(a) To calculate the gravitational potential energy of the diver, we use the formula:
Gravitational potential energy = mass * gravity constant * height
Plugging in the values:
Gravitational potential energy = 65 kg * 9.8 N/kg * 10.0 m
Gravitational potential energy = 6370 J
The gravitational potential energy of the diver is 6370 J.
(b) To calculate the kinetic energy of the diver, we use the formula:
Kinetic energy = 0.5 * mass * velocity^2
Plugging in the values:
Kinetic energy = 0.5 * 65 kg * (14 m/s)^2
Kinetic energy = 6370 J
The diver's kinetic energy is also 6370 J.
(c) The answers to parts (a) and (b) are the same. This is explained by the principle of conservation of mechanical energy. In this case, as there is no air resistance, the only energy involved is gravitational potential energy and kinetic energy. As the diver falls, gravitational potential energy is converted into kinetic energy. At the height of the water, all the potential energy is converted into kinetic energy, resulting in the same value for both.
(d) To calculate the speed of the diver 5.0 m above the water, we can use the conservation of mechanical energy:
Gravitational potential energy + Kinetic energy = constant
At the height of the water, the kinetic energy is 6370 J. Therefore:
Gravitational potential energy + 6370 J = constant
Gravitational potential energy = mass * gravity constant * height
Gravitational potential energy = 65 kg * 9.8 N/kg * 5.0 m
Gravitational potential energy = 3185 J
Therefore, the constant is 3185 J + 6370 J = 9555 J.
Using this constant and the formula for kinetic energy, we can solve for the velocity:
Kinetic energy = 0.5 * mass * velocity^2
9555 J = 0.5 * 65 kg * velocity^2
velocity^2 = 9555 J / (0.5 * 65 kg)
velocity^2 = 293.08 m^2/s^2
Taking the square root of both sides:
velocity = √293.08 m^2/s^2
velocity = 17.1 m/s
Therefore, the speed of the diver 5.0 m above the water is 17.1 m/s.
A 65 kg diver stands still on a tower, 10.0 m above the water.
(a) Calculate the gravitational potential energy of the diver, relative to the height of the water. Assume the gravitational field constant is 9.8 N/kg
(b) The diver reaches the surface of the water at a speed of 14 m/s
. Calculate the diver’s kinetic energy.
(c) Compare your answers to (a) and (b). Explain your comparison using concepts learned in this course. Assume there is no air resistance during the dive.
(d) Calculate the speed of the diver 5.0 m
above the water.
(4 points)
1 answer
1 answer