Calculating Net Force of 3 Blocks in an Elevator

AI Thread Summary
The discussion focuses on calculating the net force acting on three blocks in an elevator accelerating upwards at 3.8 m/s². The net force for the system is derived from the force of the upper spring minus the weight of all three blocks, leading to a downward displacement of 1 meter. There is confusion regarding the calculation for the middle spring, where the downward displacement was calculated as 0.83 meters, which was deemed incorrect. Participants suggest that the website used for verification may not provide the correct answer, and clarification is sought on whether the question refers to the stretch of the middle spring or its downward displacement. The conversation emphasizes the importance of correctly identifying forces acting on the system and applying Newton's second law accurately.
Hippo89
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Homework Statement
What is the distance the upper spring is streched?
Relevant Equations
Fnet = ma
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m1 = 4 kg, m2 = 12 kg, m3 = 8 kg. k = 327 N/m for all three blocks. The elevator accelerates upwards at 3.8 m/s^2.

Net force of block one would be equal to force applied by top spring minus weight of system, since top spring is holding all 3 blocks.
F1 = 4*3.8= Fs,top - Wsystem = Fs,top - 24*9.8. Fs,top = 250.4 N = -327x. x = -.76 m displacement

The correct answer is -1 m.
 
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The force acting downward on block m1 is not the weight of all three blocks. The weight of block m1 acts downward on block m1. There is one other force that acts downward on block m1. Can you identify this other force?
 
Here is another way to look at it. We are assuming that the three masses accelerate as one, i.e. they have the same acceleration at all times.

What if you took the three blocks together as your system?
What is the net force on the three-mass system?
What forces acting on the three-mass system are external to it and contribute to the net force?
What does Newton's second law say about all this?
 
kuruman said:
Here is another way to look at it. We are assuming that the three masses accelerate as one, i.e. they have the same acceleration at all times.

What if you took the three blocks together as your system?
What is the net force on the three-mass system?
What forces acting on the three-mass system are external to it and contribute to the net force?
What does Newton's second law say about all this?
Okay. I treated the system as all 3 blocks accelerating together at 3.8 m/s^2, since the top spring is carrying all three blocks.
Fnet,system = (m, system)(a) = Force of upper spring - Weight of all three blocks.
With these calculations I got a downwards displacement of 1 meter, which is the correct answer.

There was another question in this set of problems. Under these conditions, what is the distance the middle spring is streched?

I used the same logic that helped me answer the original question. I defined the blocks the spring was carrying as the system, which for the middle spring, would be blocks 2 and 3.
Fnet, system = (m2+m3)(a) = Force of middle spring - Weight of blocks 2 and 3.
With these calculations, I got a downwards displacement of 0.83 m, which apparently is the wrong answer.

What am I missing for this other question?
 
Hippo89 said:
I used the same logic that helped me answer the original question. I defined the blocks the spring was carrying as the system, which for the middle spring, would be blocks 2 and 3.
Fnet, system = (m2+m3)(a) = Force of middle spring - Weight of blocks 2 and 3.
With these calculations, I got a downwards displacement of 0.83 m, which apparently is the wrong answer.

What am I missing for this other question?
What is apparently the correct answer?
 
I get the same answer as you to two sig figs.
 
erobz said:
What is apparently the correct answer?
The website I’m using, Flipit, only states if you got the right or wrong answer. So I don’t know the correct answer.
 
Hippo89 said:
The website I’m using, Flipit, only states if you got the right or wrong answer. So I don’t know the correct answer.
I think, "we" ( @kuruman and I ) think the website is incorrect.
 
Try using an additional sig fig. if that doesn't work, ask you instructor to show you what's wrong with your answer.
 
  • #10
Hippo89 said:
what is the distance the middle spring is streched?

Hippo89 said:
I got a downwards displacement of
Just to be clear, which does the question ask for, the stretch of the middle spring or its downward displacement (which would be somewhat ambiguous)?
 
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