x.Hmce=\"CMR10\"> Two balls with masses m1 and m2 are on the x-axis. Ball m1 has
ID: 1675047 • Letter: X
Question
x.Hmce="CMR10"> Two balls with masses m1 and m2 are on the x-axis. Ball m1 has an initial velocity v1 > 0 along the positive x-axis and ball m2 is initially at rest. The balls collide elastically and remain on the x-axis after the collision. If m1 = m2, what is the final velocity v1 of the ball m1?Part (1 of 4)
In the limit, when m1 Two balls with masses m1 and m2 are on the x-axis. Ball m1 has an initial velocity v1 > 0 along the positive x-axis and ball m2 is initially at rest. The balls collide elastically and remain on the x-axis after the collision. If m1 = m2, what is the final velocity v1 of the ball m1?
Part (1 of 4)
In the limit, when m1
Explanation / Answer
in elastic collision, I. momentum will remain conserved, m1 v1+ m2 v2 = m1v'1 +m2v'2............A II. K.E. will remain constant. using above expression the relationcomes out to be: v1 +v'1 = v2 +v'2.....................................B If, m1 = m2 and v2 = 0 the 2 equation becomes: m x v1 = m x v'1 + m x v'2..........I v1 + v'1 = v'2................................II solving the 2 equations, v'1 = 0 and v'2 = v1 part 1 and part2 dividing A by m2, and putting v2 = 0 in A & B: (m1/m2)v1 +0 = (m1/m2)v'1 + v'2...................A and v1 + v'1 =v'2.......................................................B Now as m2>>m1; (m1/m2) tends to0 equation A givesus, v'2 = 0 and thus Bgives, v'1 = -v1 part 3 and part 4 dividing A by m1, and putting v2 = 0 in A & B: v1 + 0 = v'1+ (m2/m1)v'2...................A and v1 + v'1 =v'2.......................................................B Now as m1>>m2; (m2/m1) tends to0 equation A givesus, v'1 = +v1 and thus Bgives, v'2 = +2v1
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