Question

1.Linear momentum is always conserved

[ ]when kinetic energy is conserved

[ ]when total energy is conserved

[ ]in the absence of internal forces

[ ]in the absence of external forces

2. If two objects collide and there are no other forces acting on them, the momentum of each object will be independently conserved.

[ ]True

[ ]False

3.The momentum of an object is equal to the product of it mass and ______

[ ]Velocity

[ ]Speed

[ ]displacement

[ ]Acceleration

4. Two pucks collide. Puck 1 is moving in the +x-direction and puck 2 is stationary. What is true about the y component of the momenta p₁ and p₂ after the collision.

[ ]p_1y = p_2y

[ ]p_1y = p_2y = 0

[ ]p_1y = -p_2y

[ ]There is no relationship between the y-components of the two pucks after the collision.

5.Two pucks collide. Puck 1 is moving in the +x-direction and puck 2 is stationary. What must be true about the x-component of the momenta p₁ and p₂ after the collision.

[ ]p_1x = 0 and p_2x is equal to the initial momentum of the puck 1

[ ]Both pucks have a positive momentum

[ ]The first puck bounces backwards and the 2nd puck moves in the positive direction

[ ]p_1xf + p_2xf = p_1x
where p_1xf is the momentum of the first puck after the collision,
p_2xf is the momentum of the second puck after the collision and
p_1x  is the momentum of the first puck before the collision

6.Two pucks collide. Puck 1 is moving in the +x-direction and puck 2 is stationary. What might be true about the x-component of the momenta p₁ and p₂ after the collision.

[ ]The first puck bounces backwards and the 2nd puck moves in the positive direction

[ ]Both pucks have a positive momentum

[ ]Both pucks move forward after the collision at different speeds

[ ]p1_x = 0 and p_2x is equal to the initial momentum of the puck 1

7. If the total momentum is conserved then the velocity of the center of mass is ___________?

Answer 1

Answer 2

Answers[] (with explaination)

1.

[d] in the absence of external forces

(Linear momentum is always conserved when there are no external forces acting on a system. This principle is known as the law of conservation of momentum. When the net external force on a system is zero, the total linear momentum of the system remains constant. This applies to both isolated systems (where no external forces are present) and systems where the external forces cancel each other out, resulting in a net force of zero.)

2.
[b] False

(In a collision between two objects, the total momentum of the system is always conserved, but the momentum of each individual object is not necessarily conserved independently. Momentum can be transferred between the objects during the collision. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system.)

3.

[a] Velocity

(The momentum of an object is equal to the product of its mass and velocity. Mathematically, the formula for momentum (p) is:

Momentum (p) = Mass (m) × Velocity (v))

4.

[ d] There is no relationship between the y-components of the two pucks after the collision.

(In the given scenario, both pucks have no initial y-component of momentum since puck 1 is moving only in the +x-direction, and puck 2 is stationary. When they collide, the forces involved are acting in the x-direction (assuming it's a one-dimensional collision along the x-axis), so there won't be any forces or interactions that generate y-component momentum.

Thus, after the collision, both pucks will likely have no y-component of momentum. The y-components of the momenta, p1y, and p2y, would be approximately zero.)

5.

[a] p1x = 0 and p2x is equal to the initial momentum of the puck 1

(In a perfectly elastic collision, when puck 1 (moving in the +x-direction) collides with puck 2 (stationary), puck 1 will come to a complete stop after the collision (p1x = 0), and all its momentum will be transferred to puck 2. Puck 2 will then start moving with the same magnitude of momentum that puck 1 had initially.

So, after the collision:

p1x = 0 (puck 1 comes to a stop in the x-direction).

p2x = Initial momentum of puck 1 (momentum is transferred to puck 2.))

6.

[c] Both pucks move forward after the collision at different speeds

(In an inelastic collision, the two objects involved become entangled or stick together, and kinetic energy is not fully conserved. As a result, both pucks move together at a common velocity after the collision, and their individual momenta are combined into a single momentum for the combined system.

So, the correct statement about the x-component of momenta after the collision is that both pucks move forward after the collision at different speeds.)

7.

If the total momentum is conserved, then the velocity of the center of mass is [constant].

(The center of mass of a system is the point at which the system's mass can be considered to be concentrated. When external forces do not act on the system, the total momentum of the system remains constant. In such a scenario, the center of mass of the system will continue to move at a constant velocity, in accordance with Newton's first law of motion (the law of inertia))