Chapter 5 Work and Energy
Chapter Objectives Define work Identify several forms of energy Work-Kinetic Energy Theorem Conservation of Energy Power
Definition of Work W = F(x) Θ W = F(x) cos Θ F Work is the product of the magnitudes of the component of a force along the direction of displacement and the displacement. Work is only done when the component of force is parallel to the displacement. The units of work is Newton (Force) x meter (displacement) = Nm. Work is a scalar quantity that can be negative or positive. If the sign is positive, the force is in the same direction of the displacement. If the sign is negative, the force is in the opposite direction of the displacement. x Θ W = F(x) cos Θ F
Work is Confusing Work is only done when the force applied is parallel to the displacement. So carrying a bucket at constant velocity does no work on the bucket. Notice constant velocity means that the net acceleration is 0. If net acceleration is 0, then net force is 0. No force, no work! Fa Fg x
Types of Energy Kinetic energy is the energy of an object due to its motion. Kinetic energy depends on speed and mass. The units for kinetic energy is similar to work, so we keep it different by using Joule (J) for all types of energy. Potential energy is the energy associated with an object due to the position of the object relative to some other location. Potential energy is stored energy. Potential energy is present in an object that has the potential to move. The units for potential energy is the same for all forms of energy, Joule (J). KE = 1/2mv2
Gravitational v Elastic Potential Energy Gravitational potential energy is the energy associated with an object due to the position of the object relative to the Earth. This based on the object’s height above the Earth’s surface. Elastic potential energy is the potential energy in a stretched or compressed spring with the object at rest. This depends on the distance the spring is stretched or compressed. It also depends on how resistive the spring is to being stretched or compressed, called the spring constant. PEgravitational = mgh PEelastic = 1/2kx2
Joule vs. Newton-meter The joule measures the same quantity as the Newton-meter. So 1 J = 1 Nm The book will use joule for all measurements, whether work or energy. However, they list the Nm as the SI unit for work? So you can use either one and not be penalized. But, I would suggest (and prefer) that you use Nm – Work J – Energy (All Forms)
Other Forms of Energy Kinetic and both forms of Potential Energy fit into the category of mechanical energy. Mechanical Energy is any form of energy that deals with motion. Energy Mechanical Nonmechanical Electrical Heat Kinetic Potential Chemical Gravitational Elastic
Why Joule? The joule is named for the British Physicist James Prescott Joule (1818-1889). Joule made major contributions to the understanding of energy, heat, and electricity. Law of Conservation of Energy Joule’s Law That heat is produced in an electrical conductor. Helped develop the absolute scale of temperature while working with Lord Kelvin Kelvin Temperature Scale
( ) Work vs. Energy W = Fx vf2 = vi2 + 2ax W = max ax = vf2 – vi2 Work and energy are linked by one common concept They are measured in the same unit. 1 joule (J) = 1 Newton-meter (Nm) They are not only linked by their unit, but also through their formula(s). W = Fx vf2 = vi2 + 2ax W = max ax = vf2 – vi2 2 W = m vf2 – vi2 2 ( ) W = KEf - KEi W = ΔKE W = ½mvf2 – ½mvi2
Work-Kinetic Energy Theorem Remember that work is a measurement of the force used to move an object a certain distance. Since we are talking about motion, we must also think of kinetic energy. The units on both of them are similar; Joule - Nm (which are the same things!) Ultimately we can say that the net work done on an object is equal to the change in kinetic energy of the object. That is the Work-Kinetic Energy Theorem. Fx = Wnet = ΔKE = ½mvf2 – ½mvi2
Conservation of Energy Thanks to Albert Einstein’s observations about energy being related to the amount of mass of an object (E=mc2), energy is conserved because mass is conserved. That doesn’t mean the energy stays the same, just the total amount remains constant, it just changes form. Mechanical energy is conserved as long as friction is not present. If friction is present, then some energy is converted to heat, which is nonmechanical.
Conservation Equation You need to identify the initial condition of the object and its final condition. Each situation may contain more than one type of energy at the same time For instance, a parachutist jumping from an airplane. All the energy from the initial condition must be accounted for in the final condition. PEi + KEi = PEf + KEf So mghi + ½kx2 + ½mvi2 = mghf + ½kx2 + ½mvf2 If any of the three types of energy are not present, just eliminate that type from the correct location in the equation.
Power So what happens when two people do the same amount of work, but one does it faster than the other? Which person is better or stronger? Power is the rate at which work is done. Also the rate at which energy is transferred. So machines with different power ratings do the same amount of work in different time intervals. Power is measured in joules per second, which is called a Watt. W Fx P = = = Fv Δt Δt But remember that W = Fd. But remember that d/Δt = v.