Hello, I'm trying to figure out which of the following statements are TRUE.
I suspect that 2, 6, 8 are true...and that there is one more that is true, but not sure which one?
Thanks!
It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
Momentum and kinetic energy are always conserved.
Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.
It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
False
If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
False
The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
True
Momentum and kinetic energy are always conserved.
False
Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
True
The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
True
The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
True
Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
True
If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.
False
It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
1. false
If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
2. true
The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
3. true
Momentum and kinetic energy are always conserved.
4. false
Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
5. true
The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
6. true
The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
7. true
Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
8. true
If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.
9. false
ans above is incorrect, though I don't know what is wrong, just that I got it wrong
2 is false
To determine which of the statements are true, we need to analyze each one individually.
1. It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
To evaluate this statement, we need to consider what a center-of-mass is. The center-of-mass is the point where the average position of the mass of an object or system can be considered to be concentrated. In a collision, if the center-of-mass of the system is stationary before the collision, it will still be stationary after the collision, as long as no external forces are acting on the system. Therefore, this statement is TRUE.
2. If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
To analyze this statement, we need to understand the principle of conservation of momentum. According to this principle, in the absence of external forces, the total momentum of a system remains constant. Therefore, if one object's momentum decreases after a collision, the other object's momentum must increase to maintain the total momentum of the system. Hence, this statement is TRUE.
3. The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
This statement is based on the principle of conservation of momentum. If no external forces act on the system, the total momentum before the collision is equal to the total momentum after the collision. Since momentum is a vector quantity, the vector sum of the momenta before the collision should be equal to the vector sum of the momenta after the collision. Therefore, this statement is TRUE.
4. Momentum and kinetic energy are always conserved.
This statement is FALSE. Momentum is always conserved in a collision, as stated by the principle of conservation of momentum. However, kinetic energy is conserved only in elastic collisions where there is no loss of kinetic energy due to deformation, sound, heat, or other factors.
5. Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
This statement is partially TRUE. In an elastic collision, both momentum and kinetic energy are conserved. However, in an inelastic collision, momentum is still conserved, but kinetic energy is not conserved.
6. The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
According to the principle of conservation of momentum, the change in momentum for one object in a collision is equal in magnitude but opposite in direction to the change in momentum of the other object. Therefore, this statement is TRUE.
7. The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
This statement is TRUE. The motion of the center-of-mass is only affected by external forces acting on the system. The elasticity of a collision does not have an impact on the center-of-mass motion.
8. Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
This statement is TRUE. As discussed earlier, momentum is always conserved in a collision, but kinetic energy is conserved only in elastic collisions.
9. If the center-of-mass of the system is moving in one direction before the collision, it must move in the opposite direction after the collision.
This statement is FALSE. The center-of-mass of the system will continue moving in the same direction before and after the collision if no external forces are acting on it.
So, based on the analysis above, statements 1, 2, 3, 6, 7, 8 are TRUE.