Answer:
33.58794 m/s
Explanation:
[tex]F_c[/tex] = Cenrtipetal force = [tex]\dfrac{mv^2}{r}[/tex]
m = Mass of car
r = Radius of curvature = 115 m
g = Acceleration due to gravity = 9.81 m/s²
The normal force is given by
[tex]N=F_c+mg[/tex]
At the bottom N = 2N
[tex]2mg=F_c+mg\\\Rightarrow 2mg=\dfrac{mv^2}{r}+mg\\\Rightarrow v=\sqrt{gr}\\\Rightarrow v=\sqrt{9.81\times 115}\\\Rightarrow v=33.58794\ m/s[/tex]
The car was traveling at the speed of 33.58794 m/s
The speed at which the car was travelling is 33.57 m/s.
Given the following data:
We know that the acceleration due to gravity (g) of an object on planet Erath is equal to 9.8 meter per seconds square.
To find the speed at which the car was travelling:
The normal force acting on the driver and car is given by the formula:
[tex]N = F_c + mg[/tex] ....equation 1
Where:
But, [tex]F_c = \frac{mv^2}{r}[/tex]
Since, the normal force was on the driver is twice his weight:
[tex]N = 2mg[/tex]
Substituting the other eqns into eqn 1, we have:
[tex]2mg = \frac{mv^2}{r} + mg\\\\2mg - mg = \frac{mv^2}{r}\\\\mg = \frac{mv^2}{r}\\\\mgr = mv^2\\\\v = \sqrt{gr} \\\\v = \sqrt{9.8 \times 115}\\\\v = \sqrt{1127}[/tex]
Speed, v = 33.57 m/s
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