Lecture12-2A

# Lecture12-2A - Today's Lecture Lecture 12 Chapter 7 Work...

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Today Today s Lecture s Lecture Lecture 12: Lecture 12: Chapter 7 Chapter 7 Work, Energy, Power Work, Energy, Power

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What is Work? What is Work? For an object moving in one dimension, the work W done on the object by a constant force is: W F x Δ x , Where F x is the component of the force in the direction of the object’s motion and D x is the object’s displacement. Since the woman is moving horizontally only the x component of the force, F x , contributes to the work.
Work Can Be Positive Work Can Be Positive When there is a component of a force acting in the same direction as the motion of an object the work is positive. A force acting 90 o to the direction of motion does no work. A force that opposes the motion (friction) does negative work. Work Can Be Zero or Negative Work Can Be Zero or Negative

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Moving a Mass in One Dimension Moving a Mass in One Dimension When we push an object against friction, a force is required to maintain or increase its velocity. The work done is The SI unit of work is the Joule where 1J = 1 N-m . The work has been converted into heat energy via friction and any change in energy. For example the work against friction to move a block of mass m=2kg a distance 2 meters with a coefficient of kinetic friction m k = .2 is: W F x Δ x F x k N k mg .2 2  9.8 3.92 N W F x Δ x 3.92 N  2 m 7.84 Nm

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F Δ r cos , where F is a constant vector

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Work for a Spatially Varying Force Work for a Spatially Varying Force With a varying force, consider summing the work done over small displacements as shown in (a). The work done for each displacement D x is D W i . To find the total work we sum D W i . This is an approximation. Taking the limit as D x approaches zero we obtain: W i 1 N Δ W i i 1 N F x i Δ x W lim Δ x 0 i 1 N F x i Δ x x 1 x 2 F x dx This is the integral form of the work done in one-dimension by a varying force.
Work for a Spatially Varying Force in 3D Work for a Spatially Varying Force in 3D What about a force that varies

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Lecture12-2A - Today's Lecture Lecture 12 Chapter 7 Work...

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