Two identical objects, one moving twice as fast as the other, collide with each other in the following way:

0--------> 2v v <----0
m m
If the two objects stick together after the collision, will they be moving to the right, to the left, or not at all? Explain your answer.

m1•v1 – m2•v2 =(m1+m2)u.

m•2•v – mv = 2•m•u,
u = m•v/2•m = v/2 (to the right)

To determine the direction of the objects after the collision, we can use the principle of conservation of momentum. The conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces act on the system.

Let's assign some variables to better understand the problem:

Let's say the mass of each object is m, and the initial velocity of the first object (moving to the right) is 2v, while the initial velocity of the second object (moving to the left) is v.

The momentum of an object is given by the product of its mass and velocity, which can be expressed as:

momentum = mass * velocity

Using this equation, we can calculate the initial momentum of the system before the collision:

initial momentum = (mass * 2v) + (mass * -v)

Simplifying this equation, we get:

initial momentum = 2mv - mv

initial momentum = mv

Now, let's consider the situation after the collision, where the two objects stick together. Since they are moving towards each other, their velocities will add up after the collision.

Let's assume the final velocity of the combined objects is V.

The final momentum of the system after the collision can be calculated as the product of the combined mass (which is 2m since the objects stick together) and the final velocity:

final momentum = combined mass * final velocity

final momentum = (2m) * V

According to the conservation of momentum, the initial momentum and final momentum should be equal:

mv = (2m) * V

Cancelling out the mass (m) on both sides, the equation becomes:

v = 2V

From this equation, we can infer that the final velocity (V) is half the initial velocity (v).

Now, let's determine the direction of the final velocity. Since the initial velocity of the first object was to the right (2v) and the initial velocity of the second object was to the left (-v), their combined velocity after the collision will maintain the direction of the object with the greater initial velocity. In this case, the object moving to the right had the greater initial velocity (2v), so the final velocity will be to the right.

Therefore, after the collision, the objects will be moving to the right.