A 13.0 {\rm g} plastic ball is dropped from a height of 2.80 {\rm m} and is moving at 3.20 {\rm m/s} just before it hits the floor.
How much mechanical energy was lost during the ball's fall?
delta E mech = ____ J
To find the mechanical energy lost during the ball's fall, we need to calculate the initial mechanical energy and the final mechanical energy.
The initial mechanical energy is given by the formula:
E_initial = m * g * h
where
m = mass of the ball = 13.0 g = 0.013 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height = 2.80 m
E_initial = 0.013 kg * 9.8 m/s^2 * 2.80 m = 0.36344 J
The final mechanical energy is the kinetic energy just before it hits the floor, given by the formula:
E_final = (1/2) * m * v^2
where
m = mass of the ball = 13.0 g = 0.013 kg
v = velocity = 3.20 m/s
E_final = (1/2) * 0.013 kg * (3.20 m/s)^2 = 0.06656 J
The mechanical energy lost is the difference between the initial and final mechanical energy:
delta E_mech = E_initial - E_final = 0.36344 J - 0.06656 J = 0.29688 J
Therefore, the mechanical energy lost during the ball's fall is 0.29688 J.
To calculate the mechanical energy lost during the ball's fall, we need to find the initial mechanical energy before it hits the floor and subtract the final mechanical energy just before it hits the floor.
The mechanical energy of an object consists of its potential energy (PE) due to its height and its kinetic energy (KE) due to its motion. The equation for calculating mechanical energy is as follows:
E_mech = PE + KE
Potential Energy (PE) is given by:
PE = m * g * h
where m is the mass of the ball (13.0 g = 0.013 kg), g is the acceleration due to gravity (approximated as 9.8 m/s^2), and h is the height (2.80 m).
Substituting the values:
PE = 0.013 kg * 9.8 m/s^2 * 2.80 m = 0.35792 J (rounded to five decimal places)
Kinetic Energy (KE) is given by:
KE = (1/2) * m * v^2
where m is the mass of the ball (0.013 kg), and v is the velocity just before it hits the floor (3.20 m/s).
Substituting the values:
KE = (1/2) * 0.013 kg * (3.20 m/s)^2 = 0.06656 J (rounded to five decimal places)
Now, we can find the initial mechanical energy (E_initial) and the final mechanical energy (E_final) by summing the potential energy (PE) and kinetic energy (KE):
E_initial = PE + KE
E_final = KE
Mechanical energy lost (delta E_mech) is given by:
delta E_mech = E_initial - E_final
Substituting the values:
delta E_mech = (0.35792 J + 0.06656 J) - 0.06656 J = 0.35792 J (rounded to five decimal places)
Therefore, the mechanical energy lost during the ball's fall is approximately 0.358 J.
What does your \rm symbol mean? Why do you need a symbol there at all?
delta E mechanical = (Initial PE + KE) - (Final PE + KE)
= MgH - (1/2) M*Vfinal^2
H = 2.80 m is the height of the drop. Initial KE is zero