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Re: long jumping



Hi Carl,
I certainly agree that Eq (1) in the TPT article is in error. The last
term (deltaE) should not be there. Write a letter to TPT.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "Carl E. Mungan" <cmungan@UWF.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, February 23, 2000 3:07 PM
Subject: long jumping


In the March issue of The Physics Teacher on page 147, the following
equation is proposed:

E_1 = E_0 - gamma*E_0 - delta E -(1)

where E_0 is the translational KE of the jumper immediately before
takeoff, 0.5*m*v_0^2; E_1 is the jumper's translational KE after
takeoff, 0.5*m*v_1^2; gamma is the fraction of the initial energy
"wasted as heat and sound"; and delta E is the part of the initial
energy "converted into the energy of vertical motion," 0.5*m*v_1y^2.
(Quotes are verbatim from the article.)

It is this last term, delta E, that I don't understand. If we wanted
to split off the vertical part of the motion, then why aren't we left
with the horizontal part of the motion:

E_1 = 0.5*m*v_1y^2 + 0.5*m*v_1x^2 -(A)

After all, consider Eq. (1) in the limiting case of a straight
vertical jump (granted that no jumper would do that). Then v_1 = v_1y
and so we get:

E_1 = 0.5*(1-gamma)*E_0 -(B)

which appears to suggest that he could convert up to half of his
initial (horizontal) KE into final (vertical) KE. Not an obvious
result to me! (I'm not clear how gamma includes friction however, so
I'll allow that the final answer is probably lower.)

I just don't understand how to derive Eq. (1) at all. Don't I need
some model for the interaction between his foot and the ground? The
following questions may or may not help elucidate this:

What would happen if you jumped on ice?
What would happen if the ground, foot, and shoe had zero springiness?
What would happen if the foot were a single sharp point?

I need to know what simplifications I can make to start tackling all
this. Insight would be appreciated. Carl
--
Dr. Carl E. Mungan, Assistant Professor http://uwf.edu/cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu