Ch7_CantorA

= = =toc Homework=

Lesson 1a (3/5)
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. **Momentum = mass • velocity** In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as **p = m • v** where **m** is the mass and **v** is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.

The standard metric unit of momentum is the kg•m/s. While the kg•m/s is the standard metric unit of momentum, there are a variety of other units that are acceptable (though not conventional) units of momentum.

Momentum is a **vector quantity**.

From the definition of momentum, it becomes obvious that an object has a large momentum if either its mass or its velocity is large. Both variables are of equal importance in determining the momentum of an object.

A doubling of the mass results in a doubling of the momentum.Similarly, if the 2.0-kg cart had a velocity of 8.0 m/s (instead of 2.0 m/s), then the cart would have a momentum of 16.0 kg•m/s (instead of 4.0 kg•m/s). A //quadrupling// in velocity results in a//quadrupling// of the momentum.

All questions were answered successfully and efficiently.

Lesson 1b (3/6)
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.

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.

These concepts are merely an outgrowth of Newton's Second Law as discussed in an earlier unit. Newton's second law (Fnet = m • a) stated that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. Ft=m** Δ **V In physics, the quantity Force • time is known as **impulse**. And since the quantity m•v is the momentum, the quantity m•Δv must be the **change in momentum**. The equation really says that the **Impulse = Change in momentum**

One focus of this unit is to understand the physics of collisions. The physics of collisions are governed by the laws of momentum; and the first law that we discuss in this unit is expressed in the above equation. The equation is known as the **impulse-momentum change equation** .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.

Collisions in which objects rebound with the same speed (and thus, the same momentum and kinetic energy) as they had prior to the collision are known as **elastic collisions**. In general, elastic collisions are characterized by a large velocity change, a large momentum change, a large impulse, and a large force. Force and time are inversely proportional; for the same mass and velocity change. Mass and force are directly proportional Mass and velocity change are inversely proportional.

Lesson 1c (3/6)
There are four physical quantities mentioned in the above statement - force, time, mass, and velocity change.

First we will examine the importance of the collision time in affecting the amount of force that an object experiences during a collision. Observe that the greater the time over which the collision occurs, the smaller the force acting upon the object. Thus, to minimize the effect of the force on an object involved in a collision, the time must be increased. And to maximize the effect of the force on an object involved in a collision, the time must be decreased.

There are several real-world applications of these phenomena. One example is the use of air bags in automobiles. Air bags are used in automobiles because they are able to minimize the effect of the force on an object involved in a collision. The same principle explains why dashboards are padded. If the air bags do not deploy (or are not installed in a car), then the driver and passengers run the risk of stopping their momentum by means of a collision with the windshield or the dashboard.

Occasionally when objects collide, they bounce off each other as opposed to //sticking to each other// and traveling with the same speed after the collision. Bouncing off each other is known as **rebounding**. From the impulse-momentum change theorem, we could deduce that a rebounding situation must also be accompanied by a large impulse.

The importance of rebounding is critical to the outcome of automobile accidents. In an automobile accident, two cars can either collide and bounce off each other or collide, //crumple up// and travel together with the same speed after the collision. But which would be more damaging to the occupants of the automobiles - the rebounding of the cars or the crumpling up of the cars? Contrary to popular opinion, the crumpling up of cars is the safest type of automobile collision.

Lesson 2d (3/8)
The momentum lost by one object is equal to the momentum gained by another object. For collisions occurring in an isolated system, there are no exceptions to this law.

Such a motion can be considered as a collision between a person and a medicine ball. Before the collision, the ball has momentum and the person does not. The collision causes the ball to lose momentum and the person to gain momentum. After the collision, the ball and the person travel with the same velocity ( **v** ) across the ice.

The process of solving this problem involved using a conceptual understanding of the equation for __ [|momentum (p=m*v)] __. This equation becomes a guide to thinking about how a change in one variable effects a change in another variable. The constant quantity in a collision is the momentum (momentum is conserved). For a constant momentum value, mass and velocity are inversely proportional. Thus, an increase in mass results in a decrease in velocity. Mbefore*Vbefore=Mafter*Vafter

Lesson 2e (3/8)
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 conserve.

**Equal and Opposite Momentum Changes** 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. If the exploding system includes two objects or two parts, this principle can be stated in the form of an equation as: 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.

**Solving Explosion Momentum Problems** Since total system momentum is conserved in an explosion occurring in an isolated system, momentum principles can be used to make predictions about the resulting velocity of an object. Problem solving for explosion situations is a common part of most high school physics experiences.

Whether it is a collision or an explosion, if it occurs in an isolated system, then each object involved encounters the same impulse to cause the same momentum change. The impulse and momentum change on each object are equal in magnitude and opposite in direction. Thus, the total system momentum is conserved.