Textbook with spring sliding, use work-energy thm to solve

[makeAwish]

A 2.20kg textbook is forced against a horizontal spring of negligible mass and force constant 220 N/m, compressing the spring a distance of 0.270 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction 0.30. Use the work-energy theorem to find how far the textbook moves from its initial position before coming to rest.


The answer is 1.2m. Can someone help me solve?

Thanks.


My attempt was:


change in KE + change in Elastic potential energy = -friction x distance
0 + (-0.5k(x^2)) = - 0.30(mg)(L)
L = 2.48m

 

[makeAwish]

Oh. I had a careless mistake! Ahh. Okay i know le. Haha Thanks.

 

[nlightner]

Hello,

Your attempt at solving the problem is on the right track. However, there are a few things that need to be clarified and corrected.

Firstly, the work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In this case, the net work done on the textbook is equal to the work done by the spring (elastic potential energy) minus the work done by friction.

Secondly, the value of the gravitational acceleration (g) should be included in the equation for the work done by friction. Also, the distance traveled by the textbook should be represented by x, not L.

With these corrections, the equation should look like this:

Change in KE = Work done by spring - Work done by friction
0.5mv^2 = 0.5kx^2 - μmgx

Substituting the given values, we get:

0.5(2.20)v^2 = 0.5(220)(0.270)^2 - (0.30)(2.20)(9.8)x
v^2 = 3.704 - 6.804x

Since the textbook comes to rest at the end, its final velocity (v) is 0. Therefore, we can solve for x:

0^2 = 3.704 - 6.804x
x = 0.544 m or 54.4 cm

Therefore, the textbook moves 54.4 cm from its initial position before coming to rest.

I hope this helps. Keep up the good work!