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igomit [66]
3 years ago
9

a cylinder of mass 34.5 kg rolls without slipping on a horizontal surface. At a certain instant, its center of mass has a speed

9.5 m/s. Determine the rotational kinetic energy
Physics
2 answers:
Scorpion4ik [409]3 years ago
8 0

Answer:

\displaystyle 778,40625\:J

Explanation:

\displaystyle \frac{1}{2}mv^2 = KE

* For cylinders, it is unique. Since you have two circular bases, you take half the mass in the formula:

\displaystyle \frac{1}{4}mv^2 = KE \\ \\ \frac{1}{4}[34,5]9,5^2 = KE → \displaystyle \frac{1}{4}[34,5][90,25] = 778,40625\:J

I am joyous to assist you anytime.

Stolb23 [73]3 years ago
4 0

Answer:

778 J

Explanation:

Rotational energy is:

RE = ½ Iω²

For a solid cylinder I = ½ mr².

Rolling without slipping means ω = v/r.

RE = ½ (½ mr²) (v/r)²

RE = ¼ mv²

Plug in values:

RE = ¼ (34.5 kg) (9.5 m/s)²

RE ≈ 778 J

Round as needed.

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