wrong formula?

Question

A scale is fitted into the seat of a roller coaster car and a person weighing 860 N sits down on it. The car then descends along a path that has the shape of a 70.0 m radius vertical circle, with its lowest point at the bottom where the car reaches its greatest speed of 35.0 m/s. What is the maximum reading of the scale?
____kN

V^2/r gives you the a and you x that by the mass of the normal weight right....i get 1.5 kN kilonewtons? but its wrong

Answer 1

Centrifugal force = mv^2 / r

At the bottom of the path, centrifugal force pushes down, so that ADDS to weight, so

Max weight = m (g + v^2 / r)

= weight (1 + v^2 / gr)

remember, 860 N is the weight, not the mass.

Answer 2

The short answer is: you forgot to include the person's weight. The 1.5 kN would be correct if this experiment were done in a weightless environment.

To look at it strictly in terms of accelerations and forces:

The acceleration is indeed v²/r. That's a fact because of the way it's moving.

The forces on the man are only two:
1) The downward pull of gravity (= mg = 860N)
2) The upward push of the scale on his butt.

The combination of those forces MUST produce the observed acceleration. That is (choosing "up" as the positive direction) :

net force = ma
(-mg + Fs) = ma

where Fs is the upward pressure due to the scale. (The "-" in front of "mg" is because that force points down, in the negative direction.)

That means:

Fs = mg + ma
Fs = 860N + mv²/r

From that, you can get a value for Fs.

Finally, Newton's 3rd Law says, if the scale is pushing up on the guy's butt with a force of Fs, then his butt must be pushing down on the scale with the same force, Fs. So that is what the scale reads.