# 5. 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 = 3.4 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?

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5. 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 = 3.4 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?

check_circle

Step 1

The work performed by all nonconservative forces on the car as it moves around the circular track is zero. According to the work energy theorem, the total mechanical energy of the car must then remain constant. Take the lowest point in the circular track  as the initial point and the diametrically opposite point on the circular track  as the final point.  Take the origin at the center of the circular track.The diagram of motion of the car is

Step 2

The equation for the conservation of mechanical energy is

Step 3

When the car moves in the circular track the centripetal force acts on it. At the top of the track of the car, the centripetal force ac...

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