/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 How are energy and work related?... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 9

How are energy and work related?

Short Answer

Expert verified
Answer: Energy and work are related through the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. This shows that when work is done on an object, energy is transferred to the object, causing its kinetic energy to change. The work-energy theorem directly connects energy and work by demonstrating that work enables the transfer of energy between objects or systems, resulting in changes in their states.

Step by step solution

01

Define Energy

Energy is the capacity to do work or the ability to cause a change in an object's position, shape, or state. It can be classified into various forms, such as kinetic energy (energy in motion) and potential energy (stored energy).
02

Define Work

Work is the transfer of energy from one body to another. In physics, work is done when a force is exerted on an object, and the object moves a certain distance in the direction of the force. Mathematically, work (W) can be calculated as: W = F 脳 d 脳 cos(胃) where, - W is the work done, - F is the force, - d is the displacement, - 胃 is the angle between the force and the displacement.
03

Describe the Work-Energy Theorem

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be represented as: W = 螖K.E. where, - W is the work done, - 螖K.E. is the change in kinetic energy.
04

Explain the Connection between Energy and Work

When work is done on an object, energy is transferred to the object. As a result, the object's kinetic energy changes, either increasing or decreasing. The work-energy theorem directly relates the work done on an object to the change in its kinetic energy. This relationship demonstrates how energy and work are connected, as work is what enables the transfer of energy between objects or systems and causes changes in their states.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion. Whenever you see something moving, it has kinetic energy. For instance, a car speeding down the highway or a soccer ball flying through the air both have kinetic energy. The amount of kinetic energy depends on two main factors:
  • The mass of the object (m)
  • The speed of the object (v)
Mathematically, kinetic energy (\( KE \)) is calculated using the formula:\[KE = \frac{1}{2}mv^2\]This means that even a small increase in speed can significantly increase the kinetic energy because the velocity is squared in the formula. Kinetic energy will change when work is done on the object, like when you push a toy car to make it go faster.
Potential Energy
Potential energy is stored energy that depends on the position or configuration of an object. Think of it as energy waiting to be used.A classic example is a book sitting on a shelf. It has potential energy because of its height. If it falls, that potential energy converts to kinetic energy as it begins to move.Potential energy can be of different forms:
  • Gravitational potential energy, like the book on a shelf
  • Elastic potential energy, like a stretched bowstring
  • Chemical potential energy, found in batteries or food
The potential energy due to height is calculated using:\[PE = mgh\] where \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is the height. Potential energy is an essential concept in understanding how energy transforms from one type to another, particularly through the work-energy theorem.
Physics Concepts
In physics, understanding the relationship between force, work, and energy is crucial. This triangle helps us analyze and predict how objects move and interact.
  • **Force** is any interaction that, when unopposed, will change the motion of an object.
  • **Work** is done when a force causes an object to move. It's a way of transferring energy.
  • **Energy** is the capacity to do work or cause change. It's transformed from one form to another, like potential to kinetic energy.
The work-energy theorem ties these concepts together. It states that the work done on an object results in a change in the object's kinetic energy:\[W = \Delta KE\]This equation shows how energy stored as potential energy can be transformed into kinetic energy through work. As energy concepts are interconnected, mastering one makes it easier to understand the others. By learning these fundamental physics concepts, you can better understand how the physical world operates and the principles governing energy and motion.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Exactly \(10.0 \mathrm{mL}\) of water at \(25.0^{\circ} \mathrm{C}\) is added to a hot iron skillet. All the water is converted into steam at \(100.0^{\circ} \mathrm{C}\) The mass of the pan is \(1.20 \mathrm{kg}\) and the molar heat capacity of iron is \(25.19 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) .\) What is the temperature change of the skillet?

Is the fuel value of liquid propane the same as that of propane gas?

The mineral magnetite \(\left(\mathrm{Fe}_{3} \mathrm{O}_{4}\right)\) is magnetic, whereas iron(II) oxide is not. a. Write and balance the chemical equation for the formation of magnetite from iron(II) oxide and oxygen. b. Given that \(318 \mathrm{kJ}\) of heat is released for each mole of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) formed, what is the enthalpy change of the balanced reaction of formation of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) from iron(II) oxide and oxygen?

Which of the following substances has a standard enthalpy of formation equal to zero? (a) Pb at \(1000^{\circ} \mathrm{C} ;\) (b) \(\mathrm{C}_{3} \mathrm{H}_{8}(g)\) at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure; (c) solid glucose at room temperature; (d) \(\mathrm{N}_{2}(g)\) at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure.

Cleansing the Atmosphere The atmosphere contains the highly reactive molecule OH, which acts to remove selected pollutants. Use the values for \(\Delta H_{\mathrm{rxn}}\) given below to find the \(\Delta H_{\mathrm{rxn}}\) for the formation of \(\mathrm{OH}\) and \(\mathrm{H}\) from water. $$\begin{array}{rll} \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{OH}(g) & \Delta H_{\mathrm{rm}}=42.1 \mathrm{kJ} \\ \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{H}(g) & \Delta H_{\mathrm{rm}}=435.9 \mathrm{kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H_{\mathrm{rrm}}=-241.8 \mathrm{kJ} \\ \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}(g)+\mathrm{OH}(g) & \Delta H_{\mathrm{rm}}=? \end{array}$$
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.