# Homework Help: Newton's Law and Friction (Ramp problem)

1. Feb 7, 2014

1. The problem statement, all variables and given/known data
A block is placed on a incline plane. A 21 N force is required to push the block up the incline with constant velocity. What is the weight of the block? Answer in units of N

2. Relevant equations
The force pushing the block=21 N with an angle of 13 degrees. The ramp has an angle of 21 degrees. Coefficient of friction=0.17. Ramp goes up from left to right.
fs = uN, F = ma, acceleration is 0.

Angle of force = phi, Angle of ramp = theta

3. The attempt at a solution
My attempt: (after drawing my free-body diagram)

F(y-component): N-mgcos(theta) = 0 --> N=mgcos(theta) --> Fsin(phi)-mgcos(theta) = 0
F(x-component): Fcos(phi)-mgsin(theta)-fs = 0 --> Fcos(phi)-mgsin(theta)-umgcos(theta) = 0

I multiplied the y-component with the negative u (or mu) to cancel out umgcos(theta)

Then: Fcos(phi)-uFsin(phi)-mgsin(theta) = 0, So I solved for mg and my answer was incorrect. What am I doing wrong? Any help appreciated, thanks.

2. Feb 7, 2014

### BvU

What did you find when the solving was done?
I notice phi is different from the 21 degrees. Is phi wrt horizontal? Does its y component contribute to the friction force ?

3. Feb 7, 2014

Well the problem indicated that the force pushing the block up the ramp had an angle of 13 degrees. So denoting that phi, I used Fsin(phi) and Fcos(phi) respectively.

My answer in the end was about 54.85 N. Which was incorrect. No idea what I am doing wrong.

4. Feb 7, 2014

### BvU

I take it the free body diagram decomposes mg along the slope and perpendicular to it.
You want to do the same with the 21 N force. What is the angle wrt the plane ?
The component perpendicular to the plane is to be added to mg $\cos\theta$ to determine the normal force.
That times $\mu$ is the friction force, along the slope, downwards. To be added to mg $\sin\theta$, also downwards. Call the sum Fdown
No acceleration (i.e. constant speed) along the slope means the 21 N component along the slope is equal and opposite to this Fdown