chapter 11

Question 1

what is a collision ?

Answer 1

A collision is a short-duration interaction between two objects. The collision between a tennis ball and a racket, or a baseball and a bat, may seem instantaneous to your eye, but that is a limitation of your perception. A high-speed photograph reveals that the side of the ball is significantly flattened during the collision. It takes time to compress the ball, and more time for the ball to re-expand as it leaves the racket or bat.

Question 2

the duration of the collision depends on what ?

Answer 2

The duration of a collision depends on the materials from which the objects are made
The harder the objects, the shorter the contact time.

Question 3

how do you model a colliding ball ?

Answer 3

hows an object colliding with a wall. The object approaches with an initial horizontal velocity vix experiences a force of duration Δt and leaves with final velocity vfx Notice that the object, as in the photo above, deforms during the collision. A particle cannot be deformed, so we cannot model colliding objects as particles. Instead, we model a colliding object as an elastic object that compresses and then expands, much like a spring. Indeed, that’s exactly what happens during a collision at the microscopic level: Molecular bonds compress, store elastic potential energy, then transform some or all of that potential energy back into the kinetic energy of the rebounding object.

Question 4

what is an impulsive force ?

Answer 4

The force of a collision is usually very large in comparison to other forces exerted on the object. A large force exerted for a small interval of time is called an impulsive force. The graph of Figure 11.1 shows how a typical impulsive force behaves, rapidly growing to a maximum at the instant of maximum compression, then decreasing back to zero.

Question 5

what is momentum ?

Answer 5

The product of a particle’s mass and velocity is called the momentum of the particle:

(11.3)
momentum= p ≡ mv

Question 6

is momentum a vector or scalar ?

and what its units ?

Answer 6

Momentum, like velocity, is a vector. The units of momentum are kg m/s.

Question 7

can you decompose the momomentum ?

Answer 7

The momentum vector p⃗ is parallel to the velocity vector v.→ Figure 11.2 shows that p⃗ , like any vector, can be decomposed into x- and y-components. Equation 11.3, which is a vector equation, is a shorthand way to write the simultaneous equations

px=mvx
py=mvy

One of the most common errors in momentum problems is a failure to use the appropriate signs. The momentum component px has the same sign as vx. Momentum is negative for a particle moving to the left (on the x-axis) or down (on the y-axis).

Question 8

when does a object have a large momemtum ?

Answer 8

An object can have a large momentum by having either a small mass but a large velocity or a small velocity but a large mass. For example, a 5.5 kg (12 lb) bowling ball rolling at a modest 2 m/s has momentum of magnitude p=(5.5kg)(2 m/s)=11kg m/s. This is almost exactly the same momentum as a 9 g bullet fired from a high-speed rifle at 1200 m/s.

Question 9

what is impulse ?

Answer 9

Strictly speaking, impulse has units of Ns but you should be able to show that Ns are equivalent to kg m/s, the units of momentum.

jx = impulse

is the area under the curve

Question 10

what is momentum principle ?

Answer 10

This result, called the momentum principle, says that an impulse delivered to an object causes the object’s momentum to change. The momentum pfx “after” an interaction, such as a collision or an explosion, is equal to the momentum pix “before” the interaction plus the impulse that arises from the interaction:

(11.9)
pfx=pix+Jx
pix+ area under the force curve (force vs time graph)

Question 11

final velocity for momemtum

which formula ?

Answer 11

the final velocity is vfx=pfx/m.

Question 12

conservation of momentum ?

Answer 12

the momentum before the collision is the same as the momentum after the collision.
it remains constant in an isolated system.
ex: when a car hits a another car with the same mass (bit was immobile)
the momentum is the same.

this is true in an isolated system where the fnet is equal to 0 .

Question 13

newtons third law and collisions

Answer 13

you can use newtons third law to describe whats happening during the collision
when the ball hits the when, the ball exerts a force on a ball
in addition, the wall also exerts a force on the ball.
these are equal forces.
so, when the ball loses momentum, the wall will gain an equal amount of that momentum.

Question 14

choosing a system

Answer 14

be careful when choosing a system.
in order to do a conserve momentum, there must be no forces in your system. Isolated
or else you cant use that;

Question 15

what a perfectly inelastic collisions ?

and give an example

Answer 15

A collision in which the two objects stick together and move with a common final velocity is called a perfectly inelastic collision.

The clay hitting the floor and the bullet embedding itself in the wood are examples of perfectly inelastic collisions. Other examples include railroad cars coupling together upon impact and darts hitting a dart board.

Question 16

whats the key to analyzing a perfectly inelastic collisions ?

Answer 16

the key to analyzing a perfectly inelastic collision is the fact that the two objects have a common final velocity.

Question 17

is a perfectly inelastic collision an isolated system or no ?

Answer 17

A system consisting of the two colliding objects is isolated, so its total momentum is conserved. However, mechanical energy is not conserved because some of the initial kinetic energy is transformed into thermal energy during the collision.

Question 18

in a inelastic collision , what happens to the energy ?

Answer 18

In an inelastic collision, some of the mechanical energy is dissipated inside the objects as thermal energy and not all of the kinetic energy is recovered.

Question 19

whats a perfectly elastic collision ?

Answer 19

We’re now interested in “perfect bounce” collisions in which kinetic energy is stored as elastic potential energy in compressed molecular bonds, and then all of the stored energy is transformed back into the post-collision kinetic energy of the objects. A collision in which mechanical energy is conserved is called a perfectly elastic collision.

A perfectly elastic collision is an idealization, like a frictionless surface, but collisions between two very hard objects, such as two billiard balls or two steel balls, come close to being perfectly elastic.

Question 20

the collision in a perfectly elastic collision must follow 2 laws :
which one ?

