# Homework Help: Two-block system - what am I doing wrong?

1. Mar 8, 2010

### Bensky

Two-block system -- what am I doing wrong? :(

1. The problem statement, all variables and given/known data
See attempt at solution.

2. Relevant equations
f_k = u_k * N (force of kinetic friction)
W = mg (weight on the blocks)
F_net = ma (net force)

T is the tension force.

3. The attempt at a solution
See attachment. It contains all my work, and the diagram for the problem. Was I correct in assuming both T and a_x for both blocks are the same?

The answer should be 0.98 m/s^2 for the acceleration but I get 5.88 m/s^2. What am I doing wrong?

#### Attached Files:

• ###### attemptedsolution.jpg
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Last edited: Mar 8, 2010
2. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

Are you looking for someone to tell you you're correct, or is your solution wrong?

3. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

My solution is wrong. The answer I got is ~5 m/s^2 for the acceleration while I should be getting 0.98 m/s^2 for the acceleration.

4. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

What is the W term in your Fx B eqn?

5. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

mg*sin(36.87 degrees)

6. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

What does it represent? It's not Tension, it's not Friction....

7. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

Weight on the block B, sorry if I forgot to include that, edited my post.

8. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

As far as I can tell your math is good, but I don't think you need this 'weight' term in Fnetx B. Your terms in Fnetx B should be Tension - Friction - xcomponent of Gravity

9. Mar 8, 2010

### benhou

Re: Two-block system -- what am I doing wrong? :(

You made two mistakes on B. They are 1.the direction of Tension, and 2.you shouldn't have $$N_{B}$$ in the x direction.

10. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

To be clear, I meant W is the x-component of the weight of Block B, NOT the total weight of block B. I probably should have written it as W_x.

I'm not sure what you mean by x component of gravity...? How is this determined?

11. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

No your Tension looks like the right sign, but if your W is the 'x component of gravity' term then that needs to be positive, since it's directing your block to the right.

There is no x component of a Normal force so leave out N.

Keep note that your coordinate system doesn't matter, but you need to be consistent

12. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

your meaning of x component of weight of block B seems to be the same as my meaning of x component of gravity. Gravity is dragging the block down the ramp, but not at the rate mg, it is damped by a factor of sin(theta) of which you have written down correctly.

N should not be there

13. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

The reason I had N_B in the x direction is because f_k (kinetic friction force) = u_k * N_B. I think that I should have this in the x direction since friction exists in this problem. Please correct me if I'm wrong or tell me where it should be.

EDIT: Nevermind! I see where I put that in there, thank you! Will try again and see how this works.

14. Mar 8, 2010

### benhou

Re: Two-block system -- what am I doing wrong? :(

The string is pulling the block B back, therefore negative, x component of force of gravity is pointing to the right, therefore positive. Both of these should be switched.

15. Mar 8, 2010

### CaptainEvil

Re: Two-block system -- what am I doing wrong? :(

Yes, you should have Frictional force acting in the x direction = u_k * N_B

However, your leading term: N_B which stands by itself should not be there.

N_B is the force that the ramp exerts on the block, and while it is an important term in determining the frictional force, it in itself does not contribute to the acceleration of the block

Good luck!

16. Mar 8, 2010

### Bensky

Re: Two-block system -- what am I doing wrong? :(

Thank you, this makes perfect sense and I am now getting the correct answer. I don't know why I didn't see that.

Also thanks to CaptainEvil for pointing out that I included N_B in front where it should not be there.