Newton's laws / pulleys question?

[helpmeplease2]

I have uploaded the problem here: http://i36.tinypic.com/mps9i.jpg

These are the answers I have gotten so far:

a) L1 = 2*P1 - P2 - x1 + (pi*R)
L2 = 2*P2 + (pi*R) - x2

b) Forces on M1 --> M1*g downward, and T1 upward, which I think is equal to M2*g. Therefore a1 = [(M2 - M1)*g] / M1

Forces on M2--> M2*g downward, and T2 upward, which I think is equal to M1*g. Therefore a2 = [(M1 - M2)*g] / M2


If someone could tell me if I am correct so far, and also how to approach the remaining parts to the problem, I would really appreciate it.

Thank you.

 

[JoAuSc]

Part a is correct. In part b, you assume T1 = M2*g, and T2 = M1*g, but that's false. Consider a force diagram for pulley 2. You have one rope pulling up and essentially two ropes pulling down. Now, a pulley does not change the force between the two rope halves (on either side of the pulley), it just redirects the force, so the tension T1 going up from M1 is also the force going upwards above pulley 2. Also, if one half of the bottom rope for pulley 2 is pulling down on the pulley with T2, then the other half must also be pulling down with T2. Thus, on pulley #2 we have 2*T2 pulling down and T1 pulling up, and these sum to zero since m*a for the pulley is zero since it is massless. So T1 = -2*T2.

 

[baba89]

I would first commend you for attempting to solve this problem and for seeking clarification on your answers. Your equations for L1 and L2 seem correct based on the given information. However, I would recommend using the correct units for each variable (e.g. P1 and P2 should be in Newtons, x1 and x2 should be in meters).

For part b), your understanding of the forces on each mass is correct. However, your equations for a1 and a2 are incorrect. The correct equations should be:

a1 = [(M2*g - T1) / M1]
a2 = [(T2 - M1*g) / M2]

These equations can be derived from Newton's second law (F=ma) and the fact that the acceleration of the masses must be equal (since they are connected by the same rope).

For part c), you can use the equations from part b) to solve for the tensions in the ropes (T1 and T2). Then, you can use these tension values to calculate the acceleration of each mass (a1 and a2) using the equations from part b) again. Finally, you can use the equations of motion (x = x0 + v0t + (1/2)at^2) to solve for the final positions (x1 and x2) of each mass after a certain time.

For part d), you can use the equations of motion again to solve for the time it takes for each mass to reach their final positions (t1 and t2). You can also use the equations from part b) to calculate the final velocities (v1 and v2) of each mass.

I hope this helps guide you in the right direction. Remember to always double check your units and equations to ensure they are consistent and accurate. Good luck!