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Download IB 2.3 Work and Energy Jan 10 Agenda
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Physics 1 – Jan 10, 2017 P3 Challenge– (Use energy methods.)A special operations soldier parachute jumps out of an airplane moving at 45.0 m/s. How fast is the soldier moving when the parachute is opened 10.5 m below the plane? (Assume air resistance is negligible during his descent.) Today’s Objective: Review for Test on Jan 17 Get out the Cons of Energy problem set for a HW check. Agenda, Assignment IB 2.3 Work, Energy and Power Assignment: Agenda Omelet Review More Practice Problems for Exam 4 Homework Review Study for Test on Tues Jan 17 Time to work on Practice Problems Physics Work defined Work is the product of a force through a distance. Positive work When the force and the displacement are in the same direction Adds to the energy of a system. Negative work When the force and the displacement are in opposite directions Removes energy from a system Note: friction always does negative work. When is work NOT done? A perpendicular force does no work. Force applied without any change in position does no work. Work at an angle – general case Forces in the same or opposite direction do maximum work. Forces at an angle – only the component of the force in the direction of the displacement does work. IB equation: 𝑾 s may be written as x, y, r or d. W = Fd (vector dot product) = 𝑭𝒔cos𝛉 in data booklet Work by a variable force If a force is not constant over the distance, then you can plot how the force varies as a function of position. Still a force times a distance. The work done by the force over a distance is represented by the area between the graph and the x-axis on this graph. Ex: Work done by a spring force: W = ½ kx2 Practice Problems A worker pulls a cart with a 45 N force at an angle of 25 to the horizontal over a distance of 1.2 m. What work does the worker do on the cart? A 900N mountain climber scales a 100m cliff. How much work is done by the mountain climber? Angela uses a force of 25 Newtons to lift her grocery bag while doing 50 Joules of work. How far did she lift the grocery bags? Energy What is energy? The ability to do work. Comes in two varieties: EK = kinetic energy Ep = potential energy Types of kinetic energy: motion, light, sound, thermal energy, electrical energy (all are a type of motion) Types of potential energy: gravitational, chemical, nuclear, spring, electrical potential (all are reversibly stored energy) Kinetic Energy Kinetic energy – energy of motion Anything that is moving has kinetic energy EK = ½ mv2 (in data booklet) Ex: What is the Kinetic Energy of a 150 kg object that is moving with a speed of 15 m/s? Ex: An object has a kinetic energy of 25 J and a mass of 34 kg , how fast is the object moving? Ex: An object moving with a speed of 35 m/s and has a kinetic energy of 1500 J, what is the mass of the object? Work – K.E. Theorem The net work done on an object is equal to the change in kinetic energy for that object. Wnet = K.E = ½ mv2 –½ mu2 not in data booklet, need to know conceptually. a. The distance the helicopter traveled? b. The work done by the lifting force? c. The work done by the gravitational force? d. The net work done on the helicopter? e. The final kinetic energy of the helicopter? f. The final velocity of the helicopter? g. Verify this value using kinematics. Ex: A 500. kg light-weight helicopter ascends from the ground with an acceleration of 2.00 m/s2. Over a 5.00 sec interval, what is Change in energy for a system Positive work, Win Negative work, Wout Removes energy from a system Positive Heat, Qin Adds to the energy of a system. Adds to the energy of a system. Negative Heat, Qout Removes energy from a system Overall: ∆𝑬 =𝑾+𝑸 Types of Systems Depending on how you draw the boundary of your system, there are three types of systems that can occur: Open, Closed and Isolated. An open system allows both matter and energy (in the form of work and/or heat) to flow over the border of the system. A closed system prohibits matter exchange over the border, but still allows a change in energy (heat and/or work) An isolated system prohibits both matter and energy exchange over the border of the system. Conservation of Energy If you can identify an isolated system, then the E for the system will be zero. The result is a conservation of energy between any two states of the system over time. Many physical situations fall under this category. The notable exception is when there is an external force doing