How Do You Calculate Force on a Passenger in an Accelerating Elevator?

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Homework Help Overview

The discussion revolves around calculating the force exerted on a passenger in an accelerating elevator, specifically focusing on a scenario where the elevator accelerates upwards at 30 cm/s². The subject area pertains to dynamics and forces, particularly in the context of Newton's laws of motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the forces acting on the passenger and the acceleration of the elevator. There are attempts to apply Newton's second law and discussions about free body diagrams (FBDs). Questions arise regarding the correct interpretation of forces and the conversion of units from cm/s² to m/s².

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on drawing free body diagrams and clarifying the forces involved. There is a recognition of potential misunderstandings regarding the calculations, particularly in unit conversion and the application of formulas. Multiple interpretations of the problem are being explored, and some participants express uncertainty about their understanding.

Contextual Notes

There is mention of a specific mass for the passenger (100 kg) and the gravitational force acting on them, as well as the need for unit conversion in the acceleration value. Some participants express a lack of confidence in their physics knowledge, which may influence their reasoning.

amenos42
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I need a little help with this problem. I know what the answer is, but not how to get it.

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A passenger in an elevator has a mass of 100 kg. Calculate the force in Newtons exerted on the passenger by the elevator if the elevator is moving upward with an acceleration of 30 cm/s^2.
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Can anyone help me please?
 
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I would first recommend drawing an FBD. If the elevator is accelerating at 30cm/s2, what is the acceleration of the person?
 
The person should have an acceleration of 30 too, since he's inside the elevator. This gives me:

Sum of Forces = mass x acceleration
Sum of Forces = 100 (30)
Sum of Forces = 3000

When you subtract the force from gravity (-980) the normal force acting on the guy from the elevator is 3980 N, which is much too high. (the correct answer is 1010 N)

I could be misunderstanding this, I'm not great at physics.
 
Okay, your on the right lines but not quite there, did you draw a FBD? Let's first look at the forces involved, let the acceleration force be Fa and let vertically upwards be defined as positive; we therefore have;

\sum\vec{F} = F_{a} - mg

Does that make sense?
 
No, I'm sorry, it doesn't. The only formula I've learned so far is "force equals mass times acceleration" Can you show me how you got the other formula?
 
amenos42 said:
No, I'm sorry, it doesn't. The only formula I've learned so far is "force equals mass times acceleration" Can you show me how you got the other formula?
There is no formula required for this, the above step was just summing the forces or finding the net force.
 
Okay, so mg = 100(-9.8) = -980. I'm not sure about the force of acceleration. Is is 30?
 
amenos42 said:
Okay, so mg = 100(-9.8) = -980. I'm not sure about the force of acceleration. Is is 30?
30 cm/s2, you must first convert this to m/s2. So putting our forumale together;

\sum\vec{F} = m\vec{a}

F_{a} - mg = ma

Do you follow?
 
so:
Fa - mg = ma
Fa = ma + mg
Fa = (100)(3) + (100)(-9.8)
Fa = 680

That doesn't seem right.
 
  • #10
Ah. I got it. The problem was the cm - m conversion. Thanks for the help though. My teacher's a psychopath.
 
  • #11
amenos42 said:
Ah. I got it. The problem was the cm - m conversion. Thanks for the help though. My teacher's a psychopath.
No problem. Why do you say your teacher's a psychopath?
 

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