Chapter 8

Question 1

momentum

Answer 1

implies a tendency to continue on course—to move in the same direction—and is associated with great mass and speed; definition is consistent with what we think of outside of physics

Question 2

Momentum, like energy, is important because

Answer 2

it is conserved. Only a few physical quantities are conserved in nature, and studying them yields fundamental insight into how nature works, as we shall see in our study of momentum.

Question 3

Linear momentum is defined as

Answer 3

the product of a system’s mass multiplied by its velocity.

Question 4

In symbols, linear momentum is expressed as

Answer 4

p=mv

Question 5

Momentum is directly proportional to

Answer 5

the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum.

Question 6

Momentum p
is a ______ having the same direction as _______.

Answer 6

Momentum p is a vector having the same direction as velocity.

Question 7

SI unit for momentum is

Answer 7

kg⋅m/s

Question 8

Newton actually stated his second law of motion in terms of

Answer 8

momentum.

Question 9

The net external force equals the _____ in momentum of a system divided by the _____.

Answer 9

The net external force equals the change in momentum of a system divided by the change in time.

Question 10

Using symbols, the law related to net force and momentum is

Answer 10

Fnet = change in p / change in t

Question 11

Velocity equals

Answer 11

change in position / change in time

Question 12

Acceleration equals

Answer 12

change in velocity / change in time

Question 13

The quantity FnetΔt
is given the name

Answer 13

impulse.

Question 14

Impulse is the same as

Answer 14

the change in momentum.

Question 15

The assumption of a constant force in the definition of impulse is analogous to

Answer 15

the assumption of a constant acceleration in kinematics. In both cases, nature is adequately described without the use of calculus.

Question 16

The backward momentum felt by an object or person exerting force on another object is often called

Answer 16

a recoil.

Question 17

Because the changes in momentum add to zero, the total momentum of a system is

Answer 17

constant.

Question 18

An isolated system is defined to be one for which the net external force is

Answer 18

zero (Fnet=0).

Question 19

Conservation of momentum is violated only when

Answer 19

the net external force is not zero.

Question 20

Conservation of momentum is quite useful in

Answer 20

describing collisions.

Question 21

An elastic collision is one that

Answer 21

also conserves internal kinetic energy.

Question 22

Internal kinetic energy is the sum of

Answer 22

the kinetic energies of the objects in the system.

Question 23

to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for

Answer 23

conservation of momentum and conservation of internal kinetic energy.

Question 24

By definition, an elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision ______ the sum after the collision.

Answer 24

equals the sum after the collision.

Question 25

The equations for conservation of momentum and internal kinetic energy can be used to describe

Answer 25

any one-dimensional elastic collision of two objects. These equations can be extended to more objects if needed. Equation for conservation of momentum is p initial = p final. Equation for internal kinetic energy is the sum of all the kinetic energies in a system. For one object it is: KE = 1/2m x v squared

Question 26

An inelastic collision is one in which

Answer 26

the internal kinetic energy changes (it is not conserved).

Question 27

Lack of conservation (in an inelastic collision) means that the forces between colliding objects may

Answer 27

remove or add internal kinetic energy.

Question 28

Definition of inelastic collision

Answer 28

An inelastic collision is one in which the internal kinetic energy changes (it is not conserved).

Question 29

A collision in which the objects stick together is sometimes called

Answer 29

a perfectly inelastic collision because it reduces internal kinetic energy more than does any other type of inelastic collision. In fact, such a collision reduces internal kinetic energy to the minimum it can have while still conserving momentum.

Question 30

Momentum is conserved because the net external force on a system is

Answer 30

zero.

Question 31

Recall that in a collision, it is _______ and not ____ that is important.

Answer 31

it is momentum and not force that is important.

Question 32

Two-dimensional collisions: the approach taken (similar to the approach in discussing two-dimensional kinematics and dynamics) is to

Answer 32

choose a convenient coordinate system and resolve the motion into components along perpendicular axes. Resolving the motion yields a pair of one-dimensional problems to be solved simultaneously.

Question 33

point masses

Answer 33

structureless particles that cannot rotate or spin.

Question 34

The best choice for a coordinate system is one

Answer 34

with an axis parallel to the velocity of the incoming particle

Question 35

The equations of conservation of momentum along the x
-axis and y
-axis are very useful in analyzing

Answer 35

two-dimensional collisions of particles, where one is originally stationary (a common laboratory situation).

Question 36

two equations can only be used to find

Answer 36

two unknowns

Question 37

Momentum is conserved because

Answer 37

the surface is frictionless.

