CH6_braunsteinc

=lesson 1=

A:
 Motion will be approached from the perspective of work and energy. The affect that work has upon the energy of an object (or system of objects) will be investigated; the resulting velocity and/or height of the object can then be predicted from energy information. It is important to first have a solid understanding of a few basic terms. Important terms: [|mechanical energy], [|potential energy] , [|kinetic energy] , and [|power]. When a force acts upon an object to cause a displacement of the object, it is said that **work** was done upon the object. Three keys: force, displacement, and cause. In order for a force to qualify as having done //work// on an object, there must be a displacement and the force must //cause// the displacement.

Mathematically, work can be expressed by the following equation. where **F** is the force, **d** is the displacement, and the angle ( **theta** ) is defined as the angle between the force and the displacement vector. The angle measure is defined as the angle between the force and the displacement. To gather an idea of it's meaning, consider the following three scenarios.
 * Scenario A: A force acts rightward upon an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are in the same direction. Thus, the angle between F and d is 0 degrees.
 * Scenario B: A force acts leftward upon an object that is displaced rightward. In such an instance, the force vector and the displacement vector are in the opposite direction. Thus, the angle between F and d is 180 degrees.
 * Scenario C: A force acts upward on an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are at right angles to each other. Thus, the angle between F and d is 90 degrees.

==== **To Do Work, Forces Must //Cause// Displacements** It can be accurately noted that the waiter's hand did push forward on the tray for a brief period of time to accelerate it from rest to a final walking speed. But once //up to speed //, the tray will stay in its straight-line motion at a constant speed without a forward force. And if the only force exerted upon the tray during the constant speed stage of its motion is upward, then no work is done upon the tray. Again, a vertical force does not do work on a horizontally displaced object.. The angle theta in the equation is associated with the amount of force that causes a displacement. ====

**The Meaning of Theta**
When determining the measure of the angle in the work equation, it is important to recognize that the angle has a precise definition - it is the angle between the force and the displacement vector. A //force// is applied to a cart to //displace// it up the incline at constant speed. Several incline angles are typically used; yet, the force is always applied parallel to the incline. The displacement of the cart is also parallel to the incline. Since F and d are in the same direction, the angle theta in the work equation is 0 degrees. The angle is defined as the angle between the force and the displacement vector.

**The Meaning of Negative Work**
On occasion, a force acts upon a moving object to hinder a displacement. In such instances, the force acts in the direction opposite the objects motion in order to slow it down.These situations involve what is commonly called //negative work//. The //negative// of negative work refers to the numerical value that results when values of F, d and theta are substituted into the work equation. .  **Units of Work**  In the case of work (and also energy), the standard metric unit is the **Joule** (abbreviated **J** ). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words, **1 Joule = 1 Newton * 1 meter****1 J = 1 N * m** In fact, any unit of force times any unit of displacement is equivalent to a unit of work. Some nonstandard units for work are shown below. In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">Work is when a force acts on an object and causes displacement; to determine the amount of work done, three quantities must be know: force, displacement, and the angle between the force and displacement.

=<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">lesson 2: =

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">lesson 2- A:
<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">We will learn that there are certain types of forces, that when present and when involved in doing work on objects will change the total mechanical energy of the object. And there are other types of forces that can never change the total mechanical energy of an object, but rather can only transform the energy of an object from potential energy to kinetic energy (or vice versa). The two categories of forces are referred to as internal forces and external forces.

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;"> For our purposes, we will simply say that **external forces** include the applied force, normal force, tension force, friction force, and air resistance force. And for our purposes, the **internal forces** include the gravity forces, magnetic force, electrical force, and spring force.

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;"> <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;"> When net work is done upon an object by an external force, the [|total mechanical energy (KE + PE)] of that object is changed. If the work is //positive work//, then the object will gain energy. If the work is //negative work//, then the object will lose energy. The gain or loss in energy can be in the form of [|potential energy], [|kinetic energy] , or both. Under such circumstances, the work that is done will be __equal__ to the change in mechanical energy of the object. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as **nonconservative forces**.

<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">When the only type of force doing net work upon an object is an internal force (for example, gravitational and spring forces), the [|total mechanical energy (KE + PE)] of that object remains constant. In such cases, the object's energy changes form. . Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as **conservative forces**.