This problem has two parts. I will post the questions to both parts and additional info in "Description" below.

Question

A velodrome has a banking angle of 23 degrees and a curve radius of 36.5 m.

Part a) If there was no friction, what is the speed you would need to go around the corner safely?

Part b) What force is providing the centripetal force?

Answer 1

Hello Benson,

a) To calculate the speed you would need to go around the corner safely without friction, you can use the centripetal force formula:

\[F_c = \frac{mv^2}{r}\]

Where:

- \(F_c\) is the centripetal force,

- \(m\) is the mass of the object (we'll assume a typical value for a cyclist),

- \(v\) is the velocity (speed) you want to find, and

- \(r\) is the radius of the curve.

In this case, we're looking for the speed, so we can rearrange the formula to solve for \(v\):

\[v = \sqrt{\frac{F_c \cdot r}{m}}\]

Without friction, the only force providing the centripetal force is gravity. So, the centripetal force (\(F_c\)) is the gravitational force acting on the cyclist. You can calculate the gravitational force using:

\[F_c = mg\]

Where:

- \(m\) is the mass of the cyclist, and

- \(g\) is the acceleration due to gravity (approximately 9.81 m/s²).

Now, you can calculate \(v\) using this information.

b) The force providing the centripetal force is gravity (weight). It acts vertically downward, which is perpendicular to the direction of motion of the cyclist. Therefore, in this context, gravity is the force that keeps the cyclist moving in a circular path as they go around the curved track.