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

• amenos42
In summary, the passenger has a mass of 100 kg, and the elevator is moving upward with an acceleration of 30 cm/s2. The force in Newtons exerted on the passenger by the elevator is 3000 N.
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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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.

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

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?

## 1. How do elevators work?

Elevators work by using a motor and pulley system to move a cab up and down a shaft. When the elevator is called, the motor turns the pulley which moves the cab along the guide rails. Once the desired floor is reached, brakes engage to stop the cab in place.

## 2. Why do elevators sometimes get stuck?

Elevators can get stuck due to a variety of reasons, such as mechanical failures, power outages, or weight overloads. In most cases, the elevator's safety mechanisms will prevent it from falling, but it may get stuck between floors until the issue is resolved.

## 3. What should I do if I get stuck in an elevator?

If you get stuck in an elevator, the first thing to do is to remain calm. Press the emergency button or use the intercom to alert someone that you are stuck. Avoid trying to force the doors open or climbing out of the elevator, as this can be dangerous. Wait for help to arrive.

## 4. Can elevators be controlled remotely?

Yes, some elevators have remote control capabilities, allowing building managers or technicians to monitor and control the elevator's functions from a remote location. This can be useful for troubleshooting and maintenance purposes.

## 5. How often do elevators need to be serviced?

Elevators should be serviced at least once a year, but the frequency may vary depending on the elevator's usage and age. Regular maintenance is necessary to ensure the elevator's safety and proper functioning. Building owners should follow the manufacturer's recommended maintenance schedule and address any issues promptly.

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