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Chapter 5 More Applications of Newton’ s Laws

n

n

F

fs

Motion F

fk

mg

mg

(a)

(b)

| f|

Figure 5.1

fs,max

:

f s=

F

fk = µkn

0

F Static region

Kinetic region

(c)

(a ) Th e force of static friction f s between a trash can : and a concrete patio is opposite the applied force F . Th e magnitude of the force of static friction equals that of the applied force. (b ) When the magnitude of the applied force exceeds the magnitude of the force of : kin etic friction f k, the trash can accelerates to the right. (c ) A graph of the magnitude of the friction force versus that of the applied force. I n our model, the force of kin etic friction is independent of the applied force and the relative speed of the sur faces. Note that fs,max fk.

F IGURE 5.2

(Quick Quiz 5.3) A father tries to slide his daughter on a sled over snow by (a) pushing downward on her shoulders or (b) pulling upward on a rope attached to the sled. Which is easier?

F

30° F

30° (b)

(a) Gantry Bow of ship

"Umbilical cord"

Oil rig

Oil rig stops short of edge

Oil rig moves toward abyss Abyss

Abyss "Umbilical cord" is almost horizontal

(a)

F I G U R E 5.3

"Umbilical cord" is almost vertical

(b)

(Thinking Physics 5.1) An oil rig at the bottom of the ocean is dragged by a cable.

(c)

n

fk

mg g

F I G U R E 5.4

(Example 5.1) A truck skids to a stop.

y n x

f

mg sin θ mg cos θ

θ mg

θ

F I G U R E 5.5 (Example 5.2) A block on an adjustable incline is used to determine the coefficients of friction.

n

4.0 kg

4.0 kg

T

fk

m 1g

7.0 kg (a)

(b)

T

7.0 kg

m 2g (c)

F I G U R E 5.6

(Example 5.3) (a) Two objects connected by a light string that passes over a frictionless pulley. (b) Freebody diagram for the sliding cube. (c) Free-body diagram for the hanging ball.

y a

n fk mg sin θ

d

θ (a)

F I G U R E 5.7

mg cos θ

θ

x mg (b)

(Example 5.4) (a) A crate of mass m slides down an incline. (b) Free-body diagram for the sliding crate.

m Fr r

Fr

F I G U R E 5.8

Overhead view of a ball moving in a circular path in a horizontal : plane. A force F r directed toward the center of the circle keeps the ball moving in its circular path.

r

Figure 5.9 An overhead view of a ball moving in a circular path in a horizontal plane. When the string breaks, the ball moves in the direction tangent to the circular path.

(© Tom Carroll/Index Stock Imagery/PictureQuest)

F I G U R E 5.10

(Quick Quiz 5.4) A Ferris wheel located on Navy Pier in Chicago, Illinois.

L T

θ

T cos θ

θ r

mg

F I G U R E 5.11

T sin θ

mg

(Example 5.6) The conical pendulum and its free-body diagram.

fs

(a)

n

fs mg (b)

F I G U R E 5.12 (Interactive Example 5.7) (a) The force of static friction directed toward the center of the curve keeps the car moving in a circular path. (b) Free-body diagram for the car.

θ

n

θ

F I G U R E 5.13

ny

Fg

(Interactive Example 5.8) A car rounding a curve on a road banked at an angle to the horizontal. In the absence of friction the force that causes the centripetal acceleration and keeps the car moving in its circular path is the horizontal component of the normal force.

n bot Top

F I G U R E 5.14

ntop mg (b) Bottom (a)

mg (c)

(Example 5.9) (a) An aircraft executes a loop-the-loop maneuver as it moves in a vertical circle at constant speed. (b) Freebody diagram for the pilot at the bottom of the loop. In this position, the pilot experiences a force from the seat that is larger than his weight. (c) Free-body diagram for the pilot at the top of the loop. Here the force from the seat could be smaller than his weight or larger, depending on the speed of the aircraft.

F Fr

Ft

Figure 5.15

F I G U R E 5.16

(Quick Quiz 5.6) A bead slides along a curved wire.

