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

Answer 1

Answer:

A.   19.3 joules

Explanation:

The collisions is perfectly elastic: this means that both total momentum and total kinetic energy are conserved after the collision.

Therefore, we can just calculate the total initial kinetic energy before the collision, and then say that it is equal to the total kinetic energy after the collision.

The kinetic energy of object A is:

$K_A = \frac{1}{2}m_A v_A^2=\frac{1}{2}(7.2 kg)(+2.0 m/s)^2=14.4 J$

The kinetic energy of object B is:

$K_B = \frac{1}{2}m_B v_B^2=\frac{1}{2}(5.75 kg)(-1.3 m/s)^2=4.9 J$

So, the total kinetic energy before (and after) the collision is

$K=K_A + K_B=14.4 J+4.9 J=19.3 J$