Question

Object A has of mass 7.20 kilograms, and object B has a mass of 5.75 kilograms. The two objects move along a straight line toward each other with velocities +2.00 meters/second and -1.30 meters/second respectively. What is the total kinetic energy of the objects after the collision, if the collision is perfectly elastic?

A. 19.3 joules
B. 21.9 joules
C. 38.5 joules
D. 43.0 joules
E. 50.8 joules

Can someone help me please? Im too confused on this question and no one is explaining it to me right :/

Answer 1

Although, if this was perfectly inelastic, the answer would be 0. This is the equation for conservation of momentum\[m_{1i}v_{1i}+m_2iv_2i=m_{1f}v_{1f}+m_{2f}v_{2f}\]

Through a derivation you can google, the values for the final velocities \[v_{f,1} = \frac{m_1 −m_2}{ m_1 + m_2} v_{i,1}+\frac{2m_2}{ m_1 + m_2} v_{i,2}\]
\[v_{f,2} = \frac{2m_2}{ m_1 + m_2} v_{i,1}+\frac{m_1-m_2}{ m_1 + m_2} v_{i,2}\]

\[\frac{1}{2}m_{1i}v_{1i}+\frac{1}{2}m_{2i}v_{2i}=\frac{1}{2}m_{1f}v_{1f}+\frac{1}{2}m_{2f}v_{2f}\]

You should be able to calculate it out from here. Merely plug in the values to obtain v1 and v2 final then plug in the initial values and the final values in their respective locations and solve the two half equations. in theory they should be equal. Try it out. if you can't get the answer, or have any questions, let me know.

Answer 2

first of all you need to write the momentum conservation equation.
then you should write the equation of coefficient of restitution
here e(coefficient of restitution)=1 as the collision is elastic
next
you'll get the individual velocities of the objects and then you can find the k.e. by the formula (mv^2)/2
the momentum cons. equn. will be as follows
4.925=7.2v1 + 5.75v2
(+v1 is the velocity of block of mass 7.2 kg after coll. and v2 for block of mass 5.75 kg)
next for coefficient of restitution
v2-v1=3.3

now by solving these equations, you'll get the velocities and then you can calculate the k.e. of the objects

i got the nswer A

if you need any further help, please let me know

Answer 3

Thank you so much. I understand this now. Sometimes another outlook is better.