Kanji dam is about 50m high(1) calculate the potential energy of 25kg of water at top release to the bottom (2) what is the kinetic energy of the water just before it reaches bottom
(1) To calculate the potential energy of the water at the top of the dam, we can use the formula:
Potential Energy = mass * gravity * height
Given:
mass = 25 kg
gravity = 9.8 m/s^2
height = 50 m
Potential Energy = 25 * 9.8 * 50
Potential Energy = 12,250 Joules
Therefore, the potential energy of 25kg of water at the top of the dam is 12,250 Joules.
(2) To calculate the kinetic energy of the water just before it reaches the bottom of the dam, we can use the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Since the water is falling, we can calculate the final velocity using the equation of motion:
vf^2 = vi^2 + 2 * a * d
Where:
vf = final velocity (since it is falling, its initial velocity can be considered as 0)
vi = initial velocity (0 m/s)
a = acceleration due to gravity (9.8 m/s^2)
d = height (50 m)
vf^2 = 0 + 2 * 9.8 * 50
vf^2 = 980
vf = √980
vf ≈ 31.3 m/s
Now, we can calculate the kinetic energy:
Kinetic Energy = 0.5 * 25 * 31.3^2
Kinetic Energy = 0.5 * 25 * 979.69
Kinetic Energy = 12,246.13 Joules
Therefore, the kinetic energy of the water just before it reaches the bottom of the dam is approximately 12,246.13 Joules.