# Tension of a string with a pulley

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In summary, two masses of 3.00 kg and 8.00 kg are connected by a string over a frictionless pulley at a 50 degree angle from the horizontal. Using the equations of motion, the acceleration was found to be 2.79 m/s². From this, the tension in the string was calculated to be 8.37 N for m1 and 22.32 N for m2.
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## Homework Statement

Two masses are connected by a string over a pulley as shown below. The incline is
frictionless and makes a 50 degree angle from the horizontal. If m1 = 3.00 kg and m2 = 8.00 kg, find the tension in the string.

F = ma

## The Attempt at a Solution

I thought the tension in the string would be the same as the weight of m1, which is 29.4N, but that is not the correct answer. I am not sure what to try from here.

m1 accelerates, so you need to take that into consideration.
First write up the equations of motion of the two blocks.
i.e. m1*a=...
and m2*a=...

I got that that a equals 2.79m/s², so:

m1*a = 3 * 2.79 = 8.37N
m2*a = 8 * 2.79 = 22.32N

Is that what you mean? Is that right?

Yes, and now you can express the tension of the string. m1*a=m1*g-T

That got me the correct answer! Thanks so much for your help!

Last edited:

## What is the tension of a string with a pulley?

The tension of a string with a pulley is the amount of force applied to the string in order to keep it taut and in place.

## How does the angle of the pulley affect tension?

The angle of the pulley can affect the tension in the string in a few ways. If the angle is increased, it can increase the tension in the string. However, if the angle is too steep, it can cause the string to slip off the pulley, decreasing the tension.

## What factors can affect the tension in a string with a pulley?

The tension in a string with a pulley can be affected by several factors, such as the weight of the object being lifted, the angle of the pulley, and the strength and elasticity of the string itself.

## Can the tension in a string with a pulley ever be greater than the weight of the object being lifted?

Yes, the tension in a string with a pulley can be greater than the weight of the object being lifted if the pulley is configured in a way that multiplies the force applied to the string.

## How is the tension of a string with a pulley calculated?

The tension of a string with a pulley can be calculated using the formula T = (m1 + m2) x g x cosθ, where T is the tension, m1 and m2 are the masses of the objects being lifted, g is the acceleration due to gravity, and θ is the angle of the pulley.

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