Question

Question:
Two masses 2.2 Kg and 3.2 Kg connected by a rope over a massless and frictionless pulley hang at 1.8 m above the ground on either side of the pulley. The pulley is 4.8 m above the ground. What is the maximum height that the 2.2 Kg weight will rise to after the system is released.


Work so far:
A= ((m2-m1)/(m2+m1))* 9.8 = 1.81 m/sec^2

So in one second the 3.2 Kg weight is going to fall to the ground and via the rope pull the 2.2 Kg weight up to 3.6 m but it will have an initial acceleration of -1.81 m/sec and so will travel higher than 3.6 m(1.8m + 1.8m).

Gravity is pulling down on 2.2 Kg weight at 9.8 m/sec^2.

How do I know how to find the height the 2.2 Kg weight rises to given its initial acceleration of -1.81 m/sec^2.

The answer is 3.94 m

Thank you - I hope the problem description is clear.

Answer 1

"So in one second the 3.2 Kg weight is going to fall to the ground "
Not so fast, it starts from rest!

Find out the velocity of the masses when the heavier weight hits the ground, call this v0.

From this moment on, the lighter weight becomes a projectile with an initial velocity of v0 and decelerated by gravity. You can find how much higher it goes and add it onto the 3.6 m already attained.

Answer 2

The answer is not 3.94