Question

Fleas have remarkable jumping ability. a 0.60 mg flea, jumping straight up, would reach a height of 40 cm if there were no air resistance. in reality, air resistance limits the height to 20 cm . part a what is the flea's kinetic energy as it leaves the ground?

Answer 1

To answer, we determine the velocity of the flea when it leaves the ground. Using the given value for distance, the velocity can be determined through the equation,

                     2a d = (Vf)² - (Vi)²

where a is the acceleration due to gravity, d is distance, Vf is the final velocity which is equal to zero and Vi is the initial velocity. Substituting the known values,

               2(9.8 m/s²)(40cm/100cm) = (Vi)²

The value of Vi from the equation is 2.8 m/s. 

The equation for determining the kinetic energy is:
                   KE = 0.5mv²

Substituting,
                  KE = 0.5(0.60 x 10^-3g)(1 kg/1000g)(2.8 m/s)²
                        KE = 2.352 x 10^-6 J

Answer 2

The kinetic energy of the flea as it leaves the ground is $\boxed{2.352\times{{10}^{ - 6}}\,{\text{J}}}$ .

Further Explanation:

Given:

The maximum height reached by the flea in absence of air resistance is $40\,{\text{cm}}$ .

The mass of the flea is $0.60\,{\text{mg}}$ .

The height attained by the flea in presence of air resistance is $20\,{\text{cm}}$ .

Concept:

In the absence of the air resistance, the complete kinetic energy of the flea at the bottom will be converted into the potential energy of the flea at the top.

Using the conservation of energy for no air resistance case:

$\begin{aligned}KE&=PE\\\frac{1}{2}m{v^2}&=mg{h_1}\\\end{gathered}$

Substitute the values of acceleration due to gravity and the height attained by the flea.

$\begin{aligned}\frac{1}{2}{v^2}&=9.8\times\left({\frac{{40}}{{100}}}\right)\\v&=\sqrt{2\times9.8\times0.4}\\&=2.8\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}$

In the presence of the air resistance also, the flea starts with the same amount of kinetic energy but some part of energy is used in overcoming the air resistance.

The kinetic energy of the flea as it starts from the ground is:

$KE=\frac{1}{2}m{v^2}$

Substitute the value of mass and velocity in above expression.

$\begin{aligned}KE&=\frac{1}{2}\times\left({\frac{{0.60}}{{{{10}^6}}}}\right)\times{\left({2.8}\right)^2}\\&=0.5\times0.60{\kern1pt}\times{10^{-6}}\times7.84\\&=2.352\times{10^{-6}}\,{\text{J}}\\\end{aligned}$

Thus, the kinetic energy of the flea as it leaves the ground is $\boxed{2.352\times{{10}^{-6}}\,{\text{J}}}$  .

Learn More:

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Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Conservation of energy

Keywords:

Flea, remarkable jumping ability, air resistance, 0.60mg flea, height of 40cm, limits the height, to 20cm, flea’s kinetic energy, leaves the ground, potential energy.