Inclined Plane with Pulley: Finding Velocity with Tension and Acceleration

[brake4country]

Homework Statement

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?

Homework Equations

F = ma
V_f=V_i + at

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:
∑F_x = ma_x
75 N - 10 N = (10 kg) a
My acceleration is 6.5 m/s². Plugging this value into v_f=v_i + 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!

 

[ehild]

Homework Statement

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?

Homework Equations

F = ma
V_f=V_i + at

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:
∑F_x = ma_x
75 N - 10 N = (10 kg) a

Where did you get that 10 N from?

 

[brake4country]

The x component of the weight: -mgsinθ

 

[ehild]

The x component of the weight: -mgsinθ

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

 

[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

The answer is 5 m/s^2.

 

[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 into the equation Vf=Vi + at. Vf = 5 m/s.

 

[ehild]

Well done at the end!