Question

A horizontal spring with k = 72 N/m has one end attached to a wall and the other end free. An 91 g wad of putty is thrown horizontally at 3.4 m/s directly toward the free end.

Find the maximum spring compression (ignore gravity). Hint: Kinetic energy is converted into potentail energy of spring .

Express your answer to two significant figures and include the appropriate units.

Answer 1

Given horizontal spring of constant k = 72 N/m, and mass of putyy m = 91 g = 91*10^-3 kg, velocity v = 3.4 m/s

we know that the kinetic energy of the putty will be conveted in to the elastic potential energy in the spring by compressing it

equating 1/2 mv^2 = 1/2 kx^2

                       x^2 =mv^2/k

                          x = sqrt(mv^2/k)

                              = sqrt(91*10^-3*3.4^2/72)

                             = 0.12087 m

                             = 12.08 cm

spring compression is 0.1208 m = 12.08 cm