physics chapter 7 outline

# Physics chapter 7 - Chapter 7 Work and Energy W work The ork W done on a system by a force exerted on the system is a scalar dot product of two

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Chapter 7 Work and Energy

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Work The work, W , done on a system by a force exerted on the system is a scalar ( dot) product of two vectors: the applied force and the displacement of the point of application of the force or. If the force has a constant value then work W = or W =
Scalar Product of Two Vectors The scalar product of two vectors is written as It is also called the dot product θ is the angle between A and B Applied to work, this means A B r r A B cos A B r r cos W F r = = ⋅∆ F r r r

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Scalar Product, cont The scalar product is commutative The scalar product obeys the distributive law of multiplication
Dot Products of Unit Vectors Using component form with vectors: ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ⋅ = ⋅ = ⋅ = ⋅ = ⋅ = ⋅ = i i j j k k i j i k j k 1 0

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Work, summary The work, W , done on a system by an agent exerting a constant force on the system is the product of the magnitude F of the force, the magnitude r of the displacement of the point of application of the force, and cos θ, where θ is the angle between the force and the displacement vectors cos W F r = = ⋅∆ F r r r
Work W = F r cos θ A force does no work on the object if the force does not move through a displacement The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application

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Work Example The normal force and the gravitational force do no work on the object cos θ = cos 90° = 0 The force does work on the object If the surface exerts a friction force on the object then the friction force does work. The work done by friction force is negative. F r
More About Work The sign of the work depends on the direction of the force relative to the displacement Work is positive when projection of onto is in the same direction as the displacement Work is negative when the projection is in the opposite direction Work is a scalar quantity The unit of work is a joule (J) 1 joule = 1 newton . 1 meter J = N · m If more than one force acts on a system and the system can be modeled as a particle , the total work done on the system is the work done by the net force W total = F net ·Δr F r r r

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Example 1 A particle moving in xy plane undergoes displacement given by d = (15 i -12 j )m as a constant force F =(5 i +2 j )N. Calculate the work done by the force on the particle. W = F x d x +F y d y =5N·15m -2N·12m = 51 J
Example 2 A rope is used to pull a 4 kg block 10 m along a horizontal floor. The force on the block from the rope is 9.5 N and directed 25 0 above the horizontal. The coefficient of kinetic friction between block and floor is 0.22. (a) Find the work done by the rope on the block. ( b) Find the work done by the friction. ( c) Find the total work done on the block.

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Example 3 A crate of mass 10 kg is pulled up a rough 20 0 incline. The pulling force is
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## This note was uploaded on 11/11/2010 for the course PHYSICS 111 taught by Professor Wang during the Spring '09 term at NJIT.

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Physics chapter 7 - Chapter 7 Work and Energy W work The ork W done on a system by a force exerted on the system is a scalar dot product of two

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