Tension in a basic pulley system

In summary: This is because the pulley will rotate due to the unequal tensions, causing the rope to wrap around it and increasing the tension on the right side. This relates to Newton's third law, where the forces between the masses are equal and opposite.
  • #1
jasonpeng
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I've got a problem with understanding the pulley system.

In a basic pulley, if the force pulling M upwards is T, and the force pulling m upwards is also T, why is it that T is equal for both m & M? For some reason I feel inclined to believe that the T pulling m upwards is equal to the weight of M, and the T pulling M upwards is equal to the weight of m. Is that right or wrong? Why?
pulleyFBD.gif
 
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  • #2
I believe this relates to Newton's third law. If mass m is pulling on mass M with a certain force, M must be pulling on m with the same magnitude since the tension in the rope must be constant (ignoring friction).

Imagine an object hanging from the ceiling. The mass of the object itself would influence the magnitude of the upward force which is being exerted on the mass by the rope (the tension). This is because the magnitude of the force which the mass applies on the ceiling is the same as that which the ceiling applies on the mass. The same should hold true for the pulley (the force which m applies on M is the same magnitude as that which M applies on m).

I hope all of this was both correct and clear.
 
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  • #3
jasonpeng said:
I've got a problem with understanding the pulley system.

In a basic pulley, if the force pulling M upwards is T, and the force pulling m upwards is also T, why is it that T is equal for both m & M? For some reason I feel inclined to believe that the T pulling m upwards is equal to the weight of M, and the T pulling M upwards is equal to the weight of m. Is that right or wrong? Why?
View attachment 205103

If you fixed the top of the string, then you would have equilibrium. The tension on the right would support mass M and the tension on the left would suppose mass m.

However, if the string is not attached to anything (and there is no friction on the pulley), then the tension must be constant throughout. In this case, assuming mass M is larger, it will fall and pull the lower mass m upwards.
 
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  • #4
PeroK said:
However, if the string is not attached to anything (and there is no friction on the pulley), then the tension must be constant throughout. In this case, assuming mass M is larger, it will fall and pull the lower mass m upwards.

This is correct, provided that the pulley is massless. If there is mass, and more specifically a mass moment of inertia for the pulley, the tensions will not be equal on both sides.
 
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1. What is tension in a basic pulley system?

Tension in a basic pulley system refers to the force that is exerted on the rope or cable of the pulley. It is the force that is transmitted from one end of the rope to the other, and it is equal on both sides of the pulley.

2. How is tension calculated in a basic pulley system?

To calculate tension in a basic pulley system, you need to know the weight of the object being lifted, the number of pulleys in the system, and the mechanical advantage of the pulley system. The formula for tension is T = (W / n) x MA, where T is the tension, W is the weight of the object, n is the number of pulleys, and MA is the mechanical advantage.

3. What factors affect tension in a basic pulley system?

The tension in a basic pulley system is affected by several factors, including the weight of the object being lifted, the number of pulleys in the system, the angle of the rope, and the friction between the rope and the pulley.

4. How does tension change in a basic pulley system?

Tension in a basic pulley system changes depending on the weight of the object being lifted and the mechanical advantage of the system. As the weight increases, the tension also increases, but the mechanical advantage can reduce the amount of tension needed to lift the object.

5. What is the significance of tension in a basic pulley system?

Tension is a crucial component of a basic pulley system as it determines the amount of weight that can be lifted and the effort required to lift it. It is also essential for maintaining the stability and balance of the system, ensuring that the object being lifted does not fall or become unbalanced.

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