American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders 1.0 m long and 10 cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. Eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. Although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could. The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? (a) 0.5 m/s; (b) 0.7 m/s; (c) 3 m/s; (d) 5 m/s.

Question

Physics

Jax Hicks

18 September, 01:08

American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders 1.0 m long and 10 cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. Eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. Although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could. The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning? (a) 0.5 m/s; (b) 0.7 m/s; (c) 3 m/s; (d) 5 m/s.

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Rowan · Answer 1

(c) 3 m/s;

Explanation:

Moment of inertia of the fish eels about its long body as axis

= 1/2 m R ² where m is mass of its body and R is radius of transverse cross section of body.

= 1/2 x m x (5 x 10⁻²) ²

I = 12.5 m x 10⁻⁴ kg m²

angular velocity of the eel

ω = 2 π n where n is revolution per second

=2 π n

= 2 π x 14

= 28π

Rotational kinetic energy

= 1/2 I ω²

=.5 x 12.5 m x 10⁻⁴ x (28π) ²

= 4.8312m J

To match this kinetic energy let eel requires to have linear velocity of V

1 / 2 m V² = 4.8312m

V = 3.10

or 3 m / s.