Physics 604 - Simple Machines (Read objectives on screen.) At the end of our last program, your teacher showed you a cartoon of a Rube Goldberg machine. Now that you re machine savvy, you can appreciate this little gizmo. This Rube Goldberg Machine is part of a game, but you might want to build your own as a project. Check with your teacher if you re interested. Now it s time to investigate simple machines further, and that means experimentation and calculations. There are two things we can calculate about machines that will tell us how easy they are to operate in terms of our effort and how efficient they are in terms of the energy used to operate them. The first is mechanical advantage, which is the ratio of output to input forces. In other words, how much does our machine multiply the force we put into it or our effort? Here s the equation for calculating mechanical advantage. Get it into your notes. It s one of those equations that will be given to you on a quiz or test. Mechanical advantage equals the output force divided by the input force. Most machines will have a mechanical advantage greater than one unless they re just changing the direction of the force and not the magnitude. The greater the mechanical advantage of a machine, the easier it is to operate it in terms of our effort. (machine on screen) Mechanical advantage is a measure of how much a machine changes the applied force. The mechanical advantage of a machine can be found by dividing the force exerted by a machine by the force that must be applied to the machine. For example, when jacking up a car, the force that must be applied to the jack is 1500 newtons, while the output force or the weight of the car is 15,000 newtons, making the mechanical advantage of the jack ten. In an ideal machine, the work input will equal the work output. This means that if you double the distance you will cut the force in half. But that is never true of real machines. In real machines, the force times distance we put in will be less than the force times distance output of the machine. So we need to calculate something else about a machine: its efficiency. The efficiency of a machine is the percentage of energy used to operate the machine that actually produces useful work. Remember that energy is the ability to do work, but some of the energy we use to operate the machine, or work input, does not produce the desired effect, or work output. We ll talk about what happens to the lost energy later. To calculate efficiency, we divide work out by work in and multiply by 100 to change it to a percent.
(locomotive on screen) The work output of all machines is less than the work that must be put into them. The efficiency of a machine is a measure of the amount of the output work compared to the amount of work that must be put into the machine. While all machines have an efficiency of less than 100%, some machines are more efficient than others. Typically, the efficiency of most compound machines, such as car engines, are much lower that the efficiency of simple machines. The math involved in calculating mechanical advantage and efficiency is just plug and chug, so we won t do any example problems for now. Instead, let s do an experiment to determine the mechanical advantage and efficiency of this simple machine, the inclined plane. We need to be clear on what we want to accomplish, called the output. We want to raise this object from the table to the top of the plane. The most direct way to do this is to lift it straight up, like this. But what if our object was something heavy, like a piano? We couldn t lift it straight up, so we might use the inclined plane to slide it up, like this. The force I need to apply and the work I do are called input force and work. Before we go into the lab, you ll need to copy a lab table to be ready to record your data. Your teacher will give you this, and then we ll be ready to begin. (student on screen) The first step is to weigh our object. The weight is 5.0 newtons. Record this in your data table as f w. Next, the inclined plane is set at an angle of fifteen degrees. The vertical distance from the table to the top of the incline is measured. This distance, or the height, is point one seven meters. Now, the length of the inclined plane is measured, from the table to the top of the plane. This distance is point five three meters. Finally, a string is used to attach a spring scale to the object, and the object is pulled uniformly up the incline. The spring scale measures the force applied, which is two point two newtons. Record this under input force. (diagram on screen) You should have all the data for our 15-degree trial. Let s go through these calculations together. When we collect data at the 40-degree angle, you can do the calculations on your own. First, let s calculate work in, the work we put into operating the machine. Our applied force, sometimes called the effort force, was 2.2 newtons, and we applied this force over a distance of 0.53 meters up the incline. Since work is force times distance in the same direction, our work is 2.2 newtons times 0.53 meters, or 1.2 joules. Next, we ll calculate the work out. That s the desired outcome, which in this case was to raise the object up to a height of 0.17 meters. If we lifted the object straight up, we would exert a force equal to its weight, over a vertical distance, which is the height of the top of our plane. So work out is 5.0 2
