Question

Two cans of spam with identical masses collide. Before the collision, the hickory smoke flavor is moving to the left at 4m/s while the hot and spicy flavor is moving to the right at 2 m/s. After the collision, the hickory smoke is moving to the left at 1.2 m/s. What is their final velocity of the hot and spicy? Is this collision elastic?

Answer 1

1) Final velocity: 0.8 m/s to the left

2) This is not an elastic collision

Explanation:

1)

We can solve this problem by applying the law of conservation of momentum: in fact, if there are no external forces, the total momentum of the two cans must be conserved before and after the collision.

Mathematically:

$p_i = p_f\\mu_1 + mu_2 = mv_1 + mv_2$  

where:  

m is the mass of each can

$u_1 = -4 m/s$ is the initial velocity of the first can (we take to the left as negative direction)

$u_2 = 2 m/s$ is the initial velocity of the second can (to the right, positive)

$v_1 = -1.2 m/s$ is the final velocity of the first can (the hickory one)

$v_2$ is the final velocity of the 2nd can (the hot and spicy one)

Re-arranging the equation and solving for v2, we find:  

$v_2 = u_1 + u_2 - v_1 = (-4) + (+2) - (-1.2)=-0.8 m/s$

So, the final velocity of the hot and spicy can is 0.8 m/s to the left.

2)

There are two types of collisions in physics:

• Elastic collision: the total kinetic energy is conserved
• Inelastic  collision: the total kinetic energy is not conserved

In order to check if this collision is elastic or not, we need to compare the kinetic energy before the collision to the kinetic energy after the collision.

Before the collision:

$K_i = \frac{1}{2}mu_1^2 + \frac{1}{2}mu_2^2 = \frac{1}{2}m(-4)^2+\frac{1}{2}m(2)^2=10m$

After the collision:

$K_f = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2 = \frac{1}{2}m(-1.2)^2+\frac{1}{2}m(-0.8)^2=1.04m$

We see that the final kinetic energy is less than the initial kinetic energy: part of the kinetic energy has been converted into other forms of energy during the collision, therefore this is NOT an elastic collision.

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