Momentum and net external force

[Joe Armas]

Homework Statement

In the picture

Homework Equations

In the picture attached.

The Attempt at a Solution

For the firecracker problem, I believe the only net external force is gravity. Therefore using, Fnet * delta t = delta p. Change in momentum is 12 kg * m/s. Thus, the final momentum of the system is zero. Is this reasoning correct? Please let me know of any errors in my reasoning. Thank you.

 

[Nathanael]

For the firecracker problem, I believe the only net external force is gravity. Therefore using, Fnet * delta t = delta p. Change in momentum is 12 kg * m/s.

Right.

Thus, the final momentum of the system is zero. Is this reasoning correct?

How did you conclude that?

 

[Joe Armas]

Right.How did you conclude that?

The initial momentum of the system is 3kg * -4m/s = -12 kg * m/s. The change in momentum from gravity is 12 as I explained.
Pf = Pi + Delta P
Pf = -12 + 12 = 0

 

[Nathanael]

The initial momentum of the system is 3kg * -4m/s = -12 kg * m/s. The change in momentum from gravity is 12 as I explained.
Pf = Pi + Delta P
Pf = -12 + 12 = 0

By saying "-4 m/s" you have defined a direction for positive and negative.
The magnitude of the change in momentum is 12 kg.m/s, but Δp is a vector; what is it's direction?

 

[Joe Armas]

By saying "-4 m/s" you have defined a direction for positive and negative.
The magnitude of the change in momentum is 12 kg.m/s, but Δp is a vector; what is it's direction?

Gravity then should be negative since it too acts downward. So, delta p should be -30 * 0.4 or -12? So final momentum of system is actually -24 kg * m/s. The bottom piece of mass 2kg must therefore be moving at -14 m/s, since the top piece of mass 1kg is moving at +4m/s, and the sum of these two final momenta must add up to -24 kg * m/s.

 

[Joe Armas]

Is this reasoning correct?

 

[Nathanael]

Yes, it is correct.

 

[Joe Armas]

Yes, it is correct.

I know in part b there is a net external force (gravity) that does positive work, fnet > 0, thus dp/dt is positive. Does the spring in part c increase or decrease the momentum of the system? I am not too sure of my answer.