. A child hangs onto the edge of a merry-go-round that is spinning at 30 rpm. a) In your own words, explain the difference between an inertial and a non-inertial frame of reference. b) From the inertial frame of reference of the Earth, what is happening to the child on the merry go-round? From the non-inertial frame of reference of the merry-go-round, what is happening to the child?
. A child hangs onto the edge of a merry-go-round that is spinning at 30 rpm. a) In your own words, explain the difference between an inertial and a non-inertial frame of reference. b) From the inertial frame of reference of the Earth, what is happening to the child on the merry go-round? From the non-inertial frame of reference of the merry-go-round, what is happening to the child?
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1. A child hangs onto the edge of a merry-go-round that is spinning at 30 rpm.
a) In your own words, explain the difference between an inertial and a non-inertial frame of reference.
b) From the inertial frame of reference of the Earth, what is happening to the child on the merry go-round? From the non-inertial frame of reference of the merry-go-round, what is happening to the child?
2. A mass attached to a spring and allowed to oscillate horizontally on a tabletop is subject to both the restoring force of the spring and the force of friction
a) Which of these forces does work they do work, is always positive, always negative, or the sign vary ?
b) An energy is defined for only one of these two forces. Which is it, and why?
3. a) Compare and contrast elastic and inelastic collisions.
b) Another car rear-ends your car while it is stopped at a stoplight; the two cars stick together due to their mangled bumpers and move off as one . Is this collision closer to being elastic or inelastic? Why?
4. A rocket scientist must design a rocket such that it can deliver a satellite to near-Earth orbit from Earth's surface.
a) To overcome the effects of gravity and drag, the scientist needs the rocket to have as large of an acceleration as possible. Identify two ways that the rocket's acceleration can be maximized.
b) The scientist may need to design the rocket so that it has multiple stages. What is the benefit of a multi- stage rocket compared to a single stage rocket?
5. Picture 1
6. Picture 2
![**The image below presents a greatly exaggerated view of a planet in orbit around the Sun:**
**[Image Description]**
The diagram shows a planet in an elliptical orbit around the Sun. Key elements in the diagram include:
- The Sun is located at one of the foci of the ellipse, labeled as \( f_1 \), with the symbol of the Sun and its rays depicted around it.
- The planet, labeled as "Planet" with a mass \( m \), is shown at one position in its orbit.
- The variable \( r \) denotes the distance between the planet and the Sun.
- \( M \) denotes the mass of the Sun.
- A second focus point of the ellipse is labeled as \( f_2 \).
**The shape of the above orbit is an ellipse; this is in accordance with Kepler's first law of planetary motion.**
**Questions:**
a) In your own words, state Kepler's second law of planetary motion. How does this law arise from conservation of energy?
b) Again in your own words, state Kepler's third law of planetary motion, then explain how this law is derived from the laws that Newton developed.
---
**Answer Key:**
a) **Kepler's Second Law of Planetary Motion:** Kepler's second law states that the line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun. This arises from the conservation of angular momentum, which states that the product of the distance of the planet from the Sun and its velocity remains constant if no external torque acts on the system.
b) **Kepler's Third Law of Planetary Motion:** Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Mathematically, \( T^2 \propto a^3 \), where \( T \) is the orbital period and \( a \) is the semi-major axis of the ellipse. This law is derived from Newton's law of universal gravitation, which explains that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton further showed that the same force governs the motion of all celestial bodies, leading to the relationship described in Kepler's third law.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6094c4bd-a020-481f-869e-f65291d4ed64%2F329d4021-ed2e-4800-b402-87276d62e1cf%2Fympfze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**The image below presents a greatly exaggerated view of a planet in orbit around the Sun:**
**[Image Description]**
The diagram shows a planet in an elliptical orbit around the Sun. Key elements in the diagram include:
- The Sun is located at one of the foci of the ellipse, labeled as \( f_1 \), with the symbol of the Sun and its rays depicted around it.
- The planet, labeled as "Planet" with a mass \( m \), is shown at one position in its orbit.
- The variable \( r \) denotes the distance between the planet and the Sun.
- \( M \) denotes the mass of the Sun.
- A second focus point of the ellipse is labeled as \( f_2 \).