newtons times.17 meters, or 0.85 joules. Now let s calculate the mechanical advantage of this machine, which is the ratio of the force output to input. This tells us how many times the machine multiplies our effort. In this case, force out was the weight of our object, or 5.0 newtons, and force in was the force we exerted to operate the machine, or 2.2 newtons. The mechanical advantage is 2.3. Notice that ratios like these have no units. Finally, we ll calculate the efficiency of the machine, which is work out divided by work in times 100 to make it a per cent. Ours is 0.85 joules divided by 1.2 joules times 100, which is 71 percent. (student on screen) Now we ll change the angle of incline to 40 degrees and collect our data again. The weight of the object is the same as before, but this time the vertical distance, or height, is 0.37 meters. The length of the plane is the same as before, but the applied force, or input force, is 3.8 newtons. Now, you complete the calculations for the 40 degree inclined plane and answer the conclusion questions. Your teacher will check your lab reports and then we ll return to talk about what you ve learned. (table on screen) What have we learned? Let s look at some important data and calculations from the lab. We ll start with mechanical advantage. The mechanical advantage of the 15-degree inclined plane is 2.3, which means that the machine is easy to use. It greatly reduces the force needed to accomplish the task by increasing distance. As the angle of incline gets steeper, the mechanical advantage decreases. Notice that the mechanical advantage of the 40-degree incline is 1.3. If we lifted the load straight up without using a machine, force in and out would be the same, for a mechanical advantage of one, which is no advantage at all. Now look at efficiency. The greater the mechanical advantage, the less efficient the machine is. This means that the easier it is to operate a machine, the more energy we waste in using it. The only way to accomplish our task with 100 percent efficiency is to lift the box straight up without any help. You ll get all this down in your notes in a minute, but first let s talk about the reason a machine can t be 100 percent efficient. You were asked for a reason in your lab report. If you were asked for a oneword explanation, what would that word be? Tell your teacher. The word is "friction." Everyone try this. Put your hands together and rub them like this. What do you feel? Heat. A by-product of friction is always heat. Better get this into your notes. Work done to overcome friction is converted into heat. 3
This heat is released into the surroundings. For this reason, friction is called a dissipative force. The term dissipate means to disperse or scatter. So work done to overcome a dissipative force such as friction causes energy to be scattered into the surroundings. As we slide the object up the inclined plane, we have to overcome friction. The lower the angle of incline is, the greater the distance we ll have to slide the object to get it up to a certain height, and the more friction we ll have to overcome. So as the machine becomes easier to operate, it becomes less and less efficient. Better get this in your notes, too. As mechanical advantage increases, the efficiency of a machine decreases. This loss of efficiency is due to friction. Even a well-oiled machine cannot be 100-percent efficient. The problems we ll give you involving machines will be very straight-forward, and we ll give you the formulas for calculating mechanical advantage and efficiency. For example, try these calculations involving a pulley system. Local Teachers, turn off the tape and give students problem set number one from facilitator's guide The most important step in solving these problems is identifying the input and output forces and distances. Always look for at what will be accomplished by the machine, and label it output. In this problem, Doris wants to raise the 1100 newton piano 4.0 meters. This is the force out and the distance out. Labeling it right on the problem will really help. And she must put in a force of 250 newtons over a distance of 22 meters, so that s the input. Now all we have to do is use the equations given to us and plug and chug. Mechanical advantage is force out over force in, which is 1100 newtons over 250 newtons, for a mechanical advantage of 4.4. Work in is 250 newtons times 22 meters, or 5500 joules. Work out is 1100 newtons times 4.0 meters, or 4400 joules. And efficiency is work out over work in times 100, or 4400 joules divided by 5500 joules. This machine is 80 percent efficient. Now we need to talk about one more aspect of machines their power! 4
