A10 kg block is originally moving at a speed of 5 m/sec. it hits a relaxed spring of k= 3000 n/m. if the block loses 10% of its original energy, how far will the spring compress when the block stops?

0.27 m

Explanation:

The initial energy of the block (kinetic energy) is given by:

where m=10 kg is the mass of the block and v=5 m/s is the speed.

Later, the block loses 10% of its original energy, so its new energy is 90% of the original energy:

Finally, the block transfers all its kinetic energy to the spring, so the energy is converted into elastic potential energy of the spring, given by

where k=3000 N/m is the spring constant and x is the compression of the spring. Solving for x, we find