N"Simple Pulley Problem: Find Tension in String for 100N Toy on Rough Surface"

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SUMMARY

The discussion focuses on calculating the tension in a string for a 100N toy on a rough surface, with the string making a 16-degree angle with the vertical. The coefficient of friction is given as 0.8, and the toy is in limiting equilibrium. The final tension in the string, denoted as H, is calculated to be approximately 134.37N using the equations of equilibrium and friction. A correction is noted regarding the sign of the reaction force R in the calculations.

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Lokhtar
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Homework Statement



A child has a toy of weight 100N which is attached to a string. The toy is initially at rest on a rough horizontal plane. The child picks up the string and pulls it so that the string makes an angle of 16 degrees with vertical. If the coefficient of friction between the toy and the floor is 0.8 (μ) and the toy is in limitng equilibrium, find the tension in the string.



The Attempt at a Solution



Hv=(Hcos16)-100+r=0
R=(Hcos16)-100

Hh=(Hsin16)-f
Hsin- μr=0
(Hsin16)-0.8r=0
(Hsin16)-0.8[(Hcos16)-100]=0
(Hsin16)-(0.8Hcos16)+80=0
H(sin16-0.8cos16)=-80
H=-80/sin16-(0.8cos16)
H=134.37
 
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Lokhtar said:

The Attempt at a Solution



R=(Hcos16)-100


The sign of R is wrong.

ehild
 

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