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

[amenos42]

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?

 

[Hootenanny]

I would first recommend drawing an FBD. If the elevator is accelerating at 30cm/s², what is the acceleration of the person?

 

[amenos42]

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.

 

[Hootenanny]

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 F_a and let vertically upwards be defined as positive; we therefore have;

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

Does that make sense?

 

[amenos42]

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?

 

[Hootenanny]

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.

 

[amenos42]

Okay, so mg = 100(-9.8) = -980. I'm not sure about the force of acceleration. Is is 30?

 

[Hootenanny]

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?

 

[amenos42]

so:
Fa - mg = ma
Fa = ma + mg
Fa = (100)(3) + (100)(-9.8)
Fa = 680

That doesn't seem right.

 

[amenos42]

Ah. I got it. The problem was the cm - m conversion. Thanks for the help though. My teacher's a psychopath.

 

[Hootenanny]

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?