Unraveling the Flying Leap of a Flea

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Homework Help Overview

The discussion revolves around analyzing the jumping motion of a flea, specifically focusing on its maximum height and acceleration during its leap, as depicted in a graph from a scientific article. The problem involves applying kinematic equations and interpreting graphical data related to high-speed motion pictures of the flea's jump.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods for estimating the maximum height reached by the flea, including using the area under the graph and kinematic equations. Questions arise about the correctness of initial calculations and the validity of different estimation techniques.

Discussion Status

Some participants have provided estimates and shared their reasoning, leading to a collaborative exploration of the problem. While one participant claims to have arrived at the correct answer, there is no explicit consensus on the methods used, and alternative approaches are being considered.

Contextual Notes

Participants are working within the constraints of using a provided graph and are encouraged to derive answers based on visual data rather than solely relying on formulas. There is an emphasis on approximations and interpretations of the graph's features.

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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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