Chapter 10: Work and Energy 10.1 Machines and Mechanical Advantage 10.2 Work 10.3 Energy and Conservation of Energy Chapter 10 Objectives Calculate the mechanical advantage for a lever or rope and pulleys. Calculate the work done in joules for situations involving force and distance. Give examples of energy and transformation of energy from one form to another. Calculate potential and kinetic energy. Apply the law of energy conservation to systems involving potential and kinetic energy. Chapter Vocabulary chemical energy closed system law of conservation of energy electrical energy fulcrum gears input input arm input force joule kinetic energy lever machine mechanical advantage mechanical energy mechanical system nuclear energy output output arm output force potential energy pressure energy radiant energy ramp rope and pulley screw simple machine thermal energy work Inv 10.1 Machines and Mechanical Advantage Investigation Key Question: How do simple machines work? 10.1 Machines and Mechanical Advantage The ability of humans to build buildings and move mountains began with our invention of machines. In physics the term simple machine means a machine that uses only the forces directly applied and accomplishes its task with a single motion. 10.1 Machines The best way to analyze what a machine does is to think about the machine in terms of input and output. 10.1 Mechanical Advantage Mechanical advantage is the ratio of output force to input force. For a typical automotive jack the mechanical advantage is 30 or more. A force of 100 newtons (22.5 pounds) applied to the input arm of the jack produces an output force of 3,000 newtons (675 pounds) enough to lift one corner of an automobile. 10.1 Mechanical Advantage MA = F o F i Output force (N) Input force (N) Mechanical advantage 10.1 Types of simple machines The lever, wheel and axle, rope and pulleys, screw, ramp, and gears are the most common simple machines. Complex machines, combine many simple machines into mechanical systems. A mechanical system is an assembly of simple machines that work together to accomplish a task. 10.1 Mechanical Advantage of a Lever The essential features of a lever are the input arm, output arm, and fulcrum. 10.1 Three types of levers The three types of levers are classified by the location of the input and output forces relative to the fulcrum: first class lever second class lever third class lever 10.1 How a lever works A lever works by rotating about its fulcrum. The mechanical advantage can be deduced by calculating the torques created by the input and output forces. The input force creates a (positive) counterclockwise torque. The torque created by the reaction force is clockwise (negative). When the lever is in equilibrium the net torque must be zero. 10.1 Torque and mechanical advantage You are asked for the location of the fulcrum You are given input force, lever length, mass to be lifted Since you are told to assume F o = F w, use: F w = mg, MA = F o F i, MA = L i L o Solve for F o = (.5) (500 kg) (9.8 N/kg) = 2,450 N Solve for MA = 2,450 N 700 N = 3.5 Since L i = 3.5 L o, and L i + L o = 3m, then L o =.67m Calculating the position of the fulcrum Where should the fulcrum of a lever be placed so one person weighing 700N can lift the edge of a stone block with a mass of 500 kg? The lever is a steel bar three meters long. Assume a person can produce an input force equal to their own weight. Assume that the output force of the lever must equal half the weight of the block to lift one edge. 10.1 Mechanical advantage of ropes and pulleys A tension force is a pulling force acting along the direction of a rope or string. Ropes and strings carry tension forces throughout their length. If friction is small, the tension force in a rope is the same everywhere. If you were to cut a rope in tension and insert a force scale, the scale would measure the same force at any point along the rope. 10.1 Rope & Pulleys The block-and-tackle machine is a simple machine using one rope and multiple pulleys. The rope and pulleys can be arranged to create different amounts of mechanical advantage. 10.1 Wheels, gears, & rotating machines Wheels and axles provide advantages. Friction occurs where the wheel and axle touch or where the wheel touches a surface. Rolling motion creates less wearing away of material compared with two surfaces sliding over each other. With gears the trade-off is made between torque and rotation speed. An output gear will turn with more torque when it rotates slower than the input gear. 10.1 Ramps and Screws Ramps reduce input force by increasing the distance over which the input force needs to act. A screw is a simple machine that turns rotating motion into linear motion. A thread wraps around a screw at an angle, like the angle of a ramp. Chapter 10 Work and Energy 10.1 Machines and Mechanical Advantage 10.2 Work 10.3 Energy and Conservation of Energy Inv 10.2 Work Investigation Key Question: What is the trade-off for multiplying forces in a machine? 10.2 Work In physics, work has a very specific meaning. In physics, work represents a measurable change in a system, caused by a force. 