Compute acceleration on an inclined plane with friction

[Jim Bob]

Homework Statement

A 24 kg object is placed at the top of an incline with height 500m and length 375m. The coefficient of kinetic friction is 0.600
1) Find the acceleration of the object.
2) Find the speed by the time it has reached the bottom of the inclined plane.

Homework Equations

F_g = Force of gravity on the object
F_N = Normal force
F_// = Parallel force (force applied to the object parallel to the inclined plane and towards the bottom of the inclined plane)
F_p = Perpendicular force (force the object exerts on the inclined plane perpendicularly to it)
F_k = force of kinetic friction

The Attempt at a Solution

See the attachment, the answer key says acceleration=8.33646 but I got a different number

 

[haruspex]

height 500m and length 375m.

Length normally would mean the hypotenuse, but clearly that is not possible. I see you have taken the 375m as a horizontal extent, which is a reasonable interpretation.
This makes it a 3-4-5 triangle.

answer key says acceleration=8.33646

That seems to be 85% of g. It would not be that high even without friction.
I agree with your answer, but you can get there much faster. The mass is irrelevant, and it is almost always unnecessary to find the angle.
You have (4/5)g-0.6(3/5)g=(11/25)g.

 

[Jim Bob]

What about the second problem? How would I do that?

 

[haruspex]

What about the second problem? How would I do that?

What equations do you know that apply to motion under constant acceleration?

 

[Jim Bob]

Oh I got it now!, KE=mv^2/2 and PE = mgh so since all PE is transferred to KE by the end, mv^2/2=mgh and solving for v gives v=sqrt(2gh).

 

[haruspex]

all PE is transferred to KE

What about the friction?