A large block of mass 100 kg slides down an incline. The coefficient of kinetic

Question

A large block of mass 100 kg slides down an incline. The coefficient of kinetic friction between the block and the incline is 0 2. The angle that the incline makes with the horizontal is 30 degrees. A small hanging mass, 10 kg, is attached to the large box by a very light string which passes over a frictionless pulley. Draw a tree body diagram for the block and the hanging mass. Clearly label your vectors. Find the magnitude of the acceleration of the large block. Find the magnitude of the tension in the string.

Explanation / Answer

given,

mass of large block = 100 kg

mass of small block = 10 kg

coefficient of friction = 0.2

angle = 30 degree

force equation of large block

mg * sin(30) - T - kmg * cos(30) = ma

100 * 9.8 * sin(30) - T - 0.2 * 100 * 9.8 * cos(30) = 100 * a

force equation of small block

T - 10 * 9.8 = 10 * a

on solving above two equations we'll get

tension T = 118.205 N

acceleration a = 2.02 m/s^2

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