Answer:
The reduction in the mechanical energy of the Frisbee-Earth = 2.885 J
Step-by-step explanation:
From the law of conservation of energy,
Mechanical Energy = Ek + Ep
Where Ek = kinetic Energy, Ep = potential Energy.
Change in mechanical energy = change in kinetic Energy + change in potential energy.
ΔM = ΔEk + ΔEp ................................. Equation 1.
Reduction in mechanical energy = -ΔM = -(ΔEk + ΔEp)
-ΔM = -[1/2m(v₂²-v₁²) + mg(h₂-h₁)]..................... Equation 2
Where -ΔM = Reduction in mechanical Energy, m = mass of the Frisbee, v₂ = final velocity of the Frisbee, v₁ = Initial velocity of the Frisbee, h₂ = Final height of the Frisbee, h₁ = Initial height of the Frisbee.
Given: m = 77 g = 0.077 kg, v₁ = 15 m/s, v₂ = 12 m/s, h₁ = 0.99 m, h₂ = 1.3 m, g = 9.81 m/s²
Substituting these values into equation 2
-ΔM = -[1/2(0.077)(12²-15²) + 0.077(1.3-0.99)(9.81)]
-ΔM = -[(0.077)(-40.5) + (0.234)]
-ΔM = -[-3.119+0.234]
-ΔM = -[-2.8845]
-ΔM ≈ 2.885 J
Thus the reduction in the mechanical energy of the Frisbee-Earth = 2.885 J