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An 1560 kg car passes over a bump in a road that follows the arc of a circle of radius 62.9 m. The acceleration of gravity is 9.8 m/s 2 . What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 13.9 m/s? Answer in units of N.

Respuesta :

olasunkanmilesanmi

Answer:

10.5KN

Explanation:

First, we determine the total force acting on the car as it passes through the highest point of the car. The total force acting on it is the weight and the force required,i.e

Mg-F

this net force is required to cause the car to move through the bump, hence the centripetal force of the car is expressed as

[tex]C_{p}=M \frac{v^{2}}{r} \\[/tex]

since the net force must equal the centripetal force, we have

[tex]Mg-F=C_{p}\\Mg-F==M \frac{v^{2}}{r} \\F=Mg-M \frac{v^{2}}{r} \\F=M(g-\frac{v^{2}}{r})[/tex]

if we insert values,we arrive at

[tex]F=M(g-\frac{v^{2}}{r})\\F=1560(9.8-\frac{13.9^{2}}{62.9})\\F=10496N\\F=10.5KN[/tex]

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