# Tension and acceleration of a pulley sytem attached to a block

• emmaemma08
In summary: MIn summary, the tension in the rope can be calculated using the equation T = F * R = I * α, where m is the mass of the block, M is the mass of the wheel, R is the radius of the wheel, and α is the angular acceleration. The acceleration of the block can be found using the equation a = 2*m*g/M.

#### emmaemma08

A 10kg block is attached to a massless cord that doesn't stretch or sag which is wrapped around a disc-like wheel for which m=5kg, I=(1/2)mR^2. If the block is allowed to drop straight down held back only by the rotation of the wheel
a) What is the tension in the rope
b) What is the acceleration of the block

I know that the tension isn't just F=mg and so am thinking it is combined with the mass of the block but don't know how to go about it

Welcome to PF.

Consider the torque on the wheel.

What equations do you know for Torque?

I know that torque = r x F or rFsintheta
i think it needs to use the ones related to angular momentum where torque= dL/dt= Id omega/ dt= I alpha
there was a similar question but it just said the things and didnt really progress or confirm if it was right

emmaemma08 said:
I know that torque = r x F or rFsintheta
i think it needs to use the ones related to angular momentum where torque= dL/dt= Id omega/ dt= I alpha
there was a similar question but it just said the things and didnt really progress or confirm if it was right

OK. So you have

T = F * R = I * α

m*g*R = 1/2*M*R2 * α

but α = a/R

So ... m*g = 1/2*M*a

## 1. What is tension in a pulley system?

Tension is the force applied on a rope or cable that is being pulled from both ends. In a pulley system, tension is created by the weight of the object being lifted and is transmitted through the rope or cable to the other end of the pulley system.

## 2. How is tension related to acceleration in a pulley system?

In a pulley system, the tension on one side of the rope or cable is equal to the tension on the other side. This means that if one side of the rope is accelerated, the other side will also experience the same acceleration due to the equal and opposite forces acting on the rope. Therefore, tension and acceleration are directly proportional in a pulley system.

## 3. How does the number of pulleys affect tension in a pulley system?

The number of pulleys in a pulley system does not affect the tension. As mentioned before, tension is equal on both sides of the rope or cable, regardless of the number of pulleys. However, adding more pulleys can help to reduce the amount of force needed to lift an object.

## 4. Can tension be increased or decreased in a pulley system?

Yes, tension can be adjusted in a pulley system by changing the weight of the object being lifted or by changing the angle of the rope or cable. Increasing the weight or decreasing the angle will increase tension, while decreasing the weight or increasing the angle will decrease tension.

## 5. What are some real-life applications of pulley systems?

Pulley systems are commonly used in everyday life, such as in elevators, cranes, and window blinds. They are also used in more complex machines, like construction equipment and engines. Pulley systems are also used in sports, such as rock climbing and sailing, to help lift and control heavy objects.