How much mechanical energy was lost during the ball's fall?
Incomplete.
To determine how much mechanical energy was lost during the ball's fall, we need to know the change in mechanical energy. Mechanical energy is the sum of kinetic energy and potential energy.
The change in mechanical energy can be calculated using the following formula:
ΔE = E_final - E_initial
Where:
ΔE is the change in mechanical energy.
E_final is the final mechanical energy.
E_initial is the initial mechanical energy.
The initial mechanical energy of the ball can be calculated as the sum of its initial kinetic energy and potential energy. The final mechanical energy can be calculated as the sum of its final kinetic energy and potential energy.
The initial kinetic energy (K_initial) is given by the formula:
K_initial = (1/2) * m * v_initial^2
Where:
m is the mass of the ball.
v_initial is the initial velocity of the ball.
The initial potential energy (U_initial) is given by the formula:
U_initial = m * g * h_initial
Where:
m is the mass of the ball.
g is the acceleration due to gravity (approximately 9.8 m/s^2).
h_initial is the initial height of the ball.
Similarly, the final kinetic energy (K_final) and potential energy (U_final) can be calculated using the formulas:
K_final = (1/2) * m * v_final^2
U_final = m * g * h_final
Where:
v_final is the final velocity of the ball.
h_final is the final height of the ball.
Once you have the values for E_initial and E_final, you can use the ΔE formula to calculate the change in mechanical energy, which represents the amount of energy lost during the ball's fall.