**The shape of the above orbit is an ellipse; this is in accordance with Kepler's first law of planetary motion.**
**Questions:**
a) In your own words, state Kepler's second law of planetary motion. How does this law arise from conservation of energy?
b) Again in your own words, state Kepler's third law of planetary motion, then explain how this law is derived from the laws that Newton developed.
---
**Answer Key:**
a) **Kepler's Second Law of Planetary Motion:** Kepler's second law states that the line joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun and slower when it is farther from the Sun. This arises from the conservation of angular momentum, which states that the product of the distance of the planet from the Sun and its velocity remains constant if no external torque acts on the system.
b) **Kepler's Third Law of Planetary Motion:** Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Mathematically, \( T^2 \propto a^3 \), where \( T \) is the orbital period and \( a \) is the semi-major axis of the ellipse. This law is derived from Newton's law of universal gravitation, which explains that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton further showed that the same force governs the motion of all celestial bodies, leading to the relationship described in Kepler's third law.
---
**a) Assuming the slide surfaces are slick enough to be considered frictionless, identify the forms of energy a child would have and how they are changed while going down either slide.**
When a child is at the top of either slide, they possess **potential energy** due to their elevated position relative to the ground. Potential energy is dependent on the height of the slide and the child’s mass. As the child begins to slide down, the potential energy is converted into **kinetic energy**, which is the energy of motion. By the time the child reaches the bottom of the slide, almost all the initial potential energy has been converted to kinetic energy, making the child move fastest at this point.
**b) Would a child be going faster at the bottom of the red or yellow slide, and why?**
Considering that the surfaces are frictionless and assuming the yellow slide is taller than the red slide, a child would be going faster at the bottom of the yellow slide. This is due to the fact that the yellow slide, being taller, provides greater potential energy at the top. As the child slides down, the greater initial potential energy is converted into more kinetic energy, resulting in a higher speed at the bottom compared to the red slide.
---
### Diagram Description:
The image shows two playground slides side-by-side. The slide on the left is red and shorter, whereas the slide on the right is yellow and taller. Both slides are part of a playground structure set against a background of trees and pavement.
### Key Concepts:
- **Potential Energy (PE):** Energy stored due to position, PE = mgh (mass x gravitational constant x height)
- **Kinetic Energy (KE):** Energy of motion, KE = 1/2 mv² (1/2 x mass x velocity squared)
- **Energy Transformation:** Potential energy transforms into kinetic energy as the child slides down.
This visual and these explanations help illustrate the principles of energy transformation in a playground setting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6094c4bd-a020-481f-869e-f65291d4ed64%2F329d4021-ed2e-4800-b402-87276d62e1cf%2Fnt6hol9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Playground Slides: Potential and Kinetic Energy
#### The photo below depicts two playground slides.
---
**a) Assuming the slide surfaces are slick enough to be considered frictionless, identify the forms of energy a child would have and how they are changed while going down either slide.**
When a child is at the top of either slide, they possess **potential energy** due to their elevated position relative to the ground. Potential energy is dependent on the height of the slide and the child’s mass. As the child begins to slide down, the potential energy is converted into **kinetic energy**, which is the energy of motion. By the time the child reaches the bottom of the slide, almost all the initial potential energy has been converted to kinetic energy, making the child move fastest at this point.
**b) Would a child be going faster at the bottom of the red or yellow slide, and why?**
Considering that the surfaces are frictionless and assuming the yellow slide is taller than the red slide, a child would be going faster at the bottom of the yellow slide. This is due to the fact that the yellow slide, being taller, provides greater potential energy at the top. As the child slides down, the greater initial potential energy is converted into more kinetic energy, resulting in a higher speed at the bottom compared to the red slide.
---
### Diagram Description:
The image shows two playground slides side-by-side. The slide on the left is red and shorter, whereas the slide on the right is yellow and taller. Both slides are part of a playground structure set against a background of trees and pavement.
### Key Concepts:
- **Potential Energy (PE):** Energy stored due to position, PE = mgh (mass x gravitational constant x height)
- **Kinetic Energy (KE):** Energy of motion, KE = 1/2 mv² (1/2 x mass x velocity squared)
- **Energy Transformation:** Potential energy transforms into kinetic energy as the child slides down.
This visual and these explanations help illustrate the principles of energy transformation in a playground setting.
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