posted by John on .
Two blocks are released from the same height above the floor. Block A slides through a less inclined track to the floor, whereas block b slides on more inclined track to the floor. Assume no friction.Which block gets to the bottom(floor) of the incline first?
The acceleration rate down the plane is
a = g sin A,
where A is the angle the ramp makes to the horizontal. The total length L that it must travel is
L = H/sin A,
where H is the height that it must fall.
The time T required to travel the length of the ramp is such that
(1/2) a T^2 = L
T = sqrt(2L/a)
= (1/sin A) sqrt(gH)
The smaller the angle A, the longer it takes.