Wednesday, January 6, 2010

Momentum Lab Make-up

Read the following information on momentum. Once you have read the information, follow the link at the bottom to answer the momentum questions.

Momentum

If a compact car and large truck are traveling with the same velocity, it takes longer for the truck to stop than it does for the car if the same braking force is applied. Likewise, it takes longer for a fast moving car to stop than it does for a slow moving car with the same mass. The truck and the fast moving car have more momentum than the compact car and the slow moving car.
Momentum is a property of a moving object that depends on the object’s mass and velocity. The more momentum an object has, the harder it is to stop the object or change its direction.

Although the compact car and the truck are traveling with the same velocity, the truck has more mass and therefore more momentum, so it is harder to stop than the car. Similarly, the fast moving car has a greater velocity and thus more momentum than the slow moving car.
Momentum is defined as the mass of an object multiplied by its velocity. That is:

Momentum = mass x velocity

Or in shorthand notation,

Momentum = mv

We can see from the definition that a moving object can have a large momentum if either its mass is large, or its speed is large, or both. A truck has a larger momentum than a car moving at the same speed because its mass is larger. A weighty ship moving at a small speed and a lightweight bullet moving at high speed can both have the same large momentum. And, of course, a heavy object moving at a high speed, such as a massive truck rolling down a steep hill with no brakes, has a huge momentum. The same truck at rest has no momentum at all.

Momentum is Conserved

When a moving object hits another object, some or all of the momentum of the first object is transferred to the other object. If only some of the momentum is transferred, the rest of the momentum stays with the first object.
Imagine you hit a billiard ball with a cue ball so that the billiard ball starts moving and the cue ball stops. The cue ball had a certain amount of momentum before the collision. During the collision, all of the cue ball’s momentum was transferred to the billiard ball. After the collision, the billiard ball moved away with the same amount of momentum the cue ball had. This example illustrates the law of conservation of momentum. Any time two or more objects interact, they may exchange momentum, but the total amount of momentum stays the same.
Bowling is another example of how conservation of momentum is used in a game. The bowling ball rolls down the lane with a certain amount of momentum. When the ball hits the pins, some of the ball’s momentum is transferred to the pins and the pins move off in different directions. Furthermore, some of the pins that were hit by the ball go on to hit other pins, transferring the momentum again.

Conservation of Momentum and Newton’s Third Law
Conservation of momentum can be explained by Newton’s third law. In the example with the billiard ball, the cue ball hit the billiard ball with a certain amount of force. This was the action force. The reaction force was the equal but opposite force exerted by the billiard ball on the cue ball. The action force made the billiard ball start moving, and the reaction force made the cue ball stop moving. Because the action and reaction forces are equal and opposite, momentum is conserved.

Click on the following link to answer the Momentum questions
Momentum Questions

Energy Lab Make-up

Read the following information on energy. Once you have read the information, follow the link at the bottom to answer the energy questions.

Energy

When work is done by an archer in drawing a bow, the bent bow has the ability to do that amount of work on the arrow. When work is done to raise the heavy ram of a pile driver, the ram acquires the ability to do that work on the object it hits when it falls. When work is done to wind a spring mechanism, the spring acquires the ability to do work on various gears to run a clock, ring a bell, or sound an alarm.

In each case, something has been acquired. This “something” that is given to the object enables the object to do work. It may be in the form of a compression of atoms in the material of an object; it may be a physical separation of attracting bodies; it may be a rearrangement of electric charges in the molecules of a substance. This “something” that enables an object to do work is energy. Energy is measure in a unit called Joules. It appears in many forms. For now we will focus on mechanical energy – the energy due to the position or the movement of something. Mechanical energy may be in the form of either potential energy or kinetic energy.

Potential Energy
An object may store energy by virtue of its position. The energy that is stored and held in readiness is called potential energy (PE), because in the stored state it has the potential for doing work. A stretched or compressed spring, for example, has the potential for doing work. When a bow is drawn, energy is stored in the bow. A stretched rubber band has potential energy because of its position, for if it is part of a slingshot, it is capable of doing work.

The chemical energy in fuels is potential energy, for it is actually energy of position on a microscopic scale. This energy is available when the positions of the electric charges within and between molecules are altered, that is, when a chemical change takes place. Any substance that can do work through chemical action possesses potential energy. Potential energy is found in fossil fuels, electric batteries, and the food we eat.

