A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is . The effort applied parallel to the plane is given by (where = tan = Coefficient of friction between the plane and the body)

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Theory of Machine

A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is $$\alpha $$. The effort applied parallel to the plane is given by (where $$\mu $$ = $$\tan \varphi $$ = Coefficient of friction between the plane and the body)

A) $${\text{P}} = {\text{W}}\tan \alpha $$ B) $${\text{P}} = {\text{W}}\tan \left( {\alpha + \varphi } \right)$$ C) $${\text{P}} = {\text{W}}\left( {\sin \alpha + \mu \cos \alpha } \right)$$ D) $${\text{P}} = {\text{W}}\left( {\cos \alpha + \mu \sin \alpha } \right)$$

Answer & Solution

Correct Answer: Option C

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Vimala K 7 years ago

Effort applied = P (acting to the right).
Frictional force = uWcosa(acting against P).
Gravitational force = Wsina(acting downwards).

So equation will be in equilibrium as:
P = Wsina + uWcosa.
P = W(sina+ ucosa).

Kudrat Sharma 7 years ago

the answer should be P = W(sin alpha + mu cos alpha) / ( cos alpha - mu sin alpha )

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A body of weight W is required to move up the...

A body of weight W is required to move up the rough inclined plane whose angle of inclination with the horizontal is $$\alpha $$. The effort applied parallel to the plane is given by (where $$\mu $$ = $$\tan \varphi $$ = Coefficient of friction between the plane and the body)

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