The car's speed at the top if the normal force equals the magnitude of the gravitational force is 14m/s
According to the question, we are told that the normal force is equal to the magnitude of the gravitational force as a roller coaster.
N = G
The formula for calculating the normal force is expressed as:
N = mg
The formula for calculating the gravitational force is expressed as:
G = [tex]\frac{mv^2}{r}[/tex]
If they are both equal, hence;
[tex]mg=\frac{mv^2}{r}\\g=\frac{v^2}{r}[/tex]
Given the following parameters
diamater = 40m
radius = 20m
acceleration due to gravity g = 9.8m/s^2
Substitute the given parameters into the formula to get the car's speed
[tex]9.8=\frac{v^2}{20}\\v^2 = 9.8 \times 20\\v^2 = 196\\v=\sqrt{196}\\v = 14m/s\\[/tex]
Hence the car's speed at the top if the normal force equals the magnitude of the gravitational force is 14m/s
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