Two-block system - what am I doing wrong?

[Bensky]

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

Homework Statement

See attempt at solution.

Homework 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.

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?

 

[CaptainEvil]

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

 

[Bensky]

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

 

[CaptainEvil]

What is the W term in your Fx B eqn?

 

[Bensky]

What is the W term in your Fx B eqn?

mg*sin(36.87 degrees)

 

[CaptainEvil]

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

 

[Bensky]

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

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

 

[CaptainEvil]

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

 

[benhou]

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.

 

[Bensky]

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

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?

 

[CaptainEvil]

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

 

[CaptainEvil]

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

 

[Bensky]

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.

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.

 

[benhou]

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

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.

 

[CaptainEvil]

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!

 

[Bensky]

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.

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.