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Unformatted text preview: the balls’ result, as inb(4) for the limit k ,y0. ' v t & gt 2 2 . The amount of time it
24. One the correct height can e described by y % 0
0
takes to rise and fall to its initial height is therefore given by 2v0 g . If the time it takes to cycle
during
the ball The differential equation we are asked o en th is must be (2.22), in the is ""
"
210. through the juggler’s hands is ( % 0.9 s ,tthsolveereEquation 3 balls which air x $ % kx .that
Using .thesgiven ball must stay in are shownat leastfigure. the course, theis 2v0 gwill(not be able
values, the plots the air for in the 3(, so Of condition reader ) 3 , or
time ( A ingle
to distinguish 1between the results shown here and the analytical results. The reader will have to
v0 ) 13.2 m * s & .
take the word of the author that the graphs were obtained using numerical methods on a
computer. The results obtained were at most within 10 %8 of the analytical solution.
25. v (m/s) v vs t flightpath 10 N 5
er 0
plane 5 10 15 20 25
mg t (s) 30 point of maximum
accelerationx vs t 100 ! " ! " x (m) a) From the force diagram we have N & mg % mv 2 R er . The acceleration that the pilot feels is
50
N m % g ' mv R er , which has a maximum magnitude at the bottom of the maneuver.
2 b) If the acceleration felt by 0 pilot must be less than 9g, then we have
the
0 5 R) ! 10 15 &1 3 * 330 mt*(s
s)
v
%
8g
8 * 9.8 m * s &2
2 " 20 25 30 ! 12.5 km (1) v vs x 10 v (m/s) A circle smaller than this will result in pilot blackout.
26. 5 0 0 20 40 60 80 100 x (m) 211. The equation of motion is d2 x
Let the origin of our coordinate system be at $ % ktail2end of the cattle (or the closest cow/bull). 1)
m 2 the mv # mg
(
dt
a) The IAN Mare moving SINGLE PARTICLE
bales ECHANICS— initially at the speed of the plane when dropped. Describe one of 37
NEWTON
This equation can parametric equatiin the same way as in problem 212 and we find
these bales by the be solved exactly ons x % x 0 ' v0 t
2
! g # kv0 "
1
log %
x$
2&am...
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This note was uploaded on 12/14/2013 for the course PHYS 301 taught by Professor Argryes during the Fall '13 term at University of Cincinnati.
 Fall '13
 Argryes
 Physics, mechanics

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