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Question:

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively?

0.5and0.6

0.6and0.6

0.4and0.3

0.6and0.5

Solution:

Static coefficient of friction is μs=tan30°=0.577≈0.6
For kinetic friction, ma=mgsin30°−f=mgsin30°−μkmgcos30°
a=gsin30°−μk gcos30° (1)
and also using S=ut+1/2at², ⇒4=0+(1/2)a(4)² or a=0.5m/s²
Now from (1) we get, 0.5=10(1/2)−μk(10)(√3/2)
or μk=4.5/(√3)=0.5