Question
two balls collide in a head on elastic collision and rebound in opposite directions. One ball has velocity 1.2 before the collision and -2.3 after. the other ball has a mass of 1.1 kg and a velocity of -4.2 before the collision. What is the mass of the first ball? What is the velocity of the second ball after the collision?
please show work
please show work
Answers
drwls
With kinetic energy and momentum conservation, you have two equations in two unknowns, m1 and v2'
The ' symbol denotes final conditions.
m1 v1 + m2v2 = m1v1' + m2v2'
(m1/2)v1^2 + (m2/2)v2^2 = (m1/2)v1'^2 + (m2/2)v2'^2
Substitute in m2 = 1.1,
v1 = 1.2, v1' = -2.3 and v2 = 4.2
Now do the math.
It will help to prove, or know, that
v1 - v2 = v2' - v1'
(The relative velcity of the two balls changes sign but keeps the same absolute value)
The only unknown is v1 in that equation.
1.2 -4.2 = v2' + 2.3
v2 = -5.3
Now solving for m1 is easy.
You don't say what the units of velocity are. Just make sure they are the same for all.
The ' symbol denotes final conditions.
m1 v1 + m2v2 = m1v1' + m2v2'
(m1/2)v1^2 + (m2/2)v2^2 = (m1/2)v1'^2 + (m2/2)v2'^2
Substitute in m2 = 1.1,
v1 = 1.2, v1' = -2.3 and v2 = 4.2
Now do the math.
It will help to prove, or know, that
v1 - v2 = v2' - v1'
(The relative velcity of the two balls changes sign but keeps the same absolute value)
The only unknown is v1 in that equation.
1.2 -4.2 = v2' + 2.3
v2 = -5.3
Now solving for m1 is easy.
You don't say what the units of velocity are. Just make sure they are the same for all.