10.2 Work If you push a box with a force of one newton for a distance of one meter, you have done exactly one joule of work. 10.2 Work (force is parallel to distance) W = F x d Distance (m) Force (N) Work (joules) 10.2 Work (force at angle to distance) W = Fd cos ( ) Distance (m) Force (N) Work (joules) Angle 10.2 Work done against gravity W = mgh Height object raised (m) Gravity (m/sec 2 ) Work (joules) Mass (kg) You are asked for the work and time it takes to do work. You are given mass, height, and work done per second. Use: W = mgh. Solve: W = (1,500 kg) ( 9.8 N/kg) (50 m) = 735,000 J At a rate of 10,000 J/s, it takes 73.5 s to lift the beam. Calculate work done against gravity A crane lifts a steel beam with a mass of 1,500 kg. Calculate how much work is done against gravity if the beam is lifted 50 meters in the air. How much time does it take to lift the beam if the motor of the crane can do 10,000 joules of work per second? 10.2 Work done by a machine Work is usually done when a force is applied to a simple machine. All machines can be described in terms of input work and output work. In any machine, some of the input work goes to overcoming friction. The output work is always less than the input work because of the energy lost to friction. Chapter 10 Work and Energy 10.1 Machines and Mechanical Advantage 10.2 Work 10.3 Energy and Conservation of Energy Inv 10.3 Energy and Conservation of Energy Investigation Key Question: How is motion on a track related to energy? 10.3 Energy and Conservation of Energy Energy describes a systems ability to cause change. A system that has energy has the ability to do work. Energy is measured in the same units as work because energy is transferred during the action of work. 10.3 Different forms of energy Mechanical energy is the energy possessed by an object due to its motion or its position. Radiant energy includes light, microwaves, radio waves, x-rays, and other forms of electromagnetic waves. Nuclear energy is released when heavy atoms in matter are split up or light atoms are put together. The electrical energy we use is derived from other sources of energy. The workings of the universe can be viewed as energy flowing from one place to another and changing back and forth from one form to another. 10.3 Potential Energy Objects that have potential energy do not use the energy until they move. An objects potential energy comes from the gravity of Earth. Technically, energy from height is called gravitational potential energy. Other forms of potential energy also exist, such as potential energy stored in springs. 10.3 Potential Energy E p = mgh Height (m) Mass (kg) Potential Energy (joules) Acceleration of gravity (m/sec 2 ) You are asked for potential energy and time. You are given mass, height and work done per second. Use: E p = mgh. Solve for E p = (102 kg) (9.8 N/kg) (4 m) = 3,998 J. At a rate fof 50 J/s, it takes 80 s to push the cart up the ramp. Calculating potential energy A cart with a mass of 102 kg is pushed up a ramp. The top of the ramp is 4 meters higher than the bottom. How much potential energy is gained by the cart? If an average student can do 50 joules of work each second, how much time does it take to get up the ramp? 10.3 Kinetic Energy Energy of motion is called kinetic energy. The kinetic energy of a moving object depends on two things: mass and speed. Kinetic energy is proportional to mass. 10.3 Kinetic Energy Mathematically, kinetic energy increases as the square of speed. If the speed of an object doubles, its kinetic energy increases four times (mass is constant). 10.3 Kinetic Energy E k = 1 mv 2 2 Speed (m/sec) Mass (kg) Kinetic Energy (joules) 10.3 Kinetic Energy Kinetic energy becomes important in calculating braking distance. 10.3 The formula for kinetic energy A force (F) is applied to mass (m) and creates acceleration (a). After a distance (d), the ball has reached speed (v), therefore the work done is its mass times acceleration time distance: W= fd = (ma) x d = mad Also: d = at 2 Replace d in the equation for work, combine similar terms: W= ma ( at 2 ) = ma 2 t 2 Also: v = at, so v 2 = a 2 t 2 Replace a 2 t 2 by v 2 shows that the resulting work is the formula for kinetic energy: W = mv 2 You are asked for kinetic energy and stopping distance You are given mass, speed and force of brakes. Use E k = 1 / 2 mv 2 and W= fd Solve for E k = (1,300 kg) ( 30 m/s) 2 = 585,000 J To stop the car, work done by brakes = E k of car, so W = E k Solve for distance = W f = 585,000J 9,500 N = 62 m Calculating kinetic energy A car with a mass of 1,300 kg is going straight ahead at a speed of 30 m/s (67 mph). The brakes can supply a force of 9,500 N. Calculate: a) The kinetic energy of the car. b) The distance it takes to stop. 10.3 Law of Conservation of Energy As energy takes different forms and changes things by doing work, nature keeps perfect track of the total. No new energy is created and no existing energy is destroyed. 10.3 Energy in a closed system The conservation of energy is most useful when it is applied to a closed system. Because of the conservation of energy, the total amount of matter and energy in your system stays the same forever. 10.3 Energy in a closed system The total energy in the system is the potential energy of the ball at the start. Later, the ball is at a lower height (h) moving with speed (v) and has both potential and kinetic energy. Every day in the United States the average person uses about 90 million joules of electrical energy. This energy comes from many sources, including burning coal, gas and oil, nuclear power, and hydroelectric power. Hydroelectric Power In hydroelectric power, the potential energy of falling water is converted to electricity. No air pollution is produced, nor hazardous wastes created.