Question

A bicyclist is riding at a speed of 13.2m/s around a circular track with a radius of 40 m If the magnitude of the force that maintains the bike's motion is 377 N, what is the mass of the bicycle and the rider?

please give formula and thorough explanation if you can

Answer 1

To find the mass of the bicycle and the rider, we use the centripetal force formula and solve for mass.

Step-by-step explanation:

To solve this problem, we need to use the centripetal force formula. The centripetal force, F, can be calculated using the formula:

F = (mass * (velocity^2)) / radius

Where F is the force, m is the mass, v is the velocity, and r is the radius.

In this case, we want to find the mass, so we can rearrange the formula:

mass = (F * radius) / (velocity^2)

Substituting the given values:

mass = (377 N * 40 m) / (13.2 m/s)^2 = 457.57 kg

Therefore, the mass of the bicycle and the rider is approximately 457.57 kg.

Answer 2

To find the mass of the bicycle and the rider, you can use Newton's second law of motion and solve for mass by dividing the force by the acceleration. The mass of the bicycle and the rider in this case is 86.6 kg.

To find the mass of the bicycle and the rider, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).

In this case, the force is the magnitude of the force that maintains the bike's motion, which is given as 377 N. The acceleration can be calculated using the formula a =
`v^2` / r, where v is the speed of the bike (13.2 m/s) and r is the radius of the circular track (40 m).

Substituting the values into the formula, we get a =
`13.2^2`/ 40 = 4.356
`m/s^2`. Now, we can rearrange Newton's second law equation to solve for the mass: m = F / a.

Therefore, the mass of the bicycle and the rider is 377 N / 4.356
`m/s^2` = 86.6 kg.