# physics

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An obj of considerably small spatial extent (volume) slides down at a constant velocity of 2.75 m/s along an inclined board whose inclination with respect to the horizontal is 30 degrees. After reaching the bottom of the board, it travels horizontally along a surface that is made up of the same material as that of the inclined board. Find the distance that will covered by the object before coming to a stop.

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Use the fact that it goes down the incline at constant speed, together with the angle of the incline, to determine the kinetic friction coefficient, Uk.

Weight component down the incline = Friction force

M g sin 30 = M g cos30*Uk
Uk = tan30 = 0.5774

After it reaches the bottom and travels a horizontal distance X before stopping,
work done against friction = initial kinetic energy
M*g*Uk*X = (1/2)MVo^2
X = Vo^2/(2*g*Uk)
= Vo^2/[2*g*tan30]

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