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A small car of mass m and a large car of mass 4m drive along a highway at constant speeds VS and VL. They approach a curve of radius R. The small and large cars have accelerations as and aL respectively, as they travel around the curve. The magnitude of as is twice of that of aL. How does the speed of the small car VS compare to the speed of the large car VL as they move around the curve

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AMB000

Answer:

[tex]v_S=\sqrt{2}v_L[/tex]

Explanation:

The acceleration experimented while taking a curve is the centripetal acceleration [tex]a=\frac{v^2}{r}[/tex]. Since [tex]a_S=2a_L[/tex], we have that: [tex]\frac{v_S^2}{r_S}=\frac{2v_L^2}{r_L}[/tex]

They take the same curve, so we have: [tex]r_S=r_L=R[/tex]

Which means: [tex]v_S^2=2v_L^2[/tex]

And finally we obtain: [tex]v_S=\sqrt{2}v_L[/tex]

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