The total momentum of a system of two moving identical bodies is zero. What should be true about the velocities of the bodies
The velocities of the two bodies must have opposite directions in order for the total momentum to be zero. This means that if one body has a positive velocity, the other body must have an equal magnitude but negative velocity.
If the total momentum of a system of two moving identical bodies is zero, it means that the vector sum of their momenta is equal to zero. Mathematically, this can be expressed as:
m1v1 + m2v2 = 0
Where:
- m1 and m2 are the masses of the two bodies, which are assumed to be identical.
- v1 and v2 are the velocities of the two bodies.
To satisfy this condition, the velocities of the bodies should have opposite directions and magnitudes that are equal in absolute value. In other words, one body should be moving in one direction with a certain speed, while the other body should be moving in the opposite direction with the same speed. This ensures that their momenta cancel each other out, resulting in a total momentum of zero for the system.
When the total momentum of a system of two moving identical bodies is zero, it means that the momentum of one body cancels out the momentum of the other body. In order for this to happen, the bodies must have equal but opposite velocities.
To find the answer, we need to use the concept of momentum, which is defined as the product of an object's mass and velocity. The momentum (p) of an object is given by the equation:
p = m * v
Where:
p = momentum
m = mass of the object
v = velocity of the object
Let's consider two identical bodies in the system. Since they are identical, they have the same mass (m) and we can assume it to be "m" for both bodies.
If the total momentum of the system is zero, it means that the sum of the momenta of the two bodies is zero:
p1 + p2 = 0
Substituting the momentum equation for each body:
(m * v1) + (m * v2) = 0
Now, since the masses of both bodies are the same, we can factor out the mass:
m * (v1 + v2) = 0
For the equation to be true, either the mass (m) or the sum of the velocities (v1 + v2) must be zero.
Since we cannot have zero mass for both bodies in most practical scenarios, the only way to achieve a total momentum of zero is if the sum of the velocities of the two bodies is zero:
v1 + v2 = 0
This implies that the velocities must have equal magnitudes but opposite directions.
In conclusion, when the total momentum of a system of two moving identical bodies is zero, the velocities of the bodies must have equal magnitudes but opposite directions.