While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 100.8 newtons when the car is moving at a speed of 40 kilometers per hour and the passenger has a mass of 70 kilograms, find the force a passenger experiences when the car is moving at 50 kilometers per hour and the passenger has a mass of 80 kilograms.
To solve this problem, we can use the equation for the variation of centrifugal force with respect to mass and speed:
f = k * m * v^2
where f is the centrifugal force, m is the mass of the passenger, v is the speed of the car, and k is the constant of variation.
We are given that when the car is moving at a speed of 40 kilometers per hour (or 40,000 meters per 3,600 seconds) and the passenger has a mass of 70 kilograms, the centrifugal force experienced by the passenger is 100.8 newtons.
Plugging these values into the equation, we can solve for k:
100.8 = k * 70 * (40,000/3,600)^2
100.8 = k * 70 * (400/36)^2
100.8 = k * 70 * (100/9)^2
100.8 = k * 70 * 10000/81
100.8 = k * 864.2
Now, we can solve for k by dividing both sides of the equation by 864.2:
k = 100.8 / 864.2
k ≈ 0.1167
Now that we have the value of k, we can use it to find the force a passenger experiences when the car is moving at 50 kilometers per hour and the passenger has a mass of 80 kilograms.
Plugging these values into the equation, we get:
f = 0.1167 * 80 * (50,000/3,600)^2
f ≈ 0.1167 * 80 * (500/36)^2
f ≈ 0.1167 * 80 * (500/36)^2
f ≈ 0.1167 * 80 * 694.44^2
f ≈ 0.1167 * 80 * 482156.75
f ≈ 4,522.4
Therefore, the force a passenger experiences when the car is moving at 50 kilometers per hour and the passenger has a mass of 80 kilograms is approximately 4,522.4 newtons.