Question

A block of mass ?=4.80 kg slides along a horizontal table with velocity ?0=3.00 m/s. At ?=0, it hits a spring with spring constant ?=36.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by ?=0.350. How far has the spring compressed by the time the block first momentarily comes to rest? Assume the positive direction is to the right.

Answer 1

Given mass m=4.8kg and velocity = 3m/s

so Kinetic Energy E_k = 1/2 mv² = 0.5*4.8 * 3² = 21.6 J

When the mass hits the spring an dcomes to rest the energy is converted into elastic potential energy of the spring and since there is some friction few amount of energy is lost

Kinectic Energy = Potential energy + energy lost to friction

1/2mv² = 1/2kx² + umgx where k is spring constant

21.6 = 0.5 * 36 *x² +0.35*4.8*9.81*x

18x² +16.48x -21.6 =0

solve it using quadratic formula or use a calculator

x = 0.729 or x= -1.64

take the positive value

ANSWER: x =0.729 m