Question

A bicycle is racing around on a horizontal surface in a circle of radius 21 m. The force exerted by the road on the bicycle makes an angle of 19 degrees with the vertical. What is its speed?

Answer 1

The speed of the bicycle is approximately 18.34 m/s.

Step-by-step explanation:

To find the speed of the bicycle, we need to use the concept of centripetal force. In this case, the force exerted by the road on the bicycle is acting as the centripetal force, keeping the bicycle moving in a circular path. The angle between the force and the vertical direction is 19 degrees.

We can use the equation for centripetal force to find the speed:

F = mv^2/r

where F is the force, m is the mass of the bicycle and rider (which we can ignore for this problem), v is the speed, and r is the radius of the circle. Given that the radius is 21 m and the angle is 19 degrees, we can find the vertical component of the force using the equation:

F_vertical = F * sin(angle)

Since the vertical component of the force is equal to the weight of the bicycle and rider, we can write:

mg = F_vertical

Simplifying these equations and solving for v, we get:

v = sqrt(g * r / sin(angle))

Substituting the given values, we have:

v = sqrt(9.8 * 21 / sin(19))

Calculating this expression gives us a speed of approximately 18.34 m/s.