Linear Momentum and Collisions - True/False

[Melchior25]

Homework Statement

Two objects are at rest on a frictionless surface. Object 1 has a greater mass than object 2. When a constant force is applied to object 1, it accelerates throught a distance d. The force is removed from object 1 and is applied to object 2. At the moment when object 2 has accelerated through the same distance d, which statements are true? (Select all that apply.)
p1 > p2 True
K1 = K2 False
K1 < K2 True
p1 < p2 False
p1 = p2 False
K1 > K2 False

Homework Equations

Potential Energy - Stored energy; the energy an object has because of its position.
Kinetic Energy - The energy that a moving object has due to its motion, the energy of motion.

Could Someone please let me know if I am thinking about this problem wrong? And if I am, any help would be greatly appreciated.

Thanks

 

[Shooting Star]

Homework Equations

Potential Energy - Stored energy; the energy an object has because of its position.
Kinetic Energy - The energy that a moving object has due to its motion, the energy of motion.

Why do you think that potential energy is relevant to this problem?

Work done = Force X displacement. When work is done on a body by a force for a distance d, and there is no dissipation of energy, then that work done must be equal to the KE of the body at the end of the distance d.

All the answers can be found from this. Show your work this time.

 

[Moetasim]

!

Your understanding of the problem and the concepts of potential and kinetic energy seem to be correct. However, the problem is asking about linear momentum and collisions, not potential and kinetic energy.

Linear momentum is defined as the product of an object's mass and velocity. In this problem, the two objects have different masses, so their linear momenta (p1 and p2) will be different.

When the force is applied to object 1, it accelerates through a distance d. This means that its velocity increases, and therefore its linear momentum (p1) also increases. When the force is removed from object 1 and applied to object 2, it will also accelerate through the same distance d. However, since object 2 has a smaller mass, its velocity will increase more, resulting in a greater change in linear momentum (p2).

Therefore, the statement "p1 > p2" is true, as the initial linear momentum of object 1 (which is at rest) is less than the final linear momentum of object 2 (which has a greater velocity after the force is applied).

The statements "K1 = K2" and "K1 > K2" are both false, as kinetic energy is not directly related to the mass or velocity of an object.

The statement "K1 < K2" is true, as object 2 will have a greater kinetic energy due to its greater velocity.

The statements "p1 < p2" and "p1 = p2" are both false, as explained earlier.

In summary, the only true statements are "p1 > p2" and "K1 < K2".