Question

1. A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r = 28.7 m, how fast is the roller coaster traveling at the bottom of the dip?

2. A 0.21-kg ball on a stick is whirled on a vertical circle at a constant speed. When the ball is at the three o’clock position, the stick's tension is 20 N. Find the tension in the stick when the ball is (a) at the twelve o’clock and (b) at the six o’clock positions.

Answer 1

1)

.R 2 m3 Lef R se the normal reaction on the passenger at the bottom of the uscle be the speed of the passenger at the bottom of the cuscle ? R= mgt.my? 8 amg [Given R = 2mg mg + muz 2 ng = my? v=rog = √28-789.8 V = 16-77 m/s

2)

L mg At 3 o'clock position T= mv2 20 = enou r At the twelve o'clock position bart's A ses - breath T = mv.my = 20 -0.21 X 9.8 T = 17.942N

At the six o'clock position my = mg + my? 021*9.8 + 20 2058 + 20 22.058 T = 22.06 N