two bodies of different masses move such that they have equal kinetic energies. Which of the bodies, lighter or heavier one, will have more momentum? (explain please)
Answers (2)
momentum = mv
kinetic energy = (1/2)mv^2
To have equal energies, the lighter body must move at the square of the speed of the heavier one.
Ratio = (m1v^2)/m2v = m1v/m2 You have one equation with three unknowns, so there is no solution. You might find some interesting things by plotting different numbers. The first point you would want to consider would be m1v = m2.
Well, I got confused by all those variables. I said three unknowns and there are four.
KE1 = (1/2)m1(v1)^2
KE2 = (1/2)m2(v2)^2
KE1 = KE2
m1(v1)^2 = m2(v2)^2 Let m1 be the smaller mass.
(v1)^2 = (m2(v2)^2)/m1
v1 = √(m2/m1) * v2 And that is about as far as you can go without assigning some specific numbers.
Jewels, thnx for the answer, but it is still unclear to me..
how can you say that the velocity of the lighter body 'must' be the square of the heavier body's velocity ? if you take the kinetic energies of the two masses on both sides of an equation, then you don't get any such relation b/w the velocities, but actually they will depend on the masses of the bodies, to satisfy the equation. maybe u did not understand my question.