Questions
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 4.0m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively
detailed solution
Correct option is D
Let μs and μk be the coefficients of static and kinetic friction between the box and the plank respectively. When the angle of inclination θ reaches 30°, the block just slides,∴ μs=tanθ=tan30°=13=0.6If α is the acceleration produced in the block, thenma=mgsinθ-fk (where fk is force of kinetic friction) =mgsinθ-μkN as fk=μkN=mgsinθ-μkmgcosθ (as N=mgcosθa=gsinθ-μkcosθ As g=10 ms-2and θ=30°∴ a=10 ms-2sin30°-μkcos30°If s is the distance travelled by the block in time t, then s=12at2 (as u=0 or a=2st2But s = 4.0 m and t = 4.0 s (given)∴ a=2(4.0 m)(4.0 s)2=12 ms-2Substituting this value of α in eqn. (i), we get 12 ms-2=10 ms-212-μk32110=1-3μk or 3μk=1-110=910=0.9μk=0.93=0.5Similar Questions
Two blocks of mass M and m are connected with a string which passes over a smooth pulley as shown in fig. The mass M is placed on a rough
inclined plane. The coefficient of friction between the block and the inclined plane is µ. What should be the minimum mass m so that the block M slides upward ?
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