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Answer: r = 0.327m

What I tried was; before the car enters the loop it posses pure kinetic energy, and at the top of loop it posses pure potential energy.

Therefore..

1/2(m)(v)² = (m)(g)(Δh)

(1/2(v)²) / g = (Δh)

Δh = 0.816m

Since 2r = Δh

Therefore

r = 0.408m

What have I done wrong?