Question

Sheila (m=62 kg) is riding the demon roller coaster ride. The turning radius of the top of the loop is 12 m. Sheila is upside down at the top of the loop and experiencing a normal force which is one-half of her weight. Draw a free body diagram and determine Sheila's speed.

Answer 1

The free body diagram consists of weight (W), normal force (N) and centripetal force (F).

The speed of Sheila is 7.67 m/s.

How to calculate the speed of Sheila?

The speed of Sheila is calculated by considering the free body diagram of the forces acting on Sheila.

weight of Sheila (W) acting downwards

normal force of Sheila (N) acting upwards

centripetal force on Sheila (F) acting upwards

F + N = W

F = W - N

F = mg - ¹/₂(mg)

mv²/r = mg - ¹/₂(mg)

v²/r = g - g/2

v²/r = g/2

v² = rg/2

v = √ (rg/2)

where;

• r is the radius of the loop
• g is acceleration due to gravity

v = √ ((12 x 9.8/2))

v = 7.67 m/s