An object of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30° with the horizontal. the object is allowed to move and it stops on a rough horizontal surface, at a distance of 2 m from the bottom of the inclined plane. the coefficient of kinetic friction on the inclined plane is 0.4 and g = 10 m/s2. what is the coefficient of kinetic friction for the horizontal surface?

Explanation:

given,

height of the inclined plane = h

length of the inclined plane = 8 m

angle made with  the horizontal= 30°

stopped in the rough horizontal surface = 2 m

kinetic friction coefficient = 0.4

acceleration due to gravity = 10 m/s²

coefficient of kinetic friction on horizontal surface = ?

using energy conservation

v = 4.91 m/s

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force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2