At the fairground

Question 1

What is the resultant force at the bottom of a big dipper?

Answer 1

S - mg = mv²/r

Question 2

What do passengers feel at the bottom of the dipper?

Answer 2

Passengers experience an extra upwards force of mv²/r as the seats push against them.

Question 3

When an object is raised to a height equal to the length of the cable. There is a transfer of gravitational potential energy to kinetic energy as in the pendulum.

Answer 3

• ½mv² = mgh
• Its max velocity squared = 2gh
• At the lowest point the support force = S - mg = mv²/L
• Therefore the support force = mg + 2mgh/L

Question 4

At maximum height the reaction force and the weight produce the force towards the centre.

Answer 4

The result force = mg + R = mv²/r

Question 5

At what velocity is the reaction force = 0

Answer 5

v₀ = √gr