- #1
Boorglar
- 210
- 10
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?