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HomeStudy GuidesPhysics

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The Nature of Science and Physics

Kinematics

Introduction to One-Dimensional KinematicsDisplacementVectors, Scalars, and Coordinate SystemsTime, Velocity, and SpeedVideo: One-Dimensional KinematicsAccelerationMotion Equations for Constant Acceleration in One DimensionProblem-Solving Basics for One-Dimensional KinematicsFalling ObjectsGraphical Analysis of One-Dimensional Motion

Two-Dimensional Kinematics

Dynamics: Force and Newton's Laws of Motion

Introduction to Dynamics: Newton's Laws of MotionDevelopment of Force ConceptNewton's First Law of Motion: InertiaNewton's Second Law of Motion: Concept of a SystemNewton's Third Law of Motion: Symmetry in ForcesVideo: Newton's LawsNormal, Tension, and Other Examples of ForcesProblem-Solving StrategiesFurther Applications of Newton's Laws of MotionExtended Topic: The Four Basic Forces—An Introduction

Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Uniform Circular Motion and Gravitation

Introduction to Uniform Circular Motion and GravitationRotation Angle and Angular VelocityCentripetal AccelerationCentripetal ForceFictitious Forces and Non-inertial Frames: The Coriolis ForceNewton's Universal Law of GravitationVideo: GravitationSatellites and Kepler's Laws: An Argument for Simplicity

Work, Energy, and Energy Resources

Introduction to Work, Energy, and Energy ResourcesWork: The Scientific DefinitionKinetic Energy and the Work-Energy TheoremGravitational Potential EnergyVideo: Potential and Kinetic EnergyConservative Forces and Potential EnergyNonconservative ForcesConservation of EnergyPowerWork, Energy, and Power in HumansWorld Energy Use

Linear Momentum and Collisions

Rotational Motion and Angular Momentum

Introduction to Rotational Motion and Angular MomentumAngular AccelerationKinematics of Rotational MotionVideo: Rotational MotionDynamics of Rotational Motion: Rotational InertiaRotational Kinetic Energy: Work and Energy RevisitedAngular Momentum and Its ConservationVideo: Angular MomentumCollisions of Extended Bodies in Two DimensionsGyroscopic Effects: Vector Aspects of Angular Momentum

Statics and Torque

Fluid Statics

Introduction to Fluid StaticsWhat Is a Fluid?DensityPressureVariation of Pressure with Depth in a FluidPascal's PrincipleGauge Pressure, Absolute Pressure, and Pressure MeasurementArchimedes' PrincipleVideo: BuoyancyCohesion and Adhesion in Liquids: Surface Tension and Capillary ActionPressures in the Body

Fluid Dynamics and Its Biological and Medical Applications

Introduction to Fluid Dynamics and Biological and Medical ApplicationsFlow Rate and Its Relation to VelocityBernoulli's EquationVideo: Fluid FlowThe Most General Applications of Bernoulli's EquationViscosity and Laminar Flow; Poiseuille's LawThe Onset of TurbulenceMotion of an Object in a Viscous FluidMolecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

Temperature, Kinetic Theory, and the Gas Laws

Heat and Heat Transfer Methods

Thermodynamics

Introduction to ThermodynamicsThe First Law of ThermodynamicsThe First Law of Thermodynamics and Some Simple ProcessesIntroduction to the Second Law of Thermodynamics: Heat Engines and Their EfficiencyCarnot's Perfect Heat Engine: The Second Law of Thermodynamics RestatedApplications of Thermodynamics: Heat Pumps and RefrigeratorsEntropy and the Second Law of Thermodynamics: Disorder and the Unavailability of EnergyStatistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

Oscillatory Motion and Waves

Introduction to Oscillatory Motion and WavesHooke's Law: Stress and Strain RevisitedPeriod and Frequency in OscillationsSimple Harmonic Motion: A Special Periodic MotionVideo: Harmonic MotionThe Simple PendulumEnergy and the Simple Harmonic OscillatorUniform Circular Motion and Simple Harmonic MotionDamped Harmonic MotionForced Oscillations and ResonanceWavesSuperposition and InterferenceEnergy in Waves: Intensity

Physics of Hearing

- Explain work as a transfer of energy and net work as the work done by the net force.
- Explain and apply the work-energy theorem.

In this section we begin the study of various types of work and forms of energy. We will find that some types of work leave the energy of a system constant, for example, whereas others change the system in some way, such as making it move. We will also develop definitions of important forms of energy, such as the energy of motion.

Let us start by considering the total, or net, work done on a system. Net work is defined to be the sum of work done by all external forces—that is,

Figure 2a shows a graph of force versus displacement for the component of the force in the direction of the displacement—that is, an

Net work will be simpler to examine if we consider a one-dimensional situation where a force is used to accelerate an object in a direction parallel to its initial velocity. Such a situation occurs for the package on the roller belt conveyor system shown in Figure 3.

