Squids and octopuses propel themselves by expelling water. They do this by taking the water into a
cavity and then suddenly contracting the cavity, forcing the water to shoot out of an opening. A 6.50
daN squid (including the water in the cavity) that is at rest suddenly sees a dangerous predator.
(a) If this squid has 1.75 kg of water in its cavity, at what speed must it expel the water to suddenly
achieve a speed of 2.50 m/s to escape the predator? Neglect any drag effects of the surrounding
water.
(b) How much kinetic energy does the squid create for this escape maneuver?
The answers are:
a)6.79 m/s
b) 55.2J
Not too sure on how to get these answers!!Please Help!
to use conservation of momentum you must know all masses and speeds
This :::::
" cavity and then suddenly contracting the cavity, forcing the water to shoot out of an opening. A 6.50
daN squid (including the water in the cavity) that is at rest suddenly sees a dangerous predator.
..."
Is gibberish
To solve this problem, we can use the principle of conservation of momentum. We can assume that the squid and water system is initially at rest, and after expelling the water, it achieves a speed of 2.50 m/s in the opposite direction. Let's break down the problem step-by-step:
(a) First, we need to find the initial momentum of the squid and water system. Momentum is given by the formula:
momentum = mass * velocity
Since the squid and water system is initially at rest, the initial momentum is zero.
initial momentum = 0
After expelling the water, the squid achieves a speed of 2.50 m/s in the opposite direction. The final momentum of the squid is given by:
final momentum = mass * velocity
The mass of the squid is given as 6.50 daN. We need to convert it to kg by dividing it by 10, since 1 daN = 10 N.
squid mass = 6.50 daN / 10 = 0.65 kg
The final momentum of the squid is then:
final momentum = 0.65 kg * (-2.50 m/s) = -1.625 kg·m/s
This negative sign indicates the opposite direction of motion relative to the initial rest state.
Now, let's consider the water in the cavity. Its mass is given as 1.75 kg, and it's expelled in the opposite direction at some unknown speed. The momentum of the expelled water is:
expelled water momentum = 1.75 kg * v
where v is the velocity of the water being expelled.
Since momentum is conserved, the initial momentum of the squid and water system (which is zero) should be equal to the sum of the final momenta of the squid and the expelled water:
0 = -1.625 kg·m/s + 1.75 kg * v
Rearranging the equation, we can solve for the velocity of the expelled water:
v = 1.625 kg·m/s / 1.75 kg = 0.9286 m/s
So, the squid must expel the water with a velocity of approximately 0.9286 m/s to achieve a speed of 2.50 m/s in the opposite direction.
(b) The kinetic energy created by the squid for this escape maneuver can be calculated using the formula:
kinetic energy = 0.5 * mass * velocity^2
We already know the mass of the squid, which is 0.65 kg, and the velocity after expelling the water, which is 2.50 m/s.
kinetic energy = 0.5 * 0.65 kg * (2.50 m/s)^2
kinetic energy = 0.5 * 0.65 kg * 6.25 m^2/s^2
kinetic energy = 2.03125 J
Therefore, the squid creates approximately 2.03125 Joules of kinetic energy for this escape maneuver.