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Work What do you think? • List five examples of things you have done in the last year that you would consider work. • Based on these examples, how do you define work? Work • In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. W = Fd Units of Work force x N x distance 1 N·m = m = work = N·m 1 joule = 1J You perform ≈1 J of work when you lift a 100-gram apple from the floor to your table top Work • Pushing this car is work because F and d are in the same direction. • Why aren’t the following tasks considered work? – A student holds a heavy chair at arm’s length for several minutes. – A student carries a bucket of water along a horizontal path while walking at a constant velocity. Work • How would you calculate the work in this case? – What is the component of F in the direction of d? • F cos – If the angle is 90°, what is the component of F in the direction of d? • F cos 90° = 0 – If the angle is 0°, what is the component of F in the direction of d? • F cos 0° = F Net Work Done By a Constant Net Force Wnet Fnet d cos Work is a Scalar F F F F • In which direction (+ or ) is the x-component of F in each case? Classroom Practice Problem • A 20.0 kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase? • Answer: 590 J Now what do you think? • Based on the physics definition, list five examples of things you have done in the last year that you would consider work. Kinetic and Potential Energy What do you think? • You have no doubt heard the term kinetic energy. – What is it? – What factors affect the kinetic energy of an object and in what way? • You have no doubt heard the term potential energy. – What is it? – What factors affect the potential energy of an object and in what way? Kinetic Energy 1 2 KE mv 2 • What are the SI units for KE? –kg•m2/s2 or N•m or J Kinetic Energy Wnet F x max Since then or v v 2ax 2 f 2 i Wnet m( Wnet v v 2 f 2 i 2 ) 1 2 1 2 mv f mvi 2 2 Work - Kinetic Energy Theorem Wnet KE KEf KEi • KE is the work an object can do if the speed changes. • Wnet is positive if the speed increases. Classroom Practice Problems • A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? – Answer: 3.00 x 102 J or 300. J • Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed? – Answer: 1.32 x 102 J or 132 J Potential Energy • Energy associated with an object’s potential to move due to an interaction with its environment – A book held above the desk – An arrow ready to be released from the bow • Some types of PE: – Gravitational – Elastic – Electromagnetic – Chemical Gravitational Potential Energy PE g mgh • What are the SI units? – kg•m2/s2 or N•m or J • The height (h) depends on the “zero level” chosen where PEg = 0. • g = 9.80 m/s2 if h is positive Elastic Potential Energy • The energy available for use in deformed elastic objects – Rubber bands, springs in trampolines, pole-vault poles, muscles • For springs, the distance compressed or stretched = x Spring Constant (k) Visual Concept Click below to watch the Visual Concept. • The spring constant (k) depends on the stiffness of the spring. –Stiffer springs have higher k values. –Measured in N/m • Force in newtons needed to stretch a spring 1.0 meters Elastic Potential Energy PEelastic = kx2 k = the spring constant (N/m) x = the distance the spring is stretched (m) • What are the SI Units for PEelastic? –Joules (J) (N·m) –The joule is the SI unit for any form of energy Classroom Practice Problems • When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. – What is the gravitational potential energy associated with the mass relative to the table? • Answer: 9.81 J – What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? • Answer: 2.00 J