Aim: How do we characterize elastic potential energy?

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.

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

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?

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

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=2175.38 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

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

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