How Does a Roller Coaster Affect Scale Readings?

[Saad]

A scale is fitted into the seat of a roller coaster car and a person weighing 800 N sits down on it. The car then descends along a path that has the shape of a 100.0 m radius vertical circle with its lowest point at the bottom where the car reaches its greatest speed of 40.0 m/s. What is the maximum reading of the scale?

 

[HallsofIvy]

Read "Read this before posting" for forum rules: we are not here to do your homework for you. Attempt the problems first, then show us what you have done. That will help us make suggestions and give hints without just giving you the answer.

This problem is not all that challenging! You should be able to calculate the "centripetal force" the seat of the car must exert on the person (through the scale) in order to turn the person through the given curve. That will be in addition to the person's weight, of course.

 

[KSCphysics]

a) determine your variables:
V=40m/s
R=100m
F=800N = mg = m(9.8m/s^2) thus:
m=81.6N
$$a_{rad}$$ = ?


1st concept--> Force = mass x acceleration

$$F=ma$$


next, $$a_{rad}=\frac{mV^2}{R}$$

so what do you think you need to do? you know that F=ma, well, you want to know what force will be excerted onto the scale at the bottom of the curve right? well simply plug in your variables to the cent accel funtion and solve for $$a_{rad}$$ then once you get that... GO BACK to the F=ma formula, and solve for F. this F is the force the body exerts onto the scale.

 

[Saad]

Does this look ok?

Determine your variables:
V = 40m/s
R = 100m
F = 800N = mg = m (9.8m/s^2) thus:
m = 81.6kg

$$a_{rad}=\frac{mV^2}{R}$$ = (81.6kg) (40m/s)^2 / 100m
= 130560 / 100m
= 1305.6m/s^2

1st concept --> Fnet = ma
= (81.6kg)(1305.6m/s^2)
= 106537N
= 1.07 X 10^5 N

 

[Janitor]

Saad,

In post number 3 you wrote, "m=81.6N." Did you mean 81.6 kg?

Amd don't forget what HallsofIvy said about tacking on the 800 N of weight due to gravity after you do your circular acceleration calculation.