# Acceleration of a mass lowered by a motor (Help with Non-Ideal Pulley)

• Kermit_the_Phrog
In summary, the pulley has a moment of inertia of 75.7kgm^2, and the mass is lowered by 1.06E+4N. The acceleration of the mass is -0.602 m/s^2.
Kermit_the_Phrog
Summary: Non - ideal pulley question, should be easy but has got me good

Hey guys, looking for some help on this pulley question. It involves torque, and works with Newton's 2nd law in conjunction with a non-ideal pulley.

Text of question:
" When the motor in the figure below lowers the m = 1160kg mass, it produces a tension of 1.06E+4N in the cable on the right side of the pulley. The pulley has a moment of inertia of 75.7kgm^2 and a radius of 0.747m. The cable rides over the pulley without slipping. Determine the acceleration of the m = 1160kg mass. Use g=9.81m/s^2. "

Diagram:

Attempt

I found free body diagrams for both the mass and the pulley, and boiled them down to two equations, two unknowns as follows -

T2 = mg-ma

and

(r^2)T2 - (r^2)T1 = Ia

But when I added the equations together (subbed the first into the second), I got a final answer a = 0.602 m/s^2 , which was wrong.*Note - my final formula was:

a = (r^2)(mg - T1) / (I + (r^2)m)can anyone help me out?

[Moderator's note: Moved from a technical forum and thus no template.]

Last edited by a moderator:
Kermit_the_Phrog said:
But when I added the equations together (subbed the first into the second), I got a final answer a = 0.602 m/s^2 , which was wrong.

So as it Turns out, my answer was correct, BUT my sign was wrong: the correct answer was -0.602 m/s^2.

This makes me more confused honestly.

can anyone help me out explain this?

In your equations, you chose downward and ccw as the positive direction , which is fine , and that’s the way I would have done it. But apparently the solution likes downward to be in the negative direction, per typical convention. But since it was given that the mass is lowered, its picky in my mind to not consider your answer as correct.

Kermit_the_Phrog
PhanthomJay said:
In your equations, you chose downward and ccw as the positive direction , which is fine , and that’s the way I would have done it. But apparently the solution likes downward to be in the negative direction, per typical convention. But since it was given that the mass is lowered, its picky in my mind to not consider your answer as correct.

Thank you very much, it's good to know that I didn't make any sort of fatal error and that the body of my problem solving was okay. I guess the problem was just very picky on those minute details. Have a great rest of your day!

Thank you. You did a very good job in developing your equations. Ribbet, ribbet...

Kermit_the_Phrog

## 1. What is the definition of acceleration in relation to a mass lowered by a motor?

Acceleration is the rate of change of velocity of an object over time. In the case of a mass being lowered by a motor, acceleration refers to the increase in downward speed of the mass as the motor pulls it down.

## 2. How does the angle of the pulley affect the acceleration of the mass?

The angle of the pulley can affect the acceleration of the mass in two ways. First, a smaller angle will result in a greater component of the weight of the mass being directed downwards, leading to a greater acceleration. Second, a steeper angle may increase the friction between the pulley and the rope, reducing the overall acceleration.

## 3. What is the significance of a non-ideal pulley in this scenario?

A non-ideal pulley is one that has friction and other sources of resistance, whereas an ideal pulley has no friction and is perfectly smooth. In the case of a mass being lowered by a motor, a non-ideal pulley will result in a decrease in the acceleration of the mass due to the added friction and resistance.

## 4. How does the weight of the mass affect its acceleration when being lowered by a motor?

The weight of the mass has a direct effect on its acceleration. The greater the weight of the mass, the more force is required from the motor to lower it, resulting in a slower acceleration. On the other hand, a lighter mass will require less force and will have a higher acceleration.

## 5. What factors can influence the acceleration of a mass lowered by a motor?

There are several factors that can influence the acceleration of a mass lowered by a motor. These include the weight of the mass, the angle of the pulley, the type of pulley (ideal or non-ideal), the friction between the pulley and the rope, and the power and efficiency of the motor. External factors such as air resistance may also have an impact on the acceleration.

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