1. Aim: How do we characterize elastic potential energy?

2. Hooke’s Law
Hooke’s Law states that the force required to stretch a spring is equal to the product of the spring’s spring constant and the amount it is being stretched or compressed. F = - k ∆x F = force, k = spring constant ∆x = displacement from equil.

3. Elastic Potential Energy
We can show that the PE that a spring has due to being compressed or stretched can be expressed using, PE = ½ k (∆x)2 PE = elastic PE, k = spring constant, ∆x = change in length from equilibrium

4. Thought Questions
What does the elastic potential energy on a spring depend on?
The spring constant and change in spring length
2) What does a force vs ∆x graph look like?
3) What does an elastic potential energy vs ∆x graph look like?

5. Elastic Potential Energy Problems
Ex. 1 A spring has a spring constant, k, of 320 N/m. How much must the spring be compressed to store 50 J? PEs=1/2 kx2 50 J=1/2(320N/m)x2 x=0.56 m Ex. 2 A force of 10 N stretches a spring by 0.2 m. How much elastic potential energy is stored in the spring? F=kx 10 N=k(0.2 m) k=50 N/m PEs=1/2kx2=1/2(50N/m)(0.2m)2=1J

6. Elastic Potential Energy Problems
3 . When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the spring constant of the spring. F=mg=13.2kg(9.8m/s2)=129 N F=kx 129 N=k(0.0593m) k= N/m 4. If a spring has a spring constant of 400 N/m, how much work is required to compress the spring .25 m from its undisturbed position? PEs=1/2kx2=1/2(400 N/m)(0.25m)2=12.5 J

7. Turn and Talk-Before solving, explain the energy transformation that occurs
A box of mass 2 kg starts from rest and falls a distance of 1.02 m before striking a spring. If the spring has a spring constant of 500 N/m, calculate the maximum compression of the spring.
The gravitational potential energy turns into elastic potential energy.
PE=mgh=2kg(9.8m/s2)(1.02m)=19.6 J
PEs =1/2kx2=19.6 J=1/2(500N/m)x2
x=0.28 m

8. Turn and Talk- Before solving explain the energy transformation that occurs
A 0.3 kg mass collides with a spring of spring constant of 40 N/m. It is compressed 0.5 m from its initial position. Calculate the speed of the mass.
All of the kinetic energy is converted into elastic potential energy.
PEs =1/2(40 N/m)(0.5m)2
Pes=5J