# A pulley system with two objects stacked on each other

## Homework Statement

Block B, with mass 5.00kg, rests on block A, with mass 8.00kg , which in turn is on a horizontal tabletop. There is no friction between block A and the tabletop, but the coefficient of static friction between block A and block B is 0.750. A light string attached to block A passes over a frictionless, massless pulley, and block C is suspended from the other end of the string. What is mass of block C?

F=ma
FFriction = μmg

## The Attempt at a Solution

I made equations for all 3 masses:

box C:
mCa=mcg-T.

box B:
mBa=FS

box A:
mAa=T-FS

added all three equations, the internal forces (tension and friction) cancel and I get:

mCg = a(mA+mB+mC)

However I still have 2 unknowns ($a$ and mc)
I attempted to figure out acceleration using the equation for box B:

mBa=FS
mBa=μmBg
a = μg
a = (0.750)(9.8)
a = 7.35 m/s^2
but that seems to be a sketchy way to do it?

#### Attachments

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As written, the problem statement is incomplete. Without knowing how the system is moving, there is no way to determine the mass of C (as evidenced by the fact that you have 3 equations and 4 unknowns - T, FS, a, mC).

The last part of your solution is incorrect because FS will depend on the acceleration of the blocks, which is unknown.

As written, the problem statement is incomplete. Without knowing how the system is moving, there is no way to determine the mass of C (as evidenced by the fact that you have 3 equations and 4 unknowns - T, FS, a, mC).

The last part of your solution is incorrect because FS will depend on the acceleration of the blocks, which is unknown.

no when you add the 3 equations together you only have 2 unknowns. Then if you find the acceleration (7.35) and solve for mC you get 39 kg, which seems to be the correct answer.

jbunniii
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Gold Member
FFriction = μmg
You seem to be making an implicit assumption here. The friction force is at most ##\mu mg## but it can be less. For example, if mass ##C## was zero and there was no movement, then the friction force would be zero.

haruspex
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2020 Award
no when you add the 3 equations together you only have 2 unknowns. Then if you find the acceleration (7.35) and solve for mC you get 39 kg, which seems to be the correct answer.
To get that acceleration, you had to assume that the frictional force between A and B was at its maximum value. This is presumably the missing piece of information.
The question as stated does not provide any basis for such an assumption. If the normal force is N and the coefficient of friction is μ then the frictional force is anything from -μN to +μN.

no when you add the 3 equations together you only have 2 unknowns. Then if you find the acceleration (7.35) and solve for mC you get 39 kg, which seems to be the correct answer.

You have a set of 3 equations and 4 unknowns. Adding them together is a good way to isolate the variables you want, but you still are under-constrained.

Regardless, the problem is incomplete and there needs to be another piece of information (most likely about the acceleration of the blocks) to determine the mass of block C.

haruspex
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Regardless, the problem is incomplete and there needs to be another piece of information (most likely about the acceleration of the blocks) to determine the mass of block C.
No, most likely that it is the maximum mass for which the system remains static.

No, most likely that it is the maximum mass for which the system remains static.

Because the horizontal surface is frictionless, there is no static configuration for this system. The acceleration is mCg/(mA+mB+mC), which can only be zero if mC is zero or mA+mB is infinite.

haruspex
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2020 Award
Because the horizontal surface is frictionless, there is no static configuration for this system. The acceleration is mCg/(mA+mB+mC), which can only be zero if mC is zero or mA+mB is infinite.
Sorry, I should have said, for which the blocks do not slide on each other.

Sorry, I should have said, for which the blocks do not slide on each other.

Gotcha. So you're assuming that the question is asking for the maximum mass of block C such that block B doesn't slip. That would make sense.

Who knew physics question forensics would be so much fun?!