The drawing shows a version of the loop-the-loop trick for a small car. If the c

Question

The drawing shows a version of the loop-the-loop trick for a small car. If the car is given an initial speed of v = 4.1 m/s, what is the largest value that the radius r can have if the car is to remain in contact with the circular track at all times?

The drawing shows a version of the loop-the-loop trick for a small car. If the car is given an initial speed of v = 4.1 m/s, what is the largest value that the radius r can have if the car is to remain in contact with the circular track at all times?

Explanation / Answer

energy at top=0.5mv2-mg2r=0.5*m*4.12-m*9.81*2r=0.5m(vat top)2

(vat top)2=4.12-39.24r

mg=mv2/r

r=v2/g=(4.12-39.24r)/9.81

r=1.71355-4r

5r=1.71355

r=0.3428m

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