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Chapter 6 Energy and Energy Transfer F

θ F cos θ

∆r

F I G U R E 6.1 If an object :rundergoe s a displacement , the work done by the constant force :F on the object is ( F cos ) r.

n

F

θ

∆r mg

F I G U R E 6.2

When an object is displaced horizontally on a flat table, n and the the normal force : : gravitational force mg do no work.

F

F

F

(a)

F I G U R E 6.3

F

(b)

(c)

(d)

:

(Quick Quiz 6.1) A force F is applied to an object, which undergoes a displacement to the right. In each of the four cases, the magnitudes of the force and displacement are the same.

d

F

mg

F I G U R E 6.4

h

(Thinking Physics 6.1) A person lifts a heavy box of mass m a vertical distance h and then walks horizontally at constant velocity a distance d.

50.0 N

n

30.0° mg

F I G U R E 6.5

(Example 6.1) A vacuum cleaner being pulled at an angle of 30.0° with the horizontal.

the upward component of the applied

B

θ

A ⋅ B = AB cos θ

A

F I G U R E 6.6

The scalar product : A B equals the magnitude of A : multiplied by the magnitude of B and : the cosine of the angle between A : and B . : :

Area = ∆A = Fx ∆x Fx

Fx xi

xf

x

∆x (a) Fx

Work xi

xf

x

(b)

F I G U R E 6.7

(a) The work done by a force of magnitude Fx for the small displacement x is Fx x, which equals the area of the shaded rectangle. The total work done for the displacement from xi to xf is approximately equal to the sum of the areas of all the rectangles. (b) The work done by the variable force Fx as the particle moves from xi to xf is exactly equal to the area under this curve.

Fs is negative. x is positive. x

x x=0 (a) Fs = 0 x=0 x

x=0 (b)

Fs is positive. x is negative. x

x x=0 (c) Fs 2 Area = –1 kx max 2

kx max x

0 xmax

Fs = –kx

(d)

Figure 6.8 The force exerted by a spring on a block varies with the block’s displacement from the equilibrium position x 0. (a) When x is positive (stretched spring), the spring force is to the left. (b) When x is zero (natural length of the spring), the spring force is zero. (c) When x is negative (compressed spring), the spring force is to the right. (d) Graph of Fs versus x for the block – spring system. The work done by the spring force as the block moves from x max to 0 is the area 1 2 of the shaded triangle, 2 kx max .

F I G U R E 6.9

Fapp

Fs

xi = –x max

xf = 0

A block moves from xi – x max to xf 0 :on a frictionless surface as a force F app is applied to the block. If the process is carried out very slowly, the applied force is equal in magnitude and opposite in direction to the spring force at all times.

Fapp = (80 N/m)(x) Fapp

0

2

F I G U R E 6.10

4

6

x (cm)

(Example 6.3) A graph of the applied force required to stretch a spring that obeys Hooke’s law versus the elongation of the spring.

∆x

ΣF m

vi

F I G U R E 6.11

vf

An object modeled as a particle undergoes a displacement of magnitude x and a change in speed under the action of a constant net : force F .

n

vf F

∆x mg

F I G U R E 6.12

(Example 6.4) A block on a frictionless surface is pulled to the right by a constant horizontal force.

1.00 m

F I G U R E 6.13

(Example 6.5) A block is dropped onto a vertical spring, causing the spring to compress.

∆x fk

vi

vf

F I G U R E 6.14

A book sliding to the right on a horizontal surface slows down in the presence of a force of kinetic friction acting to the left. The initial : velocity of the book is v i , and its final : v f velocity is . The normal force and gravitational force are not included in the diagram because they are perpendicular to the direction of motion and therefore do not influence the speed of the book.

(a – c, e, f, George Semple; d, Digital Vision/Getty Images)

F I G U R E 6.15

Energy transfer mechanisms. (a) Energy is transferred to the block by work, (b) energy leaves the radio by mechanical waves, (c) energy transfers up the handle of the spoon by heat, (d) energy enters the automobile gas tank by matter transfer, (e) energy enters the hair dryer by electrical transmission, and (f) energy leaves the light bulb by electromagnetic radiation.

(Sinclair Stammers/Science Photo Library/Photo Researchers, Inc.)

F I G U R E 6.16

The glow worm Lampyris noctiluca is found in Great Britain and parts of continental Europe. It exhibits the phenomenon of bioluminescence. The light leaving the last three segments of its abdomen represents a transfer of energy out of the system of the worm.

n

vf F

fk

∆x mg (a) n F

vf

θ

fk

∆x mg (b)

F I G U R E 6.17

(Example 6.6) (a) A block is pulled to the right by a constant horizontal force on a surface with friction. (b) The applied force is at an angle to the horizontal.

Motor T

+

f

Mg

(a)

F I G U R E 6.18

(b)

(Example 6.8) (a) A motor lifts an elevator car. (b) Free-body diagram for the elevator. : The motor exerts an upward force T on the supporting cables. The magnitude of this force is T, the tension in the cables, which is applied in the upward direction on the elevator. The downward : forces on the elevator are the friction force f and the : gravitational force F g M : g.

y

118° x 132°

32.8 N

17.3 cm/s

Figure P6.5

Fx (N) 3 2 1 0

2

4

6

8

x (m)

10 12 14 16

Figure P6.11 Problems 11 and 24.

k2 k1

2 000 Total 1 500 force (N) 1 000 500 0

10

20 30 40 Distance (cm)

Figure P6.12

50

60

F m R

θ

Figure P6.19

View more...
θ F cos θ

∆r

F I G U R E 6.1 If an object :rundergoe s a displacement , the work done by the constant force :F on the object is ( F cos ) r.

n

F

θ

∆r mg

F I G U R E 6.2

When an object is displaced horizontally on a flat table, n and the the normal force : : gravitational force mg do no work.

