4. I drop a pufferfish of mass 5 kg from a height of 5.5 m onto an upright spring of total length 0.5 m and spring constant 3000 N/m (such that the pufferfish first encounters the spring after it has descended a distance of 5 m). a. Assuming no energy loss to friction, what is the minimum height above the ground that the pufferfish reaches? Hint: This problem will require you to use conservation of energy. When the pufferfish is dropped from rest, it has only gravitational potential energy. As it falls, it converts this gravitational potential energy into kinetic energy, until it hits the spring. Next, it converts the kinetic energy into spring potential energy. When the pufferfish reaches its minimum height above the ground, its kinetic energy is zero and it should only have spring potential energy and gravitational potential energy remaining. Call the minimum height above the ground ?. Since the spring starts with an uncompressed length of 0.5 m, when the pufferfish reaches its minimum height, it has compressed the spring by a displacement of (0.5 m - ?). How much potential energy is stored in the spring at this point? What is the change in gravitational potential energy as the pufferfish falls from a height of 5.5 m to a height of ?? Plug these values into the conservation of energy equation and solve for ?. You will need to use the quadratic formula to solve. b. Now, assume that the pufferfish begins to bounce less and less high each time as it loses energy to heat. At what height does it eventually come to rest?Hint: Eventually, the pufferfish will come to rest at a point where the net force acting on it is zero. The spring force must balance its weight. Solve for the displacement of the spring from its equilibrium position. How far above the ground is the pufferfish at this point? c. When the pufferfish reaches this equilibrium state, what quantity of each type of energy (kinetic, spring potential, gravitational potential, internal/heat) remains in the system?Hint: Use your expressions for kinetic energy, spring potential energy, and gravitational potential energy to find the values when the pufferfish is at the location determined in part b. Finally, any energy that was in the system at the beginning and is no longer in one of these forms (kinetic, spring, or gravitational) must have been lost to internal energy/heat. Calculate the initial total energy of the system (which was all gravitational). Subtract the three values you calculated above. The remainder has been converted to internal energy/heat.
4. I drop a pufferfish of mass 5 kg from a height of 5.5 m onto an upright spring of total length 0.5 m and spring constant 3000 N/m (such that the pufferfish first encounters the spring after it has descended a distance of 5 m).
a. Assuming no energy loss to friction, what is the minimum height above the ground that the pufferfish reaches?
Hint: This problem will require you to use conservation of energy. When the pufferfish is dropped from rest, it has only gravitational potential energy. As it falls, it converts this gravitational potential energy into kinetic energy, until it hits the spring. Next, it converts the kinetic energy into spring potential energy. When the pufferfish reaches its minimum height above the ground, its kinetic energy is zero and it should only have spring potential energy and gravitational potential energy remaining. Call the minimum height above the ground ?. Since the spring starts with an uncompressed length of 0.5 m, when the pufferfish reaches its minimum height, it has compressed the spring by a displacement of (0.5 m - ?). How much potential energy is stored in the spring at this point? What is the change in gravitational potential energy as the pufferfish falls from a height of 5.5 m to a height of ?? Plug these values into the conservation of energy equation and solve for ?. You will need to use the quadratic formula to solve.
b. Now, assume that the pufferfish begins to bounce less and less high each time as it loses energy to heat. At what height does it eventually come to rest?
Hint: Eventually, the pufferfish will come to rest at a point where the net force acting on it is zero. The spring force must balance its weight. Solve for the displacement of the spring from its equilibrium position. How far above the ground is the pufferfish at this point?
c. When the pufferfish reaches this equilibrium state, what quantity of each type of energy (kinetic, spring potential, gravitational potential, internal/heat) remains in the system?
Hint: Use your expressions for kinetic energy, spring potential energy, and gravitational potential energy to find the values when the pufferfish is at the location determined in part b. Finally, any energy that was in the system at the beginning and is no longer in one of these forms (kinetic, spring, or gravitational) must have been lost to internal energy/heat. Calculate the initial total energy of the system (which was all gravitational). Subtract the three values you calculated above. The remainder has been converted to internal energy/heat.
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