Question

A roller coaster car is going over the top of a 15 m- radius circular rise. At the top of the hill, the passengers "feel light" with an apparant weight only 50% of their true weight. How fast is the roller coaster moving?

Answer 1

W_apparent = m*g - m*v^2/r

0.5*m*g = m*g - m*v^2/r

m*v^2/r = 0.5*m*g

v = sqrt(0.5*g*r)

= sqrt(0.5*9.8*15)

= 8.57 m/s

Answer 2

If passengers feel only 50% of weight,

Remaining half is balanced by centripetal force.

m*g/2 = m*v²/r

v² = g*r /2 =9.8*15 /2

v =sqrt(73.5) = 8.573 m/s