Conservation of Momentum: Pulley System

In summary, the problem involves two blocks, A and B, connected by a light string and a pulley with non-negligible mass. The system is on a frictionless horizontal table and we are asked to find the magnitude of its linear acceleration. The solution involves using the equations Στ=Iα and α=a/r, as well as the moment of inertia of a disk. The provided solution appears to be correct, but there may have been a mistake with the online homework answer checker.
  • #1
Watney
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Homework Statement


Block A (of mass MA) rests on a frictionless horizontal table. It is connected via a light string to block B (of mass MB) hanging over the edge of the table. The pulley itself, a solid disc, has non-negligible mass MC. The light string does not slip over the pulley.
What is the magnitude of the linear acceleration of the system?

Edit: Messed up with the title! This problem is in the chapter of Conservation of Momentum in my book but I actually didn't use it for this problem.

Homework Equations


Στ=Iα
α=a/r
Moment of Inertia of a disk = 1/2mr^2

The Attempt at a Solution


So here's my attempt but I'm not sure where I'm messing up.
FullSizeRender 2.jpg
 
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  • #2
Your work looks correct .

Why do you think you are messing up somewhere ?
 
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  • #3
Vibhor said:
Your work looks correct .

Why do you think you are messing up somewhere ?

When I enter my answer into my online homework answer checker, it says it's wrong. I'll have to ask my professor if maybe there's a mistake with his website cause sometimes he messes up!
Thanks though!
 
  • #4
I don't know where you're messing up. I didn't see anything wrong.
 
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  • #5
Watney said:
sometimes he messes up
That is probably what happened. I went through the problem twice and got the same result both times.

Acknowledging @Vibhor who answered before me. I didn't see it until after I posted.
 
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1. What is the conservation of momentum in a pulley system?

The conservation of momentum in a pulley system is a physics principle that states that the total momentum of a closed system remains constant, meaning that the initial momentum of the system is equal to the final momentum of the system.

2. How does a pulley system conserve momentum?

In a pulley system, the rope or cable connecting the two masses is considered to be a single entity. As the rope is continuous and inelastic, the forces acting on the two masses must be equal and opposite to maintain the tension in the rope. This results in the total momentum of the system remaining constant.

3. Can the conservation of momentum be applied to all types of pulley systems?

Yes, the conservation of momentum applies to all types of pulley systems as long as there are no external forces acting on the system. This includes single pulleys, compound pulleys, and systems with multiple pulleys.

4. How does the mass of the pulley affect conservation of momentum in a pulley system?

The mass of the pulley itself does not affect the conservation of momentum in a pulley system. However, the mass of the pulley can affect the acceleration and velocity of the masses connected to it due to the force of gravity acting on the pulley.

5. Is the conservation of momentum always true in a pulley system?

The conservation of momentum is only true in a pulley system if there are no external forces acting on the system. If there is friction present or if the system is not completely closed, then the conservation of momentum may not hold true.

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