Question

A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coefficient of static friction being 05. Another horizontal force of 15 N, is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction ? If no, find the frictional force exerted by the wall on the block.

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Answer 1

Given

• Mass = 2 kg
• Force against the wall = 40 N
• µ = 0.5
• Force applied parallel to the wall = 15 N

To Find

• If the block would move and if yes the direction of motion

Solution

☯ (F_s)max = µN

• The value of µ as per the question is 0.5

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✭ According to the Question :

⇒ F = µN

⇒ F = 0.5 × 40

⇒ (F_s)max = 20 N

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• Case 1 is when the parallel force is against mg

⇒ Resultant force = mg - 15

⇒ Resultant force = (2×10) - 15

⇒ Resultant force = 20-15 = 5 N

As 5 < (F_s)max, the block will be at rest

• Case 2 is when the parallel force is along mg

⇒ Resultant force = mg + 15

⇒ Resultant force = 20+15 = 35 N

As 35 > (F_s)max, the block will move in the downward direction along the direction of mg

Answer 2

Answer:

$Net \: force = \sqrt{ {20}^{2} + {15}^{2} } - (05)x40 \\25 - 20 = 5N \\ \tan( \alpha ) = \frac{20}{15} = \frac{4}{3} \\ = > m = { \tan}^{ - 1} ( \frac{4}{3} ) = {53}^{.}$

So, the block will moveat angle 53° with the 15 N force.