# Acceleration of a hanging mass

1. Nov 14, 2013

### chillpenguin

I would rather ask a more general question then the specific hw question... Basically I am wondering how to calculate the acceleration of a hanging mass that is attached to another mass on a flat surface. Picture a mass on a table. This mass is attached to a string, which is hooked onto a pulley, and then goes off the edge of the table and is attached to a second mass. I originally thought if it was a friction-less surface that the acceleration would just be gravity no matter what. But I think varying the 2 masses would change things. Also I would like to know how to account for friction. What is the acceleration without friction? What is the acceleration with friction? I need some type of equation with variables so I can solve for any mass values and any coefficient of friction (including friction-less).

2. Nov 14, 2013

### mic*

The net force acting on the object on the table is given by;
F = ma
Where;
F is force
m is mass of the object dangling from the pulley
a is gravitational acceleration - 9.81

Accounting for friction, when the object is stationary subtract
Ffr = μsFN
Where;
Ffr is frictional force
μs is static coefficient of friction
FN is the normal force of your object on the table (mass x 9.81)

Once the object is moving/sliding...
Ffr = μkFN
Where;
μk is the kinetic coefficient of friction

3. Nov 14, 2013

### haruspex

This is wrong if things move. If the hanging mass (m2) is accelerating, the tension is less than m2g.

chillpenguin, there are two ways to address this. The safest is to consider FBDs of the two masses separately. If the string is inextensible then they will have the same acceleration. If the pulley requires no torque (frictionless and massless) then the tensions will be the same.
A shortcut is to observe that the driving force is m2g, and the mass driven (all at the same acceleration) is m1+m2. Subtract as necessary from m2g for the friction.