chapter 6 work and energy. main thrust work done by a constant force –projection, scalar product...
TRANSCRIPT
Chapter 6
Work and Energy
Main thrust
• Work done by a constant force– Projection, Scalar product (force that result in
positive work). – negative work?, force that does no work?
• Work done by varying force with displacement
6.1 Work Done by a Constant Force
FsW J joule 1 mN 1
6.1 Work Done by a Constant Force
Work, cont.•W = F r cos
– The displacement is that of the point of application of the force.
– A force does no work on the object if the force does not move through a displacement.
– The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application.
Section 7.2
6.1 Work Done by a Constant Force
sFW cos
1180cos
090cos
10cos
6.1 Work Done by a Constant Force
Example 1 Pulling a Suitcase-on-Wheels
Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m.
J 2170
m 0.750.50cosN 0.45cos
sFW
6.1 Work Done by a Constant Force
FssFW 0cos
FssFW 180cos
6.1 Work Done by a Constant Force
Example 3 Accelerating a Crate
The truck is accelerating ata rate of +1.50 m/s2. The massof the crate is 120-kg and itdoes not slip. The magnitude ofthe displacement is 65 m.
What is the total work done on the crate by all of the forces acting on it?
J102.1m 650cosN180 4W
2120 kg 1.5m s 180Nsf ma
6.1 Work Done by a Constant Force
The angle between the displacementand the friction force is 0 degrees.
J102.1m 650cosN180 4W
N180sm5.1kg 120 2 maf s
6.2 The Work-Energy Theorem and Kinetic Energy
Consider a constant net external force acting on an object.
The object is displaced a distance s, in the same direction asthe net force.
The work is simply
s
F
smasFW
6.2 The Work-Energy Theorem and Kinetic Energy
2212
2122
21
ofof mvmvvvmasmW
axvv of 222
2221
of vvax
DEFINITION OF KINETIC ENERGY
The kinetic energy KE of and object with mass mand speed v is given by
221KE mv
6.2 The Work-Energy Theorem and Kinetic Energy
THE WORK-ENERGY THEOREM
When a net external force does work on and object, the kineticenergy of the object changes according to
2212
f21
of KEKE omvmvW
6.2 The Work-Energy Theorem and Kinetic Energy
Example 4 Deep Space 1
The mass of the space probe is 474-kg and its initial velocityis 275 m/s. If the 56.0-mN force acts on the probe through adisplacement of 2.42×109m, what is its final speed?
6.2 The Work-Energy Theorem and Kinetic Energy
2212
f21W omvmv
sF cosW
6.2 The Work-Energy Theorem and Kinetic Energy
2
212
f2192- sm275kg 474kg 474m1042.20cosN105.60 v
2212
f21cosF omvmvs
sm805fv
6.2 The Work-Energy Theorem and Kinetic Energy
In this case the net force is kfmgF 25sin
6.2 The Work-Energy Theorem and Kinetic Energy
Conceptual Example 6 Work and Kinetic Energy
A satellite is moving about the earth in a circular orbit and an elliptical orbit. For these two orbits, determine whetherthe kinetic energy of the satellite changes during the motion.
6.3 Gravitational Potential Energy
sFW cos
fo hhmgW gravity
6.3 Gravitational Potential Energy
fo hhmgW gravity
6.3 Gravitational Potential Energy
Example 7 A Gymnast on a Trampoline
The gymnast leaves the trampoline at an initial height of 1.20 mand reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?
6.3 Gravitational Potential Energy
2212
f21W omvmv
fo hhmgW gravity
221
ofo mvhhmg
foo hhgv 2
sm40.8m 80.4m 20.1sm80.92 2 ov
6.3 Gravitational Potential Energy
fo mghmghW gravity
DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY
The gravitational potential energy PE is the energy that anobject of mass m has by virtue of its position relative to thesurface of the earth. That position is measured by the heighth of the object relative to an arbitrary zero level:
mghPE
J joule 1 mN 1
6.4 Conservative Versus Nonconservative Forces
DEFINITION OF A CONSERVATIVE FORCE
Version 1 A force is conservative when the work it doeson a moving object is independent of the path between theobject’s initial and final positions.