Work is required to elevate objects against earth’s gravity. The potential energy due to elevated position is called gravitational potential energy. Water in an elevated reservoir and the ram of a pile driver have gravitational potential energy.

The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward times the vertical distance it is moved (W=Fd). The upward force required (while moving at constant velocity) is equal to the weight mg of the object, so the work done in lifting it through a height h is given by the product mgh:

Gravitational potential energy = weight x height
PE = mgh

Note that the height h is the distance above some reference level, such as the ground or the floor of a building. The potential energy mgh is relative to the level and depends only on mg and the height h. The potential energy of an object on a ledge does not depend on the path taken to get it there.

Kinetic Energy
Push on an object and you can set it in motion. If an object moves, then by virtue of that motion it is capable of doing work. It has energy of motion, or kinetic energy (KE). The kinetic energy of an object depends on the mass of the object as well as its speed. It is equal to half the mass multiplied by the square of the speed.

Kinetic energy = ½ mass x speed2
KE = ½ mv2

When you throw a ball, you do work on it to give it speed when it leave your hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it to that speed from rest, or the work the object can do in being brought to rest:

net force x distance = kinetic energy

or in shorthand notation,

Fd = ½ mv2

Note that the speed is squared, so that if the speed of an object is doubled, its kinetic energy is quadrupled (22 = 4). This means it takes four times the work to double the speed; also an object moving twice as fast take four times as much work to stop. Accident investigators are well aware that a car going 60 mph has four times the kinetic energy it has at 30 mph. So a car going 60 mph will skid four times as far when its brakes are locked than it would at 30 mph. This is because speed is squared for kinetic energy.

Kinetic energy underlies other seemingly different forms of energy such as heat (random molecular motion), sound (molecules vibrating in rhythmic patterns), and light (originating from the motions of electrons within atoms). There is much in common among the various forms of energy.

Conservation of Energy
More important than being able to state what energy is, is understanding how it behaves – how it transforms. You can understand nearly every process or change that occurs in nature better if you analyze it in terms of a transformation of energy from one form to another.

As you draw back the stone in a slingshot, you do work in stretching the rubber band; the rubber band then has potential energy. When released, the stone has kinetic energy equal to this potential energy. It delivers this energy to its target, perhaps a wooden fence post. The slight distance the post is moved multiplied by the average force of impact doesn’t quite match the kinetic energy of the stone. The energy score doesn’t balance. But if you investigate further, you’ll find that both the stone and the fence post are a bit warmer. By how much? By the energy difference. Energy changes from on form to another. It transforms without net loss or net gain.

The study of the various forms of energy and their transformations from one form into another lead to one of the greatest generalizations in physics, known as the law of conservation of energy:

Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

When you consider any system in its entirety, whether it be as simple as a swinging pendulum or as complex as an exploding galaxy, there is one quantity that does not change: energy. It may change form, or it may simply be transferred from one place to another, but the total energy score stays the same.

This energy score takes into account the fact that the atoms that make up matter are themselves concentrated bundles of energy. When the nuclei (cores) of atoms rearrange themselves, enormous amounts of energy can be released. The sun shines because some of this energy is transformed into radiant energy. In nuclear reactors much of this energy is transformed into heat.

Powerful gravitational forces in the deep hot interior of the sun crush the cores of hydrogen atoms together to form helium atoms. This welding together of atomic cores is called thermonuclear fusion. This process releases radiant energy, some of which reaches the earth. Part of this energy falls on plants, and the plant energy is later stored as coal. Another part supports marine life in the ocean’s food chain that begins with plants, and part of this energy later becomes oil. Part of the energy from the sun goes into the evaporation of water from the ocean, and part of this returns to the earth as rain that may be trapped behind a dam. By virtue of its position, the water in a dam has energy that may be used to power a generating plant below, where it will be transformed to electric energy. The energy travels through wires to homes, where it is used for lighting, heating, cooking, and to operate electric toothbrushes. How nice that energy is transformed from one form to another!

Click on the following link to answer the Energy questions
Energy Questions

Force Lab Make-up

Read the following information on force. Once you have read the information, follow the link at the bottom to answer the force questions.

Force


Kick a football and it moves. Its path through the air is not a straight line – it curves due to gravity. Catch the ball and it stops. Most of the motion we see undergoes change. Most things start up, slow down, or curve as they move. Objects at rest or moving at constant velocity have no net force acting on them. Their motion is not changing. A more common case is that in which there is a change in motion – that is, accelerated motion.
Recall that acceleration describes how fast motion is changing. Specifically, it is the change in velocity per certain time interval. In shorthand notation,
Acceleration = (change in velocity)/(time interval)
This is the definition of acceleration. The cause of acceleration is a force.

