Two thin and identical steel rods move with equal speeds v=1 m/s in opposite directions and collide longitudinally. The collision is perfectly elastic and the rods swap their velocities. How long does the collision last in seconds if the length of the rods is l=30 cm. Assume that the speed of sound in the steel rods is c=5000 m/s

To determine the duration of the collision, we need to consider the time it takes for the sound wave to travel the length of the rod and reflect back.

Since the rods are moving in opposite directions, the relative velocity between them is 2v (double the individual velocities). In this case, it's 2 m/s.

When the collision occurs, a compression wave (sound wave) is generated in both rods. This wave travels through the rods until it reaches the other end, where it reflects and travels back.

The time it takes for the wave to travel the length of the rod and reflect back can be calculated using the formula:

time = distance / speed

In this case, the distance the wave travels is twice the length of the rod (2l), as it needs to travel from one end to the other and back.

The speed of sound in the steel rods (c) is given as 5000 m/s.

Plugging in the values into the formula, we get:

time = (2l) / c

Substituting the given values, we have:

time = (2 * 0.30) / 5000

time = 0.00012 seconds

Therefore, the collision lasts approximately 0.00012 seconds.