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

[Lokhtar]

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

 

[ehild]

The Attempt at a Solution

R=(Hcos16)-100

The sign of R is wrong.

ehild