Answer:
The reading on the scale is N = 9W
Explanation:
Since the roller coaster drops from a height, h of 80 m, the potential energy lost equals the kinetic energy gained as it enters the loop.
So, mgh = 1/2mv² where m = mass of rider, g = acceleration due to gravity = 9.8 m/s², h = initial height of roller coaster above ground level = 80 m and v = speed of roller coaster as it enters the loop.
So, mgh = 1/2mv²
v² = 2gh
v = √(2gh)
v = √(2 × 9.8 m/s² × 80 m)
v = √(1568 m²/s²)
v = 39.6 m/s
Now, as the roller coaster gets to the top of the vertical loop, the centripetal force, F and the weight W acts downwards. For the passenger not to fall off, this must equal the normal force, N
So, F = mv²/r where v = speed of roller coaster = 39.6 m/s and r = radius of vertical loop = 20 m and m = mass of rider = W/g
F = Wv²/gr
F = W(39.6 m/s)²/(9.8 m/s² × 20 m)
F = (1568 m²/s²)W/196 m²/s²
F = 8W
Since F + W = N
8W + W = N
9W = N
So, N = 9W
So, the reading on the scale is N = 9W