Question

A block of mass m=0.750 kg is fastened to an unstrained horizontal spring whose spring constant is k=82.0 N/m. The block is given a displacement of +0.120m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. C) What is the maximum speed of the block? Group of answer choices

Answer 1

13.12 m/s

Step-by-step explanation:

According to the law of energy conservation, the maximum speed of the block occurs when all the spring potential energy is converted to block kinetic energy. That is:

`E_s = E_k`

`(1)/(2)kx^2 = (1)/(2)mv^2`

`v^2 = (kx^2)/(m)`

`v = \sqrt{(kx^2)/(m)} = x\sqrt{(k)/(m)}`

we can substitute m = 0.75 kg, k = 82 N/m, and x = 0.12m

`v = 0.12(82)/(0.75) = 13.12 m/s`