Chapter 6 review

    Conceptual questions
      Section 6.3
      1. Consider the range equation.
        1. If the velocity doubles, what effect does this have on the range?
        2. Explain how the equation describes the range at angles of 0º and 90º.

      2. Easy Why is white paper (e.g., from a roll of white craft paper) placed underneath carbon paper when conducting a trajectory experiment with a falling marble, as in Investigation 6B on page 186?

      3. Easy You and your lab partner are given a marble and a trajectory apparatus ramp that acts as a marble launcher. You will compete with other lab groups to see who can launch their marble the furthest. With what projection angle should you set up the end of your marble launcher ramp?

      4. Easy What are the advantages of using real-time technology to generate graphs of motion (position–time or velocity–time graphs) down an inclined plane over how Galileo collected his data?

        5. How would you trace a trajectory with this apparatus?
      5. Challenging The figure above depicts a marble on a launch ramp that strikes a vertical, movable target. The carbon paper leaves a mark on the target each time a marble hits it. Describe how you would use this trajectory apparatus to graph the shape of the marble’s trajectory after it leaves the launch ramp.

      Quantitative problems
        Section 6.1
          Vector diagrams for the problem
        1. What is the net force that is the result of combining a 30 N force at a 45° angle above the horizontal and a 45 N force 37° above the horizontal?

        2. At what angle is a force directed if its horizontal component is 10 N and the vertical component is 15 N?

        3. What is the range of magnitudes that can be attained from the combination of forces with magnitudes of 7 and 5 N?

        1. What is the resultant of the following calculation adding two vectors:
          F → = F → 1 + F → 2
          where F → 1  = (a, b) and F → 2  = (c, d)?

        2. Easy Calculate the magnitude of the force with components of Fx = 12 N, Fy = 16 N, and Fz = 15 N.

        3. Easy What is the horizontal component of a force with a magnitude of 100 N that is directed 60° above the horizontal?

        4. Easy Calculate the magnitude of a force given by
          F →  = (5, 12) N.

        5. Easy What is the vertical component of a 64 N force directed 53° above the horizontal?

        6. Easy Find the components of the resultant of the following forces: 15 N up, 8 N down, 4 N left, 20 N right.

          7. What is the force vector needed to make the net force zero?
        7. Easy Determine the force F → required to make the net force zero in the diagram above.

          8. What is the force vector required to make the net force zero?
        8. Medium Determine the force F → required to make the net force zero in the diagram above.

          9. What is the magnitude of the unknown force?
        9. Medium What magnitude force at a 17° angle above the horizontal will produce a 10 N horizontal component force?

          10. What angle for this vector?
        10. Medium At what angle should a force be applied so that its x-component is three times that of its y-component?

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