Determine for each of the following statements whether it is always true or can be false.

In a perfectly inelastic collision, the kinetic energy is conserved.

Kinetic energy is conserved in an elastic collision.

Two objects of different masses but moving at the same velocity have different momentum.

In an elastic collision the momentum is not conserved.

Momentum of a system may be conserved even when mechanical energy is not.

no - in an ELASTIC collision KE is conserved

Yes as I just said

Yes m V1 is not m V2

NO -in ANY old collision momentum is conserved

Yes, in in inelastic collision momentum is conserved and energy is not (escapes as heat)

To determine whether each statement is always true or can be false, let's analyze each one individually and consider the relevant concepts.

1. In a perfectly inelastic collision, the kinetic energy is conserved.
In a perfectly inelastic collision, the objects stick together and move as one. The kinetic energy is not conserved in such collisions because some of the initial kinetic energy is converted into other forms of energy, such as heat or sound. The statement can be false.

2. Kinetic energy is conserved in an elastic collision.
In an elastic collision, the objects collide and bounce off each other without any energy loss. This means that the total kinetic energy before and after the collision remains the same. Therefore, the statement is always true.

3. Two objects of different masses but moving at the same velocity have different momentum.
Momentum depends on both mass and velocity. Since the objects have different masses but the same velocity, their momenta will differ. As momentum is a product of mass and velocity, the object with greater mass will have greater momentum. Therefore, the statement is always true.

4. In an elastic collision, the momentum is not conserved.
This statement is incorrect. In an elastic collision, both kinetic energy and momentum are conserved. The total momentum before the collision is equal to the total momentum after the collision. Therefore, the statement is false.

5. Momentum of a system may be conserved even when mechanical energy is not.
Momentum is a vector quantity that depends on the mass and velocity of an object. It can be conserved in a system as long as there are no external forces acting on it. On the other hand, mechanical energy takes into account both kinetic and potential energy and can be affected by non-conservative forces such as friction. Therefore, it is possible for momentum to be conserved even when mechanical energy is not. The statement is always true.