Question

A block of mass of 2kg 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 $\sqrt \frac {3}{2}$ a. What food should be applied to the block so that it moves down without any acceleration? b. What food should be applied to the block so that it moves up without any acceleration?

Answer 1

mass of the block , m = 2kg
Inclination angle , $\theta$ = 30°
coefficient of friction between block and the surface, $\mu$ = $\sqrt{\frac{3}{2}}$

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° - $\mu N$ = ma
mgsin30° - $\mu$ mgco30° = ma
a = gin30° - $\mu$gcos30°
a = 10 × 1/2 - √(3/2) × 10 × √3/2
a = 5 - 3/√2 × 5
a = 5(√2 - 3)/√2 m/s²

Answer 2

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