Measurement Question

Question

with no additional mass, the hanger was 30.6 cm off the ground. With 150 grams of additional mass, the hanger was 16.2 cm off the ground.

A wooden block stretched the spring so the hanger was 23.5 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

Answer 1

This is an application of Hooke's law that says the force required to stretch the spring a distance X from its equilibrium position is F = kX.

To find k, substitute the force and X into the above equation.

k = 150g x G / (30.6 - 16.2)cm = 102.1 gs^-2 (G is 980 cms^-2). The force unit is the dyne.

Assuming the 150g mass was removed and replaced with the block, the force required would be

F = mass of block x G = 102.1 gs^-2 x (30.6 - 23.5) cm which rearranges to

mass = 102.1 gs^-2 x 7.1 cm / 980 cms^-2 = 5.3 grams