When the net force acting on a particle moving in a circular path has : a tangential component vector Ft , its speed changes. The total force on the particle also has a component : vector Fr directed toward the center of the circular path. Therefore, : : : the total force is F Fr Ft.

vtop

mg

Ttop

R O T

θ

O T bot

FIGURE mg cos θ

v bot

mg sin θ

θ

mg mg (a)

(b)

5.17 (Example 5.10) (a) Forces acting on a sphere of mass m connected to a cord of length R and rotating in a vertical circle centered at O. (b) Forces acting on the sphere when it is at the top and bottom of the circle. The tension has its maximum value at the bottom and its minimum value at the top.

R v mg

(a) v vT

0.632vT

t (b)

Figure 5.18 (a) A small sphere falling through a viscous fluid. (b) The speed – time graph for an object falling through a viscous medium. The object approaches a terminal speed vT, and the time constant is the time interval required to reach 0.632vT.

R v R mg vT

mg

F I G U R E 5.19

An object falling through air experiences a resistive : drag force R and a gravitational force : : F g m g . The object reaches terminal speed (on the right) when the net force acting on it is zero, that is, when : : F g , or R mg. Before that R occurs, the acceleration varies with speed according to Equation 5.9.

(Jump Run Productions/Image Bank)

5.20 (Quick Quiz 5.7) A sky surfer takes advantage of the FIGURE

m1

r Fg –Fg m2

F I G U R E 5.21

Two particles with masses m1 and m2 attract each other with a force of magnitude Gm1m2/r2.

r

Fe

+ q2

+ q1 Fe

(a) – q2 Fe + q1

F I G U R E 5.22

Fe (b)

Two point charges separated by a distance r exert an electrostatic force on each other given by Coulomb’s law. (a) When the charges are of the same sign, the charges repel each other. (b) When the charges are of opposite sign, the charges attract each other.

(Mike Powell/Getty Images)

θ

Figure P5.3

Figure P5.8 5.00 kg

22.0° 9.00 kg

Figure P5.10

22.0°

Figure P5.4

50.0°

T

m1

P

Figure P5.13

m2

F

Figure P5.11 1.00 kg

4.00 kg

2.00 kg

θ

Figure

Figure P5.19

2.00 m 3.00 m 2.00 m

Figure P5.20 v

(Frank Cezus/FPG International)

Figure P5.22

Figure P5.24

(a) Fr

F

Ft Fr

F Ft Ft (b)

Figure QQA.5.6

View more...
n

n

F

fs

Motion F

fk

mg

mg

(a)

(b)

| f|

Figure 5.1

fs,max

:

f s=

F

fk = µkn

0

F Static region

Kinetic region

(c)

(a ) Th e force of static friction f s between a trash can : and a concrete patio is opposite the applied force F . Th e magnitude of the force of static friction equals that of the applied force. (b ) When the magnitude of the applied force exceeds the magnitude of the force of : kin etic friction f k, the trash can accelerates to the right. (c ) A graph of the magnitude of the friction force versus that of the applied force. I n our model, the force of kin etic friction is independent of the applied force and the relative speed of the sur faces. Note that fs,max fk.

F IGURE 5.2

(Quick Quiz 5.3) A father tries to slide his daughter on a sled over snow by (a) pushing downward on her shoulders or (b) pulling upward on a rope attached to the sled. Which is easier?

F

30° F

30° (b)

(a) Gantry Bow of ship

"Umbilical cord"

Oil rig

Oil rig stops short of edge

Oil rig moves toward abyss Abyss

Abyss "Umbilical cord" is almost horizontal

(a)

F I G U R E 5.3

"Umbilical cord" is almost vertical

(b)

(Thinking Physics 5.1) An oil rig at the bottom of the ocean is dragged by a cable.

(c)

n

fk

mg g

F I G U R E 5.4

(Example 5.1) A truck skids to a stop.

y n x

f

mg sin θ mg cos θ

θ mg

θ

F I G U R E 5.5 (Example 5.2) A block on an adjustable incline is used to determine the coefficients of friction.

n

4.0 kg

4.0 kg

T

fk

m 1g

7.0 kg (a)

(b)

T

7.0 kg

m 2g (c)

F I G U R E 5.6

(Example 5.3) (a) Two objects connected by a light string that passes over a frictionless pulley. (b) Freebody diagram for the sliding cube. (c) Free-body diagram for the hanging ball.

y a

n fk mg sin θ

d

θ (a)

F I G U R E 5.7

mg cos θ

θ

x mg (b)

(Example 5.4) (a) A crate of mass m slides down an incline. (b) Free-body diagram for the sliding crate.

m Fr r

Fr

F I G U R E 5.8

Overhead view of a ball moving in a circular path in a horizontal : plane. A force F r directed toward the center of the circle keeps the ball moving in its circular path.

r

Figure 5.9 An overhead view of a ball moving in a circular path in a horizontal plane. When the string breaks, the ball moves in the direction tangent to the circular path.

