Determine Mass of Pulley in Atwood's Machine

In summary: Initial and final angular velocity is 0 and 18 respectively. Find I from the expression for I for a disk. That will give you the mass of the pulley.In summary, the problem involves an Atwood's machine with two masses and a uniform disk pulley. The initial and final velocity of one mass is given, as well as the height of the other mass. The problem can be solved by finding the acceleration of the masses, which will be the same for the pulley. The net torque on the pulley can then be calculated using the expression for a disk, and the mass of the pulley can be found from the moment of inertia.
  • #1
Precursor
222
0

Homework Statement


The two masses(m1 = 5.0 kg and m2 = 3.0 kg) in the Atwood's machine shown below are released from rest, with m1 at a height of 0.75 m above the floor. When m1 hits the ground its speed is 1.8 m/s. Assuming that the pulley is a uniform disk with a radius of 12 cm, determine the pulley's mass.

http://img23.imageshack.us/img23/904/pulleyl.jpg​
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Homework Equations


Rotational kinematics


The Attempt at a Solution


I don't really know where to start here. Could someone please start me off?
 
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  • #2
Initial and final velocity of m1 is given. h is given. Find acceleration of m1. m2 and pulley will have the same acceleration. Write down the expression for a to them. Then solve for the mass of the pulley.
 
  • #3
rl.bhat said:
Initial and final velocity of m1 is given. h is given. Find acceleration of m1. m2 and pulley will have the same acceleration. Write down the expression for a to them. Then solve for the mass of the pulley.

Is the final velocity of m2 also 1.8 m/s? And is the mass of the pulley simply the mass of the disk?
 
  • #4
Precursor said:
Is the final velocity of m2 also 1.8 m/s? And is the mass of the pulley simply the mass of the disk?
Yes.
 
  • #5
So I found the acceleration to be 2.16 m/s^2.

Now is the acceleration of the pulley 2.16/0.12 = 18 rad/s^2?

So how do I find the mass?
 
  • #6
Alright! You are almost there. You can say that net torque on the disk is [tex]\tau=I\alpha[/tex]
 

Related to Determine Mass of Pulley in Atwood's Machine

1. How do you determine the mass of a pulley in Atwood's Machine?

In order to determine the mass of a pulley in Atwood's Machine, you will need to use the equation: M = (m1 - m2)a/g, where M is the mass of the pulley, m1 and m2 are the masses of the two hanging objects, a is the acceleration of the system, and g is the acceleration due to gravity (9.8 m/s^2). You will also need to measure the acceleration of the system and the masses of the hanging objects.

2. Why is it important to know the mass of the pulley in Atwood's Machine?

Knowing the mass of the pulley in Atwood's Machine is important because it affects the overall acceleration of the system. The pulley's mass adds to the total mass of the system and thus affects the acceleration according to Newton's second law (F=ma). Additionally, knowing the mass of the pulley allows for more accurate calculations and predictions in experiments.

3. Can the mass of the pulley in Atwood's Machine be ignored?

No, the mass of the pulley in Atwood's Machine cannot be ignored. As mentioned before, it affects the overall acceleration of the system and is an important factor in the calculations and predictions of the experiment. Ignoring the mass of the pulley could result in inaccurate results and conclusions.

4. Does the mass of the pulley in Atwood's Machine affect the tension in the string?

Yes, the mass of the pulley in Atwood's Machine does affect the tension in the string. The tension in the string is directly related to the acceleration of the system, and the mass of the pulley affects the acceleration. Therefore, the mass of the pulley indirectly affects the tension in the string.

5. How does the mass of the pulley in Atwood's Machine affect the final velocity of the system?

The mass of the pulley in Atwood's Machine does not directly affect the final velocity of the system. However, it does affect the acceleration of the system, which in turn affects the final velocity according to the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (usually 0 in Atwood's Machine), a is the acceleration, and s is the displacement. Therefore, the mass of the pulley indirectly affects the final velocity of the system.

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