Unraveling the Flying Leap of a Flea

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SUMMARY

The forum discussion focuses on calculating the maximum height and acceleration of a flea using high-speed motion picture data. The flea, weighing 210 μg and measuring 2 mm, jumps at a nearly vertical angle. Participants utilized kinematic equations and graphical analysis to estimate the flea's maximum height at 2.5 ms, arriving at an approximate height of 0.25 cm by calculating the area under the motion graph. The discussion emphasizes using graphical methods alongside kinematic equations for accurate estimations.

PREREQUISITES
  • Kinematic equations for motion analysis
  • Understanding of graphical representation of motion
  • Basic unit conversion skills (e.g., milliseconds to seconds)
  • Familiarity with area calculation for geometric shapes (triangles and rectangles)
NEXT STEPS
  • Study the application of kinematic equations in real-world scenarios
  • Learn about graphical methods for analyzing motion in physics
  • Explore advanced techniques for estimating areas under curves
  • Investigate the effects of mass and angle on projectile motion
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in the biomechanics of small organisms like fleas.

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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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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.
 
Last edited:
yeah that's the correct answer! :) how did you do it?
 
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
 
could you use the same concept to find the flea's height at 0.5 ms, 1.0, and 1.5 ms??
 
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.
 

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