Work done by cord on the pulley

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Homework Help Overview

The discussion revolves around calculating the work done by a cord on a pulley system involving a block on a frictionless inclined plane. The problem includes a block with a specified mass and incline angle, and a pulley with its own mass and radius. Participants are exploring the relationship between tension, torque, and work in this context.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the equations related to torque and work, questioning the unknown distance (d) required for calculations. Some express uncertainty about the problem setup and the relevance of part (a) to part (b) of the homework.

Discussion Status

There is ongoing exploration of the problem, with some participants identifying potential errors in the source material and clarifying the distance the block slides. Guidance has been offered regarding the relationship between the parts of the problem, but no consensus has been reached on the implications of these findings.

Contextual Notes

Some participants note that the distance the block slides down the incline is stated to be 50 cm, which may not have been clear in the original problem statement. There is also mention of a possible erratum in the source material being submitted.

annamal
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Homework Statement
A 2-kg block on a frictionless inclined plane with an angle 40 degrees from the hoizontal. It has a cord attached to a pulley of mass 1 kg
and radius 20 cm. The acceleration of the block down the plane is 5 m/##s^2## (b) What is the work done by the cord on the pulley?
Relevant Equations
W = F*d
##W = \Delta(0.5*I*w^2)##
Screen Shot 2022-04-01 at 5.02.42 PM.png

torque = rF = I*aT/r
F = 0.5*aT*m_p
W = F (tension in rope)*d = 0.5*aT*m_p*d

Don't know because of unknown d
 
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annamal said:
Homework Statement:: A 2-kg block on a frictionless inclined plane with an angle 40 degrees from the hoizontal. It has a cord attached to a pulley of mass 1 kg
and radius 20 cm. The acceleration of the block down the plane is 5 m/##s^2## (b) What is the work done by the cord on the pulley?
Relevant Equations:: W = F*d
##W = \Delta(0.5*I*w^2)##

View attachment 299267
torque = rF = I*aT/r
F = 0.5*aT*m_p
W = F (tension in rope)*d = 0.5*aT*m_p*d

Don't know because of unknown d
Looks like you are asking about part (b) without having shown us part (a). Maybe d is given in part (a).
 
annamal said:
Don't know because of unknown d.
It's a mistake in the book. The distance the block slides down the incline is 50 cm.
 
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kuruman said:
Looks like you are asking about part (b) without having shown us part (a). Maybe d is given in part (a).
I figured out part a.
Part a just says "What is the acceleration of the block down the plane?" which I gave as 5 m/##s^2##
 
vela said:
It's a mistake in the book. The distance the block slides down the incline is 50 cm.
I see that. I am submitting an errata to openstax.
 
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