#### Quiz

A box slides with initial velocity 10m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity?

The initial momentum is:

$\ Mv_{i} = (10) M$

The final momentum must be the same!!

The final momentum is:

$\ M_{tot} v_{f} = (2M) v_{f} = (2M) (5)$

A. 10 m/s B. 20 m/s C. 0 m/s D. 15 m/s E. 5 m/s

**Answer) E.**

The initial momentum is:

$\ Mv_{i} = (10) M$

The final momentum must be the same!!

The final momentum is:

$\ M_{tot} v_{f} = (2M) v_{f} = (2M) (5)$

#### Perfectly inelastic collision Simulation(Virtual Experiment)

When the next simulation is not visible, please refer to the following link.

(https://helpx.adobe.com/flash-player/kb/enabling-flash-player-chrome.html)

**Do the math!**

1) Consider a 2-kg fish that swims toward and swallows a 1-kg fish that is swims at –10 m/s. If the larger fish swims at 10 m/s, what is its velocity immediately after lunch?

Momentum is conserved from the instant before lunch until the instant after (in so brief an interval, water resistance does not have time to change the momentum), so we can write

$\ net~ momentum _{before~ lunch} = net~ momentum _{after ~lunch}$

$\ (net ~mv) _{before} = (net~ mv) _{after}$

$\ (2 kg)(10 m/s) + (1 kg)(-10 m/s) = (2 kg + 1 kg)(v_{after})$

$\ 10 kgm/s=(3 kg)(v_{after})$

$\ v_{after}=\frac{10}{3} m/s$

#### Let's study about the following content

**Conservation of Momentum**

From Newton’s second law you know that to accelerate an object, a net force must be applied to it. This chapter says much the same thing, but in different language. If you wish to change the momentum of an object, exert an impulse on it.

In either case, the force or impulse must be exerted on the object by something outside the object. Internal forces won’t work. For example, the molecular forces within a basketball have no effect on the momentum of the basketball, just as a push against the dashboard of a car you’re sitting in does not affect the momentum of the car. Molecular forces within the basketball and a push on the dashboard are internal forces. They come in balanced pairs that cancel within the object. To change the momentum of the basketball or the car, an outside push or pull is required. If no outside force is present, no change in momentum is possible.

Momentum, like the quantities velocity and force, has both direction and magnitude. It is a vector quantity. Like velocity and force, momentum can be canceled. So, although the cannonball in the preceding example gains momentum when fired and the recoiling cannon gains momentum in the opposite direction, the cannon–cannonball system gains none. The momenta (plural form of momentum) of the cannonball and the cannon are equal in magnitude and opposite in direction. Therefore, these momenta cancel each other out for the system as a whole. No external force acted on the system before or during firing. Since no net force acts on the system, there is no net impulse on the system and there is no net change in the momentum.

In every case, the momentum of a system cannot change unless it is acted on by external forces. A system will have the same momentum before some internal interaction as it has after the interaction occurs.

When momentum, or any quantity in physics, does not change, we say it is conserved. The law of conservation of momentum describes the momentum of a system. The law of conservation of momentum states that, in the absence of an external force, the momentum of a system remains unchanged. If a system undergoes changes wherein all forces are internal as for example in atomic nuclei undergoing radioactive decay, cars colliding, or stars exploding, the net momentum of the system before and after the event is the same.

**Collisions**

As you go about your day-to-day activities, you probably witness many collisions without really thinking about them. In some collisions, two objects collide and stick together so that they travel together after the impact. An example of this action is a collision between football players during a tackle, as shown in Figure 1.

In an isolated system, the two football players would both move together after the collision with a momentum equal to the sum of their momenta (plural of momentum) before the collision. In other collisions, such as a collision between a tennis racquet and a tennis ball, two objects collide and bounce so that they move away with two different velocities.

The total momentum remains constant in any type of collision. However, the total kinetic energy is generally not conserved in a collision because some kinetic energy is converted to internal energy when the objects deform. In this

section, we will examine different types of collisions and determine whether kinetic energy is conserved in each type.We will primarily explore two extreme types of collisions: elastic and perfectly inelastic collisions.

**Perfectly inelastic collisions can be analyzed in terms of momentum**

When two objects, such as the two football players, collide and move together as one mass, the collision is called a perfectly inelastic collision. Likewise, if a meteorite collides head on with Earth, it becomes buried in Earth and the collision is perfectly inelastic.

*Figure 1. When one football player tackles another, they both continue to fall together. This is one familiar example of a perfectly inelastic collision.*

Perfectly inelastic collisions are easy to analyze in terms of momentum because the objects become essentially one object after the collision. The final mass is equal to the combined masses of the colliding objects. The combination moves with a predictable velocity after the collision.

Consider two cars of masses $\ m_{1}$ and $\ m_{2}$ moving with initial velocities of $\ v_{1,i}$ and $\ v_{2,i}$ along a straight line, as shown in Figure 11. The two cars stick together and move with some common velocity, $\ v_{f}$ , along the same line of motion after the collision. The total momentum of the two cars before the collision is equal to the total momentum of the two cars after the collision.

*Figure 2. The total momentum of the two cars before the collision (a) is the same as the total momentum of the two cars after the inelastic collision (b).*

PERFECTLY INELASTIC COLLISION$\ m_{1}v_{1,i} + m_{2}v_{2,i} = (m_{1} + m_{2}) v_{f}$ |

This simplified version of the equation for conservation of momentum is useful in analyzing perfectly inelastic collisions.When using this equation, it is important to pay attention to signs that indicate direction. In Figure 2, $\ v_{1,i}$ has a positive value ($\ m_{1}$ moving to the right), while $\ v_{2,i}$ has a negative value ($\ m_{2}$ moving to the left).

**Kinetic energy is not conserved in inelastic collisions**

In an inelastic collision, the total kinetic energy does not remain constant when the objects collide and stick together. Some of the kinetic energy is converted to sound energy and internal energy as the objects deform during the collision.

This phenomenon helps make sense of the special use of the words elastic and inelastic in physics.We normally think of elastic as referring to something that always returns to, or keeps, its original shape. In physics, an elastic material is one in which the work done to deform the material during a collision is equal to the work the material does to return to its original shape. During a collision, some of the work done on an inelastic material is converted to other forms of energy, such as heat and sound.