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Limiting Friction

A block of ma...

Question

A block of mass $10 kg$ is at rest on a rough horizontal surface. A force of $40 N$ is applied on it as shown in figure. The acceleration of the block is: (Take $g = 10 {m/s}^{2}$ )

0 {m/s}^{2}

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10 {m/s}^{2}

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20 {m/s}^{2}

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30 {m/s}^{2}

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Solution

The correct option is A $0 {m/s}^{2}$
From the FBD
$R = 10 g - 40 sin 37^{\circ}$
$= 100 - 24 = 76 N$
$∴ (f_{s})_{max} = μ_{s} R$
$= 0.5 \times 76 = 38 N$
But applied horizontal force $= 40 cos 37^{\circ} = 32 N < (f_{s})_{max}$ .
Hence, the block does not move.

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A block of mass 10 kg is at rest on a rough horizontal surface. A force of 40 N is applied on it as shown in figure. The acceleration of the block is: (Take g=10 m/s2)

The correct option is A 0 m/s2From the FBD R=10g−40sin37∘ =100−24=76 N ∴(fs)max=μsR =0.5×76=38 N But applied horizontal force =40cos37∘=32 N<(fs)max. Hence, the block does not move.

A block of mass $10 kg$ is at rest on a rough horizontal surface. A force of $40 N$ is applied on it as shown in figure. The acceleration of the block is: (Take $g = 10 {m/s}^{2}$ )

The correct option is A $0 {m/s}^{2}$
From the FBD
$R = 10 g - 40 sin 37^{\circ}$
$= 100 - 24 = 76 N$
$∴ (f_{s})_{max} = μ_{s} R$
$= 0.5 \times 76 = 38 N$
But applied horizontal force $= 40 cos 37^{\circ} = 32 N < (f_{s})_{max}$ .
Hence, the block does not move.