Question 38

We can find two unknowns because

Answer 38

we have two independent equations.

Question 39

internal kinetic energy is less after the collision, and so

Answer 39

the collision is inelastic.

Question 40

an elastic collision conserves

Answer 40

nternal kinetic energy.

Question 41

The assumption that the scattering of billiard balls is elastic is

Answer 41

reasonable based on the correctness of the three results it produces. This assumption also implies that, to a good approximation, momentum is conserved for the two-ball system in billiards and pool. These are characteristics of two-dimensional collisions.

Question 42

Momentum is a _____ quantity.

Answer 42

It is a conserved quantity: the total momentum remains fixed within an isolated system. (It’s also a vector.)

Question 43

Momentum always points in the direction of

Answer 43

Velocity

Question 44

A positive velocity means an object is moving to the _____. And a negative velocity means an object is moving to the _____.

Answer 44

right (positive) and left (negative)

Question 45

Inelastic means

Answer 45

The objects stick to each other or their form is changed because of the collision

Question 46

Elastic means

Answer 46

Objects bounce off of each other and are unchanged by the collision.

Question 47

When objects have equal magnitudes but opposite direction, the vector sum of the momentum values is _____.

Answer 47

Zero

Question 48

Conservation of Momentum

Answer 48

Total momentum of a system stays constant if there is no net external force on it. (e.g., a moving ball collides with a ball at rest, the moving ball comes to a stop and the ball at rest moves away with the same momentum of the original moving ball. OR, two objects (one with greater mass) tied by string, with a spring between them, string is cut and the force of the spring sends smaller mass object off with higher velocity and the momentum of each object equals each other.)

Question 49

Total momentum equals

Answer 49

Vector sum of the momenta of each object

Question 50

As the time it takes for an object to experience an impulse increases, the average force on the objects ______.

Answer 50

decreases. (i.e., you meet someone, and you don’t immediately want to rip their clothes off, their force on you is less compared to someone whose clothes you want to rip off right away. Chemistry is a powerful thing! Can make you impulsive!!)

Question 51

Newton’s Second Law

Answer 51

Force acting on an object is equal to the mass of that object multiplied by its acceleration. F = ma (measured in Newtons); The greater the mass of an object, the less acceleration it will experience for a given force.

Question 52

Sum of F = change in momentum over the change in time; this equation states that the rate of change of momentum of an object is directly related to

Answer 52

the force acting on the object.

Question 53

In the context of physics, a conserved quantity is one that

Answer 53

remains unchanged under certain circumstances.

Question 54

when the total momentum is conserved, the sum of the momenta at any two moments should be

Answer 54

equal. This is the Law of Conservation of Momentum.

Question 55

for any type of collision, if the system is considered isolated, the total momentum of the system just before the collision equals ________

Answer 55

equals the total momentum just after the collision

Question 56

An elastic collision is defined as one in which

Answer 56

both momentum and kinetic energy are conserved. The collision between billiard balls is considered to be approximately elastic.

Question 57

Inelastic collisions are defined as collisions in which

Answer 57

momentum is conserved but kinetic energy is not. If the colliding objects stick together, the collision is called perfectly inelastic. After the collision the objects remain in contact. System momentum is conserved, but system energy is not conserved.

Question 58

multiple collisions of objects moving on a two-dimensional surface. For collisions like this, we apply conservation of momentum to each direction, as follows.

Answer 58

pxi = pxf
pyi = pyf

Question 59

By applying the principles of the conservation of momentum, we determine that the initial momentum in the x-direction must equal

Answer 59

the final momentum in the x-direction.

Question 60

Since the vehicles stick together after the collision, we can treat them as _______.

The mass of this body is simply ______.

We can now use our equation for the conservation of momentum to find the final velocity of the car and the truck in the x-direction.

Answer 60

a single object which contains all the momentum of the system.

the combined mass of the car and the truck.

Question 61

To solve elastic collisions, we need to use both our expression for ________, as well as an expression for __________.

Answer 61

the conservation of momentum, as well as an expression for the conservation of kinetic energy.

From this, we are able to see that the relative velocity of the two objects before the collision equals the negative of the relative velocity of the two objects after the collision. (that is, v is positive if it points right and negative if it points left.)
v1i − v2i = −(v1f − v2f)

Question 62

v1i − v2i = −(v1f − v2f)
This equation can be used in conjunction with the expression for the conservation of momentum to solve

Answer 62

problems involving elastic collisions. We can fill in all of our known values and then substitute the expressions into each other.

Question 63

It’s important to remember that in an inelastic collision,

Answer 63

the kinetic energy before the crash is greater than afterwards.