A pendulum consists of a 1.9-kg bob attached to a light 2.4-m-long string. While

Question

A pendulum consists of a 1.9-kg bob attached to a light 2.4-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 5.0 m/s. At the instant the string makes an angle of 20° with the vertical, calculate the following:

(a) the speed

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

(c) the tension in the string?

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

Explanation / Answer

1/2MV^2=1/2MU^2+ Mgl(1-cos20)

V^2=u^2+2g×2.4(1-cos20)

25=u^2+2.84

u=4.71m/s

Potential energy=mgLcos20=1.9×9.8×2.4cos20=41.99J

T=mgcos20=17.49N

-1/2mv^2+mgl=mglcos x=-12.5+23.52=23.52cosx

x=61.1approx

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