Question

1. A science teacher wanting to demonstrate centripetal acceleration holds a bucketful of water
by its handle and spins it in a vertical circle. If the teacher’s arm is 1.15m long, at what speed
must the bucket be rotated so that at the top of its path there is no tension acting through the
teacher’s arm? (2 marks)
2. An amusement park ride spins children on swings in a horizontal circle with
a radius of 6.2 m (see diagram in the top right corner of the activity). If a 21 kg
child completes 11 rotations in 2 minutes
a. identify the centripetal force acting on the child; (1 mark)
b. determine the speed of the child; and (2 marks)
c. determine the tension in the swing chain. (2 marks)
3. You are designing a model roller coaster for a school project with a loop of
radius 62 cm. What is the minimum cart speed so that the cart does not fall off
the track at the top of the loop? (4 marks)
4. A 1200 kg Indy car is travelling around a curve with a radius of 95 m. If the
curve is banked at 24° and the coefficient of friction is 0.28, what is the
maximum speed at which the car can travel without flying off?

Answer 1

1. v^2/r = g

2. omega in radians/second
= 2 pi * 11/120
a.
Ac = r omega^2
F = m Ac = m r omega^2
b.
v = omega * r
c.
same as a.

3. r = .62 meters
same as problem 1.

4. Normal force = m g cos 24
max friction force = .28 * m g cos 24
component of mass down slope = m g sin 24
so force holding car from slipping up
= m g (.28 cos 24 + sin 24)
that has to equal m v^2/R cos 24

Answer 2

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