A ball of mass 8 kg fall from rest from a height of 100m neglecting air calculate it's total energy after falling distance of 40m
total energy measured from what reference position. Think about that.
ho = 100 m above gnd.
h = 100-40 = 60 m above gnd.
KE = PE = Mgh = 8*9.8*60 = 4704 Joules.
surely, KE gained = PE lost = 40mg
PE retained = 60mg
so total energy is still the 100mg it started with
Correction: Please disregard my first post; I agree with oobleck's analysis:
The total energy does not change.
To calculate the total energy of the ball after falling a distance of 40m, we will use the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another.
The total energy of the ball at any point during its fall is the sum of its potential energy (PE) and its kinetic energy (KE).
1. Potential Energy (PE) is given by the formula: PE = m * g * h
where m is the mass of the ball (8 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
For the initial height of 100m, the potential energy is PE1 = 8 kg * 9.8 m/s^2 * 100m.
2. Similarly, for the final height of 40m, the potential energy is PE2 = 8 kg * 9.8 m/s^2 * 40m.
3. The kinetic energy (KE) is given by the formula: KE = (1/2) * m * v^2
where m is the mass of the ball (8 kg) and v is the velocity.
Since the ball falls from rest, the initial velocity is zero, so the initial kinetic energy is KE1 = 0.
4. To find the final kinetic energy (KE2), we need to calculate the final velocity. We can use the equation of motion: v^2 = u^2 + 2a * s
where u is the initial velocity (zero), a is the acceleration due to gravity (9.8 m/s^2), and s is the distance fallen (40m).
Rearranging the equation, we get v^2 = 0^2 + 2 * 9.8 m/s^2 * 40m.
5. Now that we have the final velocity, we can calculate the final kinetic energy: KE2 = (1/2) * 8 kg * (final velocity)^2.
6. The total energy after falling 40m is the sum of the final potential energy and the final kinetic energy: Total Energy = PE2 + KE2.
Using these calculations, you can find the total energy of the ball after falling 40m by plugging in the values and performing the calculations.