The force F 1 that is necessary to move a body up an inclined plane is double the force F 2 that is necessary to just prevent it from sliding down, then –
where φ = angle of F, θ = angle of inclined plane
w = weight of the body
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, d)
F 1 = mg sin θ + µmg cos θ
F 2 = mg sin θ – µ mg cos θ
But mg = w
µ = tan φ
F 1 = w (sin θ + 
cos φ )
⇒ F 1 = w sin ( θ + φ ) sec φ
Now F 1 = 2F 2
mg sin θ + µ mg cos θ = 2 (mg sin θ – µ mg cos θ )
sin θ + µ cos θ = 2 sin θ – 2 µ cos θ
⇒ 3 µ cos θ = sin θ
⇒ tan θ = 3 µ
tan θ = 3 tan φ
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