Force causes acceleration
Consider an object at rest, such as a hockey puck on ice. Apply a force and it moves. Since it was not moving before, it has accelerated – changed its motion. When the stick is no longer in contact with the puck, it moves at constant velocity. Apply another force by striking it with the stick again, and the motion changes. Again, the puck has accelerated. Forces are what produce accelerations.

Most often, the force we apply is not the only force that acts on an object. Other forces may act as well. The combination of all the forces that act on an object is called the net force. It is the net force that accelerates an object.

Forces combine to produce net forces. When more than one force acts in the same direction on an object, the net force is the sum of the forces. When forces act in opposite directions, the net force is the difference of the forces. If you pull horizontally with a force of 10 N on an object that rests on a friction-free surface, an air track for example, then the net force acting on it is 10 N. If a friend assists you and pulls at the same time on the same object with a force of 5 N in the same direction, then the net force will be the sum of these forces, 15 N. The object will accelerate as if it were pulled with a single force of 15 N. If, however, your friend pulls with 5 N in the opposite direction, the net force will be the difference of these forces, 5 N. The acceleration of the object would be the same as if it were instead pulled with a single force of 5 N.

We find that the amount of acceleration depends on the amount of the net force. To increase the acceleration of an object, you must increase the net force. This makes good sense. Double the force on an object and you will double the acceleration. If you triple the force, you’ll triple the acceleration, and so on. We say that the acceleration produced is directly proportional to the net force. (As one goes up the other goes up, as one goes down, the other goes down)

Mass Resists Acceleration
Push on an empty shopping cart. Then push equally hard on a heavily loaded shopping cart, and you’ll produce much less acceleration. This is because acceleration depends on the mass being pushed upon. For objects of greater mass we find smaller accelerations. Twice as much mass for the same force results in only half the acceleration; three times the mass results in one third the acceleration, and so forth. In other words, for a given force the acceleration produced is inversely proportional to the mass. By inversely we mean that the two values change in opposite directions
(As one goes up, the other goes down).

Newton’s Second Law
Newton was the first to realize that the acceleration we produce when we move something depends not only on how hard we push or pull (the force) but on the mass as well. He came up with one of the most important rules of nature ever proposed, his second law of motion.

Newton’s second law states:

The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is the same direction as the net force, and is inversely proportional to the mass of the body.


Or in shorter notation,

A = F/M or F = MA

The acceleration is equal to the net force divided by the mass. Rearranging the equation we get the net force equals the mass times the acceleration. From this relationship we can see that if the net force that acts on an object is doubled, the acceleration will be doubled. Suppose instead that the mass is doubled. Then the acceleration will be halved. If both the net force and the mass are doubled, then the acceleration will be unchanged.

Click on the following link to answer the force questions
Force Questions

Friction Lab Make-up

Read the following information on Friction. Once you have read the information, follow the link at the bottom to answer the friction questions.

Friction

Picture a warm summer day. You are enjoying the day by wearing shorts and tossing a ball with your friends. By accident, one of your friends tosses the ball just out of your reach. You have to make a split-second decision to dive for it or not. You look down and notice that if you dove for it, you would most likely slide across pavement rather than the surrounding grass. What would you decide?

Unless you enjoy scraped knees, you probably would not want to slide on the pavement. The painful difference between sliding on grass and sliding on pavement has to do with friction. Friction is a force that opposes motion between two surfaces that are touching.

The Source of Friction
Friction occurs because the surface of any object is rough. Even surfaces that look or feel very smooth are actually covered with microscopic hills and valleys. When two surfaces are in contact, the hills and valleys of one surface stick to the hills and valleys of the other surface. This contact causes friction even when the surfaces appear smooth.
The amount of friction between two surfaces depends on many factors, including the roughness of the surfaces and the force pushing the surfaces together.
Rougher Surfaces create more friction
Rougher surfaces have more microscopic hills and valleys. Thus, the rougher the surface, the greater the friction. Think back to the pavement vs. grass example. Pavement is much rougher than grass. Therefore, more friction is produced when you slide on the pavement than when you slide on grass. This increased friction is more effective at stopping your sliding, but it is also more painful! On the other hand, if the surfaces are smooth, there is less friction. I you were to slide on ice instead of on grass, your landing would be even more comfortable – but also much colder!
Greater Force Creates More Friction
The amount of friction also depends on the force pushing the surfaces together. If this force is increased, the hills and valleys of the surfaces can come into closer contact. This causes the friction between the surfaces to increase. Less massive objects exert less force on surfaces than more massive objects do. For example, there is more friction between a more massive book and the table than there is between a less massive book and a table. A harder push is needed to overcome friction to move the more massive book. However, changing the amounts of the surfaces that touch does not change the amount of friction.

