Calculating Net Force of 3 Blocks in an Elevator

In summary, the conversation discusses the calculation of net force and displacement for three blocks with different masses and a spring with a spring constant of 327 N/m. The elevator they are in is accelerating upwards at 3.8 m/s^2. It is determined that treating the three blocks as a system and using Newton's second law can help solve the problem. However, when calculating the stretch of the middle spring, there may be a discrepancy between the answer obtained and the answer expected by the website used. Further clarification or adjustments may be needed to solve this issue.
  • #1
Hippo89
4
2
Homework Statement
What is the distance the upper spring is streched?
Relevant Equations
Fnet = ma
791DE92B-F813-4C2A-8F82-0D7BBED33B20.jpeg

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.
 
Physics news on Phys.org
  • #2
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?
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 
  • #6
I get the same answer as you to two sig figs.
 
  • Like
Likes erobz
  • #7
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.
 
  • #8
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.
 
  • #9
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)?
 

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
6
Views
955
  • Introductory Physics Homework Help
Replies
4
Views
770
  • Introductory Physics Homework Help
Replies
7
Views
577
  • Introductory Physics Homework Help
Replies
14
Views
1K
  • Introductory Physics Homework Help
Replies
24
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
2K
Back
Top