Question

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal. At the bottom of the plane, the block continues to move on a flat surface with a coefficient of friction u = 0.30. How far does the mass move on the flat surface?

Answer 1

Gravitational acceleration = g = 9.81 m/s2

Mass of the block = m

Height from which the block is released = h = 1 m

Angle the incline makes =

Speed of the block at the bottom of the incline = V

By conversation of energy the initial potential energy of the block is converted into the kinetic energy of the block at the bottom of the incline.

V = 4.43 m/s

Normal force on the block from the flat surface = N

N = mg

Coefficient of friction between the block and the flat surface = = 0.3

Friction force on the block = f

f = N

f = mg

Distance the block slides on the flat surface = L

By conservation of energy the kinetic energy of the block at the bottom of the incline is lost to the work done against friction as it slides on the flat surface.

L = 3.33 m

Distance the block moves on the flat surface = 3.33 m