A racecar drives on a dry circular track of radius R = 600 m...

A racecar drives on a dry circular track of radius R = 600 m with coefficients \(\mu_s = 0.9\) (static) and \(\mu_k = 0.7\) (kinetic). Problem 9 If the track is flat, draw the FBD of the system and determine the max speed (mph) the car can drive without drifting. Problem 10 If the track is banked at angle \(\theta = 25\) deg, draw the FBD of the system and determine the max speed (mph) the car can drive without drifting.

Transcript

00:01 In this question it is given that a thousand kilogram car is slowly picking up the speed as it goes around a horizontal curve which radius is 100 meter.

00:12 Okay, so this is some curve of radius 100 meter and this is some car that is moving along this curve its weight is thousand kilograms.

00:26 Okay, so as we know when we draw its free body diagram, if this is the right of the curve, it's weight is 1 ,000 kilograms.

00:32 Direction okay so there will be a net force that will be accelerating it along this direction downward direction there will be m g okay and upward direction there would be a normal force also when it is moving towards right if this is the plane inside and out's outward of the paper there will be a net force a centrifugal force that would be acting outside of the plane then outside of the circle, okay, this is the center, away from the center there will be a force of centrifugal force acting that would be mb square by r, okay, that must be balanced by what? another friction force? okay, this would be the situation.

01:24 So this is the free body diagram.

01:26 Okay, now let me see what is the next part says.

01:30 It says that we might write the nuisance law of equation for this situation.

01:34 Okay, so along horizontal direction this mv square bar r is the frixional force that is acting on the body okay so that must be balanced by this is not a actual force acting this is a imaginary force okay this force is used to calculate the fictional force this is the actual force acting on it now okay, so mv square by r is the friction force acting so, net force must be equal to mass into acceleration.

02:11 So this would be equal to acceleration from here will be equal to v square by r.

02:16 Okay, so this is not an actual force.

02:19 This is a imaginary force that we assume that it will be acting because as we know that when a body will be moving in a circle, there is a force that must be acting inwards that is changing direction of the vehicle.

02:33 Okay, because direction of the most, moving vehicle will change only when there is a net force acting in that direction...

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