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I don’t understand why the answer is the first choice, please explain!

I don’t understand why the answer is the first choice, please explain!-example-1

1 Answer

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(a) Take into account that the centrifugal force experienced by each car is given by:


\begin{gathered} F_1=m(v^2_1)/(R_1) \\ F_2=m(v^2_2)/(R_2) \end{gathered}

where v1 and v2 are the speed of both cars and R1 and R2 are the radius of the curve traveled by each car, m is the mass of the cars.

If you solve for m, you obtain:


\begin{gathered} m=(F_1R_1)/(v^2_1) \\ m=(F_2R_2)/(v^2_2) \end{gathered}

due to the masses of the cars are identical, you have:


(F_1R_1)/(v^2_1)=(F_2R_2)/(v^2_2)

(b) Now, consider that:

R1 = 2R

v1 = v

R2 = 6R

v2 = 3v

Now, divide the equation for F1 over the equation for F2, replace the previous expressions for the parameters and simplify for F1:


\begin{gathered} \frac{F_1_{}}{F_2}=(m(v^2_1)/(R_1))/(m(v^2_2)/(R_2)) \\ \frac{F_1_{}}{F_2}=(v^2_1R_2)/(v^2_2R_1)=(v^2\cdot6R)/((3v)^2\cdot2R) \\ (F_1)/(F_2)=(1)/(3) \\ F_1=(1)/(3)F_2 \end{gathered}

User Konstantin Yovkov
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