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ICP “Work, Energy and Momentum” Core Content SC-HS-1.2.1 Students will: select or construct accurate and appropriate representations for motion (visual, graphical and mathematical); defend conclusions/explanations about the motion of objects and real-life phenomena from evidence/data. Objects change their motion only when a net force is applied. Newton’s Laws of motion are used to describe the effects of forces on the motion of objects. Conservation of mechanical energy and conservation of momentum may also be used to predict motion. DOK 3 Work work - the product of a net force and the distance through which it acts work = force x distance W = Fd The unit for work is the joule, J. joule = newton x meter (J = Nm) joule - the amount of energy expended when a 1N force acts through 1m Sample Problem How much work is done on a vacuum cleaner pulled 3.0m by a force of 50N applied on the horizontal? W = Fd = 50N x 3m = 150 Nm = 150J Challenge! An acceleration of 2 m/s2 acts on a 10kg mass through a distance of 8m. How much work is done? W = Fd = ma d = 10kg x 2 m/s2 x 8m = 160 Nm = 160J Energy Energy is measured in terms of the work it does or can do. Energy has the same units as work, SI joule. Like work, energy is a scalar quantity. Energy is either potential or kinetic. Potential energy (PE) - energy of position Kinetic energy (KE) - energy of motion Kinetic Energy F = ma F d = ma d F d = mv2/2 KE = 1/2 mv2 Sample Problem - Calculate the kinetic energy of a 2kg object moving at 5 m/s. KE = 1/2mv2 = .5(2kg x (5 m/s)2) = 25kg m2/s2 = 25J Potential Energy The increase in the potential energy of any system is equal to the work done on the system. Gravitational potential energy depends on the mass and height of the object in question. PE = Fd = mg d = mgh A 5.0 kg bowling ball is lifted to a height of 1.5m. What is its increase in potential energy? PE = mgh = 5kg x 9.8 m/s2 x 1.5m = 73.5kg.m/s2.m = 73.5J Work, Energy, and Power energy - the capacity to do work energy = work (same units) power - the time rate at which work is done P=W/t The SI unit for power is the watt. watt - the power required for 1 joule of work to be done in 1 second Sample Problem A machine produces 80N of force through a distance of 10m. How much work is done? W = Fd = 80N x 10m = 800 J If the work is done in 5 seconds, how much power is used? P = W/t = 800J/5s = 160 J/s = 160 watts Momentum and Impulse momentum - the product of the mass of an object and its velocity unit for momentum.......kg m/s impulse - the product of a force and the length of time during which it acts unit for impulse.............N s Using the units, find the relationship between impulse and momentum. Newton’s Third Law of Motion Newton’s Third Law of Motion states that for every action there is an equal and opposite reaction. Object A Object B Ft = -Ft mv = -mv Law of Conservation of Momentum The Law of Conservation of Momentum states that the total momentum of an isolated system cannot change. mv before collision = mv after collision m1v1 + m2v2 = m1v’1 + m2v’2 Sample Problem A mass of 5.0g moves with a velocity of 20cm/s. This mass collides with a second mass of 10g which is moving along the same line with a velocity of 10cm/s. After the collision, the 5.0g mass is moving at 8cm/s. What is the velocity of the 10g mass after the collision? Conservation of Matter and Energy The Law of Conservation of Matter and Energy states “Matter and energy are interchangeable and the total amount of matter and energy in the universe remains constant. E = mc2 (c = 3 X 108 m/s) Calculate the energy released when 5g of mass is converted to energy. Open Response Suppose you are in a canoe two feet from a boat dock. If you want to get out of the canoe, describe, using Newton’s Laws of motion and any vector diagrams you choose; A. The effect of jumping onto the ramp. B. The effect of stepping onto the ramp.