If a block moving up at `Theta` equal to 30 degree with a velocity 5m/s, stops after 0.5 sec, then `mu` is..??

A block is moving up a slope inclined at 30 degrees to the horizontal. The initial velocity of the block is 5 m/s and it stops after 0.5 seconds. We need to determine the coefficient of friction between the block and the surface on which it is moving.

As the block moves up the slope there is a deceleration of the block due to frictional force. Let the mass of the block be m. The normal force of the block on the surface is `(m*g)/sin 30` . If the coefficient of friction is `mu` , the frictional force is equal to `((m*g)/sin 30)*mu` . The acceleration of the block is `(g/sin 30)*mu` = `19.6*mu`

As the block stops moving after 0.5 seconds, using the equation v = u + a*t gives:

`0 = 5 - 19.6*mu*0.5`

`mu = 25/49`

The coefficient of friction between the block and slope is approximately 0.5102