Version 2 A force is conservative when it does no work on an object moving around a closed path, starting andfinishing at the same point.
6.4 Conservative Versus Nonconservative Forces
6.4 Conservative Versus Nonconservative Forces
Version 1 A force is conservative when the work it doeson a moving object is independent of the path between theobject’s initial and final positions.
fo hhmgW gravity
6.4 Conservative Versus Nonconservative Forces
Version 2 A force is conservative when it does no work on an object moving around a closed path, starting andfinishing at the same point.
fo hh fo hhmgW gravity
6.4 Conservative Versus Nonconservative Forces
An example of a nonconservative force is the kinetic frictional force.
sfsfsFW kk 180coscos
The work done by the kinetic frictional force is always negative.Thus, it is impossible for the work it does on an object that moves around a closed path to be zero.
The concept of potential energy is not defined for a nonconservative force.
6.4 Conservative Versus Nonconservative Forces
In normal situations both conservative and nonconservativeforces act simultaneously on an object, so the work done bythe net external force can be written as
ncc WWW
KEKEKE of W
PEPEPE fogravity foc mghmghWW
6.4 Conservative Versus Nonconservative Forces
ncc WWW
ncW PEKE
THE WORK-ENERGY THEOREM
PEKE ncW
6.5 The Conservation of Mechanical Energy
ofof PEPEKEKEPEKE ncW
ooff PEKEPEKE ncW
of EE ncW
If the net work on an object by nonconservative forcesis zero, then its energy does not change:
of EE
6.5 The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an objectremains constant as the object moves, provided that the network done by external nononservative forces is zero.
6.5 The Conservation of Mechanical Energy
6.5 The Conservation of Mechanical Energy
Example 8 A Daredevil Motorcyclist
A motorcyclist is trying to leap across the canyon by driving horizontally off a cliff 38.0 m/s. Ignoring air resistance, findthe speed with which the cycle strikes the ground on the otherside.
6.5 The Conservation of Mechanical Energy
of EE
2212
21
ooff mvmghmvmgh
2212
21
ooff vghvgh
6.5 The Conservation of Mechanical Energy
2212
21
ooff vghvgh
22 ofof vhhgv
sm2.46sm0.38m0.35sm8.92 22 fv
6.5 The Conservation of Mechanical Energy
Conceptual Example 9 The Favorite Swimming Hole
The person starts from rest, with the ropeheld in the horizontal position,swings downward, and then letsgo of the rope. Three forces act on him: his weight, thetension in the rope, and theforce of air resistance.
Can the principle of conservation of energybe used to calculate hisfinal speed?
6.6 Nonconservative Forces and the Work-Energy Theorem
THE WORK-ENERGY THEOREM
of EE ncW
2212
21
ooffnc mvmghmvmghW
6.6 Nonconservative Forces and the Work-Energy Theorem
Example 11 Fireworks
Assuming that the nonconservative forcegenerated by the burning propellant does425 J of work, what is the final speedof the rocket. Ignore air resistance.
2
21
221
oo
ffnc
mvmgh
mvmghW
6.6 Nonconservative Forces and the Work-Energy Theorem
2212
21
ofofnc mvmvmghmghW
2
21
2
kg 20.0
m 0.29sm80.9kg 20.0J 425
fv
221
fofnc mvhhmgW
sm61fv
6.7 Power
DEFINITION OF AVERAGE POWER
Average power is the rate at which work is done, and itis obtained by dividing the work by the time required to perform the work.
t
WP
Time
Work
(W)watt sjoule
6.7 Power
Time
energyin ChangeP
watts745.7 secondpoundsfoot 550 horsepower 1
vFP
6.7 Power
6.8 Other Forms of Energy and the Conservation of Energy
THE PRINCIPLE OF CONSERVATION OF ENERGY
Energy can neither be created not destroyed, but can only be converted from one form to another.
6.9 Work Done by a Variable Force
sFW cos
Constant Force
Variable Force
2211 coscos sFsFW