What fraction of the total mechanical energy of a SHO is kinetic and what fraction potential when the displacement is one third the amplitude?

Chapters 11 and 14 Written Homework

Be sure to show all your work, particularly for odd-numbered questions. If you end up looking at a solution cite the source of your information.

11 – 10: A person of mass 75 𝑘𝑔 stands at the center of a rotating merry-go-round platform of radius 3.0 𝑚 and moment of inertia 920 𝑘𝑔 ∙ 𝑚2. The platform rotates without friction with angular velocity 0.95 𝑟𝑎𝑑/𝑠. The person walks radially to the edge of the platform.

a) Calculate the angular velocity when the person reaches the edge.

b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk

14 – 30: a) At what displacement of a SHO (Simple Harmonic Oscillator) is the mechanical energy half kinetic and half potential?

B) What fraction of the total mechanical energy of a SHO is kinetic and what fraction potential when the displacement is one third the amplitude?

14 – 43: A musician wishes to construct a metronome based on a simple pendulum design where a “beat” is sounded when the bob reaches each opposite extreme of its swing. (This means two beats are sounded for each cycle of the pendulum.)

How long must the pendulum be so that this metronome is set for 104 beats per minute?