- #1
h6872
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If the first ball in problem 7) has a mass of 10 kg and the second ball is traveling at it with a speed of 14 m/s, what is the velocity, to one decimal place, of the first ball after collision?
Problem (7) says A 9.8 kg steel ball, traveling left to right at 12 m/s, undergoes an elastic collision with a 5 kg steel ball at rest. To the nearest Joule, what is the Total Kinetic Energy of the two balls after collision?
So I derived equations using the conservation of momentum and kinetic energy and I got the two formulas:
from Ek = Ek1+ Ek2
1) 980 = 10 v1(prime)^2 + 5 v2 (prime) ^2
-------------- ---------------
2 2
from m1v1 + m2v2 = m1v1 (prime) + m2v2 (prime)
2) 190 = 10v1(prime) + 5 (v2) (prime)
so then I divided them all by 5 and rearranged to solve for v2(prime) getting:
v2 (prime) = 2v1(prime) - 38
I substituted this eqn back into the first and got
980 = 10v1(prime)^2 + 5 (2v1(prime) - 38)^2
This rearranges into a quadratic eqn (i think) the after I solve for v1 prime I keep getting the wrong answer! I'm not sure if it's just a math error or if I interpreted the question wrong... please help me!
thank you
Problem (7) says A 9.8 kg steel ball, traveling left to right at 12 m/s, undergoes an elastic collision with a 5 kg steel ball at rest. To the nearest Joule, what is the Total Kinetic Energy of the two balls after collision?
So I derived equations using the conservation of momentum and kinetic energy and I got the two formulas:
from Ek = Ek1+ Ek2
1) 980 = 10 v1(prime)^2 + 5 v2 (prime) ^2
-------------- ---------------
2 2
from m1v1 + m2v2 = m1v1 (prime) + m2v2 (prime)
2) 190 = 10v1(prime) + 5 (v2) (prime)
so then I divided them all by 5 and rearranged to solve for v2(prime) getting:
v2 (prime) = 2v1(prime) - 38
I substituted this eqn back into the first and got
980 = 10v1(prime)^2 + 5 (2v1(prime) - 38)^2
This rearranges into a quadratic eqn (i think) the after I solve for v1 prime I keep getting the wrong answer! I'm not sure if it's just a math error or if I interpreted the question wrong... please help me!
thank you