9 in. beyond its natural
length.
II Rope problems
3. # 12 in Stewart A uniform cable hanging over the edge of a tall building is 40 ft long
and weighs 60 lb. How much work is required to pull 10 ft of the cable to the top?
4. #14 in Stewart. A bucket that weighs 4 lb and a rope of negligible weight are used to
draw water from a well that is 80 ft deep. The bucket starts with 40 lb of water and is
pulled up at a rate of 2 ft/sec. Water leaks out of the bucket at the rate of 0.2 lb/sec. Find
the work done in pulling the bucket to the top of the well.
III Pumping water out of a tank.
Please see the link, Setting up tank problems on my webpage.
5. A trough has an isosceles triangular face that is 5m high and 4m wide at the top. The
trough is 12m long and is full of water. Find the work done in pumping all the water out a
spout that is 1m above the top of the tank.
6. A tank in the shape of a right circular cylinder rests on its 8 m length. The radius of
face of the tank is 2m. The tank is full of water. How much work is done in pumping all
the water out a spout that is 2m above the top of the tank?