Dynamical Equations & Free Body Diagrams: Solving for Net Force and Torque

[~christina~]

Homework Statement

A car of mass m_c is connected to mass m2 by a string. The string passes over a solid cylindrical pulley, which has a frictionless bearing, of radius R and mass M. when the system is released from rest the string doesn't slip, the car moves down the incline, and m2 moves upward through a distance h' .

a) draw a free body diagram for m_c, m_2, and M

b) Use the dynamical equations of motion to find the components of the net force aceting on m_c and m_2 and net torque acting on M.

c) Use the results of b) to derive a expression for the translational aceleration for the masses in terms of m_c, m_2, M, h', 2 and the coefficient of friction \mu

http://img263.imageshack.us/img263/7160/carhj5.th.jpg

Homework Equations

dynamical equations ==> what is that exactly??

The Attempt at a Solution

a) a) draw a free body diagram for m_c, m_2, and M

I drew it in with a picture of the drawing but I'm not sure the free body diagram of the pulley since I've never drawn a free body diagram of a pulley before. What forces would be on it other than that of the car and block?

b) b) Use the dynamical equations of motion to find the components of the net force aceting on m_c and m_2 and net torque acting on M.I have no clue how to do this part at all.

What are the dynamical equations of motion?

HELP Please

 

[rl.bhat]

Dynamic equation is the equation of the body under motion. In this problem it is possible that Mc and M2 can remain at rest. You can describe this condition by some static equation. In this problem the tension in the string and acceleration of the car and the mass is same. Using free body diagram calculate acceleration. From that you can find the torque acting on the pully.

 

[aq1q]

hey
for a) it should be McA (in your free-body diagram on M, the Mc needs an acceleration)

for c) is H' the distance, or the rate at which the height is changing. and what is "2"?

 

[aq1q]

you should also note that, since the tension is uniform and the mass of the string is negligible, both of the masses will be accelerating with the same magnitude, but different direction, right?

 

[~christina~]

hey
for a) it should be McA (in your free-body diagram on M, the Mc needs an acceleration)

for c) is H' the distance, or the rate at which the height is changing. and what is "2"?

I'm not sure what is "2" but thanks for catching the Mc A

Dynamic equation is the equation of the body under motion. In this problem it is possible that Mc and M2 can remain at rest. You can describe this condition by some static equation. In this problem the tension in the string and acceleration of the car and the mass is same. Using free body diagram calculate acceleration. From that you can find the torque acting on the pully.

I have no idea what you are talking about...is it involving sum of F in one direction of one object?

you should also note that, since the tension is uniform and the mass of the string is negligible, both of the masses will be accelerating with the same magnitude, but different direction, right?

Yes...

but I'm thinking the whole wording of "dynamic equation" is messing with me since I know how to do tension and etc. but I've not heard of "dynamic equation" and I'm not sure what they want...or how to relate that to torque...