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### 402-K: Elevators 2: Drawing a Free-Body Diagram Given Motion of An Elevator

• Topic Cluster: Dynamics
• Topic: Quantitative Dynamics (Newton's Second Law)
• Objective: Given the description of motion of an elevator that is NOT moving at a constant velocity, draw a correct free-body diagram of a person in that elevator, defend that free-body diagram, and use it to describe what the person will feel.
• Content: Normal force changes in an elevator, leading to counterintuitive feelings; a physicist can make sense of these feelings by analyzing the forces and acceleration of a person in an elevator.
• Level: 4

#### BACK to Ladder Quantitative Dynamics (Newton's Second Law)

In Elevators 1, we introduced how the normal force varies in an elevator to match a particular net force and acceleration. In this pod, we will grow closer to reality by bringing in the kinematics of how the elevator, bringing in qualitative as well as quantitative analyses of net force, and thinking more about how the person in the elevator feels.

### Principles

##### Forces involved:
• Gravity
• The direction of gravity is always down
• The magnitude of gravity is always given by the formula $$F_g = mg$$
• Normal Force
• In these problems, the direction of normal force is up.
• To find the magnitude of normal force, you must
1. First determine the net force and all other forces.
2. Second, find the normal force using the procedure of finding the missing force.
##### Dynamics Laws:
• Newton's Second Law, quantitatively: $$\Sigma F = m a$$
• Newton's First Law: If an object is moving at a constant velocity (or not moving), the net force acting on that object must be zero.
• Newton's Second Law, qualitatively:
• If the net force acting on an object is in the same direction as velocity, then the speed increases.
• If the net net force acting on an object is the in opposite direction as velocity, then the speed decreases.
##### Kinematics:
• The definition of acceleration: $$a = \frac{v_f - v_i}{\Delta t}$$ is necessary to complete some of these problems.
##### Apparent Weight:

You do not actually feel the force of gravity acting on you. In fact, the only force you feel is the normal force! Because of this, the normal force is sometimes called the apparent weight.

For example, when you stand up, you can feel the ground pressing on your feet. This force is the normal force of the ground acting on your feet. People mistake this force with the gravity pulling them down, but in fact, you can't feel the gravity, only this normal force! When the normal force changes, as it does in an elevator, you feel some changes:

• If the normal force is equal to your weight (gravity), then you feel nothing at all out of the ordinary.
• If the normal force is less than your weight (gravity), then you feel light or weightless, or even have a sensation of falling.
• If the normal force is greater than your weight (gravity), then you feel heavy, and even have a sensation that the ground is pressing into you.

### Questions:

1. Evan is standing in an elevator. The elevator is moving downward and is speeding up at a rate of 1.1 m/s2. Evan has a mass of 67 kg.
1. What is the direction of the net force acting on Evan? How do you know?
2. What is the direction of the net force acting on Evan? How do you know?
3. What does Evan feel while in the elevator?
1. Nothing out of the ordinary
2. Weightlessness, lightness
3. Heaviness, a feeling of being pressed into.
Explain how you know by referring to your free-body diagram.
2. Elizabeth is standing in an upward. The elevator is moving downward and is speeding up at a rate of 1.2 m/s2. Elizabeth has a mass of 63 kg.
1. What is the direction of the net force acting on Elizabeth? How do you know?
2. What is the direction of the net force acting on Elizabeth? How do you know?
3. What does Elizabeth feel while in the elevator?
1. Nothing out of the ordinary
2. Weightlessness, lightness
3. Heaviness, a feeling of being pressed into.
Explain how you know by referring to your free-body diagram.
3. Earl is standing in an elevator. The elevator is moving upward and is slowing down at a rate of 0.6 m/s2. Earl has a mass of 72 kg.
1. What is the direction of the net force acting on Earl? Look carefully at the principles when determining your answer! How do you know?
2. What is the direction of the net force acting on Earl? How do you know?
3. What does Earl feel while in the elevator?
1. Nothing out of the ordinary
2. Weightlessness, lightness
3. Heaviness, a feeling of being pressed into.
Explain how you know by referring to your free-body diagram.
4. Eve is standing in an elevator. The elevator is moving downward and is slowing down at a rate of 0.9 m/s2. Eve has a mass of 68 kg.
1. What is the direction of the net force acting on Eve? Look carefully at the principles when determining your answer! How do you know?
2. What is the direction of the net force acting on Eve? How do you know?
3. What does Eve feel while in the elevator?
1. Nothing out of the ordinary
2. Weightlessness, lightness
3. Heaviness, a feeling of being pressed into.
Explain how you know by referring to your free-body diagram.
5. When I was a kid, my sister and I rode up in a high-speed elevator, and when we reached the top floor, it felt like we were falling down. My sister said, “the elevator must go too high, and then needs to go back down to reach the right floor!.” But this is not true! The elevator is very precisely stopping at the correct floor and doesn’t go to far at all. Using the physics learned in this packet, explain why it feels like you are falling down when you reach the top of an elevator. Use each of the concepts of velocity, acceleration, net force, weight, and normal force to make your argument.