Acceleration down an inclined plane

[jakerue]

Homework Statement

A 25-kg box slides, from rest, down a 9.0-m-long incline that makes an angle of
15° with the horizontal. The speed of the box when it reaches the bottom of the
incline is 2.4 m/s. (a) What is the coefficient of kinetic friction between the box
and the surface of the incline? (b) How much work is done on the box by the
force of friction? (c) What is the change in the potential energy of the box?

Homework Equations

F_x = mg * sin15
F_n = mg * cos15
F_fr = u_k * Fn = u_k * mg * cos15
Vf²-Vo² = 2 *a*d

The Attempt at a Solution

Having an issue with kinetic friction calculation here

Taking the force components and applying Newton's 2nd law -> ƩF = ma
F_x - F_fr = ma_x
mg * sin 15 - u_k (mg * cos 15) = m * a_x

Since I want uk and the final velocity is given, I calculate accel -> Vf² - Vo² = 2*a*d so a = 2.4m/s / (2*9.0m) = 0.32 m/s^2
Can I put it into mg * sin 15 - u_k (mg * cos 15) = m * a_x and end up with u_k = 0.2345 ?

I can't get over that a_x isn't constant acceleration and I don't think I can use it in this case...

 

[TaxOnFear]

I would assume constant acceleration, since there is no external forces acting on the box and it's sliding under its own mass. Therefore, I believe your method is correct.

 

[gneill]

What makes you think that the acceleration is not constant? Can you identify a force that changes during the slide?

If you're leery about the acceleration you could always check the result by using an energy conservation approach. You know the potential energy (due to gravity) at the top of the slope, and the kinetic energy at the bottom (i.e. velocity). The difference of the two will be the energy lost to friction.