# Calculating Acceleration and Tension in a Pulley System

• dtesselstrom
In summary, in this problem, there are two blocks connected by a massless string over a pulley. The pulley has a mass and radius, and one block is released while the other is on a horizontal, frictionless surface. The acceleration of the block on the surface can be found using the formula a=2m2*g/(m1+m2) and the tensions in the upper and lower portions of the string can be found using the equations T1=m2\1*a for m1 and T2-m2*g=m2*a for m2. However, there is also a need to calculate the moment of inertia and torque of the wheel, and relate the angular acceleration of the wheel to the tangential acceleration of its
dtesselstrom
Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in the figure. The pulley turns on frictionless bearings, and mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest.
Suppose the pulley has mass mp and radius R. Find the acceleration of m1.
Find the tension in the upper portion of the string.
Find the tension in the lower portions of the string.
Ive tried R*g*m2/(1/2*mp*r^2)*R and it said it needs mass1 in the problem but I couldn't figure out where it is needed

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Draw three free body diagrams. One for mass on table. One for hanging mass. One for wheel. You need the moment of inertia of the wheel (looks like you have it) and the torque on the wheel,which comes from the two tensions in the string (not the weights of the masses). The acceleration of both masses and the tangential acceleration of the rim of the wheel have the same magnitude. Relate the angular acceleration of the wheel to the tangential acceleration of its rim.

Ive already drawn out the free body diagrams and in class our teacher told us that this problem is solved with a=-m2*g/(1/2mp+m1+m2) but it told me that was wrong too
so the equations I have are T2-m2*g=m2*a for m2 T1=m2\1*a for m1 and 1/2mpR^2*angular acc.=RT1-RT2

Last edited:
a=2m2*g/(m1+m2) can anyone verify if that is correct because I only have one more guess to get the answer right.

dtesselstrom said:
a=2m2*g/(m1+m2) can anyone verify if that is correct because I only have one more guess to get the answer right.
There has to be an mp in the answer for the acceleration. This cannot be right.

## 1. What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove around its circumference. It is used to change the direction of a force, making it easier to lift heavy objects. The rope or belt that runs around the pulley can distribute the weight of the object between multiple ropes, reducing the amount of force needed to lift it.

## 2. How does a pulley affect the acceleration of a mass?

In a system with a mass attached to a pulley, the acceleration of the mass is affected by the number of pulleys used. With a single pulley, the acceleration of the mass will be equal to the force applied divided by the mass. With multiple pulleys, the acceleration of the mass will be reduced due to the distribution of the force among the different ropes or belts.

## 3. Can a pulley increase the acceleration of a mass?

Yes, a pulley can increase the acceleration of a mass by reducing the amount of force needed to lift it. This is because with a pulley, the force applied is distributed among multiple ropes, reducing the overall force needed to lift the mass. However, the acceleration will still depend on the mass of the object and the force applied.

## 4. What is the formula for calculating the acceleration of a mass on a pulley system?

The formula for calculating the acceleration of a mass on a pulley system is a = F/m, where a is the acceleration, F is the force applied, and m is the mass of the object. This formula assumes there is no friction in the system and the rope or belt is massless.

## 5. How does the direction of the force affect the acceleration of a mass on a pulley?

The direction of the force applied to a pulley affects the direction of the acceleration of the mass. If the force is applied upwards, the mass will accelerate upwards, and if the force is applied downwards, the mass will accelerate downwards. The magnitude of the acceleration will depend on the force and the mass of the object, as well as the number of pulleys used in the system.

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