Answer 20

The collision must obey two conservation laws: conservation of momentum (obeyed in any collision) and conservation of mechanical energy (because the collision is perfectly elastic). Although the energy is transformed into potential energy during the collision, the mechanical energy before and after the collision is purely kinetic energy.

Question 21

are perfectly elastic and inelastic collisions happens in real life ?

Answer 21

No collision is perfectly elastic, although collisions between two very hard objects (metal spheres) or between two springs (such as a collision on an air track) come close. Collisions can be perfectly inelastic, although many real-world inelastic collisions exhibit a small residual bounce. Thus perfectly elastic and perfectly inelastic collisions are models of collisions in which we simplify reality in order to gain understanding without getting bogged down in the messy details of real collisions.

Question 22

what is an explosion ?

Answer 22

An explosion, where the particles of the system move apart from each other after a brief, intense interaction, is the opposite of a collision. The explosive forces, which could be from an expanding spring or from expanding hot gases, are internal forces. If the system is isolated, its total momentum during the explosion will be conserved.

Question 23

momentum definition in words

Answer 23

Momentum can be defined as “mass in motion.” All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.

Question 24

an object with momentum is hard to stop ? why ?

and how do you stop it ?

Answer 24

Any object with momentum is going to be hard to stop. To stop such an object, it is necessary to apply a force against its motion for a given period of time. The more momentum that an object has, the harder that it is to stop. Thus, it would require a greater amount of force or a longer amount of time or both to bring such an object to a halt. As the force acts upon the object for a given amount of time, the object’s velocity is changed; and hence, the object’s momentum is changed.

Question 25

momentum and the direction of the force

Answer 25

A force acting for a given amount of time will change an object’s momentum. Put another way, an unbalanced force always accelerates an object - either speeding it up or slowing it down. If the force acts opposite the object’s motion, it slows the object down. If a force acts in the same direction as the object’s motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed.

Question 26

impulse-momentum equation

explain in words what it means

Answer 26

In a collision, an object experiences a force for a specific amount of time that results in a change in momentum. The result of the force acting for the given amount of time is that the object’s mass either speeds up or slows down (or changes direction). The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m • Δ v.

Question 27

newtons third and second law for momentum

Answer 27

Newton’s third law of motion is naturally applied to collisions between two objects. In a collision between two objects, both objects experience forces that are equal in magnitude and opposite in direction. Such forces often cause one object to speed up (gain momentum) and the other object to slow down (lose momentum). According to Newton’s third law, the forces on the two objects are equal in magnitude. While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude. In accord with Newton’s second law of motion, the acceleration of an object is dependent upon both force and mass. Thus, if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force that results during the collision.

Question 28

explain a collision between 2 billiards ball

Answer 28

Consider the collision between a moving seven ball and an eight ball that is at rest in the sport of table pool. When the seven ball collides with the eight ball, each ball experiences an equal force directed in opposite directions. The rightward moving seven ball experiences a leftward force that causes it to slow down; the eight ball experiences a rightward force that causes it to speed up. Since the two balls have equal masses, they will also experience equal accelerations. In a collision, there is a force on both objects that causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction. For collisions between equal-mass objects, each object experiences the same acceleration.

Question 29

Consider the interaction between a male and female figure skater in pair figure skating. A woman (m = 45 kg) is kneeling on the shoulders of a man (m = 70 kg); the pair is moving along the ice at 1.5 m/s and the man throw her into a spin

explain what happens ?

Answer 29

he man gracefully tosses the woman forward through the air and onto the ice. The woman receives the forward force and the man receives a backward force. The force on the man is equal in magnitude and opposite in direction to the force on the woman. Yet the acceleration of the woman is greater than the acceleration of the man due to the smaller mass of the woman.

Question 30

how to tell if a system is isolated ?

Answer 30

A system is a collection of two or more objects. An isolated system is a system thatF is free from the influence of a net external force that alters the momentum of the system. There are two criteria for the presence of a net external force; it must be…

a force that originates from a source other than the two objects of the system
a force that is not balanced by other forces.
A system in which the only forces that contribute to the momentum change of an individual object are the forces acting between the objects themselves can be considered an isolated system.

Consider the collision of two balls on the billiards table. The collision occurs in an isolated system as long as friction is small enough that its influence upon the momentum of the billiard balls can be neglected. If so, then the only unbalanced forces acting upon the two balls are the contact forces that they apply to one another. These two forces are considered internal forces since they result from a source within the system - that source being the contact of the two balls. For such a collision, total system momentum is conserved.

Question 31

is momentum the same before and after the collision ?

Answer 31

For collisions occurring in isolated systems, there are no exceptions to this law. This same principle of momentum conservation can be applied to explosions. In an explosion, an internal impulse acts in order to propel the parts of a system (often a single object) into a variety of directions. After the explosion, the individual parts of the system (that is often a collection of fragments from the original object) have momentum. If the vector sum of all individual parts of the system could be added together to determine the total momentum after the explosion, then it should be the same as the total momentum before the explosion. Just like in collisions, total system momentum is conserved.

Question 32

in explosions, does the to object follows newtons third law ?

Answer 32

Just like in collisions, the two objects involved encounter the same force for the same amount of time directed in opposite directions. This results in impulses that are equal in magnitude and opposite in direction. And since an impulse causes and is equal to a change in momentum, both carts encounter momentum changes that are equal in magnitude and opposite in direction.

Question 33

if the masses are the same or different in an explosion,

what happens to their velocity and momentum ?

Answer 33

If the masses of the two objects are equal, then their post-explosion velocity will be equal in magnitude (assuming the system is initially at rest). If the masses of the two objects are unequal, then they will be set in motion by the explosion with different speeds. Yet even if the masses of the two objects are different, the momentum change of the two objects (mass • velocity change) will be equal in magnitude.