Question

A body of weight 500 N is lying on a rough plane inclined at an
angle 25° with the horizontal. It is supported by an effort P parallel
to the plane. Determine the minimum value of P for which the
equilibrium can exist, the coefficient of friction is 0.25​

Answer 1

Explanation:

100

6. Calculate 'Intermediate Consumption' from the following data:

Items

(i) Subsidies

(ii) Opening stock

(iii) Closing stock

(iv) Sales

(v) Consumption of fixed capital

600

5,000

700

angle 25° with the horizontal. It is supported by an effort P parallel

to the plane. Determine the minimum value of P for which the

equilibrium can exist, the coefficient

Answer 2

Answer: Minimum value of P is 97.5 Newtons

Explanation:

When body is placed on inclined plane, there is tendency of body to slip down along the plane because of its weight.

Friction opposes the slipping of body on the plane.

If the frictional force is not sufficient to stop the body, then we need to apply external force.

Weight of the body (W) = 500 N

Coefficient of friction (μ)  = 0.25

Balancing the forces on the body :

N = Wcos(25)                 (direction perpendicular to plane)

P + f = Wsin(25)             (direction along the plane)

For minimum P , f should be maximum

Maximum friction = μN

P +  μN = Wsin(25)

P +  μWcos(25) = Wsin(25)

P  = W ( sin(25) - μcos(25) )

P = 500 ( 0.42 - 0.25(0.90) )

P = 500 ( 0.195)

P = 97.5 Newtons

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