Question

A spring with k=45 N/m is oriented vertically with one end fixed to the ground. A 0.5 kg mass on top of the spring compresses it.

1. Provide a conceptual explanation of what is happing for each of the following cases :

a. You hold the mass while you gently compress the spring, and when you release the mass it sits at rest atop the spring.

b. You place the mass on the uncompressed spring and release it.

c. You drop the mass from 10 cm above the spring.

2. Find the spring’s maximum compression in each of the cases above.

Answer 1

1 (a) When i compress the spring, work is done by me and that work is stored in the form of potential energy.and when I release, that potential energy will start converting into kinetic energy.

(b) When I placed the mass on uncompressed spring, it will compress due to the weight of mass until it was balanced by restoring force.

(c) The falling mass will gain kinetic energy and when it will come into contact with spring, spring will start compressing and gain potential energy untill all the kinetic energy gain by mass will convert into potential energy of spring.

2. (b) When mass is placed and released then

(c) Let the compression in spring is

ignioring -ve value we have

x=0.292 m