(man with lawn mower on screen) A man brags to his neighbor that his new lawnmower is very powerful. He says, This machine can cut an acre of grass. The neighbor tries it and is impressed. But then he says, Wait a minute. My old lawnmower can cut an acre of grass, too. So it must be just as powerful. What other quantity do the neighbors need to measure to describe the power of each lawnmower? Tell your teacher. There is more to power than just how much work is done. Power involves time, too. Did you get it? Watch this and then we ll take some notes. (car on screen) Another term we hear frequently in association with machines and their performance is power. Power is the rate at which work can be done. Power is calculated by dividing work by time. To demonstrate the usefulness of the steam engine, James Watt, a Scottish engineer, compared the amount of work a steam engine could do in 1 day to the amount of work a horse could do in the same time. From these experiments, the term horsepower was developed. Even today, the output of car engines is calculated in horsepower. In standard international units, power is measured in watts. One watt of power is defined as work being done at the rate of 1 joule per second. One horsepower equals seven hundred forty six watts. In physics, power is defined as the amount of work done per unit time. We use a capital P as the symbol for power, and the equation for calculating power is power equals work divided by time. In the MKS system, the unit for measuring power is the watt, which is abbreviated with a lower case w. One watt equals one joule per second. Let s try this power problem together. A box weighing 580 newtons is lifted 22 meters straight up in 15 seconds by a machine. What is the power of the machine? We know that power equals work divided by time and that work is force times displacement. So the power of our machine equals 580 newtons times 22 meters divided by 15 seconds. The answer is 850 joules per second, or 850 watts. You can expect all the problems involving the mechanical advantage, efficiency, and power of machines to be straightforward. And remember that we ll give you the equations. Now your teacher will give you some more practice in calculating mechanical advantage, efficiency, 5
and power. You ll go over the solutions in class. When you ve had enough time to practice, I mean come back and we ll go on to our next topic. Well, so far, we ve concentrated our study of energy on work and simple machines. But there s a lot more to energy that you need to know. So now it s time to dive a little deeper into the study of energy. (fire on screen) Energy comes in many forms. Heat Light Electric energy and Sound (Sound Effect: thunder) are just a few. Since this semester of physics is devoted to the study of mechanics, we ll concentrate our study of energy on mechanical energy. Mechanical energy is any energy due to the motion or position of an object. You might not have heard of mechanical energy, but it s pretty easy to figure out. You know that mechanics is the study of objects and their motion. So mechanical energy is the energy an object has because of its motion or because its position can lead to motion. You also know that all energy can be divided into two types, kinetic energy and potential energy. That s true of mechanical energy, too. Let s get this in your notes. There are two types of mechanical energy. Kinetic energy is an object s energy due to its motion. Potential energy is the energy stored by an object because of its position. Look at these examples of kinetic and potential energy. (roller coaster on screen) All forms of energy can be classified as either kinetic or potential. Kinetic energy is energy in motion. To understand kinetic energy, consider a bowling ball. When a bowling ball is thrown down the lane, it posses kinetic energy. When it strikes the pins, it transfers some of the energy to them. Thus it can be said that the ball does work on the bowling pins. (rock formation on screen) Another broad category of energy is potential energy. An object may also have the ability to do wrok because of its state or position. The skydivers about to jump out of this plane have potential energy. 6
Do you remember how we defined energy in a previous program? It s the ability to do what? (Brief Pause) You re right if you said "work.". Well, work and energy are very closely connected. They re even measured in the same unit, the joule. And the connection goes farther than just using the same unit. Work and energy are interchangeable or transferable. When work is done on an object, the object gains kinetic or potential energy. And when work is done by an object, the object loses kinetic or potential energy. (bulldozer on screen) Energy is defined as the ability to do work. This front-end loader performs about 40,000 J of work, lifting a 10,000 N pile of dirt 4 m. The amount of work done on an object is a measure of the amount of energy needed to do that work. Whenever work is done, energy is transferred. In the previous example, approximately 40,000 J was required to lift 10,000 N of dirt 4 m. The loader used 40,000 J of energy, while the dirt gained 40,000 J. Note that the amount of work needed to lift an object equals the amount of energy gained by the object. We ll learn more about the relationship between work and energy in the next program. But now, it s time to SHOW WHAT YOU KNOW!! Jot down your choice for each question. Your local teacher will go over the correct answers with you. (Read Show What You Know questions on screen) Well, that s it for this program. Next time, you ll use the relationship between work and energy to derive equations for calculating both kinetic energy and potential energy. And we ll finally get around to explaining this toy. See you later. 7