Posted by Elisa on Monday, July 7, 2008 at 9:34am.
well since everything is in cm and seconds and grams we can stay in the centimeter, gram, second or"cgs" units.
Initial momentum = 10*25 - 15*36
= -290 (to the right is positive)
final momentum =same = -290 = 10 U + 15 V
elastic so initial KE = final KE
(1/2) 10 (625) + (1/2) 15 (1296)
3125+9720
=12,845 dynes
final KE =12,845 = 5 U^2 + 7.5 V^2
so two equations, two unknowns:
-290 = 10 U + 15 V
12,845 = 5 U^2 + 7.5 V^2
U = - (1.5 V + 29)
U^2 = 2.25 V^2 + 87 V + 841
12,845 = 5(2.25 V^2 + 87 V + 841) + 7.5 V^2
You can solve the quadratic I think
in 3 seconds from 0 to 2*10^4 revs/min
first change rev/min to radians/sec
2*10^4rev/min (1 min/60 s)(2 pi rad/rev)
=2094 radians/s
alpha = change in speed/change in time = 2094/3 = 698 radians/s^2
angle = (1/2) alpha t^2
=349*9 = 3141 radians
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