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Question

# A block of mass 10Kg is placed on a rough horizontal table whose coefficient of static friction μs is equal to 0.5. A Force F acting on the block at angle of 37∘ is gradually increased from zero. Determine whether the block will first slide or lift up?

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Solution

## There is minimum a magnitude of forces required, both in horizontal and vertical direction, either to slide or lift up the block. The block will first slide or lift up would depend upon which minimum magnitude of force is lesser.For block to start lifting up, in vertical direction Fsin37∘+N−Mg≥0N becomes zero on just lifting condition.Flift≥10g3/5∴Flift≥5003NFor horizontal direction to start slidingFcos37≥μsNFcos37∘>0.5[10g−Fsin37∘](∵N=10g−Fsin37∘)Hence fslide>50cos37∘+0.5sin37∘fslide>50011NFlift>5003N⇒fslide<FliftTherefore the block will begin to slide before lifting.

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