A 2.0 kg rock falls from a height of 25 m to a point 20 m above the ground.
a) how much potential energy does it lose?
b) How much kinetic energy does it gain?
Thanks.
It loses mgh PE
it gains mgh KE
You can calculate those.
You can also calculate the KE from the final velocity .
To find the potential energy lost by the rock, we can use the formula:
Potential energy = mass * gravity * height
Where:
mass = 2.0 kg (given)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 25 m - 20 m = 5 m (height difference)
a) Potential energy lost by the rock:
Potential energy = 2.0 kg * 9.8 m/s^2 * 5 m
= 98 J
Therefore, the rock loses 98 Joules of potential energy.
To find the kinetic energy gained by the rock, we can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Since the rock falls freely, all its potential energy is converted into kinetic energy just before it hits the ground. Therefore, we can use the formula for potential energy to find the kinetic energy gained.
b) Kinetic energy gained by the rock:
Kinetic energy = 98 J
Therefore, the rock gains 98 Joules of kinetic energy.
To find the answers to these questions, we need to use the equations for potential energy and kinetic energy.
a) The potential energy lost by the rock can be calculated using the equation:
Potential energy lost = mass × acceleration due to gravity × height
In this case, the mass of the rock is given as 2.0 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is the difference between the initial height and the final height, which is 25 m - 20 m = 5 m.
Therefore, the potential energy lost by the rock is:
Potential energy lost = 2.0 kg × 9.8 m/s^2 × 5 m
b) The kinetic energy gained by the rock can be calculated using the equation:
Kinetic energy gained = 1/2 × mass × velocity^2
To find the velocity, we need to calculate the final velocity of the rock when it reaches the ground.
The final velocity can be found using the equation:
Final velocity = √(2 × acceleration due to gravity × height)
In this case, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is 20 m.
Therefore, the final velocity of the rock is:
Final velocity = √(2 × 9.8 m/s^2 × 20 m)
Once we have the final velocity, we can calculate the kinetic energy gained by the rock:
Kinetic energy gained = 1/2 × 2.0 kg × (final velocity)^2
By plugging in the values and performing the calculations, you will be able to find the answers to both parts of the question.