Length a Block on Pulley Moves - (Basic Energy Question)

AI Thread Summary
The discussion revolves around a physics problem involving two connected masses and their energy dynamics. The 6-kg mass is initially moving upwards while the 4-kg mass descends, both at 2 m/s. Participants clarify that despite both blocks moving at the same speed, there is acceleration involved, and energy conservation principles should be applied to solve for how far the 6-kg mass rises before stopping. The initial kinetic and potential energies of both blocks are calculated, but confusion arises regarding the forces acting on the blocks and the final energy states. Ultimately, it is emphasized that energy considerations alone are sufficient to solve the problem without needing to analyze internal forces or free body diagrams.
Alyssa Eiger
Messages
7
Reaction score
2

Homework Statement



Two masses are connected by a string that is passed over a massless pulley. At t=0, the 6-kg mass is moving upwards at 2m/s, while the 4-kg mass is descending at the same speed.

How far will the 6-kg mass rise before it stops?

Homework Equations



KE= 1/2*m*v^2
PEg: m*g*h

The Attempt at a Solution


- I considered the entire system (both blocks) as the system, with no external forces acting - only gravity is at play.
- Same speed is mentioned, so there is no acceleration.
- The tension between the two blocks is the same, as the string is massless.
- I determined that initially: there is KE and PEg - and final state only has PEg. I set both equal to each other, (as indicated on the attached photo tweet), but am having a difficult time determining next-steps.

Any input is appreciated.
1001147259503890432
 
  • Like
Likes M. M. Fahad Joy
Physics news on Phys.org
Alyssa Eiger said:
Same speed is mentioned, so there is no acceleration.
This is not correct. The blocks having the same speed does not mean that they cannot change speed.
Alyssa Eiger said:
I determined that initially: there is KE and PEg - and final state only has PEg. I set both equal to each other, (as indicated on the attached photo tweet), but am having a difficult time determining next-steps.
Please post your work in text.
 
They will be traveling at the same rate, for any given time, but there will be acceleration. I would draw a Free Body Diagram for each block, then do as you said by setting the magnitude of the tensions equal (and the magnitudes of the velocities equal).
 
You could call the location of the 6 kg block (at time 0) to be location zero, so the potential energy of that block is zero there. You could also set the smaller block up to have zero PE at a certain point to maybe help your calculations.
 
@scottdave @Orodruin - thank you for your invaluable input.

Initial States:
6KG Block: If I set the 6-kg block at t=0 to be location zero, with a potential energy of zero - then all my energy at that point in time for the block is KE (1/2*6kg*4m/s) = 12 Joules.

4KG Block: At the initial point t=0, there is both KE and PEg. KE is: (1/2)(4kg)(4m/s) = 8 Joules. There is also PEg: (4kg)(10m/s)(h) which is equal to 4 Joules (the difference between 12J-8J). If PEg = 4Joules, then: 4J = (4kg)(10m/s)(h). Height = .1m

Final States:
6KG Block: When the block comes to rest - the only energy acting is PEg - also at 12 J.
4KG Block: When the block comes to rest - the only energy acting is PEg - also at 12 J.Photo of my FBD: https://twitter.com/wrongedauthor/status/1001152490635644929

I also don't quite understand how the FBD is possible, if the 6KG block is moving UP - the force of the tension on the strong has to be greater than 60N - but that is the same value of tension on the 4KG block, which is larger than the Weight of the Earth on the block (40N) - which indicates there's no way the 4kg block could move down.

The back of the book reports the answers is 1M, but all my calculations have either reflected .2M or .1M. This is my first physics course.
 
Alyssa Eiger said:
6KG Block: When the block comes to rest - the only energy acting is PEg - also at 12 J.
4KG Block: When the block comes to rest - the only energy acting is PEg - also at 12 J.
There is no reason to assume that each block has the same total energy as it had before. The blocks by themselves do not form a closed systen.

Alyssa Eiger said:
I also don't quite understand how the FBD is possible, if the 6KG block is moving UP - the force of the tension on the strong has to be greater than 60N
This is not correct. The tension can be lower than 60 N while it moves up. All this tells you is that the acceleration is in the opposite direction compared to the velocity - which it must be to eventually stop!

Anyway, energy considerations should be sufficient. There is no reason to start considering the internal forces and drawing FBDs.
 
  • Like
Likes M. M. Fahad Joy
Orodruin said:
...Anyway, energy considerations should be sufficient. There is no reason to start considering the internal forces and drawing FBDs.
Yes I agree, after rereading the problem.
 
Back
Top