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

AI Thread Summary
The problem involves calculating the tension in a string attached to a 100N toy on a rough surface, with the string pulled at a 16-degree angle from vertical. The coefficient of friction is 0.8, and the toy is in limiting equilibrium. The equations derived include balancing vertical and horizontal forces, leading to a tension calculation. An error was noted in the sign of the reaction force (R) in the solution attempt. The correct tension in the string is ultimately found to be approximately 134.37 N.
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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