Final answer:
The correct number of revolutions per minute at which riders experience a centripetal acceleration equal to gravity, given an 8.00 m radius ride, is approximately 17.7 rpm.
Step-by-step explanation:
To find out at how many revolutions per minute (rpm) the riders on a fairground ride are subjected to a centripetal acceleration equal to that of gravity, we need to establish a relationship between centripetal acceleration and angular velocity. The centripetal acceleration (ac) experienced by an object moving in a circular path of radius r at a constant speed v is given by ac = v2 / r. The acceleration due to gravity (g) is 9.81 m/s2. As we want the centripetal acceleration to be equal to g, we have: v2 = g • r. To find the speed v, we take the square root giving us v = √(g • r).
The relationship between linear velocity v and angular velocity ω (in radians per second) is v = ω • r. We can express angular velocity in revolutions per minute by using the conversion 1 revolution = 2π radians and 1 minute = 60 seconds. Solving for ω in rpm, we get: ω = v / (2πr) • 60.
Substituting the values r = 8.00 m and g = 9.81 m/s2 into the equations, first to find v, then ω yields the number of revolutions per minute at which the ride must spin to create a centripetal acceleration equal to the acceleration due to gravity. The calculation results in a speed of approximately 17.7 rpm, which means the correct answer is b) 17.7 rpm.