Question

06.** A block takes twice as long to slide down an inclined plane that makes an angle of 35 with the horizontal as it does to fall freely through the same vertical distance h. What is the coefficient of kinetic friction? [μ = 0.16] ​

Answer 1

The coefficient of kinetic friction between the block and the incline is 0.168.

Coefficient of kinetic friction

The coefficient of kinetic friction is determined from the principle of conservation of energy as follows;

distance traveled on the incline = L

L = h/sin35

L = 1.743 h

Since it takes twice the time travel down,

velocity to slide = 1.743 h/2t = 0.871 v

• v is the velocity to drop from the vertical height

K.E of the block when it slides = ¹/₂mv₁²  = ¹/₂m(0.871v)² = 0.871²(K.E to fall) = 0.758K.E to fall straight down

Energy lost to friction

1 - 0.758 = 0.24

Conservation of energy

μmgcos(35) = 0.24(mgsin(35)

μcos(35) = 0.24(sin(35)

μ = 0.168

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