Riding a Bike in a Pipe: Physics Stunt Challenge
What are the physics behind riding a bike inside a pipe for a film stunt?
a) What is the acceleration of the bike at the bottom of the pipe?
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:
a) The acceleration at the bottom of the pipe is 6.25 m/s^2.
b) The force on the bike at an angle of 30° up from the bottom is 3,464 N.
c) The minimum velocity at the top for the bike and rider to stay moving in a circle is 6.26 m/s.
d) Yes, the bike and rider have sufficient velocity to stay moving on a circle at the top.
In a film stunt where a person is trying to ride a bike inside a pipe, there are interesting physics concepts at play. The diameter of the pipe is 8 m, and the mass of the bike and rider is 400 kg. The rider maintains a constant speed of 5 m/s for the stunt.
a) To calculate the acceleration at the bottom of the pipe, we utilize the centripetal acceleration formula: a = v^2 / r. Substituting the given values, we find the acceleration to be 6.25 m/s^2.
b) The force on the bike at an angle of 30° up from the bottom can be calculated using the centripetal force formula: F = m * a. After computation, the force is determined to be 3,464 N.
c) The minimum velocity required at the top for the bike and rider to stay moving in a circle is found by equating the centripetal acceleration to the acceleration due to gravity. The calculated minimum velocity is 6.26 m/s.
d) By comparing the minimum velocity to the constant speed of 5 m/s, we confirm that the bike and rider indeed have sufficient velocity to maintain circular motion at the top of the pipe.