#2) A solid cylindrical pulley has a radius of 0.20 m and mass of 2.0 kg. It is mounted
on a horizontal axle through its center. A corn cob hanging at the end of string and
the string is wrapped around the pulley. The mass of a corn cob is 0.20 kg. Hikaru
lunges toward the corn cob and the pulley starts to turn. Mass of Hikaru is 0.11 kg.
Find the speed of the corn cob/Hikaru combination after it has fallen through a height
of 0.50 m. The magnitude of gravitational acceleration is 9.8 m/s².

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MathPhys MathPhys · Answer 1 · 2024-03-26T15:47:03+01:00

Answer:

1.5 m/s

Explanation:

Initial potential energy = final kinetic energy + final rotational energy

PE = KE + RE

mgh = ½ mv² + ½ Iω²

Moment of inertia for a solid disk is I = ½ MR².

mgh = ½ mv² + ½ (½ MR²) ω²

mgh = ½ mv² + ¼ MR²ω²

The tangential speed of the pulley is v = ωR:

mgh = ½ mv² + ¼ Mv²

mgh = ¼ v² (2m + M)

v² = 4mgh / (2m + M)

Plug in values and solve:

v² = 4 (0.20 kg + 0.11 kg) (9.8 m/s²) (0.50 m) / (2 × (0.20 kg + 0.11 kg) + 2.0 kg)

v = 1.5 m/s