Since the radius of the circle is 2 m the ball

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does perform work on the ball, according the height it reaches. Since the radius of the circle is 2 m, the ball reaches a height of 4 m, and experiences work from the gravitational force of - mgh = - 2 mg . Remember the sign is negative because the force acts in a direction opposite the motion of the ball. This work causes a change in velocity from the bo " om of the loop to the top of the loop, which can be calculated by the work-energy theorem: W = Δ K Thus - mgh = mv f2 - mv o2 Canceling the mass and solving for v o , v o = = = 7.7 m/s Thus the ball must enter the vertical loop of at least 7.7 m/s. Prev Section Next Section
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