Find Acceleration for Pulley Homework

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In summary: B]1/2MR^2*(A/R) = (56-33)*9.8*RThis equation should by1/2MR^2*(a/R) =[ T1- T2]*R...(1)You have to write two more equations.56*g - T1 = 56*a ...(2)T2 - 33*g = 33*a...(3)From these three equations, you can get the required result.In summary, the at-tached pulley rotates with no friction about its pivot and has a net torque of 23 newton metres. The masses are connected by a massless
  • #1
shangri-la89
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Homework Statement


A pulley (in the form of a uniform disk)
with mass 79 kg and a radius 14 cm is at-
tached to the ceiling in a uniform gravita-
tional field and rotates with no friction about
its pivot. The masses are connected by a
massless inextensible cord.
Determine the acceleration of the mass
33 kg. The acceleration of gravity is 9.8 m/s2 .
Assume up is positive. Answer in units of
m/s2.

Homework Equations


Net Torque = Moment of Inertia *Angular Acceleration
Torque = Force * Radius



The Attempt at a Solution



I attempted this:
I*Alpha = net toque
1/2MR^2*(A/R) = (56-33)*9.8*R
M*A=23*9.8*2
A=(23Kg*9.8m/s/s*2)/(79Kg)

Unfortunately that didnt work...
Thanks for any help.
 
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  • #2
If I understand the situation correctly, the rope tensions are not simply equal to the weights of the masses.

Maybe try applying F=mA to each mass, and see if that helps.
 
  • #3
Redbelly98 said:
If I understand the situation correctly, the rope tensions are not simply equal to the weights of the masses.

Maybe try applying F=mA to each mass, and see if that helps.

Youre right, I tried just using the tensions and such and that didnt work either. Thanks for your help, and Ill try that.
 
  • #4
Oh, also note that the 2 rope sections can have different tension.
 
  • #5
Redbelly98 said:
Oh, also note that the 2 rope sections can have different tension.

Not only can they, but they do. As one mass is accelerating up, and the other down.
 
  • #6
I messed up typing it originally.
The pulley has two masses attached. One of mass 56 kg on one side of the pulley and one of mass 33 kg on the other side.
 
  • #7
shangri-la89 said:
I messed up typing it originally.
The pulley has two masses attached. One of mass 56 kg on one side of the pulley and one of mass 33 kg on the other side.

Don't forget to write the rotational equation of motion for the pulley too!
 
  • #8
shangri-la89 said:
Not only can they, but they do. As one mass is accelerating up, and the other down.

Just on a conceptual note, from this it does not follow that the tension is different on each side of the pulley. If it were a mass-less pulley, one mass would be accelerating up, and the other down, but the tension in the rope would still be the same throughout.
 
  • #9
shangri-la89 said:
1.

Homework Equations


Net Torque = Moment of Inertia *Angular Acceleration
Torque = Force * Radius

The Attempt at a Solution



I attempted this:
I*Alpha = net toque
1/2MR^2*(A/R) = (56-33)*9.8*R
M*A=23*9.8*2
A=(23Kg*9.8m/s/s*2)/(79Kg)
.

1/2MR^2*(A/R) = (56-33)*9.8*R
This equation should by
1/2MR^2*(a/R) =[ T1- T2]*R...(1)
You have to write two more equations.
56*g - T1 = 56*a ...(2)
T2 - 33*g = 33*a...(3)
From these three equations, you can get the required result.
 

1. What is acceleration in the context of a pulley?

Acceleration in the context of a pulley refers to the change in velocity of an object as it moves along the pulley system. It is a measure of how quickly the object's speed is increasing or decreasing.

2. How is acceleration calculated for a pulley system?

Acceleration for a pulley system can be calculated using the equation a = (m2 - m1g) / (m1 + m2), where m1 is the mass of the object on one side of the pulley, m2 is the mass on the other side, and g is the acceleration due to gravity.

3. Can the acceleration for a pulley system ever be negative?

Yes, acceleration for a pulley system can be negative. This would occur if the object on one side of the pulley is moving downwards and the object on the other side is moving upwards, causing a decrease in speed.

4. How does the angle of the pulley affect the acceleration?

The angle of the pulley affects the acceleration by changing the direction of the force acting on the object. The greater the angle, the more the force is directed horizontally and the less it is directed vertically, resulting in a change in acceleration.

5. What are some real-world examples of pulleys and acceleration?

A common real-world example of pulleys and acceleration is a weightlifting machine. The weights on either side of the pulley system represent the different masses, and as the weight is lifted, the acceleration changes as the weights move up and down. Another example is a flagpole, where the flag is pulled up and down by a rope and pulley system, causing changes in acceleration.

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