Elevator Physics Problem - Normal Force on a Scale & Apparent Weight
TLDRThis video script delves into the physics of elevator problems, focusing on the concept of weight and normal force. It explains that a scale inside an elevator reads the normal force, which can vary if the elevator is moving. The weight of an 80 kg person is calculated as 784 newtons, and it's shown that at rest or constant speed, the scale reads the true weight. However, during acceleration or deceleration, the scale detects changes in apparent weight, which is when passengers feel heavier or lighter. The video also touches on the sensation of free fall, akin to being in space, where the normal force is zero and the scale would not register any weight.
Takeaways
- 📈 When an elevator is at rest or moving at a constant speed, the scale reads the true weight of the person, which is the product of mass and gravitational acceleration (mg).
- 🔄 The apparent weight detected by the scale changes when the elevator is accelerating, either upward or downward, affecting the normal force exerted on the person.
- ⏳ At rest or constant speed, the normal force equals the gravitational force (mg), and the scale reads the actual weight of the person.
- 🚀 When the elevator accelerates upward, the scale reads a weight greater than the person's natural weight due to the additional acceleration factor.
- 📉 Conversely, when the elevator accelerates downward, the scale reads a weight less than the person's natural weight because of the reduced acceleration component.
- 💺 The discomfort felt in an elevator is due to the changes in acceleration, not constant speed motion. This sensation is experienced during the initial acceleration and deceleration phases.
- 🌌 In free fall, both the person and the elevator fall at the same rate, resulting in no contact between the person and the scale, and thus the normal force, and the scale reading, become zero.
- 🤸♂️ The sensation of weightlessness during free fall is akin to floating in space, as experienced by astronauts, where there is no net acceleration detected by the body.
- 📚 Newton's second law (F=ma) is fundamental in understanding the relationship between forces, mass, and acceleration in the context of the elevator problem.
- 🔢 The weight of the 80 kg person is 784 newtons (80 kg * 9.8 m/s²), which is the baseline weight the scale would read under normal conditions.
- 🔄 Understanding the concept of apparent weight and how it varies with the elevator's motion is crucial for solving problems involving scales inside elevators.
Q & A
What is the weight of the 80 kg man in newtons?
-The weight of the 80 kg man is 784 newtons, calculated as 80 kg multiplied by the acceleration due to gravity (9.8 m/s^2).
What force does the scale read when the elevator is at rest?
-When the elevator is at rest, the scale reads the true weight force, which is the normal force equal to the person's weight (784 newtons).
Does the scale read the same weight when the elevator moves at a constant speed, either upward or downward?
-Yes, when the elevator moves at a constant speed, whether upward or downward, the scale reads the same weight of 784 newtons, which is the person's true weight.
What happens to the apparent weight when the elevator accelerates upward?
-When the elevator accelerates upward, the apparent weight increases because the scale detects a force greater than the person's natural weight due to the additional acceleration force.
What happens to the apparent weight when the elevator accelerates downward?
-When the elevator accelerates downward, the apparent weight decreases because the scale detects a force less than the person's natural weight due to the negative acceleration force.
What is the formula for calculating the normal force in the y direction?
-The normal force in the y direction can be calculated using the formula: Normal Force = mass (m) times the sum of gravitational acceleration (g) and the acceleration in the y direction (a_y).
What is the normal force when the elevator accelerates upward with an acceleration of 3 m/s^2?
-When the elevator accelerates upward with an acceleration of 3 m/s^2, the normal force is 80 kg multiplied by the sum of 9.8 m/s^2 (gravitational acceleration) and 3 m/s^2 (upward acceleration), which equals 1,024 newtons.
What is the normal force when the elevator accelerates downward with an acceleration of 4 m/s^2?
-When the elevator accelerates downward with an acceleration of 4 m/s^2, the normal force is 80 kg multiplied by the difference of 9.8 m/s^2 (gravitational acceleration) and 4 m/s^2 (downward acceleration), which equals 464 newtons.
What would happen to the scale reading if the elevator cable snaps and the elevator is in free fall?
