Consider a giant pendulum with a bowling ball (w=16.0lb) suspended by a very lig

Question

Consider a giant pendulum with a bowling ball (w=16.0lb) suspended by a very light rope of length 8.0ft. The ball is initially pulled up to an angle of 60 degrees relative to the vertical, then released.

(1) neglecting friction, what will be the speed of the ball at the bottom of the swing?

(2) to determine the work done by friction, we find after one full swing the ball rises up to an angle of 59.0 degrees relative to vertical. What is the work done by friction?

(3) what percent of the total mechanical energy is lost in one swing?

Explanation / Answer

1) neglecting friction ,we can use law of conservation of energy

Energy at the extreme = energy at the mean position

cos(60) = (l-h)/l

l-h = l*cos(60)

h = l*(1-cos(60)) = 0.5*l

h = 0.5*8ft = 4 ft =

weight is mg = 16*4.45 = 71.2 N

4ft = 1.22 m

m*g*(h) = 0.5*m*v^2

71.2*1.22 = 0.5(71.2/9.81)*v^2

v = 4.89 m/sec

2) work done by friction is W = U1 -U2 = m*g*(h1-h2)

h1 = 4 ft = 1.22 m

h2 = 4*(1-cos(59)) = 3.87 ft = 1.179 m

W = 71.2*(1.22-1.179) = 2.92 J

3) lost in mechanical energy = 2.92/(m*g*h) = 2.92/(71.2*1.22) = 0.0336

required percentage is 3.36 %

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