Question

You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move down and find that it hangs at rest with the spring stretched by 23.0 cm. Next, you lift the block back up and release it from rest with the spring unstretched. What maximum distance does it move down?

Answer 1

Maximum distance moved = 0.46 m = 46 cm

Step-by-step explanation:

Doing a force balance in this initial setup,

The weight of the block = Elastic force on the spring.

mg = kx

where m = mass of the block

g = acceleration due to gravity

k = spring constant

x = extension = 23 cm = 0.23 m

(mg/k) = 0.23 (eqn 1)

But when the block is lifted back up and released with the spring unstretched,

The maximum change in potential energy = maximum work done on the spring.

If the maximum distance moved = X

Maximum Change in potential energy = mgX

Maximum workdone on the spring = (1/2)kX²

mgX = (1/2)kX²

X = (2mg/k)

Recall eqn 1; (mg/k) = 0.23

X = 2(mg/k) = 2 × 0.23 = 0.46 m = 46 cm.

Hope this Helps!!!