Can you solve this equation for me? Step-by-step?

Question

Please tell me how to solve it!!!! A student of mass M = 82 kg takes a ride in a frictionless loop-the-loop at an amusement park. The radius of the loop-the-loop is R = 15 m. The force due to the seat on the student at the top of the loop-the-loop is FN = 696 N and is vertically down. What is the apparent weight of the student at the bottom of the loop-the-loop? I'm in college by the way.

Answer 1

fawls quesshun.   If foers on yu at top be "vertikally DOWN" yu wood fall.   Foers from spin gotta be > 1 g tu hold

yu in plaes at the top av the loop.  That meen the net foers gotta be UP at the top.

???? "seet" ???? yu hav sumthun tu hold onto?????  wotz the purpus av that????

???? yu hav seet belt ????

Comments

The force experienced at the apex of rotation is greater than the force of gravity downwards, so with or without a seatbelt the passenger would remain in the seat. By Newton's third law, action and reaction are equal and opposite, the experienced force is the resistance of the fixed seat. Centrifugal force constrains all fixed parts of the ride to be attracted towards the centre. Any unattached parts would be flung out tangentially, but the back and sides of the passenger seat itself, rather than a seatbelt, act as constraints that prevents the passenger from being ejected.

(A bucket full of water without a lid can be spun in a vertical centrifuge without spilling any water, for the same reason. Care to try it?)

Answer 2

The centrifugal force, given by the expression mw^2r, where m=mass, w=angular acceleration (radial component) and r=radius, is actually radially directed towards the centre of rotation, but is experienced by a reactive force acting outwards, because of the pressure of the seat against the passenger's body. At the apex of the rotation, gravity is pulling the passenger vertically downwards with a force mg, where g=9.81m/s/s, the acceleration of gravity, so the net effect is m(w^2r-g)=696 N. Therefore, 82(15w^2-9.81)=696. From this w^2=(696/82+9.81)/15=1.22 approx. At the lowest point the force is m(w^2r+g)=82(1.22*15+9.81)=2305 N approx.

We need to convert this force into a weight by dividing by 9.81: 2305/9.81=235kg approx. (2.9g).