# Rigid Bodies and Free Body Diagrams (w pulley)

1. Nov 30, 2005

### moo5003

Question: "A block of mass m1 = 1.87 kg and a block of mass m2 = 5.84 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.180m and mass M = 12.7 kg. These blocks are allowed to move on a fixed block-wedge of angle 31.4 degrees as in the figure. The coefficient of kinetic friction is .357 for both blocks.

A) Using free-body diagrams of both blocks and of the pulley, determine the acceleration of the two blocks.

B) Determine the tensions in the string on both sides of the pulley.
"
Diagram

BLOCK(m1) Pulley
__________________\
\\
\\\\
\\\\\BLOCK (m2)
\\\\\
ANGLE\\\\
_________________________\\

My basic question here is how I factor in the pulley. I'm assuming I need to incorporate torques with the pulley and convert them to forces such that I can find a F(net)=ma for each block.

Block m1 WORK DONE:
X: F(net) = T1(Tension of string) - F(friction)
Y: F(net) = -m1g + N = 0

Block m2 WORK DONE:
X: F(net) = m2gsin(Theta) - T2(String) - F(friction)
Note: X is directed along the slope of the ramp.
Y: F(net) = -m2gcos(Theta) + N = 0
Perpindicular to ramp.

Thats as far as I got. Any help is appreciated.

2. Dec 1, 2005

### Staff: Mentor

So far, so good. Write F(friction) in terms of the normal force and the coefficient of friction.

Treat the pulley as a rotating disk with the two tensions exerting torques on it.

Now apply Newton's 2nd law to all three objects. Be sure to incorporate the system constraint relating the motion of all three: Since they are attached by a string, the linear acceleration of both masses must be the same (in magnitude). What's the relationship between the linear acceleration of the masses and the angular acceleration of the pulley?