Analyzing a Pulley System: Solving for Energy and Work

[minimario]

Homework Statement

Homework Equations

$W_{nc} = \Delta KE + \Delta PE$
$PE = mgh$
$KE = \frac{1}{2} mv^2$

The Attempt at a Solution

For Block B, $\Delta KE + \Delta PE = \frac{1}{2} 100 v^2 + (-20)(g)(100)$

For Block A, $\Delta KE + \Delta PE = \frac{1}{2} 50 v^2 + (20 \sin 37^{\circ})(g)(100)$

Therefore, we have the total change in energy is $75 v^2 - 13702$. This is the total work done by nonconservative forces.

The only nonconservative force is friction on the A block. The normal force on the A block is $50g \cos 37^{\circ}$, so the friction force is $(0.25)(50g \cos 37^{\circ})$ The work done by friction is then $- 20 \cdot (0.25)(50g \cos 37^{\circ}) = 1956.66$, so $75v^2-13702 = 1956.66 \Rightarrow v^2 = 208.77$, so the Kinetic Energy change is $\frac{1}{2} (50)(208.77) = 5219.25$

This is incorrect, can anyone find what's wrong?

 

[Chestermiller]

Well, for one thing, in the PE of A, the mass is 50 kg, not 100 kg. Is this a typo, or did you really use 100?

Chet

 

[NTW]

I suggest a simpler approach: determine the net force; from that and from the masses involved, find the acceleration, and you have solved a half of the problem...

 

[minimario]

Well, for one thing, in the PE of A, the mass is 50 kg, not 100 kg. Is this a typo, or did you really use 100?

Chet

That was a typo.

 

[Chestermiller]

There should be a sin 37 in the potential energy term of block B also.

Chet

 

[minimario]

Then the P.E.s of A and B cancel out?

That doesn't give the right ans either... (do you get v^2 = 52.1776)

 

[Chestermiller]

Then the P.E.s of A and B cancel out?

That doesn't give the right ans either... (do you get v^2 = 52.1776)

No, they don't cancel out. Don't forget your typo on the masses.

Chet

 

[minimario]

So now v^2 = 104.73, is that right?

 

[Chestermiller]

So now v^2 = 104.73, is that right?

Shouldn't the friction decrease the kinetic energy?

Chet

 

[minimario]

Yes, but the 100 kg block provides the energy and accelerates it.

 

[Chestermiller]

Yes, but the 100 kg block provides the energy and accelerates it.

If there were no friction, the velocity of the blocks would be higher.

Chet

 

[minimario]

What do you mean? The 100 kg provides a force to counteract the friction...

 

[Chestermiller]

What do you mean? The 100 kg provides a force to counteract the friction...

What I mean is that you have the wrong sign on the friction term.

One way to be sure is to solve the problem using force balances rather than the energy balance. At the very least, you should check to see that they both give the same answer.

Chet