Answer:
a) the initial potential energy = 541.95J
b) the final kinetic energy = 87.991 J
Explanation:
<u>Step 1</u>: Data given
The ball has a mass of 0.145 kg and is at a height of 381m
<u>Step 2</u>: Calculate potential energy
The potential energy = m * g * h
with m = the mass of the ball = 0.145 kg
with g = Gravitational acceleration = 9.81 m/s²
with h = the height of the building = 381m
The potential energy = 0.145 Kg * 9.81 m/s² * 381m = 541.95 J
FD = 1/2ρCDAv²
⇒ with FD = the drag force = the force component in the direction of the flow velocity
⇒ with ρ = density of the fluid (air in our case: ρ≈1.1839 Kg/m3 at 1 atm and 25 °C)
⇒ with v = velocity of the ball
⇒ with A = reference area, which in our case is just the cross sectional area of the ball: A=πr2
⇒ with CD is the drag coefficient - a dimensionless coefficient, that in the case of a sphere, CD=0.47
Following Newton's second law:
ΣFy = may = -mg +Dv²
Here is D=1/2ρCDA ( for convenience) = 0.001172
The terminal speed we can define as the speed of the ball where ay = 0
Therefore: -mg + Dvt² = 0
⇒vt = √(mg/D)
vt = √(0.145 * 9.8 / 0.001172) ≈ 34.837
Uinitial=mgh≈541.951 J (see first question)
Kfinal=1/2*mvt²=(m²g)/2D ≈ 87.991 J
The final kinetics energy is 87.991 J
