# Springs

I am confused about spring blocks in vertical motion and the energy at each position. Can we go over a spring block when it’s vertical…

Can we please go over this question again^

Hi Enyero,
Let me try to clear this up. First when we look at the system, we can only have energies that exist in that system.

• System #1 - there’s no Earth or Spring included so we can’t have any PEg or PEs in that system. So the only energy in the system is KE
• System #2 - We have the Spring and the Block, so we can have PEs and KE. No Earth so we can’t include PEg
• System #3 - Now we finally have the Earth so we can have PEg and KE. But no spring, so PEs isn’t in the system.

Second if there are any external forces on the system, those can do work and change the total energy of the system.

• System #1 - There are 2 external forces on the system, the weight of the block (mg), and the spring force (Fs). We’re told that the block is moving upwards towards the equilibrium position so Fs > mg and the net force is directed upwards. This is the same direction as the motion of the block, so the work done is positive and adds KE to the system.
• System #2 - There’s 1 external force on the system, the weight of the block (mg). (The spring force is an internal force and can’t change the total energy). The weight is acting downwards on the block and is opposite the direction of motion, so it does negative work on the system and removes energy.
• System #3 - There’s 1 external force acting on the system, the Spring Force (Fs). (The weight is an internal force because it’s acting between the 2 members of the system). Fs is acting upwards, in the same direction as the motion of the block, and does positive work to add KE and PEg into the system.

Hope that helps a bit!

I guess you can think of each system (1, 2, 3) as the object itself. For example, system 1 only the block is the object. In the instance that it is being shot back up, the spring is giving the block energy to move upward, which is why there is an increase in energy.

For system 2, the “object” is the spring and the block. Within the spring and block, energy is constantly being converted from spring PE to kinetic energy. However, gravity is not a part of the object, and therefore taking away some of that spring PE to give to gravity, so gravity is sapping some of that energy from the system, hence why there is a net downward force.

If you understand where I’m going with this for system 3, then that means gravity and the block are one object, and the spring force is the external force. And since the block is being pulled upward, or accelerating upward, the spring is giving energy to the block, and in effect the system as a whole.

Hope that helped.

Thanks Peter and @PinaColada that was very helpful I get it now.

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