Chapter 6: Work and Energy

1
The Spring

• Consider a spring, which we apply a force FA to
  either stretch it or compress it

FA
x
k is the spring constant, units of N/m, different
for different materials, number of coils
unstretched
-FA
-x
x0
2
From Newtons 3rd Law, the spring exerts a force
that is equal in magnitude, but opposite in
direction
Hookes Law for the restoring force of an ideal
spring. (It is a conservative force.)

• Work done by a spring
• We know that work equals force times displacement

3
But the force is not constant
xi
Take the average force
xf
x0
Then the work done by the spring is
4
Units of N/m m2 N m J

• Total potential energy is

Example Problem A block (m 1.7 kg) and a spring
(k 310 N/m) are on a frictionless incline (?
30). The spring is compressed by xi 0.31 m
relative to its unstretched position at x 0 and
then released. What is the speed of the block
when the spring is still compressed by xf 0.14
m?
5
xi
xf
x0
x0
?
?
Given m1.7 kg, k310 N/m, ?30, xi0.31 m,
xf0.14 m, frictionless Method no friction, so
we can use conservation of energy
Initially
6
Finally
7
Interesting to plot the potential energies
E
Energy
K
?
Utotal
Ug
Us
xf
xf
xf
xi
xi
xi