Answer:
A) V = 0.324 m/s
B) V = 0.56 m/s
Explanation:
A) Change in gravitational potential energy = mass * gravity * height change
Change in G.P.E = 2.85 * 9.81 * 0.058 = 1.6215 J
Energy transferred to spring = 0.5 * k * x^2
Here k = 875 N/m
And x = 0.058 m
Thus energy transferred to spring = 1.47175 J
The G.P.E is converted to spring potential energy and kinetic energy as it moves down. So the difference in energy is accounted by kinetic energy as follows:
Kinetic energy = G.P.E - Spring P.E
Kinetic energy = 1.6215 - 1.47175 = 0.14975 J
We can now find the speed using this kinetic energy:
Kinetic energy = 0.14975
0.5 * mass * velocity^2 = 0.14975
0.5 * 2.85 * V^2 = 0.14975
V = 0.324 m/s
B) The fish accelerates because the force on it are unbalanced. These forces are the weight of the fish, and the force of the spring stopping it.
As long as the weight of the fish is more than the upward force of the spring, the fish will continue to accelerate. Using this knowledge, we can deduce that the speed is maximum when the weight and spring force are equal. Thus we set them equal and find out the displacement first:
Weight = spring force
2.85 * 9.81 = 875 * Displacement
Displacement = 0.03195 m
Similarly as (A):
Change in G.P.E = 2.85 * 9.81 * 0.03195 = 0.8933 J
Spring P.E = 0.5 * 875 * 0.03195^2 = 0.4466 J
Kinetic energy = 0.8933 - 0.4466 = 0.4467 J
0.5 * mass * V^2 = 0.4467
0.5 * 2.85 * V^2 = 0.4467
V = 0.56 m/s
