A ball with a mass m = 0.20 kg is pushed against the end of thespring with a spr

Question

A ball with a mass m= 0.20 kg is pushed against the end of thespring with a spring constant k= 2.0 105N/m. The spring is compressed to a distanceof x = -1.0 cm from theequilibrium point, and then released. When the ball is back at theequilibrium point, the ball and the spring separate.

a) What is the work done on the spring when compressing it from theequilibrium point to the x= -1.0 cm position?
b) What is the speed of the ball immediately after it separatesfrom the spring? A ball with a mass m= 0.20 kg is pushed against the end of thespring with a spring constant k= 2.0 105N/m. The spring is compressed to a distanceof x = -1.0 cm from theequilibrium point, and then released. When the ball is back at theequilibrium point, the ball and the spring separate.

a) What is the work done on the spring when compressing it from theequilibrium point to the x= -1.0 cm position?
b) What is the speed of the ball immediately after it separatesfrom the spring?

Explanation / Answer

a) work done W is equal to the potential energy stored in thespring. W = (1/2)kx2 = (1/2)*2.0*105N/m*(-1.0*10-2m)2 = 10.0J b) let the speed is v, after release, the kinetic energy will beequal to the energy stored in the spring. (1/2)mv2 =(1/2)kx2 =10.0J v = (2*10.0J/m) = (2*10.0J/0.20kg) =10.0m/s

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