Types of Friction
The friction you observe when sliding books across a tabletop is called sliding friction. Other types of friction include rolling friction, fluid friction, and static friction. As you will learn, the name of each type of friction is a big clue as to the conditions where it can be found.

Sliding Friction
If you push an eraser across your desk, the eraser will move for a short distance and then stop. This is an example of sliding friction. Sliding friction is very effective at opposing the movement of objects and is the force that causes the eraser to sop moving. You can feel the effect of sliding friction when you try to move a heavy dresser by pushing it along the floor. You must exert a lot of force to overcome the sliding friction.
You use sliding friction when you go sledding, when you apply the brakes on a bicycle or a car, or when you write with a piece of chalk.
Rolling Friction
If the same heavy dresser were on wheels, you would have an easier time moving it. The friction between the wheels and the floor is an example of rolling friction. The force of rolling friction is usually less than the force of sliding friction. Therefore, it is generally easier to move objects on wheels than it is to slide them along the floor.
Rolling friction is an important part of almost all means of transportation. Anything with wheels-bicycles, skateboards, cars, trains and planes – use rolling friction between the wheels and the ground to move forward.
Fluid Friction
Why is it harder to walk on a freshly mopped floor than on a dry floor? The reason is that on the wet floor the sliding friction between your feet and the floor is replaced by fluid friction between your feet and the water. In this case, fluid friction is less than sliding friction, so the floor is slippery. The term fluid includes liquids, such as water and milk, and gases, such as air and helium.
Fluid friction opposes the motion of objects traveling through a fluid. For example, fluid friction between air and a fast moving car is the largest force opposing the motion of the car. You can observe this friction by holding your hand out the window of a moving car.
Static Friction
When a force is applied to an object but does not cause the object to move, static friction occurs. The object does not move because the force of static friction balances the force applied. Static friction disappears as soon as an object starts moving, and then another type of friction immediately occurs like sliding friction.

Friction Can Be Harmful or Helpful
Think about how friction affects a car. Without friction, the tires could not push against the ground to move the car forward and the brakes could not stop the car. Without friction, a car is useless. However, friction can cause problems in a car too. Friction between moving engine parts increases their temperature and cause the parts to wear down. A liquid coolant is added to the engine to keep it from overheating, and engine pars need to be changed as they wear out.
Friction is both harmful and helpful to you and the world around you. Friction can cause holes in your socks and in the knees of your jeans. Friction by wind and water can cause erosion of the topsoil that nourishes plants. On the other hand, friction between your pencil and your paper is necessary for the pencil to leave a mark. Without friction, you would just slip and fall when you tried to walk. Because friction can be both harmful and helpful, it is sometimes necessary to reduce or increase friction.

Some Ways to Reduce Friction
One way to reduce friction is to use lubricants. Lubricants are substances that are applied to surfaces to reduce the friction between them. Some examples of common lubricants are motor oil, wax, and grease.
Friction can also be reduced by switching from sliding friction to rolling friction. Ball bearings are place between the wheels and axles of in-line skates and bicycles to make it easier for the wheels to turn by reducing friction.
Another way to reduce friction is to make surfaces that rub against each other smoother. For example, rough wood on a park bench is painful to slide across because there is a large amount of friction between your leg and the bench. Rubbing the bench with sandpaper makes it smoother and more comfortable to sit on because the friction between your leg and the bench is reduced.
Some ways to Increase Friction
One way to increase friction is to make surfaces rougher. For example, sand scattered on icy roads keeps cars from skidding. Baseball players sometimes wear textured batting gloves to increase the friction between their hands and the bat so that the bat does not fly out of their hands.
Another way to increase friction is to increase the force pushing the surfaces together. For example, you can ensure that your magazine will not blow away at the park by putting a heavy roc on it. The added mass of the rock increases the friction between the magazine and the ground. Or if you are sanding a piece of wood, you ca sand the wood faster by pressing harder on the sandpaper.

Click on the following link to answer the friction questions
Friction Questions