Pulling force making an angle θ to the horizontal is applied on a bloc...
Solution:
Given,
Weight of the block, W
Angle of friction, α
Angle of pulling force with horizontal, θ
To find,
Magnitude of force required to move the block
1. Free body diagram
Draw the free body diagram of the block with all the forces acting on it.
The weight of the block acts vertically downwards.
The normal reaction force acts perpendicular to the table surface.
The pulling force acts at an angle θ to the horizontal.
The friction force acts opposing the motion of the block.
2. Equations of motion
Resolve all the forces in the horizontal and vertical directions.
In the vertical direction,
N - W = 0
In the horizontal direction,
F cos θ - f = 0
where,
N = Normal reaction force
f = Friction force
3. Friction force
The friction force can be calculated using the equation,
f = μN
where,
μ = coefficient of friction
N = Normal reaction force
Here,
μ = tan α
Substituting the value of N,
f = tan α * W
4. Force required to move the block
The force required to move the block can be calculated using the equation,
F = f / sin (θ - α)
Substituting the value of f,
F = (tan α * W) / sin (θ - α)
Simplifying,
F = W sin α / cos (θ - α)
Hence, option C is the correct answer.
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