An ideal spring is used to stop blocks as they slide along a table without friction. A 0.80 kg block traveling at a speed of 2.2 m/s can be stopped over a distance of 0.11 m once it makes contact with the spring. A rectangular block on a level surface moves at velocity v to the right towards a spring that rests on the surface and is attached to a fixed mount on the right.

What distance would a 1.40 kg block travel after making contact with the spring if the block is traveling at a speed of 3.0 m/s before it makes contact with the spring?

Use the work-energy theorem: the total work done on the 0.80 kg block by the spring to make it come to a stop is equal to the change in the block's kinetic energy.

If we take the block's initial direction of motion to be positive, then the spring does negative work on the block, and

-1/2 k (0.11 m)² = 0 - 1/2 (0.80 kg) (2.2 m/s)²

Solve for the spring constant k :

k = (1/2 (0.80 kg) (2.2 m/s)²) / (1/2 (0.11 m)²) = 320 N/m

We can use the same equation as above to find the distance the 1.40 kg block would travel as it is slowed down by the same spring:

-1/2 (320 N/m) x ² = 0 - 1/2 (1.40 kg) (3.0 m/s)²

Solve for the displacement x :

x = √((1/2 (1.40 kg) (3.0 m/s)²) / (1/2 (320 N/m))) ≈ 0.20 m

force tends to be low and long diustance masses are high