Question

VI. On another planet, a spring with constant 4.7 n/m is set up and allowed to expand verticaly freely. 8.4kg mass is placed on the spring and the spring extends 5.28m. Calculate the exected extension on earth.

Answer 1

The mass is attached to the spring vertically, so at equilibrium the force of gravity pulling down on the mass will equal the spring force acting upwards on the mass.

For gravity:

F = mg

m is the mass.

g is the acceleration due to earth's gravity.

For the spring:

F = kΔx

k is the spring constant.

Δx is the spring extension.

Set the force of gravity and spring force equal to each other:

mg = kΔx

Given values:

m = 8.4 kg

g = 9.81 m/s²

k = 4.7 N/m

Substitute the terms in the equation with the given values and solve for Δx:

8.4×9.81 = 4.7Δx

Δx = 17.53 m