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The theorem of conservation of mechanical energy is used
a) The initial kinetic energy is, K = 1.33 10⁻⁶ J
b) The fraction of kinetic energy converted to potential energy, U/K = 1.96
The total mechanical energy which is defined as the sum of kinetic energy plus potential energies, is given as
E = K + U
To find the speed of the flea jump when there is no friction,
Initial point
E₁ = K = ½ m v²
Final point.
At the highest height h = 30 cm = 0.30 m because there is no friction
E₂ = U = mgh
Energy is conserved
E₁ = E₂
½ mv² = mgh
v = [tex]\sqrt{2gh}[/tex]
v = [tex]\sqrt{2(10)(0.4)}[/tex]
v = [tex]\sqrt{4}[/tex] m/s
v = 2 m/s
A) Now we have to find the initial kinetic energy
K = ½ m v²
K = ½ (0.5 × 10⁻⁶) (2)²
K = 1 × 10⁻⁶ J
B) Now we have to find the fraction of energy lost if we take into account the friction of the air
The initial kinetic energy
K = ½ m v²
Now we have to look for the potential energy until h’= 20 cm = 0.20 m
U = mgh'
The fraction of energy lost,
U/K = mgh'/½ mv²
= 2gh'/v²
= 2 × 9.8 × 0.2/ 2
= 1.96
Therefore,
a) The initial kinetic energy is, K = 1 × 10⁻⁶ J
b) The fraction of kinetic energy converted to potential energy, U/K = 1.96
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