Question

.. A 15.0-kg fish swimming at 1.10 m>s suddenly gobbles up a 4.50-kg fish that is initially stationary. Ignore any drag effects of the water. (a) Find the speed of the large fish just after it eats the small one. (b) How much mechanical energy was dis- sipated during this meal?

Answer 1

The speed of the large fish just after eating the small one is 0 m/s. No mechanical energy is dissipated during this meal.

Step-by-step explanation:

(a) To find the speed of the large fish just after it eats the small one, we can use the law of conservation of momentum. The initial momentum of the system is zero because the small fish is initially stationary. The final momentum of the system is equal to the momentum of the large fish after eating the small one. Momentum is given by the equation:

momentum = mass x velocity

The initial momentum of the system is 0. The mass of the large fish is 15.0 kg and its velocity is unknown. The mass of the small fish is 4.50 kg and its velocity is 0 m/s. The equation can be rewritten as:

0 = (15.0 kg + 4.50 kg) x v

Solving for v, we find that the velocity of the large fish after eating the small one is 0 m/s.

(b) To find the amount of mechanical energy dissipated during this meal, we need to consider the change in kinetic energy of the system. The initial kinetic energy of the system is given by:

KE = 0.5 x mass x
`velocity^2`

Since the small fish is initially stationary, its initial kinetic energy is 0. The final kinetic energy of the system is equal to the kinetic energy of the large fish after eating the small one. Assuming a positive direction for velocity, the equation can be written as:

KE = 0.5 x (15.0 kg + 4.50 kg) x
`0^2`

Simplifying, we find that the amount of mechanical energy dissipated during this meal is 0 Joules.

Answer 2

(a) 0.846 m/s

(b) 2.097J

Step-by-step explanation:

Parameters given:

Mass of big fish, M = 15 kg

Mass of small fish, m = 4.5 kg

Initial speed of big fish, U = 1.1 m/s

Initial speed of small fish, u = 0 m/s (it is stationary)

(a) We apply the principle of conservation of momentum:

Total initial momentum = Total final momentum

Since both fish have the same final speed, V, (the small fish is in the mouth of the big fish), we have:

MU + mu = (M + m)*V

(15 * 1.1) + (4.5 * 0) = ( 15 + 4.5) * V

16.5 = 19.5V

=> V = 16.5/19.5

V = 0.846 m/s

The speed of the large fish after the meal is 0.846 m/s.

(b) We need to find the change in Kinetic energy of the entire system to find the total mechanical energy dissipated.

Initial Kinetic energy:

KEini = (½ * M * U²) + (½ * m * u²)

KEini = (½ * 15 * 1.1²) + (½ * 4.5 * 0²)

KEini = 9.075 J

Final Kinetic Energy:

KEfin = (½ * M * V²) + (½ * m * V²)

KEfin = (½ * 15 * 0.846²) + (½ * 4.5 * 0.846²)

KEfin = 5.368 + 1.610 = 6.978 J

Change in kinetic energy will be:

KEfin - KEini = 9.075 - 6.978

ΔKE = 2.097 J

The energy dissipated in eating the meal is 2.097 J