A roller coaster car speeds down a hill past point A and then rolls up a hill past hill B.The car has a speed of 16.9 m/s at point A. THe acceleration of gravity is 9.81 m/s^2.If at point A the track exerts a force on the car that is 2.45*10^4 N greater than the car's weight, what is the mass of the car?
To find the mass of the car, we need to use the concept of force and acceleration. We'll use the equation F = ma, where F is the net force acting on the car, m is the mass of the car, and a is the acceleration.
At point A, the net force acting on the car is the sum of the gravitational force (car's weight) and the force exerted by the track.
Given that the force exerted by the track is 2.45 x 10^4 N greater than the car's weight, we can write the equation as:
F(track) = F(gravity) + deltaF
Where F(track) is the force exerted by the track, F(gravity) is the gravitational force (mg), and deltaF is the additional force exerted by the track.
The gravitational force can be calculated using the formula:
F(gravity) = mg
Given that the acceleration of gravity (g) is 9.81 m/s^2, we can rewrite the equation as:
mg = mg + deltaF
Now, we can isolate the mass (m) in the equation to find the answer:
m = deltaF / g
Substituting the given values, we have:
m = (2.45 x 10^4 N) / (9.81 m/s^2)
Calculating this expression gives us the mass of the car.