A block of mass of 2 kg slides on an inclined plane that makes an angle of `30^(@)` with the horizontal . The coefficient of friction between the block and the surface is `sqrt(3)//2` . What force should be applied to the block so that it moves up without any acceleration ?
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Explanation:
Mass of the block , m = 2kg
Inclination angle , = 30°
coefficient of friction between block and the surface, =
Block moves downward without any acceleration,
use Newton's law of motion,
fnet = 0
mgsin30° - fr = 0
fr = mgsin30° = 2 × 10 × 1/2 = 10N
block moves downward with an acceleration, a
From Newton's law of motion,
mgsin30° - fr = ma
mgsin30° - = ma
mgsin30° - mgco30° = ma
a = gin30° - gcos30°
a = 10 × 1/2 - √(3/2) × 10 × √3/2
a = 5 - 3/√2 × 5
a = 5(√2 - 3)/√2 m/s²
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