A pendulum consists of a 1.7-kg bob attached to a light 2.3-m-long string. While

Question

A pendulum consists of a 1.7-kg bob attached to a light 2.3-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 4.6 m/s. At the instant the string makes an angle of 30° with the vertical, calculate the following:

(a) the speed
m/s

(b) the gravitational potential energy (relative to its value is at the lowest point)
J

(c) the tension in the string?
N

(d) What is the angle of the string with the vertical when the bob reaches its greatest height?
°

Explanation / Answer

The mass of the bob is m = 1.7 kg The length of the string is l = 2.3 m The horizontal velocity of the bob is u = 4.6 m/s The angle made by the string is A = 30o = (pi/6) radians (a)We know from the relation S = l * A We know that v^2 - u^2 = 2gS where v is final velocity of the bob and g = 9.8 m/s^2 (b) the gravitational potential energy is equal to the kinetic energy of the bob K = (1/2)m * v^2 (c)the tension in the string is F = (K/S) (d)Let the angle be B We know that v = l * (B/t) where t is time and S = ut + (1/2)gt^2 solve above equation for time

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