Pully/block system on an incline

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Homework Help Overview

The problem involves a block of mass on an incline connected to a pulley system. The incline has a specified angle, and the pulley has a defined moment of inertia and radius. The block is released from rest, and the problem requires finding the acceleration of the block and the tension in the cable, while considering friction between the block and the ramp.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss drawing free body diagrams for both the block and the pulley to apply Newton's laws. There are attempts to set up equations based on forces acting on the block and the rotational dynamics of the pulley. Some participants express uncertainty about their equations and seek clarification on their correctness.

Discussion Status

Several participants have provided equations based on their understanding of the problem. There is ongoing exploration of the relationships between the forces and torques involved. Some participants have noted discrepancies in their results and are seeking feedback on their approaches. No explicit consensus has been reached regarding the correct method or solution.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is also a discussion about the interpretation of variables and terms, such as the distinction between torque and tension.

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Homework Statement


A block of mass m = 10 Kg is attached to a cable that wraps around the pulley. The pulley is pivoted at the center, and the angle of incline is θ = 30°. The radius of the pulley is R = 0.5 m and its moment of inertia is I = 0.4 Kgm2. The block is released from rest and slides down the ramp, and the coefficient of friction is μk= 0.2 between the block and the ramp.
(a) Find the acceleration of the block. a = _______________________
(b) Find the tension in the cable. T = ______________________

I have no idea where to start.
 
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1. Draw a free body diagram for the mass on the incline.
2. Use your FBD to apply Newton's Law to the mass.
3. Draw a free body diagram for the pulley.
4. Use this FBD to apply Newton's Second Law (for rotations) to the pulley. Note that the tangential acceleration of a point on the pulley's rim is the linear acceleration of the rope and, of course, the mass.
5. Steps 2 and 4 will give two equations and two unknowns, the acceleration a and the tension T.
6. Solve the system of two equations and two unknowns to find what the problem asks.
 
For my equation, I got mgsin(theta)-I(a/r)-umgcos(theta)=ma however this does not give me the correct answer. Any ideas?
 
b577phaty said:
For my equation, I got mgsin(theta)-I(a/r)-umgcos(theta)=ma however this does not give me the correct answer. Any ideas?
Unless you show what answer you got and how, I have no ideas because I don't know what you did. The equation seems correct.
 
For the block
Fx=mgsin(theta)-T-Ff=ma
Fy=-mgcos(theta)+N=0

For the pully
T=Ialpha
T=I(a/r)

10*9.8*sin30-.8a-.2*10*9.8*cos30=10a

a=2.72 ?
 
b577phaty said:
For the pully
T=Ialpha
T=I(a/r)
In the above equations "T" stands for "Torque" not "Tension". You treat it as if it were tension. What is the torque τ if the tension is T and the lever arm is r?
 

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