A pendulum consists of a 2.3-kg bob attached to a light 2.7-m-long string. While

Question

A pendulum consists of a 2.3-kg bob attached to a light 2.7-m-long string. While hanging at rest with the string vertical, the bob is struck a sharp horizontal blow, giving it a horizontal velocity of 4.7 m/s. At the instant the string makes an angle of 30

Explanation / Answer

(a) The vertical height (h) at 30* =>h = L - Lcos? =>h = 2.3[1-cos30*] =>h = 0.31m =>Let the velocity is (v) of the bob at 30* =>By the law of energy conservation:- =>KE(initial) = KE(final) + PE(final) =>1/2mu^2 = 1/2mv^2 + mgh =>v^2 = u^2 - 2gh =>v^2 = (4.2)^2 - 2 x 9.8 x 0.31 =>v = v11.60 =>v = 3.41 m/s (b) By PE = mgh =>PE = 2 x 9.8 x 0.31 =>PE = 6.04 J (c) By T = mgcos? =>T = 2.3 x 9.8 x cos30* =>T = 19.52 N (d) Let the maximum height attained is H =>By the law of energy conservation:- =>KE(initial) = PE(final) =>1/2mu^2 = mgh =>H = u^2/2g =>H = (4.3)^2/(2 x 9.8) =>H = 0.94 =>By h = L - Lcos? =>H = 2.3[1-cos?] =>0.94/2.3 = [1-cos?] =>cos? = 0.5898 ˜ cos54* =>? ˜ 54*

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