Question
I'm not very sure at all that I'm doing this right... so helpwould be much appreciated A ball of mass M attached to a string of length L moves in acircle in a vertical plane. At the top of the circular path, thetension in the string is twice the weight of the ball. At thebottom the ball just clears the ground. Air resistance isnegligible. Ecpress all answers in terms of M, L, and g. a. Determine the magnitude and direction of the net force onthe ball when it is at the top. b. Determine the speed vo of the ball at thetop. c. Determine the time it takes the ball to reach theground. d.Determine the horizontal distance the ball travels beforehitting the ground. THANKS!! I'm not very sure at all that I'm doing this right... so helpwould be much appreciated A ball of mass M attached to a string of length L moves in acircle in a vertical plane. At the top of the circular path, thetension in the string is twice the weight of the ball. At thebottom the ball just clears the ground. Air resistance isnegligible. Ecpress all answers in terms of M, L, and g. a. Determine the magnitude and direction of the net force onthe ball when it is at the top. b. Determine the speed vo of the ball at thetop. c. Determine the time it takes the ball to reach theground. d.Determine the horizontal distance the ball travels beforehitting the ground. THANKS!!
Explanation / Answer
T + M g = M v2 / L centripetal force on ball equals centripetal acceleration 3 M g = M v2 /L where 3 M g is thetotal force on the ball and is directed downward v = (3 g L) 1/2 m vB2 = 1/2 m v2 + 2 m gL kinetic energy gained by ball is 2 m g Lthe distance the ball falls vB2 = v2 + 4 g L = 3 g L + 4g L Speed at bottom = (7 g L) If we use vav = (v + vB) / 2 asthe average speed of the ball on its circular downward path then t = L / vav The total horizontal distance traveled by the ball is 2L. The net horizontal distance traveled by the ball iszero. I think this question could be worded morespecifically. The total horizontal distance traveled by the ball is 2L. The net horizontal distance traveled by the ball iszero. I think this question could be worded morespecifically.