Find the least force required to pull a body of weight W placed on a rough horizontal plane when the force is applied at angle theta with the horizontal
Answers
Explanation:
Given :
Weight W rest on a rough horizontal plane.
Angle of friction = theta
We know that,
F = mg
mg = W
Angle of friction = Angle of repose
Since,
When a body is kept on an inclined plane inclined at an angle equal to angle of repose then it will be ready to move.
Therefore,
F = mg × sin theta
F = W sin theta
Hence,
W sin theta is the required answer.
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Answer:
P = w sinλ is the least force required to pull a body
Explanation:
Let P be force applied to pull a body of weight w placed on a rough horizontal surface.
As per the given data, we have the diagram as shown below.
From the figure,
Pcosθ = μR
R+Psinθ = w
Pcosθ = μ(w-Psinθ)
P(cosθ+μsinθ) = μw
P = (μw)/(cosθ+μsinθ)
since μ = tanλ
P = (w tanλ)/(cosθ+tanλsinθ)
P = (w sinλ)/(cosθcosλ+sinλsinθ)
P = (w sinλ)/cos(θ-λ)
P is minimum, when cos(θ-λ) is maximum
If cos(θ-λ) is maximum then cos(θ-λ) = 1
Hence, P = w sinλ is the least force required to pull a body.
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