Question

A block is released from rest at the top of an inclined plane. The height of the plane is 5.00 m and it makes an angle of 30.0 degrees with the horizontal . The coefficient of kinetic friction between block and surface is 0.200. What is the speed of the block (in m/s) when it reaches the bottom of the incline?

Answer 1

Horizontal direction :
IF angle is measured from y axis (vertical line) -> a(horizontal) = Fsin(32)/m
IF angle is measured from horizontal -> a(horizontal) = Fcos(32)/m

Vertical direction:
[ here positive a means acceleration down, negative a means up]
IF angle is measured from vertical:
If force is down -> a(vertical) = (Fcos(32) + mg)/m
if force is up -> a(vertical) = (Fcos(32) - mg)/m

If angle is measured from horizontal
force is down -> a = (Fsin(32) + mg)/m
force is up -> F = (Fsin(32) - mg)/m

Then magnitude of acceleration = SQRT[acceleration(horizontal) ^ 2 + acceleration(vertical) ^ 2]