A block is moving on an inclined plane making an angle with the horizontal and the coefficient of friction is . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define , th

Question

A block is moving on an inclined plane making an angle $45 °$ with the horizontal and the coefficient of friction is $μ$ . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define $N = 10 μ$ , then $N$ is [2011]

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(5)

For upward moving of block, pushing force $F_{1} = m g \sin θ + f$

$∴$ $F_{1} = m g \sin θ + μ m g \cos θ = m g (\sin θ + μ \cos θ)$

The force required to just prevent it from sliding down or block just remains stationary,

$F_{2} = m g \sin θ - μ N = m g (\sin θ - μ \cos θ)$

Given, $F_{1} = 3 F_{2}$

$∴$ $\sin θ + μ \cos θ = 3 (\sin θ - μ \cos θ)$

$∴$ $1 + μ = 3 (1 - μ)$ $[∵ \sin θ = \cos θ]$

$∴$ $4 μ = 2 \Rightarrow μ = 0.5$

$∴$ $N = 10 μ = 10 \times 0.5 = 5 N$

Solution

Q.
A block is moving on an inclined plane making an angle $45 °$ with the horizontal and the coefficient of friction is $μ$ . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define $N = 10 μ$ , then $N$ is [2011]

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Solution

Q. A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N=10μ, then N is [2011]

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Q.
A block is moving on an inclined plane making an angle $45 °$ with the horizontal and the coefficient of friction is $μ$ . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define $N = 10 μ$ , then $N$ is [2011]