A 2.50-kg mass is pushed against a horizontal spring of force constant 25.0 N/cm on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any way. When the spring has been compressed enough to store 11.5 J of potential energy in it, the mass is suddenly released from rest. (a) Find the greatest speed the mass reaches. When does this occur? (b) What is the greatest acceleration of the mass, and when does it occur?

Solution 23E Step 1 of 5: In the given problem, a block of mass m=2.5 kg is placed in front of the spring with force constant k= 25 N/cm as shown in the figure below. Step 2 of 5: (a) Find the greatest speed the mass reaches. When does this occur The potential energy stored in the spring when it is compressed is 11.5 J and when the spring is released this potential stored energy will be converted into kinetic energy of the block in front of the spring. The maximum speed v the block attains as it leaves the spring, That is, PE = KE Using PE= 11.5 J and KE= mv 2 2 11.5 J= mv 2 2 Step 3 of 5: Substituting m=2.5 kg and solving for v, 11.5 J= (2.5 kg)v 2 2 v = 2×11.5 J (2.5 kg) v = 9.2 v = 3.03 m/s Therefore, as the block leaves the spring, block attains maximum speed of 3.03 m/s.