F

F

F

(a)

F I G U R E 6.3

F

(b)

(c)

(d)

:

(Quick Quiz 6.1) A force F is applied to an object, which undergoes a displacement to the right. In each of the four cases, the magnitudes of the force and displacement are the same.

d

F

mg

F I G U R E 6.4

h

(Thinking Physics 6.1) A person lifts a heavy box of mass m a vertical distance h and then walks horizontally at constant velocity a distance d.

50.0 N

n

30.0° mg

F I G U R E 6.5

(Example 6.1) A vacuum cleaner being pulled at an angle of 30.0° with the horizontal.

the upward component of the applied

B

θ

A ⋅ B = AB cos θ

A

F I G U R E 6.6

The scalar product : A B equals the magnitude of A : multiplied by the magnitude of B and : the cosine of the angle between A : and B . : :

Area = ∆A = Fx ∆x Fx

Fx xi

xf

x

∆x (a) Fx

Work xi

xf

x

(b)

F I G U R E 6.7

(a) The work done by a force of magnitude Fx for the small displacement x is Fx x, which equals the area of the shaded rectangle. The total work done for the displacement from xi to xf is approximately equal to the sum of the areas of all the rectangles. (b) The work done by the variable force Fx as the particle moves from xi to xf is exactly equal to the area under this curve.

Fs is negative. x is positive. x

x x=0 (a) Fs = 0 x=0 x

x=0 (b)

Fs is positive. x is negative. x

x x=0 (c) Fs 2 Area = –1 kx max 2

kx max x

0 xmax

Fs = –kx

(d)

Figure 6.8 The force exerted by a spring on a block varies with the block’s displacement from the equilibrium position x 0. (a) When x is positive (stretched spring), the spring force is to the left. (b) When x is zero (natural length of the spring), the spring force is zero. (c) When x is negative (compressed spring), the spring force is to the right. (d) Graph of Fs versus x for the block – spring system. The work done by the spring force as the block moves from x max to 0 is the area 1 2 of the shaded triangle, 2 kx max .

F I G U R E 6.9

Fapp

Fs

xi = –x max

xf = 0

A block moves from xi – x max to xf 0 :on a frictionless surface as a force F app is applied to the block. If the process is carried out very slowly, the applied force is equal in magnitude and opposite in direction to the spring force at all times.

Fapp = (80 N/m)(x) Fapp

0

2

F I G U R E 6.10

4

6

x (cm)

(Example 6.3) A graph of the applied force required to stretch a spring that obeys Hooke’s law versus the elongation of the spring.

∆x

ΣF m

vi

F I G U R E 6.11

vf

An object modeled as a particle undergoes a displacement of magnitude x and a change in speed under the action of a constant net : force F .

n

vf F

∆x mg

F I G U R E 6.12

(Example 6.4) A block on a frictionless surface is pulled to the right by a constant horizontal force.

1.00 m

F I G U R E 6.13

(Example 6.5) A block is dropped onto a vertical spring, causing the spring to compress.

∆x fk

vi

vf

F I G U R E 6.14

A book sliding to the right on a horizontal surface slows down in the presence of a force of kinetic friction acting to the left. The initial : velocity of the book is v i , and its final : v f velocity is . The normal force and gravitational force are not included in the diagram because they are perpendicular to the direction of motion and therefore do not influence the speed of the book.

(a – c, e, f, George Semple; d, Digital Vision/Getty Images)

F I G U R E 6.15

Energy transfer mechanisms. (a) Energy is transferred to the block by work, (b) energy leaves the radio by mechanical waves, (c) energy transfers up the handle of the spoon by heat, (d) energy enters the automobile gas tank by matter transfer, (e) energy enters the hair dryer by electrical transmission, and (f) energy leaves the light bulb by electromagnetic radiation.

(Sinclair Stammers/Science Photo Library/Photo Researchers, Inc.)

F I G U R E 6.16

The glow worm Lampyris noctiluca is found in Great Britain and parts of continental Europe. It exhibits the phenomenon of bioluminescence. The light leaving the last three segments of its abdomen represents a transfer of energy out of the system of the worm.

n

vf F

fk

∆x mg (a) n F

vf

θ

fk

∆x mg (b)

F I G U R E 6.17

(Example 6.6) (a) A block is pulled to the right by a constant horizontal force on a surface with friction. (b) The applied force is at an angle to the horizontal.

Motor T

+

f

Mg

(a)

F I G U R E 6.18

(b)

(Example 6.8) (a) A motor lifts an elevator car. (b) Free-body diagram for the elevator. : The motor exerts an upward force T on the supporting cables. The magnitude of this force is T, the tension in the cables, which is applied in the upward direction on the elevator. The downward : forces on the elevator are the friction force f and the : gravitational force F g M : g.

y

118° x 132°

32.8 N

17.3 cm/s

Figure P6.5

Fx (N) 3 2 1 0

2

4

6

8

x (m)

10 12 14 16

Figure P6.11 Problems 11 and 24.

k2 k1

2 000 Total 1 500 force (N) 1 000 500 0

10

20 30 40 Distance (cm)

Figure P6.12

50

60

F m R

θ

Figure P6.19

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