A spring with a constant of 4 (kg)/s^2 is lying on the ground with one end attached to a wall. An object with a mass of 3 kg and speed of 3 m/s collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Mar 12, 2016

color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"

Explanation:

This is a routine case for using law of the conservation of energy

color(red)("The kinetic energy possessed by the body when it collides transfers to the springs potential energy")

color(Blue)("KE of body = PE of spring")

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

cancel(1/2) mv^2 = cancel(1/2)kx^2

m = 3, v = 3, k = 4 x = ?

3 *3^2 = 4x^2

3^3 /2^2 = x^2

3 *3^2 /2^2 = x^2

x = sqrt(3 *3^2 /2^2 ) = 3/2 sqrt 3

color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"