Question

a car having a mass of 1,520 kilograms maneuvers around a curve at a velocity of 24.0 m/s. The radius of the curve is 455 meters. What is the centripetal force required to keep the car following the curve?

Answer 1

When an object is moving around in circles, there are two forces that keeps it in its circular orbit. These are the centripetal and the centrifugal forces. They are equal in magnitude, but they differ in the direction. The centripetal force is the force that pulls the object toward the circle's center. The centrifugal force is the force that pushed the object away from the circle's center. 

Applying Newton's Second Law of Motions, any force is equal to its mass times its acceleration. For an object moving in circles, the force here is centrifugal or centripetal force, and the acceleration is the centripetal or centrifugal acceleration which is equal to

a = v²/r,
where v is the linear or tangential velocity
r is the radius of the circle

Applying this to Newton's Second Law of Motion,

F = mv²/r
Substituting the values,
F = (1,520 kg)(24 m/s)²/455 m
F = 1,924.22 N

Answer 2

Answer:

Centripetal force = 1924.2 N

Explanation:

It is given that,

Mass of the car, m = 1520 kg

Velocity around a curve, v = 24 m/s

Radius of the circular curve, r = 455 m

The centripetal force is given by :

$F_c=\dfrac{mv^2}{r}$

$F_c=\dfrac{1520\ kg\times (24\ m/s)^2}{455\ m}$

$F_c=1924.2\ N$

Hence, this is the required solution.