A ball of mass 8 kg falls from a height of 100 m. Neglecting air resistance, calculate it's total energy after falling a distance of

40 m

the gravitational potential energy from the 40 m fall becomes kinetic energy

K.E. = m * g * h = 8 * 9.8 * 40

the ball still has 60 m worth of gravitational potential energy

P.E. = M*g*h = 8*9.8*100 = 7840 J. = Potential Energy = Total energy.

P.E. = Mgh = 8*9.8*(100-40) = 4704 J. = Total energy after falling 40 m.

K.E.= 7840 - 4704 = 3136 J.

To calculate the total energy of the ball after falling a certain distance, we need to consider two types of energy: potential energy and kinetic energy.

1. Potential Energy:
The potential energy of an object at a height h is given by the equation:
Potential Energy = mass x gravity x height
where mass is the mass of the object, gravity is the acceleration due to gravity (9.8 m/s² on Earth), and height is the distance from the reference point (in this case, the ground).

Using the given values:
mass = 8 kg
gravity = 9.8 m/s²
height_1 = 100 m (initial height)
height_2 = 40 m (final height)

Potential Energy_1 = mass x gravity x height_1
Potential Energy_2 = mass x gravity x height_2

2. Kinetic Energy:
The kinetic energy of an object is given by the equation:
Kinetic Energy = 0.5 x mass x velocity²
where mass is the mass of the object and velocity is its speed.

Assuming the ball falls freely without air resistance, its potential energy at the initial height will convert into kinetic energy at the final height.

To calculate the velocity of the ball at the final height, we can use the conservation of energy principle, which states that the total mechanical energy (sum of potential and kinetic energy) remains constant in the absence of external forces.

Total Energy_1 = Potential Energy_1
Total Energy_2 = Potential Energy_2 + Kinetic Energy_2

Equating the two equations and rearranging, we get:
Kinetic Energy_2 = Total Energy_1 - Potential Energy_2

Now, we can substitute the given values and calculate the total energy of the ball after falling a distance of 40 m.

Let's go through the calculations step by step:

1. Calculate the initial potential energy:
Potential Energy_1 = mass x gravity x height_1
Potential Energy_1 = 8 kg x 9.8 m/s² x 100 m
Potential Energy_1 = 7840 J

2. Calculate the final potential energy:
Potential Energy_2 = mass x gravity x height_2
Potential Energy_2 = 8 kg x 9.8 m/s² x 40 m
Potential Energy_2 = 3136 J

3. Calculate the final kinetic energy:
Total Energy_1 = Potential Energy_1
Total Energy_1 = 7840 J

Kinetic Energy_2 = Total Energy_1 - Potential Energy_2
Kinetic Energy_2 = 7840 J - 3136 J
Kinetic Energy_2 = 4704 J

Therefore, the total energy of the ball after falling a distance of 40 m is 4704 Joules.