If a pushing force making an angle with horizontal is applied on a block off mass m placed on horizontal table and angle of friction is beta, then what is the minimum magnitude of force required to move the block ?
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Let us first resolve the pushing force F. The vertical component is F sinβ and the horizontal component is F cos β.
The net normal reaction is, N = mg + F sinβ
The firctional force f is, f = µN = µ(mg + F sinβ)
Since, β is the angle of friction, so, µ = tanβ
Therefore, f = (tanβ)( mg + F sinβ)
The applied force will be able to move the block when the minimum force is,
F/ = f
=> F cos β = (tanβ)( mg + F sinβ)
=> F = (tanβ)( mg + F sinβ)/(cos β)
The net normal reaction is, N = mg + F sinβ
The firctional force f is, f = µN = µ(mg + F sinβ)
Since, β is the angle of friction, so, µ = tanβ
Therefore, f = (tanβ)( mg + F sinβ)
The applied force will be able to move the block when the minimum force is,
F/ = f
=> F cos β = (tanβ)( mg + F sinβ)
=> F = (tanβ)( mg + F sinβ)/(cos β)
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