A stone is thrown from the edge of a cliff into the ocean below. It is thrown somewhat upward, but mostly outward. The stone has a mass of 2.0kg and is thrown with a speed of 10m/s from an initial height of 5.0m above the ocean.
A. What is the kinetic energy of the stone when it is thrown?
B. What is the Potential energy of the stone relative to the ocean when it is first thrown?
C. What is the kinetic energy of the stone just as it hits the water?
D. What is the speed with which the stone hits the water?
(a)KE=mv²/2
(b) PE=mgh
(c) KE1=KE+PE
(d) mv₁²/2= mv²/2+mgh
v₁= sqrt(v² +2gh)
To solve these problems, we'll need to use the concepts of kinetic energy, potential energy, and conservation of energy.
A. To find the kinetic energy of the stone when it is thrown, we use the formula:
Kinetic energy = (1/2) * mass * velocity^2
The mass of the stone is given as 2.0kg and the velocity is given as 10m/s. Plugging these values into the formula, we get:
Kinetic energy = (1/2) * 2.0kg * (10m/s)^2 = 100 Joules
Therefore, the kinetic energy of the stone when it is thrown is 100 Joules.
B. To find the potential energy of the stone relative to the ocean when it is first thrown, we use the formula:
Potential energy = mass * gravity * height
The mass of the stone is still 2.0kg, the acceleration due to gravity is approximately 9.8m/s^2, and the height is given as 5.0m. Plugging these values into the formula, we get:
Potential energy = 2.0kg * 9.8m/s^2 * 5.0m = 98 Joules
Therefore, the potential energy of the stone relative to the ocean when it is first thrown is 98 Joules.
C. To find the kinetic energy of the stone just as it hits the water, we know that all the potential energy of the stone has been converted into kinetic energy at this point. Therefore, the kinetic energy just before the stone hits the water is equal to the potential energy it had when it was first thrown.
So, the kinetic energy of the stone just as it hits the water is also 98 Joules.
D. To find the speed with which the stone hits the water, we can use the conservation of energy principle. We know that the total mechanical energy (sum of kinetic energy and potential energy) is conserved.
The total mechanical energy at the initial position (where the stone is thrown) is the potential energy:
Potential energy = mass * gravity * height = 2.0kg * 9.8m/s^2 * 5.0m = 98 Joules
The total mechanical energy at the position where the stone hits the water is the sum of kinetic energy and potential energy:
Total mechanical energy = Kinetic energy + Potential energy = 98 Joules + 0 Joules = 98 Joules
Since the potential energy is zero when the stone hits the water, the total mechanical energy is equal to the kinetic energy:
Kinetic energy = 98 Joules
Using the kinetic energy formula, we can solve for the velocity:
Kinetic energy = (1/2) * mass * velocity^2
98 Joules = (1/2) * 2.0kg * velocity^2
velocity^2 = 98 Joules / (1kg * 2.0) = 49
velocity = √49 = 7 m/s
Therefore, the speed with which the stone hits the water is 7 m/s.