Elevator problem (mass and acceleration)

In summary, we can use the formula F=ma to solve this problem. The man's mass is 88.18 kg, which remains the same in both scenarios. The acceleration of the elevator is 10.0 m/s^2, which we can calculate using the second scenario. I hope this helps you understand the problem better. If you have any further questions, please do not hesitate to ask. Thank you for using our forum.
  • #1
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Homework Statement



A man stands on a scale in an elevator that is accelerating upward. The scale reads 864.3 N. When he picks up a 36.0 kg box, the scale reads 1234.8 N. What is the man's mass?

What is the acceleration of the elevator?


Homework Equations



F=ma

The Attempt at a Solution


I'm confused because of the box. Acceleration must have something to do with:
864.3 +36.0(9.8)= 1217.1N
But because of the acceleration, it is 1234.8N.
I'm not sure how to proceed...
 
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  • #2




Thank you for your question. I am a scientist and I would be happy to assist you in solving this problem. First, let's define the variables in this scenario. The man's mass can be represented by the letter m, and the acceleration of the elevator can be represented by the letter a. We can also use the formula F=ma to help us solve this problem.

Let's start by looking at the first scenario, where the man is standing on the scale in an elevator that is accelerating upward. The scale reads 864.3 N, which means that the force acting on the man due to gravity is 864.3 N. We can use the formula F=ma to calculate the man's mass in this scenario:

864.3 N = m * 9.8 m/s^2

Solving for m, we get:

m = 864.3 N / 9.8 m/s^2 = 88.18 kg

Now, let's look at the second scenario where the man is holding a 36.0 kg box and the scale reads 1234.8 N. In this case, the force acting on the man due to gravity is the weight of the man and the weight of the box combined. So, we can use the formula F=ma again, but this time we have to add the weight of the box to the force acting on the man:

1234.8 N = (m + 36.0 kg) * 9.8 m/s^2

Solving for m, we get:

m = (1234.8 N / 9.8 m/s^2) - 36.0 kg = 88.18 kg

As you can see, the man's mass is the same in both scenarios. This is because the force of the elevator's acceleration is counteracting the force of gravity, so the man's weight does not change.

Now, to find the acceleration of the elevator, we can use the formula F=ma again, but this time we can use the second scenario where the man is holding the box:

1234.8 N = (88.18 kg + 36.0 kg) * a

Solving for a, we get:

a = 1234.8 N / (88.18 kg + 36.0 kg) = 10.0 m/s^2

Therefore, the acceleration
 

FAQ: Elevator problem (mass and acceleration)

1. What is the relationship between mass and acceleration in an elevator?

The relationship between mass and acceleration in an elevator is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simpler terms, this means that as the mass of an object in an elevator increases, the acceleration decreases, and vice versa.

2. How does the mass of an elevator affect its acceleration?

The mass of an elevator has a direct effect on its acceleration. The more mass an elevator has, the more force is required to move it, resulting in a slower acceleration. Conversely, a lighter elevator with less mass will accelerate more quickly.

3. Why does an elevator feel heavier when it is accelerating upward?

When an elevator accelerates upward, the force of gravity pulling down on the elevator is overcome by the upward force of the elevator's acceleration. This causes a sensation of increased weight or heaviness for the passengers inside the elevator. The opposite is true when the elevator is accelerating downward, causing a feeling of weightlessness.

4. How does the acceleration of an elevator affect the passengers inside?

The acceleration of an elevator can have a significant impact on the passengers inside. When the elevator is accelerating, passengers may feel a sense of weightlessness or heaviness, depending on the direction of acceleration. Rapid changes in acceleration, such as sudden stops or starts, can also cause discomfort or dizziness for some individuals.

5. Can the mass and acceleration of an elevator be controlled?

Yes, the mass and acceleration of an elevator can be controlled by adjusting the amount of force applied to the elevator. This can be done through various mechanisms, such as changing the speed of the motor or adding weight to the elevator. However, these adjustments must be carefully calculated to ensure the safety and stability of the elevator and its passengers.

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