Aceleration & tension in a system involving pulley

In summary, the conversation discusses a problem involving tension, acceleration, friction, and a pulley. The person is unsure how to incorporate the pulley into their solution and asks for help. They receive hints on drawing free body diagrams and determining the tensions on either side of the pulley. The conversation ultimately concludes that the tensions on either side of the pulley are caused by the frictional force and weight of the masses in the system, and that the pulley must be accelerating to maintain motion.
  • #1
jb007
18
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1. Homework Statement
I am stuck on this problem involving tension, acceleration of a system, friction and a pulley. I have an idea of how to find the acceleration of the system neglecting the mass of the pulley, but it is not the solution. How does adding a frictionless pulley in the system change its acceleration?

Homework Equations


F=ma
torque = I(alpha)
rotational equations?

The Attempt at a Solution


For the tension T1 from the pulley disk downwards to mass m, the tension is mg.
For the tension T2 from the mass M rightward to the pulley disk, would the tension be equal to T1?

I drew FBD's for the two masses.
For M, by applying Newton's 2nd Law, Fnet=Ma: T2-f = Ma
For m, applying F=ma: mg-T1 = ma

I know the acceleration of the system should be equal. But how do I incorporate the pulley disk in the system to find the acceleration of the system?

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  • #2
You draw free body diagrams for both blocks and the pulley ... hint: what sort of motion does the pulley undergo?
 
  • #3
So the pulley disk is rotating. The string wraps around the top of the disk, and it rotates in the same direction as the acceleration of the two blocks (the same way the string is moving). Would this be a torque force acting on pulley disk? Because the force on the disk by the string is perpendicular to the radius?
 
  • #4
The disk must be accelerating (unless the rope is slipping) so there must be an unbalanced torque in the direction of the acceleration.
The free body diagram for the pulley has two forces on it - from each straight section of string.
The forces produce opposing torques. The tension on either side of the pulley will be different.
 
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  • #5
So the tension on the left side of the pulley would be the tension caused by the frictional force acting on M, and the tension on the right side of the pulley would be caused by the weight of m? (They are in opposite directions)
 
  • #6
As far as the free body diagram of the pulley is concerned, there is no mass m or mass M.
Just write in T1 and T2 for the two tensions ... they come from the interactions between parts of the overall system.
 

1. What is the relationship between acceleration and tension in a system involving pulleys?

The acceleration of a system involving pulleys is related to the tension in the ropes or cables. As the acceleration of the system increases, the tension in the ropes also increases.

2. How does the number of pulleys in a system affect the acceleration and tension?

The number of pulleys in a system can affect the acceleration and tension in different ways. Generally, more pulleys will lead to a lower tension in the ropes and cables, but can also increase the overall acceleration of the system.

3. What is the role of friction in a system involving pulleys?

Friction plays a significant role in a system involving pulleys. It can decrease the efficiency of the system by converting some of the input energy into heat. Friction also affects the tension in the ropes, as it can create a resistive force that opposes the motion of the system.

4. How can the direction of the applied force affect the acceleration and tension in a system involving pulleys?

The direction of the applied force can have a significant impact on the acceleration and tension in a system involving pulleys. If the force is applied in the same direction as the motion of the system, it can increase the acceleration and tension. However, if the force is applied in the opposite direction, it can decrease the acceleration and tension.

5. What is the difference between linear and angular acceleration in a system involving pulleys?

Linear acceleration refers to the change in velocity of an object in a straight line, while angular acceleration refers to the change in angular velocity of an object around a central axis. In a system involving pulleys, both types of acceleration may be present, depending on the direction of motion and the configuration of the pulleys.

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