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## Homework Statement

A string is attached on a pulley, with Mass 1 (2 kg) hanging from the left and Mass 2 (5 kg) hanging from the right. The pulley itself is being pulled upwards with a force of 100N.

Find the tension T in the string, and the accelerations of both masses.

We consider the pulley and string to be massless, and no friction. Gravitational acceleration is g=9.8 m/s^2

F = 100N

m1 = 2kg

m2 = 5kg

a1 = acceleration of Mass 1

a2 = acceleration of Mass 2

a = acceleration of the whole system

T = tension in the string

## Homework Equations

m1 a1 = T - m1 g

m2 a2 = T - m2 g

## The Attempt at a Solution

First I found the acceleration of the system:

the total force on the system is F - (m1+m2)g (because gravity pulls it downwards). So

a = F/(m1+m2) - g.

Since the string is not extendable, the relative accelerations of the masses with respect to the pulley are equal in magnitude and with opposite signs:

a1 - a = -(a2 - a)

a2 = 2a - a1 = 2F/(m1+m2) - 2g - a1

Replacing a2 in the Relevant equations:

m1 a1 = T - m1 g

m2 [2F/(m1+m2) - 2g - a1] = T - m2 g

After solving this system for T (by multiplying the second equation by m1/m2 and adding both equations to eliminate the a1 term), I get:

T = 2m1m2F/(m1+m2)^2 = 2000/49 = 40.82 N

But the answer is supposed to be 50N. And the accelerations I get are also not the same as in the answers.

Where did I go wrong?