A block is placed on a plane inclined at 35 degrees relative to the horizontal. If...

A block is placed on a plane inclined at 35 degrees relative to the horizontal. If the bloc k slides down the plane with an acceleration of magnitude g/3, determine the coefficient of the kinetic friction between the block and plane.

Solutions

Expert Solution

Gravitational acceleration = g = 9.81 m/s²

Mass of the block = m

Angle of incline = = 35^o

Acceleration of the block = a = g/3

Normal force on the block from the incline = N

Coefficient of kinetic friction between the block and plane =

Friction force on the block = f

From the free body diagram,

N = mgCos

f = N

f = mgCos

ma = mgSin - f

ma = mgSin - mgCos

a = gSin - gCos

g/3 = gSin - gCos

1/3 = Sin - Cos

1/3 = Sin(35) - Cos(35)

= 0.293

Coefficient of kinetic friction between the block and plane = 0.293

genius_generous answered 2 weeks ago

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