As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of m and a mass of kg. If this fish is moving upward at m/s as its head first breaks the surface and has an upward speed of m/s after two-thirds of its length has left the surface, assume constant acceleration and determine (a) the salmon’s acceleration and (b) the magnitude of the force F during this interval.

Question

11-10-2019
Physics

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As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of m and a mass of kg. If this fish is moving upward at m/s as its head first breaks the surface and has an upward speed of m/s after two-thirds of its length has left the surface, assume constant acceleration and determine (a) the salmon’s acceleration and (b) the magnitude of the force F during this interval.

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SaniShahbaz SaniShahbaz · Answer 1 · 2019-10-15T00:54:30+02:00

Complete Question:

As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 48.0 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.30 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following. (a) the salmon's acceleration m/s2 upward (b) the magnitude of the force F during this interval N

Answer:

(a) acceleration = 15.3 ms⁻²

(b) Magnitude of net force = 734.4 N

Magnitude of upward force exerted by tail fin = 1204.8 N

Explanation:

Mass of the salmon fish = 48 kg

Length of the Salmon Fish = 1.5 m

g = 9.8 ms⁻²

(a) salmon's acceleration during the time interval N:

Downward Force on the fish is equal to the Force due to gravity and is given as:

F₂ = mg

= 48 * 9.8

= 470.4 N

The direction of movement of the fish is upward and the acceleration is constant. We are given two different velocities of fish at two different instances.

- When the head breaks out of the water surface first:

Initial velocity = v₁ = 3 m/s

- When two third of its body length is out = d = 1 m

Final Velocity = v₂ = 6.3 m/s

Using the third equation of motion:

2*a*d = v₂² - v₁²

a = (6.3² - 3²)/2*1

a = 15.3 ms⁻²

(b) magnitude of force F during this interval N = ?

We are assuming that F is the net force consisting of both the upward and the downward force.

According to Newton's 2nd law of motion, Force is given as:

F = ma

F = 48 kg * 15.3

F = 734.4 N

Magnitude of upward Force = Fₓ

Force Fₓ exerted by the tail fin of the fish is given by

F = Fₓ - F₂

That is the net force is the sum of the upward and downward forces acting on the fish body. Fₓ is positive because it is in upward direction and F₂ is negative because it is in downward direction. F which is the net force here is positive as Fₓ > F₂.

=> Fₓ = F + F₂

Fₓ = 734.4 + 470.4

Fₓ = 1204.8 N