# Acceleration of falling balls

## Homework Statement

Two small balls with masses 3M and M hang on elastic massless rubber bands (with the M ball attached to and suspended beneath the 3M ball with one rubber band; the 3M ball is suspended from the ceiling by a seperate rubber band). When the band between the balls is cut, what are the accelerations of the balls immediately after?

F(GRAVITY)=mg

## The Attempt at a Solution

I think the M ball would simply move downward at acceleration g=9.8 m/s^2. But would the 3M ball move upwards due to the release of the tension when the rubber band is cut? And would that upward acceleration be equal to the force of gravity on the M ball? How do you take the force of gravity on the 3M ball into account?

## Answers and Replies

ideasrule
Homework Helper
Why would the rubber band have any effect on the ball after it's cut? The rubber band would snap up & away from the ball to relieve the tension, and gravity would be the only force on the ball.

nasu
Gold Member
What is the upward force on the 3M ball before cutting the lower rubber band?
This force will act on the ball right after cutting the band. There is also a downward force that is balanced by the upward force before cutting the band but won't be balanced anymore after cutting.

The nature of the rubber bands is not explained and I don't think relevant; I gave all the information given in the problem. The 3M ball (on top) has the downward force of gravity and the downward tension from the M ball (below it) and the upward tension from the top rubber band (the tension being from the masses of both of the balls, so 4M) initially, correct? So when you remove the M ball on the bottom, I believe the 3M ball has just the downward force of gravity from its own mass and the upward 4M tension from the rubber band. (Please correct if I'm wrong about this). So the M ball will fall normally, but the 3M ball will accelerate upwards due to the 4M tension. But how fast is that?

ideasrule
Homework Helper
Oh, I didn't read the question properly. Apologies.

What's the net force on the 3M ball if there's an upwards force of 4M and a downwards force of 3M? (Of course, it's actually 4Mg and 3Mg.) Fnet=ma will give you the answer.

So the M ball falls at 9.8 m/s^2 and the 3M ball falls at 1/3 g (or 3.27 m/s^2). Did I understand you correctly?

nasu
Gold Member
The 3M ball does not fall but moves upwards (right after cutting the lower band).

Of course, sorry. That's what I meant. Thanks for the help!