Example 5-9: A rope of length 60 cm is tied to the handle of a bucket (whose mas

Question

Example 5-9: A rope of length 60 cm is tied to the handle of a bucket (whose mass is 3 kg), and th bucket is then whirled in a vertical circle. At the bottom of its path, the tension in the rope is 50 N. Wh is the speed of the bucket at this point? Solution: First, let's draw a diagram. L- 60 an W mg Because we call toward the center the positive direction when doing circular motion problems, we see that the tension Fr, is a positive force, and the bucket's weight, w, is a negative force. (Because w points away from the center, we count it as negative. Therefore, the net force on the bucket at this point is FT w. Because the net force directed toward the center is called the centripetal force, we'd write

Explanation / Answer

T - mg = mv^2/r (The net forces equal the mass times the centripetal acceleration) . So solving yields v = sqrt((T-mg)r/m) = sqrt((50-3x9.8)(.60)/3) = 2.03m/s

How to find T

T= mv^2/r +mg

= m( v^2/r+g)
= 3(2^2/.60 +9.8)
T = 50 N

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