Question

The instructions for your toy car set say that the max centripetal acceleration the cars can withstand without falling out of the track is 3.8 m/s. You notice that the toy cars fly off the track when they move faster than 1.1 m/s, so what is the radius in meters of the curve in your track?

Answer 1

To find the radius of the toy car track's curve, use the formula for centripetal acceleration, a = v^2 / r, with the provided maximum acceleration (3.8 m/s^2) and the speed at which the car flies off (1.1 m/s). The radius r is approximately 0.3184 meters.

Step-by-step explanation:

The question involves finding the radius of the curve in a toy car track given the maximum allowable centripetal acceleration and the speed at which the cars fly off the track. The centripetal acceleration a can be calculated using the formula:

a = v^2 / r

Where v is the velocity of the car and r is the radius of the curve. We know the maximum centrifugal acceleration a car can withstand is 3.8 m/s^2 and the velocity v at which the car flies off is 1.1 m/s. Using these values, we can rearrange the formula to solve for r as follows:

r = v^2 / a

Substituting the given values:

r = (1.1 m/s)^2 / 3.8 m/s^2

r = 1.21 m/s^2 / 3.8 m/s^2

r = 0.3184 meters

Therefore, the radius of the curve in your track is approximately 0.3184 meters.