The force of gravity and the normal force acting on the package are perpendicular to the displacement and do no work. Moreover, they are also equal in magnitude and opposite in direction so they cancel in calculating the net force. The net force arises solely from the horizontal applied force

The effect of the net force

To get a relationship between net work and the speed given to a system by the net force acting on it, we take

$\displaystyle{a}=\frac{v^2-v_0^2}{2d}\\$

. When $\displaystyle{W}_{\text{net}}=m\left(\frac{v^2-v_0^2}{2d}\right)d\\$

The $W=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2\\$

.
This expression is called the $\frac{1}{2}mv^2\\$

. This quantity is our first example of a form of energy.$\frac{1}{2}mv^2\\$

.$W_{\text{net}}=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2\\$

$\frac{1}{2}mv^2\\$

in the work-energy theorem is defined to be the translational $\text{KE}=\frac{1}{2}mv^2\\$

, is the energy associated with translational motion. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together.We are aware that it takes energy to get an object, like a car or the package in Figure 3, up to speed, but it may be a bit surprising that kinetic energy is proportional to speed squared. This proportionality means, for example, that a car traveling at 100 km/h has four times the kinetic energy it has at 50 km/h, helping to explain why high-speed collisions are so devastating. We will now consider a series of examples to illustrate various aspects of work and energy.

$\text{KE}=\frac{1}{2}mv^2\\$

.$\text{KE}=\frac{1}{2}mv^2\\$

.Entering known values gives KE = 0.5 (30.0 kg)(0.500 m/s)

KE = 3.75 kg ⋅ m^{2}/s^{2} = 3.75 J.

- Calculate the net work done on the package.
- Solve the same problem as in part 1, this time by finding the work done by each force that contributes to the net force.

$\begin{array}{lll}W_{\text{net}}&=&F_{\text{net}}d=(115\text{ N})(0.800\text{ m})\\\text{ }&=&9.20\text{ N}\cdot{\text{m}}=92.0\text{ J}\end{array}\\$

$\begin{array}{lll}W_{\text{app}}&=&F_{\text{app}}d(\cos0^{\circ})=F_{\text{app}}d\\\text{ }&=&(120\text{ N})(0.800\text{ m})\\\text{ }&=&96.0\text{ J}\end{array}\\$

The friction force and displacement are in opposite directions, so that $\begin{array}{lll}W_{\text{fr}}&=&F_{\text{fr}}d(\cos180^{\circ})=F_{\text{fr}}d\\\text{ }&=&-(5.00\text{ N})(0.800\text{ m})\\\text{ }&=&-4.00\text{ J}\end{array}\\$

So the amounts of work done by gravity, by the normal force, by the applied force, and by friction are, respectively,$\begin{array}{lll}W_{\text{gr}}&=&0,\\W_{\text{N}}&=&0,\\W_{\text{app}}&=&96.0\text{ J},\\W_{\text{fr}}&=&-4.00.\text{ J}\end{array}\\$

The total work done as the sum of the work done by each force is then seen to be $\frac{1}{2}mv_0^2\\$

. These calculations allow us to find the final kinetic energy, $\frac{1}{2}mv^2\\$

, and thus the final speed $W_{\text{net}}=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2\\$

.
Solving for$\frac{1}{2}mv^2\\$

gives $\frac{1}{2}mv^2=W_{\text{net}}+\frac{1}{2}mv_0^2\\$

.
Thus,$\frac{1}{2}mv^2=92.0\text{ J}+3.75\text{ J}=95.75\text{ J}\\$

.
Solving for the final speed as requested and entering known values gives$\begin{array}{lll}v&=&\sqrt{\frac{2(95.75\text{ J})}{\text{m}}}=\sqrt{\frac{191.5\text{ kg}\cdot\text{m}^2\text{s}^2}{30.0 \text{ kg}}}\\\text{ }&=&2.53\text{ m/s}\end{array}\\$

$\displaystyle{d}\prime=-\frac{W_{\text{fr}}}{f}=-\frac{-95.75\text{ J}}{5.00\text{ N}}\\$

and so - The net work
*W*_{net}is the work done by the net force acting on an object. - Work done on an object transfers energy to the object.
- The translational kinetic energy of an object of mass
*m*moving at speed*v*is$\text{KE}=\frac{1}{2}mv^{2}\\$. - The work-energy theorem states that the net work
*W*_{net}on a system changes its kinetic energy,${W}_{\text{net}}=\frac{1}{2}mv^{2}-\frac{1}{2}{mv}_0^2\\$.

- The person in Figure 4 does work on the lawn mower. Under what conditions would the mower gain energy? Under what conditions would it lose energy?

- A person pushing a lawn mower with a force F. Force is represented by a vector making an angle theta below the horizontal and distance moved by the mover is represented by vector d. The component of vector F along vector d is F cosine theta. Work done by the person, W, is equal to F d cosine theta.

Work done on a system puts energy into it. Work done by a system removes energy from it. Give an example for each statement. - When solving for speed in Example 3, we kept only the positive root. Why?

- Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an 80.0-kg astronaut in orbit moving at 27,500 km/h.
- (a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would relate to metabolic rates.
- What is the value for the kinetic energy of a 90,000-ton aircraft carrier at 30 knots? You will need to look up the definition of a nautical mile (1 knot = 1 nautical mile/h).
- (a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
- A car’s bumper is designed to withstand a 4.0-km/h (1.1-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.
- Boxing gloves are padded to lessen the force of a blow. (a) Calculate the force exerted by a boxing glove on an opponent’s face, if the glove and face compress 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s. (b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm. (c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?
- Using energy considerations, calculate the average force a 60.0-kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him.

$\frac{1}{2}{\text{mv}}^{2}\\$

for the translational (i.e., non-rotational) motion of an object of mass $\frac{1}{250}\\$

3. 1.1 × 10

5. 2.8 × 10

7. 102 N