What is the force of a roller coaster? Please check my work.

[Dmitri10]

Homework Statement

A rollercoaster car and passengers have a combined mass of 1620 kgm, and they descend the first hill at an angle of 45o to the horizontal. With what force is the roller coaster pulled down the hill?

Homework Equations

The Attempt at a Solution

Vertical force = 1620 kg * 9.81 = 15892.2 N
With a triangle in mind: cos(45) = 15892.2 / x
x[cos(45)] = 15892.2
x = 22475 N

Is this correct?

 

[Delphi51]

mg is straight down. Part of that is straight into the track and part is along the track, mg*cos(45). The answer must be smaller than the whole 15892.

 

[tomcue]

I would like to commend your attempt at solving this problem. However, your solution is not entirely correct. The force of a roller coaster is not a constant value, as it varies throughout the ride due to changes in speed, direction, and other factors. Instead, we can calculate the force at a specific point on the roller coaster using Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma). In this case, the force pulling the roller coaster down the hill would be equal to the mass of the roller coaster and passengers multiplied by the acceleration due to gravity (9.81 m/s^2), multiplied by the cosine of the angle of the hill. So the correct equation would be F = (1620 kg * 9.81 m/s^2) * cos(45) = 11492.3 N. This means that the roller coaster is being pulled down the hill with a force of approximately 11492.3 Newtons. Keep up the good work!