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.
 
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  • #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)?
 

FAQ: Calculating Net Force of 3 Blocks in an Elevator

What is net force and how is it calculated?

Net force is the overall force acting on an object when all the individual forces acting on it are combined. It is calculated by summing up all the forces in a particular direction. If multiple forces are acting in different directions, you need to consider their vector sum. The formula is \( F_{\text{net}} = ma \), where \( m \) is the mass of the object and \( a \) is its acceleration.

How do you determine the forces acting on the blocks in an elevator?

To determine the forces acting on the blocks in an elevator, you need to consider the gravitational force (weight) acting downward and the normal force exerted by the floor of the elevator acting upward. If the elevator is accelerating, you also need to include the pseudo-force due to the acceleration of the elevator. The gravitational force is calculated as \( F_g = mg \), where \( m \) is the mass of the block and \( g \) is the acceleration due to gravity (9.8 m/s²).

How do you calculate the net force if the elevator is accelerating upwards?

If the elevator is accelerating upwards, the net force on each block is the difference between the upward normal force and the downward gravitational force. The formula is \( F_{\text{net}} = m(a + g) \), where \( a \) is the acceleration of the elevator and \( g \) is the acceleration due to gravity. This is because the effective acceleration acting on the blocks is the sum of the elevator's acceleration and gravity.

How do you calculate the net force if the elevator is accelerating downwards?

If the elevator is accelerating downwards, the net force on each block is the difference between the downward gravitational force and the upward normal force. The formula is \( F_{\text{net}} = m(g - a) \), where \( a \) is the acceleration of the elevator and \( g \) is the acceleration due to gravity. This is because the effective acceleration acting on the blocks is the difference between gravity and the elevator's acceleration.

What happens to the net force if the elevator is moving at a constant velocity?

If the elevator is moving at a constant velocity, the acceleration is zero. Therefore, the net force on each block is zero because the forces are balanced. In this case, the normal force is equal to the gravitational force, so \( F_{\text{net}} = 0 \). This means the blocks are in a state of dynamic equilibrium.

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