# What is the acceleration of the crate?

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1. Dec 6, 2014

### Sylvia

Problem: A 22.0-kg crate is pulled along a horizontal floor by the ideal arrangement
shown in figure below. The force F is 300 N. The coefficient of friction between the crate and
the floor is 0.270. What is the acceleration of the crate?

2. Relevant equations
F = ma
Friction = (coefficient)(normal force)

3. The attempt at a solution

2. Dec 6, 2014

### ehild

Welcome to PF! :)

F acts on the pulley, not on the crate. The crate is connected to a rope. What is the force the rope pulls the crate with?
Note that the pulley is ideal, massless. What forces act on it, and what should be the resultant force?

3. Dec 7, 2014

### Sylvia

Thank you! :)
That's the tension force, right? So would I set it up as F + T - Friction = ma?
I also wondered this at first, but I got confused because how would you know what the value of T is?

4. Dec 7, 2014

### haruspex

Yes.
No. Consider the pulley and the crate separately. What forces act directly on the crate? (Hint: F does not.) What forces act on the pulley?
You can write a $\Sigma F_x = m a_x$ equation for each, but in the case of the pulley the mass is zero.

5. Dec 7, 2014

### ehild

F does not act on the crate. F is applied at the pulley. So what equations you have both for the crate and for the pulley?

6. Dec 7, 2014

### Sylvia

See, that's where I'm confused. For the crate would I have -Friction + Tension = ma? And then for the pulley I would have F + Tension = ma? I'm not sure where the tension is playing a role.

7. Dec 7, 2014

### ehild

Correct.
Think: There are two pieces of the string pulling the pulley. The tension is the same in both pieces. And what is the direction of force one string exerts on the pulley?
And the pulley is massless.

8. Dec 7, 2014

### Sylvia

Since the mass of the pulley is 0 and since the tension in both pieces is the same, I would get F - 2T = 0?

9. Dec 7, 2014

### ehild

Exactly! You can solve the problem now. :)

10. Dec 7, 2014

### Sylvia

Thank you very much for the help!

11. Dec 7, 2014

### ehild

You are welcome. What did you get for the acceleration?

12. Dec 7, 2014

### Sylvia

I actually had a different version of this question; I googled the question and found this version so I could copy and paste it (the question was the same, just the numbers were different). I had 24 kg and coeff. of friction was 0.290. But I ended up getting the right answer, which was 3.41 m/s^2 :)

13. Dec 7, 2014

### ehild

Correct! Good work.:)