Finding Force Constant of a Spring

[court2011]

Homework Statement

A 1.80 kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 1.95 m/s and compresses it a distance of 14.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is µk = 0.560, what is the force constant of the spring?

Homework Equations

k=2U/x^2

The Attempt at a Solution

k=2(0.560)/0.14^2

 

[rl.bhat]

Hi court2011, welcome to PF.
The kinetic energy of the block is utilized to do the work to overcome the friction and compress the spring.
What is the frictional force?

 

[court2011]

hi! the problem doesn't say so I am assuming i have to find it given the coefficient of kinetic friction?

 

[rl.bhat]

Kinetic energy of the block = Potential energy of the spring + work done against the frictional force.

 

[court2011]

ok so potential energy is = mgy but if its going horizontal isn't y=0 so the potential energy is 0?

 

[rl.bhat]

Potential energy stored in the spring is 1/2*k*x^2.

 

[court2011]

ok i need to find k so how do i get the potential energy without having k in the equation?

 

[rl.bhat]

First of all find the frictional force.
Then using 1/2*m*v^2 = Fr*x + 1/2*k*x^2 find k.

 

[court2011]

is Fr where i am supposed to insert the frictional force? because i did and I still got the problem wrong but equation seems right how do i find the frictional force isn't it f_k=u_kN?

 

[rl.bhat]

I am refereeing Fr as fk which is equal to μk*N. Now what is the normal force?

 

[court2011]

ma which is 1.8*1.95=3.51

 

[rl.bhat]

The normal force is mg.
Frictional force is μk*mg.