-If the elevator cable snaps and the elevator is in free fall, the scale reading will be zero because there is no normal force exerted on the person as they are in a state of weightlessness, both the person and the elevator are falling at the same rate.
Why do we feel weightless in a free-falling elevator?
-We feel weightless in a free-falling elevator because both the person and the elevator are accelerating downward at the same rate due to gravity, resulting in no relative acceleration between them, and thus no normal force is exerted on the person by the elevator floor or scale.
How does the sensation of weight in an elevator relate to the sensation of weightlessness in space?
-The sensation of weight in an accelerating elevator and the sensation of weightlessness in space are similar because in both cases, there is no effective normal force acting on the person. In a free-falling elevator, the person and the elevator are falling at the same rate, and in space, an astronaut is continuously falling towards Earth without feeling the gravitational pull due to the lack of resistance or contact with a surface.
Outlines
📈 Understanding Elevator and Weight Forces
This paragraph introduces the concept of solving elevator problems, specifically focusing on the forces involved when an 80 kg man stands on a scale inside an elevator. It explains the weight force exerted by the person and the normal force exerted by the scale. The key point is that the scale reads the normal force, which can fluctuate based on the elevator's movement. The paragraph establishes that at rest, the scale reads the true weight force and provides a formula to calculate the normal force based on the person's mass, gravitational acceleration, and the elevator's acceleration.
🏃 Constant Speed Movement and Elevator Scale Readings
This section discusses the behavior of the elevator scale when the elevator moves at a constant speed, either upward or downward. It clarifies that during constant speed movement, the acceleration is zero, and thus the scale reads the same weight force of 784 newtons, which is the person's actual weight. The paragraph emphasizes that regardless of the direction of constant speed movement, the scale will always read the original weight, as there is no acceleration to change the normal force.
🚀 Acceleration and the Feeling of Weight
The paragraph explores the effects of acceleration on the scale readings and the person's sensation of weight. It explains that during acceleration, whether upward or downward, the scale detects a change in the normal force, leading to a change in the apparent weight. The paragraph uses the example of traveling to the Empire State Building to illustrate when passengers feel the change in weight due to acceleration and deceleration. It concludes with a discussion on free fall, explaining that if the elevator cable snaps, the person would feel weightless as they and the elevator fall at the same rate, and the scale would read zero normal force.
Mindmap
Keywords
💡Elevator
💡Weight Force
💡Normal Force
💡Free Body Diagram
💡Acceleration
💡Newton's Second Law
💡Apparent Weight
💡Constant Speed
💡Free Fall
💡Scale
💡Deceleration
Highlights
The problem focuses on solving elevator scenarios involving a man weighing 80 kg standing on a scale inside the elevator.
When the elevator is at rest, the scale reads the weight force, which is the normal force.
A free body diagram is used to illustrate the weight force and the normal force acting on the person.
The normal force can fluctuate based on the elevator's movement, but at rest, it equals the weight force.
An expression is derived to calculate the normal force: Normal Force = m(g + ay), where m is mass, g is gravitational acceleration, and ay is the acceleration in the y-direction.
The weight of the 80 kg person is calculated to be 784 newtons (80 kg * 9.8 m/s^2).
When the elevator moves at a constant speed, the scale reads the same weight (784 newtons) regardless of the direction of movement.
During acceleration or deceleration, the scale detects changes in the normal force, leading to a change in the apparent weight.
The discomfort in an elevator is felt during the initial acceleration or deceleration, not during constant speed movement.
When the elevator accelerates upward, the scale reads a weight greater than the person's natural weight.
Conversely, when the elevator accelerates downward, the scale reads a weight less than the person's natural weight.
In the event of the elevator cable snapping and the elevator in free fall, the scale will not read the person's weight as there is no contact between the person and the scale.
The sensation of weightlessness during free fall is akin to floating in space, as experienced by astronauts.
The video aims to provide a comprehensive understanding of how an elevator's movement affects the reading of a scale.
The content is engaging and educational, offering practical insights into the physics of everyday experiences.
The video concludes by encouraging viewers to explore more content on the channel for further learning.
Transcripts
5.0 / 5 (0 votes)
Thanks for rating: