A block of mass 2 kg is pushed against a rough vertical wall with a force of 40 N, coeffirient of static friction being 0.5 Another horizontal force of 15, is applied on the block iin the 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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Solution

Net force $= \sqrt{(20^{2} + 15^{2})} - (0.5) \times 40 = 25 - 20 = 5 N ∴ tan θ = \frac{20}{15} = \frac{4}{3} \Rightarrow m = {tan}^{- 1} (\frac{4}{3}) = 53^{\circ}$
So, the block will move at angle $53^{\circ}$ with the 15N force.

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A block of mass 2 kg is pushed normally against a rough vertical wall with a force of 40 N, co-efficient of static friction being 0.5. 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 and with what acceleration? If no, find the frictional force exerted by the wall on the block.

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Net force =√(202+152)−(0.5)×40=25−20=5N∴tanθ=2015=43⇒m=tan−1(43)=53∘ So, the block will move at angle 53∘ with the 15N force.

Net force $= \sqrt{(20^{2} + 15^{2})} - (0.5) \times 40 = 25 - 20 = 5 N ∴ tan θ = \frac{20}{15} = \frac{4}{3} \Rightarrow m = {tan}^{- 1} (\frac{4}{3}) = 53^{\circ}$
So, the block will move at angle $53^{\circ}$ with the 15N force.