work on the system, usually in the form of friction. Note: This is a conservation of energy for a given system. Contrast this to the general idea of conservation of energy in the universe. Conservative Forces and Potential E If a force does no net work during any closed loop sequence of events, then the force is conservative. If work is done, the force is nonconservative. Consider a swinging pendulum. The work done by gravity over a complete swing is zero. It has positive work as the pendulum falls, but does an equal amount of negative work as the pendulum rises again. Therefore, gravity is a conservative force. For every conservative force, there is a corresponding potential energy defined. Ug = – Wg Ug = mgh (Note IB uses the general symbol Ep for all potential energies) Conservative Forces and Potential E Consider a mass oscillating on a spring on a horizontal frictionless table. For one complete cycle, the spring does zero work. As the mass is being compressed, the spring does negative work, as it moves back to equilibrium it does an equal amount of positive work. As is becomes extended, the spring again does negative work until it turns around. As the mass returns to equilibrium an equal amount of positive work is done. Therefore, the spring force is a conservative force. Us = – Ws Us = ½ kx2 (Note IB uses the general symbol Ep for all potential energies) Problem Solving with Cons of Energy As long as only conservative forces are present, then the total amount of energy in an isolated system will be constant. Problem solving strategy is to inventory the types of energy present at time 1 and set their sum equal to the inventory of types of energy present at time 2. The types of problems one can solve this way are similar to problems we previously solved with kinematics. Hint: Choose a convenient point to set Ep = 0 to make life easy. (Here: Ug= 0 at bottom of hill.) Ex: A 55 kg sled starting at rest slides down a virtually frictionless hill. How fast will the sled be moving when it reaches the field 1.2 m below? Ex: What if the sled had an initial speed of 1.5 m/s? When there is friction…. Friction is a nonconservative force that does negative work on a system. The change in energy of the system E = W is equal to the work done by friction. Or Ek1 + EP1 + Wnc = EK2 + EP2 Ex: A 62.9-kg downhill skier is moving with a speed of 12.9 m/s as he starts his descent from a level plateau at 123-m height to the ground below. The slope has an angle of 14.1 degrees and a coefficient of friction of 0.121. The skier coasts the entire descent without using his poles; upon reaching the bottom he continues to coast to a stop; the coefficient of friction along the level surface is 0.623. How far will he coast along the level area at the bottom of the slope? (Use energy methods) Power Power is defined as the rate at which work is done. 𝑷= ∆𝑾 ∆𝒕 In mathematics this is a time derivative or Power is measured in Watts, (W) with 1 W = 1 J/s An alternative formula for power is easily derived if one considers Work as a force times a change in displacement. Change in displacement over change in time we know as velocity. So 𝑷 = ∆𝑾 ∆𝒕 =𝑭∙ ∆𝒙 ∆𝒕 𝑷 = 𝐅 ∙ 𝐯 = 𝐅𝐯𝐜𝐨𝐬 𝛉 Power problems Ex: Running late to class, Jerome runs up the stairs, elevating his 102 kg body a vertical distance of 2.29 meters in a time of 1.32 seconds at a constant speed. What power did Jerome generate? Ex: At what velocity is a car moving at the instant its engine is using 2,250 watts to exert 130 N of force on the car’s wheels? Efficiency A related idea to the power of a motor is its efficiency. In the real world, all motors that provide power that can do work, run at less than 100% efficiency. There is always some loss to nonconservative forces. 𝑼𝒔𝒆𝒇𝒖𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒐𝒖𝒕 𝑨𝒄𝒕𝒖𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒊𝒏 = 𝑼𝒔𝒆𝒇𝒖𝒍 𝒑𝒐𝒘𝒆𝒓 𝒐𝒖𝒕 𝑨𝒄𝒕𝒖𝒂𝒍 𝒑𝒐𝒘𝒆𝒓 𝒊𝒏 𝑬𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 = Ex: A certain motor uses 1300J of energy to raise a 30kg mass to a height 2.4 meters above where it started. a. How much potential energy does the mass gain during the lift? b. Calculate the efficiency of this motor. Exit Slip - Assignment Exit Slip- A certain celling fan uses 2400 J of energy to bring the 4.3 kg blades from rest to a speed of 23 m/s. What is the efficiency of the fan motor? What’s Due on Jan 12? (Pending assignments to complete.) Work on the Extra Practice Problems Study for the Test on Jan 17 What’s Next? (How to prepare for the next day) Read 2.3 p78-95 about Work and Energy
