Work and Energy Unit 5 Work • Issues talked about have the same meaning in everyday life as they do in physics • In everyday life, work means to do something that takes physical or mental effort • In physics work has a different meaning Ex: holding a heavy chair at arms length for several minutes No work is done on the chair Ex: carry a bucket of water along a horizontal path while walking at constant velocity No work is done on the bucket Work • Work is done on an object when a force causes a displacement of the object • Work-the product of the component of a force along the direction of displacement and the magnitude of the displacement W=Fd Where W is work, F is force, and d is displacement Work is not done on an object unless the object is moved with the action of a force The object must move otherwise no work is done on the object Work • Work is done only when components of a force are parallel to a displacement Components of the force perpendicular to a displacement do not do work If I push on a crate on a horizontal surface at an angle, , below horizontal, only the horizontal component of the force causes a displacement and contributes to the work W=Fd cos() If many forces are acting on an object, you can find the net work done by finding the net force on the object first Wnet=Fnetd cos() Work • Work has dimensions of force times length Units for work 1 Nm=1J 1 joule of work is about the amount of work needed to raise an apple from your waist to the top of your head Work • The sign of work is important Work is a scalar quantity and can be positive or negative Work is positive when the component of force is in the same direction as the displacement • Also for when an object speeds up Work is negative when the force is in the direction opposite the displacement • Ex: kinetic friction, work done by friction is negative • Also for when an object slows down Work • Ex: How much work is don on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0 degrees above the horizontal? Energy • Kinetic energy-the energy of an object that is due to the object’s motion Kinetic energy depends on speed and mass KE=(1/2)mv2 Mass is measured in kg, velocity in m/s Kinetic energy is a scalar quantity and is measured in units of joules If a bowling ball and a volleyball are traveling at the same speed, which do you think has the grater kinetic energy? Energy • Ex: A 7.00 kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g table tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis player? Energy • The net work done on a body equals its change in kinetic energy Work-kinetic energy theorem - the net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy Wnet=KE Wnet=(1/2)mvf2-(1/2)mvi2 When using this theorem, you must include all the forces that do work on the object in calculating the net work done The work-kinetic theorem allows us to think of kinetic energy as the work that an object can do while the object changes speed or as the amount of energy stored in the motion of an object Energy • Ex: On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10? Energy • Potential Energy-the energy associated with an object because of the position, shape, or condition of the object Potential energy is stored energy Associated with an object that has the potential to move because of its position relative to some other locations Depends on properties of the object and its interaction with its environment Energy • Gravitational potential energy-the potential energy stored in the gravitational fields of interacting bodies Gravitational potential energy depends on height from a zero level PEg=mgh Only for when free-fall acceleration is constant over the entire height Zero level can be arbitrarily set Ex: marble falls off a table Potential energy is converted to kinetic energy Energy • Elastic potential energy-the energy available for use when a deformed elastic object returns to its original configuration Elastic potential energy depends on distance compressed or stretched Ex: a spring The length of a spring when no external forces are acting on it is called the relaxed length of the spring When an external force compresses or stretches the spring, elastic potential energy is stored in the spring PEelastic=(1/2)kx2 Where k is called the spring constant and x is the distance the spring is compressed or stretched Energy • Ex: A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling? Conservation of Energy • The description of the motion of many objects often involve a combination of kinetic and potential energy as well as different forms of potential energy Ex: pendulum clock At the highest point of its swing, there is only gravitational potential energy associated with its position At other points in the swing, the pendulum has motion so it has kinetic energy as well Conservation of Energy • We can ignore other forms of energy (I.e. chemical, heat, etc.) if their influence is negligible or if they are not relevant to the situation being analyzed • Mechanical Energy-the sum of kinetic energy and all forms of potential energy ME=KE+PE Nonmechanical energy types: nuclear, chemical internal, and electrical MECHANICAL ENERGY IS NOT A UNIQUE FORM OF ENERGY. IT IS ONLY A WAY OF CLASSIFYING ENERGY! Conservation of Energy • Mechanical energy is conserved (assuming no friction) Conserved means is converted between different forms, but not lost The total potential energy and kinetic energy of an object will be the same anywhere along its path MEi=MEf (in the absence of friction) Depends on the forms of potential energy (1/2)mvi2+mghi=(1/2)mvf2+mghf Conservation of Energy • Energy conservation occurs even when acceleration varies We can apply a new method of solving problems because of this instead of worrying about constant acceleration We set up the initial mechanical energy equal to the final mechanical energy and ignore the information in between Conservation of Energy • Mechanical energy is not conserved in the presence of friction Total energy is always conserved However, when friction is involved, the mechanical energy is converted into forms of energy that are much more difficult to account for Therefore that energy is considered to be “lost” Conservation of Energy • Ex: Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg. Power • Power-a quantity that measures the rate at which work is done or energy is transformed P=W/t An alternate form is substituting W=Fd into the equation P=Fd/t d/t is another way of writing the speed of an object P=Fv Power • SI unit is the watt, W One joule per second Horsepower is another unit of power 1 hp=746 watts Power • Ex: A 193 kg curtain needs to be raised 7.5 m, at constant speed, in as close to 5.0 s as possible. The power rating for three motors are listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job?