Question

A block slides down a smooth ramp, starting from rest at a height h. When it reaches the bottom it’s moving at speed v. It then continues to slide up a second smoothramp.

At what height is its speed equal to v/2?

a.)h/4
b.)h/2
c.)3h/4
d.)2h

Please show which formula you used.

Answer 1

ΔE = 0

m g h - ½ m vi² = 0

vi² = 2 g h

and then, continue slide up to the second ramp,

ΔE = 0

-m g h' - ½ m v² +  ½ m vi² = 0

v = ½ vi and canceled out of mass "m"

-g h' - ½ (½ vi)² +  ½ vi² = 0

(3/8) vi² = g h'

but please remember that :

2 g h = vi²

(3/8) (2 g h) = g h'

h' = (3/4) h