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Published byKimberly Shaw Modified over 9 years ago
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Work - Work is calculated by multiplying the force applied by the distance the object moves while the force is being applied. W = Fs
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The unit of work is the Newtonmeter, also called the joule (J). The equation we will use is: W = (F cosϴ)s
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Ex. 1 - Find the work done by a 45.0 N force in pulling a luggage carrier at an angle ϴ = 50.0° for a distance s = 75.0 m.
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Ex. 2 - A weight lifter is bench pressing a 710 N barbell. He raises the barbell 0.65 m above his chest and then lowers it the same distance. What work is done on the barbell during the lifting and lowering phase.
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Ex. 4 - A flatbed truck accelerating at a = +1.5 m/s 2 is carrying a 120 kg crate. The crate does not slip as the truck moves s = 65 m. What is the total work done on the crate by all the forces acting on it?
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Work done to an object results in a change in the kinetic energy of the object. This relationship is called the work-energy theorem.
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W = Fs = mas v f 2 = v 0 2 +2as can be solved for as. as = 1/2 (v f 2 - v 0 2 ), this second term is substituted in the first equation. Fs = 1/2 m v f 2 - 1/2 m v 0 2
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Fs = 1/2 m v f 2 - 1/2 m v 0 2 Work equals final kinetic energy minus initial kinetic energy. KE = 1/2 mv 2 The unit is the joule.
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The Work-Energy Theorem. W = KE f - KE 0 = 1/2 mv f 2 - 1/2 mv 0 2
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Ex. 5 - A space probe of mass m = 5.00 x 10 4 kg is traveling at a speed of v 0 = 1.10 x 10 4 m/s through deep space. The engine exerts a constant external force of F = 4.00 x 10 5 N, directed parallel to the displacement. The engine fires continually during the displacement of s = 2.50 x 10 6 m. Determine the final speed of the probe.
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Ex. 6 - A 54 kg skier is coasting down a 25° slope. A kinetic frictional force of f k = 70 N opposes her motion. Her initial speed is v 0 = 3.6 m/s. Ignoring air resistance, determine the speed v f at a displacement 57 m downhill.
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The work-energy theorem deals with the work done by the net external force, not an individual force (unless its the only one).
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The gravitational force is a force that can do positive or negative work. W = (mg cos ϴ°)(h 0 - h f ) = mg(h 0 - h f )
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Ex. 8 - A gymnast leaves a trampoline at a height of 1.20 m and reaches a height of 4.80 m before falling back down. Determine (a) the initial speed v 0 with which the gymnast leaves the trampoline and (b) the speed of the gymnast after falling back to a height of 3.5 m.
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Gravitational Potential Energy is energy due to the distance an object is able to fall. PE = mgh PE is also measured in joules.
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W gravity = mgh 0 - mgh f = PE 0 - PE f
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The work done by the gravitational force on an object does not depend on the path taken by the object. This makes gravitational force a conservative force.
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A force is conservative when the work it does on a moving object is independent of its path. A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point.
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Nonconservative forces are those where the work done does depend on the path. Kinetic frictional forces and air resistance are two examples.
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In the work-energy theorem both conservative and nonconservative forces act on an object. So: W = W c + W nc.
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If work done is equal to the change in KE and W c is due to gravitational force, then W nc = (KE f – KE 0 ) + (PE f – PE 0 )
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Conservation of Mechanical Energy W nc = (KE f - KE 0 ) + (PE f - PE 0 ) becomes: W nc = (KE f + PE f ) - (KE 0 + PE 0 ) or: W nc = E f - E 0
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Conservation of Mechanical Energy The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external nonconservative forces is zero.
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Ex. 9 - A motorcyclist drives horizontally off a cliff to leap across a canyon. When he drives off, he has a speed of 38.0 m/s. Find the speed with which the cycle strikes the ground on the other side if he is 35 m below his starting point when he strikes the ground.
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Ex. 10 - A 6.00-m rope is tied to a tree limb and used as a swing. A person starts from rest with the rope held in a horizontal orientation. Determine how fast the person is moving at the lowest point on the circular arc of the swing.
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Ex. 12 - The roller coaster Magnum XL-200 includes a vertical drop of 59.4 m. Assume that the coaster has a speed of nearly zero as it crests the top of the hill. Find the speed of the riders at the bottom of the hill.
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