Acceleration and forces?

Question

a 12kg box is released from the top of an incline that is 5.0m long and makes an angle of 40deg. to the horizontal. a 60-N friction force impedes the motion of the box.

A. what is the acceleration of the box?

B. how long will it take to reach at the bottom of the incline?

Answer 1

The weight of the box is:

W = mg

Since the box is on an inclined plane, you must resolve the weight into two components.  One component acts normanl to the plane (Wn) and the other acts parallel (Wp) down the plane.

Wn=WCos(theta)

Wp=WSin(theta)

The friction force (F) acts parallel up the plane.

Using Newtons Law:

Wp-F=ma

Solve for a.

a = 1.306m/s^2

Use the equations od rectilinear motion to solve for t.  Use vo=0, s=5m

t=2.77s