In Figure 10-53, two blocks, of mass m1 =400 g and m2 =600 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 500 g and radius R = 12.0 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. (a) Find the magnitude of the acceleration of the blocks. m/s2 (b)

Question

In Figure 10-53, two blocks, of mass m1 =400 g and m2 =600 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 500 g and radius R = 12.0 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. 



(a) Find the magnitude of the acceleration of the blocks. 
m/s2 
(b) Find the tension T1 in the cord at the left. 
N 
(c) Find the tension T2 in the cord at the right. 
N

First, calculate the moment of inertia for the pulley. 

Then, notice on the pulley that angular acceleration is related to cord acceleration by 

alpha*radius= linear acceleration. 

Now, writing a system equation... 


m2*(g-a)= pulling force by gravity 
I*alpha= Torque on pulley 
I*alpha/radius = force on pulley extreme 
I*acceleration/radius^2 
m1*a= tension on m1 

or 
m2*(g-a)=I*a /r^2+m1*a 

solve for a. 

check my thinking.

i need help with writing system of equations for ages

Answer

To write a system of equations for this problem, you will need to consider the forces acting on each block and the pulley. For the blocks, you will need to consider the force of gravity and the tension in the cord. For the pulley, you will need to consider the torque due to the tension in the cord.

For the block on the left, the equation would be: 
m1*a = T1 - m1*g

For the block on the right, the equation would be: 
m2*a = T2 - m2*g

For the pulley, the equation would be: 
I*alpha = T1*R - T2*R

Where I is the moment of inertia of the pulley, alpha is the angular acceleration, T1 and T2 are the tensions in the cord, and R is the radius of the pulley.

Once you have written the equations, you can solve them simultaneously to find the acceleration, tension in the cord, and angular acceleration of the pulley.

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