Homework Help: Did I do this question correctly?

1. Nov 22, 2008

lanvin

Question is:
"A box with a mass of 22kg is at rest on a ramp inclined at 45° to the horizontal. The coefficients of friction between the box and the ramp are µ(s) = 0.78 and µ(k) = 0.65

Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to remain at rest."

What I was thinking, is that if the object is at rest, then the net force on the x axis is zero. So, the magnitude would be the same as the gravity parallel to the ramp...? My calculations:

(22kg)(9.8N/kg)sin45° - F(applied) = 0N
F(applied) = 152N

Is that right, or wrong? Hints or suggestions...?

2. Nov 22, 2008

naresh

You did not include the effect of friction.

Also, you should be clear when you say "x axis". What is the x axis in your solution?

3. Nov 22, 2008

PhanthomJay

You forgot that the friction force on the box is also acting down the plane.

4. Nov 22, 2008

lanvin

152N - F(f)
152N - (0.65)(22kg)(9.8N/kg) = 11.86N

did I do it right?

5. Nov 22, 2008

PhanthomJay

No. Why did you use the kinetic friction coefficient when it is given that the box is to remain at rest? Also, the normal force acts perpendicular to the incline; it is not equal to its weight. Have you defined your x axis, and identified all the components of the forces acting on the box along and perpendicular to the incline?

6. Dec 9, 2008

KOKA

Without any added parallel or perpendicular forces, the force of gravity acting parallel to the ramp will move the box downwards. In this case, you're looking for a larger normal force to keep the box in place (think about adding pressure from a hand to prevent the box from slipping). Remember that F = uFN? Add an unknown force to the FN to symbolize the applied force added to the top of the box.