Question

Assume the HZ Amp pendulum is 12 m long and that the bowling ball has a mass of 7 kg. You pull the bowling ball to the right by 5 m of arc length and release it. Using the "small angle approximation" and treating the resulting motion as simple harmonic motion, what is the kinetic energy of the ball when it swings through its original resting position in J?

Answer 1

Answer:

Explanation:

Given

Length of String $L=12 m$

mass of ball $m=7 kg$

length of arc $l=5 m$

using small angle approximation

$\tan \theta \approx \theta \approx \frac{5}{12}$

Now kinetic energy at resting Position will be equal to Potential Energy acquired by ball

height Gained by ball is $L-L\cos \theta$

$K.E.=mgL(1-\cos \theta )$

$K.E.=mgL\times 2\sin ^2\frac{\theta }{2}$

$K.E.=7\times 9.8\times 12\times 2\times \frac{\theta ^2}{4}$

$K.E.=7\times 9.8\times 12\times \frac{\theta ^2}{2}$

$K.E.=72.91 J$