Can anyone help out with this? I have been stuck on this problem for over an hour now.

The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In the video, 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 21.8 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

Question

Can anyone help out with this? I have been stuck on this problem for over an hour now.

The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In the video, 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 21.8 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

SmokeyBrown · Answer

The amount stretched by a spring should be proportional to the tension applied to the string.
We see that the spring stretches a distance of (30.6 - 16.2) centimeters == 14.4 centimeters due to tension applied by 150 grams of mass.
We can say that the spring stretches by 14.4 centimeters for 150 grams, or, to simplify, 
14.4/150 == 0.096 centimeters per gram

The same spring is then stretched 21.8 cm by a block of unknown mass.
Since we know that the spring stretches 0.096 centimeters per gram, we can find out the mass of the block by calculating how many (0.096 cm) it takes to equal 21.8 cm:
21.8/0.096 = 227.083

In this way, we have found that the wooden block which caused the spring to stretch 21.8 centimeters had a mass of 227.083 grams.