I had one person answer this, but it did not make sense. Can someone else, pleas

Question

I had one person answer this, but it did not make sense. Can someone else, please try to help. I would appreciate steps and formulas used to solve the problem. Thank you.

Loop You are designing a new roller-coaster. The main feature of this particular design is to be a vertical circular loop-the-loop where riders will feel like they are being squished into their seats even when they are in fact upside-down at the top of the loop). The coaster start at rest a height of 80m above the ground, speeds up as it descends to ground level, and then enters the loop which has a radius of 20m. Suppose a rider is sitting on a bathroom scale that initially reads W (when the coaster is horizontal and at rest). What will the scale read when the coaster is moving past the top of the loop? (You can assume that the coaster rolls on the track without friction)

Explanation / Answer

Velocity with which the coaster enters the loop = velocity of the coaster when it reaches the ground from 80 m.
Using the conservation of energy, mgH = 1/2 mv2., H = 80 m
v = sqrt[2gH] ...(1)
We need to know the velocity when the coaster is at the top of the loop,
Again using energy conservation,
mg(2R) + 1/2 mV2 = 1/2 mv2
V is the velocity of the coaster at the top of the loop.
1/2 mV2 = 1/2 mv2 - mg (2R)
= mgH - mg(2R) [From (1)
V = sqrt [2g x (H - 2R)]
= 28 m/s.

m = W/g
Outward centripetal force = mV2/R = W/9.8 x( V2/R) = 4W
Downward gravitational force = W
Net force on the scale = 4W - W = 3W

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