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A block of mass m = 4 kg is placed over ...

A block of mass `m = 4 kg` is placed over a rough inclined plane as shown in fig . The coefficient of friction between the block and the plane `mu = 0.5 ` A force `F = 10N` is applied on the block at an angle of `30^(@)`. Find the contact force between the block and the plane.
`k`

Text Solution

Verified by Experts

The correct Answer is:
` = 13.5 sqrt(5) N`

Drawing free - body diagram of block , we get
`N + F sin 30^(@) = mg cos 37^(@)`
`N = mg cos 37^(@) - F sin 30^(@)`
`= (4)(10) ((4)/(5)) - (10) ((1)/(2)) = 27 N `…(i)
` f_(max) = mu N = 0.5 xx 27 = 13.5 N`
` mg sin 37^(@) = (4)(10)((3)/(5)) = 24 N`
`and F cos 30^(@) = (10)(sqrt(3)/(5)) = 5 sqrt(3) N`
Now since `mg sin37^(@) gt f_(max) = F cos 30^(@)`
Therefore , block will slide down and friction will be maximum .Therefore net contact force is

`F_(c) = sqrt(N^(2) + (f_(max))^(2))`
`= sqrt((27)^(2) + (13.5)^(2)) = 13.5 sqrt(5) N`
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Knowledge Check

  • A block of mass m=4kg is placed oner a rough inclined plane as shown in figure. The coefficient of friction between the block and the plane is mu=0.5 . A force F=10N is applied on the block at an angle of 30^(@) .

    A
    static in nature in the direction up the plane and have the value `30.2N`
    B
    static in nature in the direction down the plane and have the value `30.2N`
    C
    kinetic in nature in the direction up the plane and have the value `30.2N`
    D
    None of these
  • A block of mass m = 4 kg is placed over a rough inclined plane as shown in figure. The coefficient of friction between the block and the plane is u=0.5. A force F= 10 N is applied on the block at an angle of 30°. The friction force between the block and wedge is

    A
    static in nature in the direction up the plane and have the value 30.2 N
    B
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    C
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  • A block is stationary on an inclined plane If the coefficient of friction between the block and the plane is mu then .

    A
    `mu gttan theta`
    B
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    C
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    D
    the reaction of the ground on the block is mg cos `theta`
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