Unraveling the Flying Leap of a Flea

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In summary, at 0.5, 1.0, and 1.5 ms, the flea reached a height of .0031, .0068, and .0098 cm, respectively.
  • #1
MozAngeles
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Homework Statement


High-speed motion pictures 3500 (frames/second) of a jumping, 210 μg flea yielded the data used to plot the graph given in the figure . (See "The Flying Leap of the Flea" by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical take-off angle. Use the graph to answer the questions.
YF-02-42.jpg


Find the maximum height the flea reached in the first 2.5 {\rm ms}.
Find the flea's acceleration at 0.5 {\rm ms}.

Homework Equations



the kinematics equations
x= .5at2+ v0+ x0
v= at + v0
...

The Attempt at a Solution


hmax=1/2g*t
after converting everything to the right units i got .0031 cm which was wrong... help meh please?
 
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  • #2
how do you know it was wrong? do you have the answer? I've done a quick estimate giving 0.25ish cm. if that's closer I'll explain how I did it.
 
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  • #3
yeah that's the correct answer! :) how did you do it?
 
  • #4
Well... I didn't use any formulae in my estimation really, I just used the fact that the distance traveled = the area under the graph...

if you do it in two halves (triangular and rectangular)
you get height (distance traveled upwards buy flea) = (1/2)*(1/1000 sec)*(125 cm/sec) + ((2.5-1)/1000 sec)*(125 cm/sec) = about 0.25cm

this is actually a fair approximation as the extra bit added to the rectangle at the top left corner by taking the left hand edge as 1ms compensates for the bit missing from the triangle caused by the fact that the slope upwards in concave

There may be a more "mathsy" way of doing this, perhaps more accurately, but the question does after all say "Use the graph to answer the questions."

Hope this helps!

Will
 
  • #5
could you use the same concept to find the flea's height at 0.5 ms, 1.0, and 1.5 ms??
 
  • #6
I don't see why not? just work out the area under the graph in terms of triangles and rectangles up to those times on the x-axis.
 

1. What makes fleas able to jump so far?

Fleas have a special anatomical feature called resilin, which is a protein-based elastic material found in their hind legs. This allows them to store and release energy quickly, giving them the ability to jump up to 200 times their body length.

2. How do fleas control their jumping direction?

Fleas have small claws at the end of their legs that they use to grip onto surfaces. By adjusting the angle of their legs and claws, they can control the direction of their jump.

3. Can fleas jump higher than their body length?

Yes, fleas can jump much higher than their body length. In fact, some species of fleas can jump up to 12 inches vertically and 33 inches horizontally.

4. How does the flea's size affect its jumping ability?

The size of a flea does not seem to affect its jumping ability. Even the smallest fleas have the same anatomical features and jumping mechanism as larger fleas, allowing them to jump similar distances.

5. Are there any other animals that can jump like fleas?

Fleas have one of the most impressive jumping abilities in the animal kingdom, but there are a few other animals that can jump relatively far compared to their body size. These include grasshoppers, kangaroos, and frogs.

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