# Homework Help: Inclined plane with pulley

1. Apr 4, 2015

### brake4country

1. The problem statement, all variables and given/known data
A 10 kg mass is on a frictionless inclined plane 30 degrees to the horizontal. At the top of the plane is a pulley that has a rope attached to mass with tension T = 75 N. If the mass starts from rest, what is its velocity after 2 seconds?

2. Relevant equations
F = ma
Vf=Vi + at

3. The attempt at a solution
So my book lists the formula as T = mgsinθ + ma. I set the problem up pretty much the same as:
∑Fx = max
75 N - 10 N = (10 kg) a
My acceleration is 6.5 m/s2. Plugging this value in to vf=vi + at, I get 13.0 m/s but my book says it's supposed to be 5 m/s. What am I doing wrong? Thanks in advance!

2. Apr 4, 2015

### ehild

Where did you get that 10 N from?

3. Apr 4, 2015

### brake4country

The x component of the weight: -mgsinθ

4. Apr 4, 2015

### ehild

m=10 kg, g=10 m/s2, θ=30° . How would it give 10 N ?????

5. Apr 5, 2015

### brake4country

I see. Well, I redid this problem and I did a force table. My T is 75 N, my x component of the force is -50 N. If I set up the problem I get:
T - mgsinθ = ma
75-50 = 10 a
a = 2.5 m/s^2

6. Apr 5, 2015

### brake4country

I totally misread this problem and it serves me right for not paying close attention. This is a two part problem. I solved for the acceleration using F=ma, which is 2.5 m/s^2. Then with the known time (2 s), I plugged it in to the equation Vf=Vi + at. Vf = 5 m/s.

7. Apr 5, 2015

### ehild

Well done at the end!