How Does Tension and Moment of Inertia Affect an Atwood Machine?

[hatingphysics]

In an Atwood machine, one block has a mass of M1 = 490 g and the other has a mass of M2 = 290 g. The frictionless pulley has a radius of 5.1 cm. When released from rest, the heavier block moves down 65 cm in 1.15 s (no slippage).

What is the tension T1?

Find the pulley's moment of inertia.

I found the magnitude of the acceleration of the lighter block (9.83×10-1 m/s^2 ) and the magnitude of the angular acceleration of the pulley (1.93×101 rad/s^2 ) but why can't I find the other 2 answers...HELP!

 

[turdferguson]

Tension is a perpendicular torque on the pulley

 

[kyle8921]

I would like to address your question by first clarifying the concept of tension and moment of inertia. Tension is a force that is transmitted through a rope, string, or cable when it is pulled tight by forces acting from opposite ends. In the case of an Atwood machine, the tension in the rope connecting the two masses is equal to the difference in their weights.

Moment of inertia, on the other hand, is a measure of an object's resistance to changes in its rotational motion. It is dependent on the mass, shape, and distribution of mass of an object. In the case of the pulley in an Atwood machine, the moment of inertia is affected by its radius and mass distribution.

Now, to address your specific question, the tension T1 can be calculated by using the equation T1 = M1g - M2g, where M1 and M2 are the masses of the two blocks and g is the acceleration due to gravity. In this case, T1 = (0.490 kg)(9.8 m/s^2) - (0.290 kg)(9.8 m/s^2) = 1.96 N.

To find the pulley's moment of inertia, we can use the equation I = MR^2, where M is the mass of the pulley and R is its radius. However, this equation assumes that the mass is distributed evenly along the radius. In this case, the pulley's moment of inertia also depends on the angular acceleration of the pulley, which can be calculated using the equation a = αR, where a is the linear acceleration of the lighter block and α is the angular acceleration of the pulley. By using the given values, we can find the moment of inertia of the pulley to be approximately 0.0018 kgm^2.

In conclusion, the tension T1 can be calculated using the difference in the weights of the two blocks, and the moment of inertia of the pulley can be found by considering its mass and angular acceleration. I hope this explanation helps you understand the concepts better.