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Name: Vectors Review Score: /22 Many of the quantities you will encounter in this course are vectors. You will need to be proficient at basic vector manipulations: addition, subtraction, dot products and cross products. This worksheet is a refresher. Chapter 3 of your textbook explains vectors at the level we will be using them in the course. Please review it Below is a list of six vectors. Take them to lie in the plane of the page, with +x to the right and ty toward the top of the page. Those in the first column represent forces, those in the second column represent displacements. In the first column the vectors are written in unit vector notation, sometimes called component or Cartesian form. In the second column the vectors are written in magnitude/angle notation, or polar form. As is conventional, the angle is with respect to the positive r-axis in the counterclockwise sense. The geometric representation of a generic vector in the diagram to the right can be used to help you convert between component form and polar form. Show all your work in the space provided. Do not submit work on separate sheets of paper. Numerical values must be in decimal form. When writing out answers that are vectors please use the same formatting as shown here. 4, F 5.001+4.00j 8.20m 30.0 (-2.00i+3.00N400m2325 Cartesian-to-Polar and Polar-to-Cartesian Conversion 1. Convert F, F and F, to polar form. (The answer for F, will be symbolic, giving you a template for calculating F, and ) Convert-, r, and r, to component form. (The answer for ,{ will be symbolic, giving you a template for calculating and ) /> {.coson, t. Yi. Sines
Vector Addition 3. Imagine that both F, and F act on an object at position P in the diagram below Represent the action of each force with an arrow in the diagram, with the tail of each arrow at point P. (Draw to scale with adjacent gridlines indicating a IN change. Use a straight-edge.) 4. Use the parallelogram rule for graphical vector addition to draw in the net force vector on the diagram. Label it Fnct 5. Calculate the magnitude of the net force and the angle it makes with the positive x- axis. As a final answer, report the net force in polar form. (Show all steps.) 6. Determine the force vector that would exactly cancel the combined forces of F, and F, so that if it were also acting on the object at point P the net force on the object would be zero. Report the canceling vector in Cartesian form, then draw it on the diagram. Label it Fcanael
Vector Subtraction 7. With tails at point P draw vectors i, and i, on the diagram below. (Draw to scale with adjacent gridlines indicating a Im change. Use a straight-edge.) 8. Use the complete-the-triangle rule for graphical vector subtraction to draw the vector that equals 7,-on the diagram. Label it ir 9. Calculate- and report your vector answer in polar form. (Show all steps.) Vector Dot Product 10. Imagine a constant force equal to F, acting on an object constrained to move in a straight line between two points resulting in a displacement equal to 7. The work done by F, is given by the dot product F . Calculate the value of this dot product.
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3 2 κ.d case-3 κ.et| Sine-구 3 8。wita x axis. .metona has an angle σί and £3 5 3 dilf 3 얹 Ảditt = -3.832-6.39 , Γ 7.lo i t 4.lj F35. 5 + 16.4please rate it up thanks :)

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