For its size, the common flea is one of the most accomplished jumpers in the ani

Question

For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.00mm -long, 0.500mg critter can reach a height of 20.0cm in a single leap.

Part A

Neglecting air drag, what is the takeoff speed of such a flea?

Part B

Calculate the kinetic energy of this flea at takeoff and its kinetic energy per kilogram of mass.

Part C

K/m = ____ J/kg

Part D

If a 77.0kg , 1.70m -tall human could jump to the same height compared with his length as the flea jumps compared with its length, how high could he jump, and what takeoff speed would he need?

Part E

v = ____ m/s

Part F

In fact, most humans can jump no more than 60.0cm from a crouched start. What is the kinetic energy per kilogram of mass at takeoff for such a 77.0kg person?

Part G

Where does the flea store the energy that allows it to make such a sudden leap?

Explanation / Answer

Part A:

The ground potential energy of the Flea is given by;

P.E=mgh=KE=0.5m*v^2
so takeoff speed of flea is v=sqrt(2gh)=sqrt(19.6*0.2 m)=1.98 m/s(independent of its mass)       

Part B:

Kinetic energy of the flea is given by;

Kinetic energy=Potential energy

Kinetic energy=m*g*h

Kinetic energy=0.5*10-6 kg*9.8 m/s2*0.2 m

Kinetic energy=0.98 *10-6J

Also, kinetic energy per kilogram of mass is given by;

K=0.98*10-6J/0.5*10-6 kg=1.96 J/kg

Part D:

Human jump relative height is given by;

H=0.2 m*1.76*1000 mm/2 mm

H=0.2 m*1.76*1000 mm/2 mm

H=176 m

Part E:

The take off speed of human is given by;

V=sqrt (2gH)=sqrt(2*9.8 m/s^2*176 m)=Sqrt(3449.6 )=58.73 m/s

Part F:

Energy=g* H=9.8 m/s2*176 m=1724.8 J

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