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A car of mass m travels around a particular highway curve at speed v. If a truck of mass 3 m travels around this same corner but at half the speed of the car, then the new centripetal force required must be what multiple of the original force?

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boffeemadrid

Answer:

[tex]\dfrac{3}{4}[/tex]

Explanation:

m = Mass of car

3m = Mass of truck

v = Velocity of car

[tex]\dfrac{1}{2}v[/tex] = Velocity of truck

r = Turn radius

Centripetal force is given by

For car

[tex]F_1=\dfrac{mv^2}{r}[/tex]

For truck

[tex]F_2=\dfrac{3m(\dfrac{1}{2}v)^2}{r}\\\Rightarrow F_2=\dfrac{3m\dfrac{1}{4}v^2}{r}[/tex]

Dividing the forces we get

[tex]\dfrac{F_1}{F_2}=\dfrac{\dfrac{mv^2}{r}}{\dfrac{3m\dfrac{1}{4}v^2}{r}}\\\Rightarrow \dfrac{F_1}{F_2}=\dfrac{4}{3}\\\Rightarrow F_2=\dfrac{3}{4}F_1[/tex]

So, the multiple of the original force is [tex]\dfrac{3}{4}[/tex]

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