(© Tom Carroll/Index Stock Imagery/PictureQuest)

F I G U R E 5.10

(Quick Quiz 5.4) A Ferris wheel located on Navy Pier in Chicago, Illinois.

L T

θ

T cos θ

θ r

mg

F I G U R E 5.11

T sin θ

mg

(Example 5.6) The conical pendulum and its free-body diagram.

fs

(a)

n

fs mg (b)

F I G U R E 5.12 (Interactive Example 5.7) (a) The force of static friction directed toward the center of the curve keeps the car moving in a circular path. (b) Free-body diagram for the car.

θ

n

θ

F I G U R E 5.13

ny

Fg

(Interactive Example 5.8) A car rounding a curve on a road banked at an angle to the horizontal. In the absence of friction the force that causes the centripetal acceleration and keeps the car moving in its circular path is the horizontal component of the normal force.

n bot Top

F I G U R E 5.14

ntop mg (b) Bottom (a)

mg (c)

(Example 5.9) (a) An aircraft executes a loop-the-loop maneuver as it moves in a vertical circle at constant speed. (b) Freebody diagram for the pilot at the bottom of the loop. In this position, the pilot experiences a force from the seat that is larger than his weight. (c) Free-body diagram for the pilot at the top of the loop. Here the force from the seat could be smaller than his weight or larger, depending on the speed of the aircraft.

F Fr

Ft

Figure 5.15

F I G U R E 5.16

(Quick Quiz 5.6) A bead slides along a curved wire.

When the net force acting on a particle moving in a circular path has : a tangential component vector Ft , its speed changes. The total force on the particle also has a component : vector Fr directed toward the center of the circular path. Therefore, : : : the total force is F Fr Ft.

vtop

mg

Ttop

R O T

θ

O T bot

FIGURE mg cos θ

v bot

mg sin θ

θ

mg mg (a)

(b)

5.17 (Example 5.10) (a) Forces acting on a sphere of mass m connected to a cord of length R and rotating in a vertical circle centered at O. (b) Forces acting on the sphere when it is at the top and bottom of the circle. The tension has its maximum value at the bottom and its minimum value at the top.

R v mg

(a) v vT

0.632vT

t (b)

Figure 5.18 (a) A small sphere falling through a viscous fluid. (b) The speed – time graph for an object falling through a viscous medium. The object approaches a terminal speed vT, and the time constant is the time interval required to reach 0.632vT.

R v R mg vT

mg

F I G U R E 5.19

An object falling through air experiences a resistive : drag force R and a gravitational force : : F g m g . The object reaches terminal speed (on the right) when the net force acting on it is zero, that is, when : : F g , or R mg. Before that R occurs, the acceleration varies with speed according to Equation 5.9.

(Jump Run Productions/Image Bank)

5.20 (Quick Quiz 5.7) A sky surfer takes advantage of the FIGURE

m1

r Fg –Fg m2

F I G U R E 5.21

Two particles with masses m1 and m2 attract each other with a force of magnitude Gm1m2/r2.

r

Fe

+ q2

+ q1 Fe

(a) – q2 Fe + q1

F I G U R E 5.22

Fe (b)

Two point charges separated by a distance r exert an electrostatic force on each other given by Coulomb’s law. (a) When the charges are of the same sign, the charges repel each other. (b) When the charges are of opposite sign, the charges attract each other.

(Mike Powell/Getty Images)

θ

Figure P5.3

Figure P5.8 5.00 kg

22.0° 9.00 kg

Figure P5.10

22.0°

Figure P5.4

50.0°

T

m1

P

Figure P5.13

m2

F

Figure P5.11 1.00 kg

4.00 kg

2.00 kg

θ

Figure

Figure P5.19

2.00 m 3.00 m 2.00 m

Figure P5.20 v

(Frank Cezus/FPG International)

Figure P5.22

Figure P5.24

(a) Fr

F

Ft Fr

F Ft Ft (b)

Figure QQA.5.6

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