Understanding Work, Energy, and Displacement in a Spring System

[Joe Armas]

Homework Statement

In the pictures.

Homework Equations

KE = 1/2mv^2.
PE = 1/2kx^2
Work external = Delta KE + Delta PE
W = F* d

The Attempt at a Solution

In the pictures.Comments:

On Problem 3 ai, I am not sure whether I have identified the correct horizontal forces. The hint gave two, but I believe there could also be a force that the wall exerts on the spring.

I am also not sure which way the force points when a spring is stretched and extended. I believe it is in the direction of the equilibrium unextended position. Please let me know if my answers/reasoning is correct. Thank you.

 

[haruspex]

On Problem 3 ai, I am not sure whether I have identified the correct horizontal forces. The hint gave two, but I believe there could also be a force that the wall exerts on the spring.

They want you to identify the forces acting on the SB system from outside that system. Is the force between spring and block such a force?

 

[NascentOxygen]

Bear in mind that forces always occur in pairs: an action and an equal and opposite reaction. You can't exert a force on anything if it doesn't push back.

 

[Joe Armas]

I see, so the force on the spring by the block is equal and opposite to the force by the block on the spring?. So is what I have for 3 a i correct?

 

[Joe Armas]

They want you to identify the forces acting on the SB system from outside that system. Is the force between spring and block such a force?

No, correct? The only force that I can see is the wall.

 

[haruspex]

No, correct? The only force that I can see is the wall.

That's right, the external forces are from string and wall.

 

[Joe Armas]

That's right, the external forces are from string and wall.

The wall does zero work while the String does positive work right? Since displacement and force is in the same direction?

 

[haruspex]

The wall does zero work while the String does positive work right? Since displacement and force is in the same direction?

Yes.

 

[Joe Armas]

Yes.

Ok thanks for the help. Do you see any discrepancies on the back side?

 

[haruspex]

Ok thanks for the help. Do you see any discrepancies on the back side?

Have another think about a iv. This is the work done by external forces on SB.

 

[Joe Armas]

It should be positive right? The string does positive work while work does negative work. But why is the work net external not equal to delta potential energy here?

 

[Joe Armas]

Have another think about a iv. This is the work done by external forces on SB.

What situations can we use conservation of energy for net external work?

 

[haruspex]

What situations can we use conservation of energy for net external work?

No, I'm suggesting you need to distinguish between work done on a system and and work done by a system. They have opposite signs.

 

[Joe Armas]

The system gains potential energy because the spring is stretched. Isn't Wnet external equal to - delta PE? So it would be indeed be negative? That was my reasoning and it makes sense.

 

[lightgrav]

system gains PE because spring is stretched (spring PE is always positive, like KE is always positive).
but no, Wnet,external (positive) is where that Energy comes from that is stored in the spring as PE (positive).

 

[haruspex]

The system gains potential energy because the spring is stretched. Isn't Wnet external equal to - delta PE? So it would be indeed be negative? That was my reasoning and it makes sense.

Work done on the system equals gain of work by the system. Both positive in this case.