ch-8

Chapter 8 Momentum and Collisions v1

m1

F 21 F 12 m2 v2

F I G U R E 8.1

Two particles interac t with each other. Accordin g to Newton’s third law, we must have : : F 12 F 21.

FIGURE

8.2 (Example 8.2) An archer fires an arrow horizontally. Because he is standing on frictionless ice, he will begin to slide across the ice.

Κ0

Before decay (at rest)

p–

p+ π–

π+ After decay

F I G U R E 8.3

(Example 8.3) A kaon at rest decays into a pair of oppositely charged pions. The pions move apart with momenta of equal magnitudes but opposite directions.

F

ti

tf

t

(a)

F

Favg Area = Favg ∆t ti

tf

t

(b)

F I G U R E 8.4

(a) A net force acting on a particle may vary in time. The impulse is the area under the curve of the magnitude of the net force versus time. (b) The average force (horizontal dashed line) gives the same impulse to the particle in the time interval t as the time-varying force described in part (a). The area of the rectangle is the same as the area under the curve.

(Courtesy of Saab)

F I G U R E 8 .5

A test dummy is brought to rest by an air bag in an automobile.

Before –15.0 m/s

After

(a)

F I G U R E 8.6

(Tim Wright/CORBIS)

+2.60 m/s

(b)

(Example 8.4) (a) The car’s momentum changes as a result of its collision with the wall. (b) In a crash test, the large force exerted by the wall on the car produces extensive damage to the car’s front end.

F21

F12 m1

m2 (a)

p + ++ 4 He

(b)

F I G U R E 8.7

(a) A collision between two objects as the result of direct contact. (b) A “collision” between two charged particles that do not make contact.

Before collision m1

v1i

m2

v2i (a)

After collision

m1 + m2

vf

(b)

Figure 8.8 A perfectly inelastic head-on collision between two particles: (a) before the collision and (b) after the collision.

Before collision v1i

m1

v2i

m2

(a) After collision v1f

v2f (b)

Figure 8.9 An elastic head-on collision between two particles: (a) before the collision and (b) after the collision.

v1i = (4.00iˆ) m/s

k m1

v2i = (–2.50iˆ) m/s

v1f = (3.00iˆ) m/s

m2

m1

v2f

k

m2

x (a)

(b)

F I G U R E 8.10

(Example 8.8) A moving block collides with another moving block with a spring attached: (a) before the collision and (b) at one instant during the collision.

v1f v1f sin θ m1

θ

v1i

φ m2

v1f cos θ v2f cos φ

–v2f sin φ (a) Before the collision

(b) After the collision

v2f

Figure 8.11 A glancing collision between two particles.

y vf (25.0iˆ) m/s

θ

x

(20.0jˆ) m/s

F IGURE

8.12

eastbound car northbound van.

(Example 8.10) An colliding with a

CM

(a)

Figure 8.13 CM

(b)

CM

(c)

Two particles of unequal mass are connected by a light, rigid rod. (a) The system rotates clockwise when a force is applied between the less massive particle and the center of mass. (b) The system rotates counterclockwise when a force is applied between the more massive particle and the center of mass. (c) The system moves in the direction of the force without rotating when a force is applied at the center of mass.

y ∆mi CM

ri rCM

x

z

F I G U R E 8.15

An extended object can be modeled as a distribution of small elements of mass mi . The center of mass of the object is located at the vector position : r CM, which has coordinates x CM, y CM, and z CM.

A

B

C

A B

Center of mass D

FIGURE

8.16 An experimental technique for determining the center of mass of a wrench. The wrench is hung freely from two different pivots, A and C. The intersection of the two vertical lines AB and CD locates the center of mass.

F I G U R E 8.17

(Quick Quiz 8.5) A baseball bat cut at the location of its center of mass.

y

4m

h

CM

2m O

m d

F I G U R E 8.18

x

b

(Example 8.11) Locating the center of mass for a system of three particles.

y dm c

b

y dx O

x

x

a (a)

F I G U R E 8.19

(b)

(Example 8.12) (a) A triangular sign to be hung from a single wire. (b) Geometric construction for locating the center of mass.

(Richard Megna, Fundamental Photographs)

F I G U R E 8.20

Strobe photograph showing an overhead view of a wrench moving on a horizontal surface. The center of mass of the wrench (marked with a white dot) moves in a straight line as the wrench rotates about this point. The wrench moves from left to right in the photograph and is slowing down due to friction between the wrench and the supporting surface. (Note The decreasing distance between the white dots.)

F I G U R E 8.22 (Example 8.13) When a projectile explodes into several fragments, where does the center of mass of the fragments land? F I G U R E 8.21

(Thinking Physics 8.1) A boy takes a step in a canoe. What happens to the canoe?

(© Bill Stormont/The Stock Market)

Figure Q8.13 Firefighters attack a burning house with a hose line.

3M

M Before (a) v

2.00 m/s

3M

M After (b)

Figure P8.5

F (N)

F = 18 000 N

20 000 15 000 10 000 5 000 0

1

2

3

t (ms)

Figure P8.7 y 60.0˚ x 60.0˚

Figure P8.9

Figure P8.11

A

m1

5.00 m

B

m2

C

Figure P8.16

m

M v/2

v

Figure P8.18

5.00 m/s 4.00 kg

3.00 m/s 10.0 kg

Figure P8.22

–4.00 m/s 3.00 kg

Figure P8.23

y

y (cm) 30

20

10

10

20

30

Figure P8.33

x (cm)

H 0.100 nm

53° O 53° 0.100 nm H

Figure P8.34

Figure P8.35