Question

At a waterpark, sleds with riders are sent along a slippery, horizontal surface by the release of a large, compressed spring. The spring with a force constant 42.0 N/cm and negligible mass rests on the frictionless horizontal surface. One end is in contact with a stationary wall. A sled and rider with total mass 68.0 kg are pushed against the other end, compressing the spring 0.390 m. The sled is then released with zero initial velocity.What is the sled's speed when the spring returns toits uncompressed length?m/s

Answer 1

The sleds speed when the spring returns toits uncompressed length is v = 0.03 m/s.

Explanation:

Given,

force constant = 42 N/cm = 0.42 N/m,   mass m = 68 kg, spring x = 0.39 m

The potential energy, U, stored in the spring is

                     U = 1/2 kx^2  

                       = 1 / 2 $\times$ 0.42 $\times$ (0.39)^2

                       = 0.032 J

All its potential energy has been converted into kinetic energy since it has a uncompressed length.

                    K = 1/2 mv^2

                     v = sqrt (2K / m)

                       = √(( 2 $\times$ 0.032) / 68)

                    v = 0.03 m/s .