How do you calculate acceleration and angular acceleration with pulleys?

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Homework Help Overview

The problem involves two blocks connected by a pulley system, where one block is heavier than the other. The scenario describes the motion of the blocks as the heavier block falls a certain distance over a specified time, prompting questions about calculating both linear and angular acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using kinematic equations to find the acceleration of the falling block and relate it to the angular acceleration of the pulley. There are attempts to derive relationships between tension, weight, and acceleration.

Discussion Status

Some participants have provided guidance on using kinematic formulas, while others express confusion about the relationship between linear and angular acceleration. There is acknowledgment of the challenges posed by the unknown mass of the pulley and the need for clarity in understanding the problem setup.

Contextual Notes

Participants note that the mass of the pulley is not provided, which complicates the calculations. There is also a mention of the initial conditions of the system being released from rest, which is relevant to the kinematic analysis.

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Homework Statement


A block has a mass of 500 g, another block has a mass of 460 g. Both are attached to a pulley with a frictionless wire that does not slip. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 seconds. What is the magnitude of the blocks' acceleration? What is the magnitude of the pulley's angular acceleration?

Fig: http://i212.photobucket.com/albums/cc150/deadfishfactory/1.jpg


Homework Equations


Torque = Moment of Inertia * Angular Acceleration
Force = Mass * Acceleration
Acceleration = Angular Acceleration / Radius
Moment of Inertia = (1/2)MR^2

The Attempt at a Solution


T=tension; W=weight; A=acceleration; R=radius; I=moment of inertia
M(1) = left box; M(2) = right box; M(3) = pulley

A(1) = A(2) = a/R = A

1. T(1) - W(1) = m(1) * A; T(1) = W(1) + M(1) * A
2. T(2) - W(2) = -m(2) * A; T(2) = W(2) - M(2) * A
3. T(1)R - T(2)R = I * A / R
T(1) - T(2) = M(3) * A
W(1) + M(1) * A - W(2) + M(2) * A = M(3) * A
Solved for A.

Well, I started plugging things in and stuff, but I can't solve the problem because the mass of the pulley is unknown. I'm pretty sure I did it wrong so can someone point out my mistake or show me how to do it if I did it completely wrong? Thanks!

answer: a) 6.00 cm/s^2 b) 1.20 rad/s^2
 
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Using kinematic formula, find the acceleration of the falling body. Using this value find the angular acceleration of the pully. In this problem mass of any object is not needed
 
Last edited:
Still having trouble finding the acceleration of the blocks.

I found the angular acceleration of the pulleys by using the constant acceleration equation like you said. I got 1.22 rad/s^2, which is close enough. I can't figure out how to find the acceleration of the blocks since I used gravity for the block's acceleration to find the angular acceleration. My physics skills aren't too good, can you explain it to me very precisely since I'm kinda slow.
 
Heavier block falls 75.0 cm in 5.00 sec. (The system was released from rest.) Can you find A from the basic equations of Kinematics. (Remember those s-u-v-a-t equations??)
 
Ohhhh. Pfft. When you said "heavier block falls 75.0 cm in 5.00 sec," it immediately smacked into me. Haha. I'm such an idiot for not noticing. Anyways, I got the answer. Thank you very much!
 

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