Download The Ferris Wheel: Answers

The Ferris Wheel: Answers
Measurements
Period T = 52 sec
Measuring and Calculating Average Speed
Measure the period of rotation: T = 52 sec
Average Speed = 2 x x R / T = 2 x x 9.0 / 52 = 1.1 ms-1
Speed (or linear velocity) varies with the radius, even though the angular velocity (or revolution
per minute) stays the same. Calculate the linear velocity (speed) of the rotating Ferris wheel at
half the radius. v = 0.55 m/s
Observing the Mechanism of the Ride.
Describe in detail (use a drawing) how the propulsion mechanism propels this ride?
The Ferris wheel uses a belt drive
Explain the safety design features of the ride (and associated equipment) and any safety
procedures that you can observe?
Feature/Procedure
Seat belts
Brakes
Explanation (How it makes the ride safe)
Calculating Acceleration on a Ferris Wheel
Acceleration can be computed quite easily for objects that are moving in a circular motion using
the following formula.
Acceleration = v2 / R = (4 x 2 x R) / T2
Question 1:
a)
Work out the centripetal acceleration of a passenger on the Ferris Wheel using the value
for velocity that you calculated above? Since you already know v and R you can use the
first part of the equation. a = 0.13 m/s2
b)
When would you use the second? When you cannot easily measure the speed, but can
measure the period
Examining Centripetal Acceleration
Question 2: Draw on the large circle representing the orbit of the ride.
a.
Label with dots the position of occupant at the following points at 12:00 and 6:00 o’clock
b.
c.
Draw in the acceleration vector for each position.
Draw with arrows the direction of the 2 forces acting on the occupants at each position.
Label each force as “Force by A on You”, e.g the weight force is the Force by Earth on You
N1 = Force by Seat on You
a
mg = Force by Earth on You
N2 = Force by Seat on You
a
mg = Force by Earth on You
The net force on the occupant is in the same direction as the centripetal acceleration. This
enables you to determine which of the two forces acting on the occupant is the larger.
d)
Using mg for the weight and N1 and N2 for the reaction forces write an expressions for the
net force at the 12 o’clock and at the 6 o’clock position.
At 12 o’clock mg - N1 = ma
At 6 o’clock
N2 - mg = ma
e)
Since Net Force = ma, use your value of the acceleration calculated above to determine the
size of the reaction force, N, at these two positions for an occupant with a mass of 65 kg.
12 o’clock position
d) Net Force expression N1 = mg -ma
e) Calculation of N
N1 = 65 x (9.80 - 0.13)
N1 = 629 N
6 o’clock position
N2 = ma + mg
N2 = 65 x (0.13 + 9.8)
N2 = 645 N