# Homework Help: Maximum Acelleration of a System of Masses

1. Aug 10, 2009

### liuquinlin

1. The problem statement, all variables and given/known data
A mass on a horizontal friction-free air track is accelerated by a string attached to another 10kg mass hanging vertically from a pulley. Suppose the masses described are 1kg and 100kg. Compare the acellerations when the masses are interchanged, that is, for the case when the 1kg mass dangles over the pulley and then the case where the 100kg mass dangles over the pulley. What does this indicate about the maximum acceleration of such a system of masses?

2. Relevant equations
Fg=mg
a=f/m

3. The attempt at a solution
I found the two acellerations (.099m/s^2 and 9.9m/s^2 respectively). However I do not understand what they mean by maximum acceleration or what the two acellerations indicate.

2. Aug 10, 2009

### pgardn

It will be easier if the pulley is frictionless. I guess I will assume it is ....

Can you draw a picture of each mass and the forces on each and then the net force on each mass (free body diagram)? If you can then you can make some mathematical statements that include a (acceleration). You know the two masses and g... all thats left is a... You might use T to signify tension since each mass will have this "force" as the masses are attached to each other.

Do this with the 100 kg mass on the horizontal plane and the 1 kg mass (hanging) and accelerating which way?

Then reverse the two masses. It should be obvious that the accelerations will be very different. So you did the above using g=10 m/s/s and now you see that one situation is very close to that and the other situation is a lot less than that? (If you used 9.8 for g you did something wrong). Hint one situation is close to freefall acceleration but not quite there...

3. Aug 10, 2009

### PhanthomJay

That 9.9m/sec^2 value looks awful close to a well known acceleration value of an object subject to a certain force on Planet Earth. Hint: If the mass on the table is close to zero and the hanging mass is much greater than zero, what's the acceleration of the system?

4. Aug 10, 2009

### liuquinlin

Ohhh, I understand now. Thanks!