Elevator Problem: Max Mass Calculation (10kN, 2m/s2)

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In summary, to determine the maximum mass of the elevator and participants, we can use Newton's 2nd law, F_net = ma, where F_net is the net force acting on the elevator and participants, and a is the maximum acceleration of 2m/s2. The elevator cable can hold a maximum of 10kN, which is the known force. By solving for m, we can determine the maximum mass. The correct answer is A. 1050kg.
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Homework Statement



An elevator cable can hold a maximum of 10kN and has a maximum accelleration of 2m/s2. Determine the maximum mass of the elevator and participants.


i need some help, can't figure this out at all. thanks in advance
 
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  • #2
The obvious thing here is to use F = ma
You know F and you know a... find m.
If you get stuck get back to me
 
  • #3
I tryed putting them just straight in but that does not work.

I forgot to put the multiple choice, it might help

A. 1050kg
B. 1280kg
C. 0.8466kg
D. 1.28kg
E. 890kg
F. 10009.81kg
G. 846.74kg
H. 9.901kg
I. 650kg
 
  • #4
Identify the magnitude and direction of the forces acting on the elevator, both known and unknown. There are 2 forces acting in the vertical direction. Find the net force, and use Newton's 2nd law, F_net = ma.
 
  • #5


I can provide you with a solution to this elevator problem. The maximum mass that the elevator and its participants can have is determined by the maximum force that the cable can withstand and the maximum acceleration that the elevator can have.

To calculate the maximum mass, we can use the formula F=ma, where F is the force, m is the mass, and a is the acceleration. Since we know the force (10kN) and acceleration (2m/s2), we can rearrange the formula to solve for the mass.

m = F/a

Substituting the values, we get:

m = 10,000 N / 2 m/s2 = 5000 kg

Therefore, the maximum mass of the elevator and its participants should not exceed 5000 kg (or 5 metric tons) in order to stay within the safe limits set by the maximum force and acceleration. I hope this helps with your homework. Good luck!
 

1. What is the maximum mass that an elevator can safely carry?

The maximum mass that an elevator can safely carry depends on a few factors, including the maximum load capacity of the elevator and the acceleration rate of the elevator. In the given scenario, the maximum mass that the elevator can safely carry is 10,000 Newtons (or approximately 1,020 kilograms).

2. How is the maximum mass of an elevator calculated?

The maximum mass of an elevator is calculated using the formula M = F/a, where M is the maximum mass, F is the maximum force (in this case, 10,000 Newtons), and a is the acceleration rate (in this case, 2 meters per second squared). This formula is derived from Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.

3. What is the significance of the acceleration rate in determining the maximum mass of an elevator?

The acceleration rate is a crucial factor in determining the maximum mass of an elevator because it affects the amount of force that is exerted on the elevator. The higher the acceleration rate, the more force is exerted on the elevator, and therefore, the lower the maximum mass it can safely carry.

4. Can an elevator safely carry more mass if it has a slower acceleration rate?

Yes, an elevator can safely carry more mass if it has a slower acceleration rate. This is because a slower acceleration rate means less force is exerted on the elevator, allowing it to carry a greater maximum mass.

5. Are there any other factors that can affect the maximum mass of an elevator?

Yes, there are other factors that can affect the maximum mass of an elevator, such as the structural strength of the elevator, the weight and distribution of the mass within the elevator, and any external forces acting on the elevator (such as wind or turbulence). It is important for elevator engineers to consider all of these factors when determining the maximum mass that an elevator can safely carry.

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