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Chapter 3: Problem 53

You are riding along on your bicycle at \(20 \mathrm{km} / \mathrm{h}\) and eating an apple. You pass a bystander. a. How fast is the apple moving in your frame of reference? b. How fast is the apple moving in the bystander's frame of reference? c. Whose perspective is more valid?

Short Answer

Expert verified
a. 0 km/hb. 20 km/hc. Both perspectives are valid.

Step by step solution

01

Define the Frame of Reference

A frame of reference is a point of view from which measurements are taken. Here, we'll consider two frames of reference: one from the perspective of the rider and one from the perspective of the bystander.
02

Speed of the Apple in Rider's Frame of Reference

In the rider's frame of reference, the apple is at rest relative to the rider. Therefore, the velocity of the apple as seen by the rider is the same as the rider’s speed relative to the apple. Hence, the velocity is 0 km/h.
03

Speed of the Apple in Bystander's Frame of Reference

In the bystander's frame of reference, both the rider and the apple are moving together at the same speed. So, the velocity of the apple relative to the bystander is the same as the rider’s speed, which is 20 km/h.
04

Validity of Perspectives

Both perspectives are equally valid within their own frames of reference. There is no objective measure that makes one perspective more correct than the other—they are simply different points of view.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

relative velocity
Relative velocity is a way to understand how different observers perceive the speed of an object in motion. Imagine two people, one standing still and another moving on a bike. The observer who is moving would have a different perspective on the speed of an apple they’re holding, compared to the observer who is stationary. To find the relative velocity, we compare the speed of the moving object (apple) from both the rider’s point of view and the bystander’s point of view.

In this context, the calculation becomes simple.
  • From the rider’s frame of reference, the apple is at rest because it moves along with the rider. Thus, its relative velocity is 0 km/h.
  • From the bystander's frame of reference, the apple moves along with the rider. Hence, its relative velocity is 20 km/h, the same as the rider's speed.
perspective in physics
Perspective in physics deals with understanding how different observers see the same event differently, based on their position and motion. When you're riding a bike and holding an apple, from your perspective, the apple isn’t moving. However, for someone standing on the sidewalk, the apple moves with you at your bike’s speed. Both perspectives are equally correct because they rely on different frames of reference.

Here’s what makes perspectives significant in physics:
  • They help us understand relative motion without needing to find an absolute state of rest or movement.
  • They are crucial in many areas of physics, including mechanics and relativity.

Recognizing that both perspectives are valid reminds us that motion is relative and can only be described correctly within a given frame of reference.
frames of reference in motion
Frames of reference in motion help us describe the motion of objects as seen by different observers. A frame of reference can be stationary or in motion.

Here’s a simple way to think about it:
  • If you're riding a bicycle, your frame of reference moves with you. The apple you're holding appears to stand still because both you and the apple share the same velocity.
  • For a bystander who is not moving, their frame of reference is stationary. They see both you and the apple moving at the same speed.

This concept is important because it allows us to analyze and understand physical phenomena from multiple viewpoints. Whether an object is at rest, in motion, or how fast it’s moving can change based on the chosen frame of reference.

Use the concept of frames of reference to solve problems in physics by identifying the observer’s position and their velocity relative to the moving object. This makes it easier to calculate the relative velocities accurately.

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Most popular questions from this chapter

Suppose you watch a car sliding on ice down a hill. As it slides, it slowly drifts to your right across the road, speeding up in that direction until it bumps into the curb. In this situation, which of the following is more likely, and why? a. The car was already traveling diagonally across the street before it hit the patch of ice. b. The road surface is rounded (or "crowned"), causing the car to be pushed across the street.

For Earth, \(P^{2} / A^{3}=1.0\) (in appropriate units). Suppose a new dwarf planet is discovered that is 14 times as far from the Sun as Earth is. For this planet, a. \(P^{2} / A^{3}=1.0\) b. \(P^{2} / A^{3}>1.0\) c. \(P^{2} / A^{3}<1.0\) d. you can't know the value of \(P^{2} / A^{3}\) without more information.

Go to the online "Extrasolar Planets Encyclopedia" (http://exoplanet.eu/catalog-all.php), and find a planet with an orbital period similar to that of Earth. What is the semimajor axis of its orbit? If it is very different from 1 AU, then the mass of the star is different from that of the Sun. Click on the star name in the first column to see the star's mass. What is the orbital eccentricity? Now select a star with multiple planets. Verify that Kepler's third law applies by showing that the value of \(P^{2} / A^{3}\) is about the same for each of the planets of this star. How eccentric are the orbits of the multiple planets?

Galileo observed that Venus had phases that correlated with its size in his telescope. From this information, you may conclude that Venus a. is the center of the Solar System. b. orbits the Sun. c. orbits Earth. d. orbits the Moon.

When riding in a car, we can sense changes in speed or direction through the forces that the car applies on us. Do we wear seat belts in cars and airplanes to protect us from speed or from acceleration? Explain your answer.
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