Question

A block of mass m = 4.30 kg slides along a horizontal table with speed v0 = 8.50 m/s. At x = 0 it hits a spring with spring constant k = 31.00 N/m and it also begins to experience a friction force. The coefficient of friction is given by μ = 0.150. How far has the spring compressed by the time the block first momentarily comes to rest?

I'm not really sure where to go with this question. I've drawn a free body diagram and calculated the net work by the equation W=1/2m(v^2-vi^2) and got -155 J. I'm not sure where to go from there.

Answer 1

Looking at energy:
initial KE=final spring PE+workdoneFriction

1/2 m*vo^2=1/2 k x^2 + 1/2 mg(mu)x

0=1/2 k x^2 + 1/2 .150 *4.3*9.8*x

so it is a quadratic, put it in standard form, and solve for x.

Answer 2

That did not give me the correct answer.