A ball of mass 8kg falls from a height of 100m,neglecting air resistance calculate it total energy after falling a distance
total energy is constant until it hits the ground. Potential turns to kinetic.
m g h = 8 * 9.81 * 100 Joules
To calculate the total energy of the ball after falling a certain distance, we need to take into account its potential energy and kinetic energy.
1. Potential Energy:
The potential energy of an object at a certain height is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the mass of the ball is 8 kg, the height it falls from is 100 m, and we can take g as approximately 9.8 m/s² (acceleration due to gravity on Earth).
So, the potential energy of the ball before falling is:
PE = mgh = (8 kg) * (9.8 m/s²) * (100 m)
2. Kinetic Energy:
The kinetic energy of an object is given by the formula KE = (1/2)mv², where m is the mass of the object, and v is its velocity.
Since the ball is falling freely, without air resistance, it will only have kinetic energy when it reaches its final velocity just before hitting the ground. At that point, all of its potential energy will be converted into kinetic energy.
The final velocity can be calculated using the equation v = √(2gh), where g is the acceleration due to gravity and h is the height.
So, the velocity of the ball just before hitting the ground is:
v = √(2 * 9.8 m/s² * 100 m)
Now, we can calculate the kinetic energy of the ball just before hitting the ground:
KE = (1/2) * m * v² = (1/2) * 8 kg * [√(2 * 9.8 m/s² * 100 m)]²
3. Total Energy:
Finally, the total energy of the ball after falling a certain distance is the sum of its potential energy and kinetic energy.
Total Energy = Potential Energy + Kinetic Energy
Now, substitute the values into the equations and solve to find the total energy of the ball after falling.