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Work, Energy, and Power A. Work B. Work: Practice Problems C. Potential Energy D. Potential Energy: Springs E. Kinetic Energy F. Mechanical Energy G. Power A. Work A force acting upon an object to cause a displacement F = force d = displacement theta is the angle between the force and the displacement vector A. Work A. Work A force acts upward upon an object as it is displaced rightward The force vector and the displacement vector are at right angles to each other The angle between F and d is 90 degrees Calculate Work cos 90 = 0 A vertical force can never cause a horizontal displacement A. Work Determining the angle It is the angle between the force and the displacement vector A force is applied to a cart to pull it up an incline at constant speed Several incline angles were used; yet, the force was always applied parallel to the incline The displacement of the cart was also parallel to the incline Since F and d are in the same direction, the angle was 0 degrees A. Work Measured in Joules (J) The Joule is the unit of work. 1 Joule = 1 Newton * 1 meter 1J = 1 N * m One Joule is equivalent to one Newton of force causing a displacement of one meter B. Work: Practice Problems B. Work: Practice Problems A = 500 J B = 433 J C = 750 J B. Work: Practice Problems A 10-N forces is applied to push a block across a friction free surface for a displacement of 5.0 m to the right Calculate Work. W = 50 J B. Work: Practice Problems A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right Calculate work. W = -50 J C. Potential Energy the stored energy of position possessed by an object 2 Types Gravitational PE Elastic PE C. Potential Energy Gravitational PE the energy stored in an object as the result of its vertical position (height) dependent on two variables mass of the object height C. Potential Energy Elastic PE the energy stored in elastic materials as the result of their stretching or compressing Stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow the more stretch, the more stored energy C. Potential Energy Elastic PE the amount of force is directly proportional to the amount of stretch or compression (x) the constant of proportionality is known as the spring constant (k). C. Potential Energy Elastic PE D. Potential Energy: Springs Hooke’s Law If a spring is not stretched or compressed, then there is no elastic potential energy stored in it The spring is said to be at its equilibrium position The equilibrium position is the position that the spring naturally assumes when there is no force applied to it E. Kinetic Energy The energy of motion An object which has motion - whether it be vertical or horizontal motion - has kinetic energy E. Kinetic Energy Types of KE: vibrational (the energy due to vibrational motion) rotational (the energy due to rotational motion) translational (the energy due to motion from one location to another) E. Kinetic Energy Translational KE Depends upon two variables the mass (m) of the object the speed (v) of the object m = mass of object v = speed of object E. Kinetic Energy Kinetic energy is a scalar quantity; it does not have a direction The kinetic energy of an object is completely described by magnitude alone KE is measured in Joules (J) F. Mechanical Energy The energy which is possessed by an object due to its motion or its stored energy of position Can be PE or KE An object which possesses mechanical energy is able to do work F. Mechanical Energy F. Mechanical Energy The mechanical energy of an object can be the result of its motion and/or the result of its stored energy of position The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy TME = PE + KE TME = PEgrav + PEspring + KE G. Power The rate at which work is done The work/time ratio The standard metric unit of power is the Watt Watt is equivalent to a Joule/second G. Power Most machines are designed and built to do work on objects All machines are typically described by a power rating The power rating indicates the rate at which that machine can do work upon other objects The power of a machine is the work/time ratio for that particular machine G. Power G. Power Suppose that Ben elevates his 80-kg body up the 2.0 meter stairwell in 1.8 seconds. If this were the case, then calculate Ben's power rating G. Power Suppose that Ben elevates his 80-kg body up the 2.0 meter stairwell in 1.8 seconds. If this were the case, then calculate Ben's power rating