Introduction to Momentum and Energy, Circular Motion PDF

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The concepts of motion covered include objects turning or going in complete circles. The understanding of gravitation not only explains forces on the surface of Earth but also the motion of satellites and planets. Finally, the concepts of momentum and energy are another way to analyze and understand...

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PHY-102 Lecture 2 Introduction to Momentum and Energy Introduction to Circular Motion Topic 1 discussed how changes in motion (acceleration) are caused by a non-zero net force. In fact, Newton's first law of motion stated that when all forces are balanced (the net force is zero), an object in motion will remain in motion at a constant speed in a straight line. An interesting application of Newton's laws of motion arises when considering objects moving in circles, including objects turning even if it is only a fraction of a circle. In order to make an object turn right, it must have a change in velocity toward the right. This by definition means that it needs to have acceleration toward the right, which can only be caused by a net force toward the right. For an object that continues to turn, making a circle, the force needs to continually point toward the center. This net force toward the center is often called the centripetal force or center-seeking force, as opposed to a centrifugal force, or center-fleeing force. Examples include swinging an object around on a string, where the centrifugal force is caused by the tension force in the string, or a car turning on a flat road, where the centripetal force is caused by the friction. The planets of the Solar System move in almost circular orbits as do most of the satellites around Earth. These circular motions are caused by the force of gravity. Sir Isaac Newton recognized that the forces on the planets are in fact the same forces that hold people to the ground on Earth's surface. He correctly argued that the force of gravity between two masses is proportional to the masses and inversely proportional to the distance between the masses squared, i.e., if the distance between two masses increases by a factor of two, then the force decreases by a factor of four (two squared).

Introduction to Momentum The quantity obtained as a product of mass and velocity is called momentum. This may also be referred to as inertia in motion - more mass and/or more velocity result in more momentum. In other words, momentum is a measure of how hard it is to stop something. The concept of momentum is useful to understand a variety of real-life phenomena. First, there is the impulse-momentum theorem, which states that impulse - defined as the product of force and time - equals the change in momentum. Some examples

include pitching a baseball. The greater the force and the greater the time during which the force is exerted on the ball, the greater the change in momentum, which in this case translates to the greater speed. Likewise, in a car crash, the car is designed to buckle and crumble, which serves to increase the time for a person inside to stop, and thus decrease the necessary force. A second useful application of momentum arises from the fact that the total momentum in a system is conserved, as long as no outside forces are acting on the system. This not only explains, but also facilitates calculations in situations such as the firing of a bullet. Before the bullet was shot the bullet and the gun both had zero momentum, thus after the explosion the sum of the momentum of the bullet and the momentum of the gun must still be zero. This can only be possible if the gun has a backward momentum equal to the bullet's forward momentum. The gun has a much larger mass than the bullet and thus will have a much smaller backward velocity. A collision between two cars is another example of a complicated interaction, where the law of conservation of momentum can be very useful. A general benefit of a conservation law is its ability to relate the situation before some event to the situation after the event, without a need to know about the sometimes very complicated interactions occurring during the event.

Introduction to Energy Energy is usually defined as the ability to do work. This definition is only useful if work is first defined in science terms. Work is defined as the product of force and distance, where only the force acting in the direction of the motion is used. With this definition, work is done when lifting an object, while no work is done if the object is held at the same height. Similarly, work is done if an object is pushed for some distance, such as kicking a ball or moving a table across the floor. Doing work is a way of transferring energy. If someone kicks a ball, that person did some work. This was accomplished by burning some calories (chemical energy) in their body and giving the ball some energy as a result. In other words, energy was transferred from one form in the body to another form possessed by the ball. The energy possessed by the ball in this case is called kinetic energy (energy of motion). Similarly, if a box is lifted from the floor onto a shelf, work is done. This is accomplished by transferring energy from one form in the body to another form possessed by the box. The energy possessed by the box by virtue of its position is called potential energy. Potential energy is stored energy with the potential of doing some work (transferring energy) later. The water behind a dam has large amounts of potential energy that can be transferred to kinetic energy in the turbines of a hydroelectric power plant.

The total amount of energy in the universe is constant. This is referred to by scientists as the law of conservation of energy. When gasoline burns to make engines run, chemical energy is being transferred from the gasoline to heat and then to motion in the cylinders of the engine, which in turn gives the car its kinetic energy. No energy was lost or created in these processes. Energy was just transferred between different forms. It should be noted that the transfer from chemical energy to the final kinetic energy of the car is not very efficient - only a relatively small percentage of the initial chemical energy ends as useful kinetic energy. A much larger part is transferred to the environment as heat.

Simple Machines A group of devices known as simple machines provides a great illustration of the law of conservation of energy in a smaller and simpler setting. A machine is a device that allows people to control the forces and the distances of the work they do, but the machine does not do any work. As much energy has to be put into the machine as is wanted to get out. In fact, in most cases more energy has to be put in, since some of the energy initially put in is transferred to the environment in the form of heat, rather than to the final object of focus. Lifting a large boulder can be accomplished by applying a large force for a relatively small distance, or a lever can be used to lift the boulder. With the lever the force can be significantly reduced, but now a force needs to be applied for a considerably longer distance. Other examples of simple machines include the wheel and axle, which is employed in the gears of a bicycle, the jackscrew, which allows you to lift a car to change a flat tire, and the ramp , which allows you to load a moving truck with considerable ease.

Conclusion The concepts of motion covered include objects turning or going in complete circles. The understanding of gravitation not only explains forces on the surface of Earth, but also the motion of satellites and planets. Finally, the concepts of momentum and energy are another way to analyze and understand the motion of objects....