A metal ball of mass 2kg is allowed to fall freely from rest from height of 5m. Calculate potential energy it possesses and kinetic energy before it reaches the ground. What happens to mechanical energy of the ball after it hits the ground?
PE=2*9.8*heightinMeters joules
KE=1/2 *2*v^2
but v^2=vi^2+2 g* (5-h)
so KE= gh
total energy=PE+KE=2*9.8*h+2*9.8*(5-h)
= 2*9.8*5 joules
so it starts our at h=5 with all PE, then that energy changes to KE as it falls. At the bottom, it is converted to heat, sound.
=
100J
To calculate the potential energy possessed by the metal ball, we can use the formula:
Potential Energy = mass * acceleration due to gravity * height
Given:
Mass (m) = 2 kg
Height (h) = 5 m
Acceleration due to gravity (g) = 9.8 m/s²
Potential Energy = 2 kg * 9.8 m/s² * 5 m
= 98 Joules
So, the potential energy possessed by the metal ball is 98 Joules.
To calculate the kinetic energy of the ball just before it hits the ground, we can use the formula:
Kinetic Energy = 1/2 * mass * velocity²
Just before hitting the ground, the ball has no potential energy left, so its potential energy is converted entirely into kinetic energy.
The ball has fallen freely from rest, which means its initial velocity is 0. We can calculate the final velocity just before hitting the ground using the formula:
Final Velocity (v) = sqrt(2 * acceleration due to gravity * height)
Final Velocity (v) = sqrt(2 * 9.8 m/s² * 5 m)
= sqrt(98 m²/s²)
= 9.9 m/s (approx.)
Using this velocity value, we can now calculate the kinetic energy:
Kinetic Energy = 1/2 * 2 kg * (9.9 m/s)²
= 97.02 Joules (approx.)
So, the kinetic energy of the ball just before it hits the ground is approximately 97.02 Joules.
After the ball hits the ground, it comes to a stop. This means that all of its mechanical energy (potential energy and kinetic energy) is converted into other forms of energy, such as heat and sound energy. So, the mechanical energy of the ball is completely lost or transformed into non-mechanical forms.