Question

A person is trying to ride a bike all the way round the inside of

a pipe for a stunt in a film. The filmmaker wants to know what

speeds are involved. The pipe has a diameter of 8 m.

The mass of the bike and rider is 400 kg. The rider goes at a

constant speed of 5 m/s.

a) What is its acceleration at the bottom?

b) What is the force on the bike at an angle of 30° up from the

bottom?

c) What is the minimum velocity at the top for the bike and

rider to stay moving in a circle?

d) Do the bike and rider have sufficient velocity to stay moving

on a circle at the top?�

Answer 1

(a) $a=g+2v^2/d=16.05\text{ m/s}^2.$

(b) $F=m\bigg(g\cos\theta+\dfrac {2v^2}d\bigg)=5895\text{ N}.$

(c) $u=\sqrt{gd/2}=6.26\text{ m/s}.$

(d) No, because the chosen velocity (5 m/s) is smaller than the required velocity (6.23 m/s).