A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is:
A) 14 m/s
B) 20 m/s
C) 28 m/s
D) 80 m/s
E) 120 m/s

Question

A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is: 
A) 14 m/s 
B) 20 m/s 
C) 28 m/s 
D) 80 m/s 
E) 120 m/s

Quizplus · Accepted Answer

When the cage is at X, the centripetal force acting on the man is equal to his weight. The centripetal force is given by:

F = mv²/r

where m is the mass of the man, v is his speed, and r is the radius of the wheel.

When F = w (the man's weight), we have:

w = mv²/r

Solving for v, we get:

v = sqrt(wr/m)

Substituting the given values, we get:

v = sqrt(9.81 x 20) = 14 m/s

Therefore, the speed of the man is 14 m/s. The answer is B.

A Giant Wheel, 40 M in Diameter, Is Fitted with a Cage