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Vector Projections: Calculating Components for Work Problems

Learn to find vector projections for calculating forces and work done in physics problems involving displacement vectors.

vaughan-cantrell
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Vector Projections: Calculating Components for Work Problems

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  1. Calculating Components

  2. Vector Projections It often becomes necessary to find the projection of one vector across the length of another. When this is required, the procedure is denoted as:

  3. Calculate the following components of u along v • <1,4> and <-2,1> 2. <-2,3> and <1,1>

  4. Work Problems

  5. Let’s try it! A force is given by the vector F = <2,3> and moves an object from the point (1,3) to the point (5,9). Find the work done. -First we calculate the Displacement vector D -Now we calculate So the work done is 26 ft-lbs.

  6. Pulling a Wagon A man pulls a wagon horizontally by exerting a force of 20lbs. On the handle. If the handle makes an angle of 60 degrees with the horizontal, find the work done in moving the wagon 100ft. -Displacement vector. The force on the handle can be written as:

  7. This gives us two vectors to work with: Now we can find the Work done:

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