5 Work Physics - F r Work By examining the definition of...

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By examining the definition of work above, we see that: Even if a force is applied to an object, if there is no movement (displacement Δr ) of the object, then there is no work done on the object. Second, there must be at least a component of the force parallel to the direction of the displacement . Recall the dot product of two vectors also means: Work r F Work r F θ cos
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Be careful when you are using the expression for work. The angle θ is not the usual angle on a coordinate system measured from the x-axis. Instead, it is the angle between r and F .
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Review Work The definition for work is given by: W = ΣF r cos θ As you discovered, the cos θ in the work equation is very important. For angles between 0 o and 90 o , cos is positive and has a value less than one. This indicates that the force pulls at least partly in the direction of the displacement and does positive work.
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If the angle equals 0 o between the force and displacement then the force “pulls or pushes” completely in the same direction of the displacement; thus it does the maximum positive work. But if the angle equals 90 o , the force does no work since the force has no component parallel to the displacement. For angles between 90 o and 180 o , cos θ is negative and has a value less than one. This indicates that the force at least partly opposes the displacement and does negative work. The sum of the forces dotted with the displacement gives the total work done on the object .
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Example A crane is used to lower a log (weight = 22,000 N ) 10 meters down a slope as shown. If the tension in the cable is 7,000 N and a 4,000 N frictional force opposes the motion, calculate the total work done by all the forces acting on the log. Note friction is opposing motion
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1) First draw a sketch and circle the system . Then identify the forces and draw them on the sketch. 2) Draw a free-body diagram . Identify the displacement vector and include it in the diagram. Note that it is directed down the incline and has different units than the force vectors.
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3) Find the angle between each force and the displacement . Calculate the work done by each separate force: W = F r cos θ W T = 7,000(10) cos 180 o = -70,000 J W N = N(10) cos 90 o = 0 W W = 22,000(10) cos 60 o = 110,000 J W f = 4,000(10) cos 180 o = - 40,000 J
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W Total = -70,000 J + 0 J + 110,000 J – 40,000 J = 0 Joules Why can we add the different works together?
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W = F r cos θ The reason we add the various works done on the log lowered down the slope is from the definition of work given above. F is the net or sum of all forces acting on the log, hence: F = ΣF i = Friction Force + Tension force + Gravity Force + Normal Force Thus work equals the sum of all forces, each being multiplied by r cos θ : [ ΣFi] r cos θ
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A tow truck is dragging a stalled car of mass 1000 kg a distance of 0.5 km . The cable makes an angle of
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This note was uploaded on 10/05/2011 for the course PHYS 4A taught by Professor Ernest during the Summer '10 term at Irvine Valley College.

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5 Work Physics - F r Work By examining the definition of...

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