Body slides down from rest from the top of a 6.4 m long rough inclined plane at 30° with horizontal find the time taken by the block in reaching the bottom given coefficient of kind attic fiction ass .2 and acceleration due to gravity is 9.8
Asked by deepamajulal
24th August 2019,
5:21 PM
Answered by Expert
Answer:
Figure shows the different forces, i.e., weight = mg, normal reaction force N and friction force f
acting on the sliding block of mass m.
Gravitational force mg is resolved into two componenets such a way one component mg cos30
normal to inclined plane and other component mg sin30 parallel to inclined plane.
Normal reaction force N = mg cos30
friction force f = μN = μ mg cos30
net downward force F acting on block in the direction parallel to inclined plane,
F = m g sin30 - μ mg cos30 ...............................(1)
Hence acceleration = F/m = g sin30 - μ g cos30 = 9.8 [ (1/2) - 0.2(√3/2) ] = 3.2 m/s2
Time duration t for reaching ground is calculated from formula, " S = (1/2)a t2 "
where S is the distance ( length of inclined plane) travelled by the block.
Hence t = [ 2S/a ]1/2 = [ 2×6.4/3.2 ]1/2 = 2 s
Answered by Expert
24th August 2019,
8:43 PM
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