Analyzing Acceleration and Forces in a Pulley System

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Homework Help Overview

The discussion revolves around analyzing the acceleration and forces in a pulley system involving a motor and a mass. The problem includes parameters such as mass, tension in the cable, moment of inertia of the pulley, and the setup of the system as described in a diagram.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the forces acting on the mass and the pulley, including the calculation of weight and tension. There are questions about how to relate angular acceleration to linear acceleration and the proper application of Newton's laws.

Discussion Status

Participants are actively engaging with the problem, with some offering guidance on breaking down the steps needed to analyze the system. There is a focus on ensuring that all relevant forces and torques are considered, but no consensus has been reached on the correct procedure yet.

Contextual Notes

There is an emphasis on not skipping steps in the analysis, and participants are encouraged to clarify their reasoning and calculations as they progress through the problem.

Corky
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A motor raises a mass (m = 1100kg), it produces a tension of 1.46 *10^-4 in the cable on the right side of the pulley. the pulley has a moment of inertia of 73.8Kg*m^2 and a radius of 0.712m. The cable rides over the pulley without slipping. Determine the acceleration of mass m.

The question come with diagram with a motor beside the mass on the group, a rope goes up from the motor - around a pulley - and then back down to attach to the mass.
 
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Well, give it a shot. Show your work and you'll get some help.
 
Oh right forgot about that detail. Well I caculated weight = mass * gravity for the tension on the leftn side of the pully to be (1100kg) * (9.81) and from there I am not really sure. I would expect to have to subtract the given motion of inertia from the tention on the right, and then subtract the tension on the left side from that number to get the upward force on the mass. Is that right?
 
Let's do it step by step. The picture I have is a pulley with a rope hanging over it. The mass (m) is attached to the left end of the rope; a motor is attached to the right. Correct?

What you know: The tension in the right-side rope: Tright.

You also should realize: the acceleration is the same at all points along the rope. So how does the angular acceleration of the pulley relate to the acceleration of the rope? Figure that out first.

Now consider the forces on the mass: its weight pulls down, the tension in the left side rope (Tleft) pulls up. Apply F=ma to this body.

Do something similar for the pulley. There are two forces on it: the tensions of the two sides of rope. (Note: those tensions are not equal--if they were, the pulley (and rope) would not accelerate!) Now figure out what torques those tensions give to the pulley. Then apply the torque equation to this body: Torquenet = Ix(angular acceleration).
 
All right, at this point I have subtract tention left (w = 10791N) from tention right (14600N)and got a net force of 3809N. I used the equation [I(moment of intertia)= 0.5mr^2] to calculate the mass of the disk to be 291.2kg. Then I used the net force, 3809, with the equation F=ma to find the acceleration of the system to be 13.08m/s^2. Is this the correct procedure?
 
Don't skip steps. I asked you to do three things. Start with the first thing. Then we'll go from there.

1) First answer my question about how the angular acceleration of the pulley relates to the linear acceleration of the mass.

2) Then analyze the forces on the mass.

3) Then the pulley.
 

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