circular motion bicycle problem( physics 12).

Question

Bicycle racetracks, or velodromes, are banked at the ends. If we ignore friction, and the banking angle is  θ= 25 degrees.

a) what is the maximum speed of a bicycle if it is to move around the end of the track at a constant radius r=25m? Include FBD, and show all work!

b) if the bicycle goes faster than this value what must he do to compensate? what will happen? if the bicycle goes slower? (show any equations to help justify the answer.)

c) how slow could the bicycle ride and still travel in a circle on the track? the radius at the top of the ramp is 25m and at the bottom it is 15m>

Answer 1

First, draw a circular racetrack. Then show two acting forces: gravity and normal force. Gravity will not contribute to acceleration, but the horizontal component of the normal force does. Re-cast the normal force into horizontal and vertical components. Use Newton's second law to figure out the vertical component of the normal force in terms of gravity. Then use the horizontal component of it to figure out the acceleration. Remember the acceleration is centripetal. This should leave you the speed v in terms of the radius and the angle only. You can then answer parts a), b), and c). Good luck!