Answer:
We need 4 times more force to keep the car in circular motion if the velocity gets double.
Explanation:
Lets take the mass of the car = m
The radius of the arc = r
[tex]F=\frac{m\times v^2}{r}[/tex]
Given that speed of the car gets double ,v' = 2 v
Then the force on the car = F'
[tex]F'=\frac{m\times v'^2}{r}[/tex] ( radius of the arc is constant)
[tex]F'=\frac{m\times (2v)^2}{r} [/tex]
[tex]F'=4\times \frac{m\times v^2}{r}[/tex]
We know that [tex]F=\frac{m\times v^2}{r}[/tex]
Therefore F' = 4 F
So we can say that we need 4 times more force to keep the car in circular motion if the velocity gets double.
The magnitude of centripetal force will become four times with the twice the greater speed of car.
Given data:
The magnitude of centripetal force on car is, Fc.
The force acting on any object undergoing the motion around the circular path, such that the motion is balanced is known as centripetal force. It is also known as the center-seeking force. And the expression for the centripetal force is given as,
Fc = mv²/r
Here,
m is the mass of car.
v is the speed of car.
r is the radius of circular track.
If the speed of car is twice as great, then the new centripetal force is given as,
F'c = m(2v)²/r
F'c = 4 × mv²/r
F'c = 4 × Fc
Thus, we can conclude that the magnitude of centripetal force will become four times with the twice the greater speed of car.
Learn more about the centripetal force here:
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