The passengers in a roller coaster car feel 50% heavier than their true weight as the car goes through a dip with a 10 m radius of curvature. What is the car's speed at the bottom of the dip?

7 ms⁻¹

Explanation:

When the weight is 50% more, if the actual weight is W, the weight at the dip will be 1.5 Mg. At the bottom, the forces acting are

Weight Mg, vertically downwards

Centripetal force towards the center of the circle

and the normal force N = 1.5 Mg, that acts towards the center

N - Mg = Mv²: r

1.5 Mg - Mg = M v² : r

0.5 g = v² : 10

⇒ v = 7 ms⁻¹ Car's speed at the bottom of the dip.