Question

A block–spring system vibrating on a frictionless, horizontal surface with an amplitude of 9.0 cm has a total energy of 22 J. If the block is replaced by one whose mass is twice the mass of the original block and the amplitude of the motion is again 9.0 cm, what is the energy of the more massive system?

a. 11j
b. 22j
c. 44j
d. 88j
e. none of above

Answer 1

The energy of the more massive block-spring system with the same amplitude is 22 J.

Step-by-step explanation:

In a block-spring system, the total energy is given by the sum of potential energy stored in the spring and the kinetic energy of the block, which is proportional to the square of the amplitude. Therefore, in this case, the total energy is equal to (1/2)kA².

If we replace the block with one whose mass is twice the mass of the original block but keep the amplitude the same, the energy of the system will still be given by (1/2)kA². So the energy of the more massive system will also be 22 J.

Therefore, the correct answer is

(b) 22 J

.