Applied Science 151 Computer-Aided Engineering Graphics

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Applied Science 151
         Computer-Aided Engineering Graphics
                          Quiz 2: October 30, 2002

Question 1: Sailboat
Figure 2 shows a sailboat heeling (tilting) over in the wind. The wind exerts a
force perpendicular to the sail, at the location shown. The water exerts an equal
and opposite force onto the keel at the second location shown. The other two
forces acting on the sailboat are its weight and the buoyancy of the hull, which act
vertically through the centre of gravity and the centre of buoyancy respectively.
The weight of the sailboat, including crew, is 30,000 N.
 Sketch a free-body diagram of the sailboat, showing all of the
   forces and where each acts.
 Graphically determine the magnitude of the wind force that must
   be acting on the sailboat.

Question 2: Aquaduct
In ancient times, canals were used to transport water from springs, rivers and
other sources to cities where the water was needed. Figure 3 shows a source of
water some distance from the city that needed the water.
 Select a route for the canal to follow from the source to the city.
    Note that it is important when selecting the route to ensure that
    the canal has a uniform grade (slope) along its entire route so
    that the water flows at a constant rate. It may also be necessary
    to incorporate an aqueduct (bridge to carry the canal) along part
    of its length.
 What is the grade of the canal?
                Applied Science 151
         Computer-Aided Engineering Graphics
                            Quiz 1: Marking Guide

Solution 1:
This problem is a simple non-concurrent force problem. There are three
unknown forces in this problem, the buoyancy of the sailboat, the wind force on
the sail and the hydrodynamic force on the keel. Students will need to consider
lines of action when solving this problem.
Following is a marking guide for the problem.
                          Correct free-body diagram sketch 2
                     Lines of Action Constructed Correctly 2
                       Force Polygon Constructed Properly 2
                                  Correct Solution ( 10%) 2
                                                       Neat 2


Solution 2:
This is quite a difficult problem in the use of a topographic map. The difficulty is
to maintain a constant slope along the entire length of the canal, including the
aquaduct. However, it is not possible to know what slope to use without knowing
the length of the canal. An iterative solution is required; fortunately the solution
converges very rapidly.
The canal should follow a route such that there is equal distances between
crossings of adjacent contour lines and that grade should be the same as the
grade of the aquaduct. Give one bonus mark if the solution minimizes the length
of the aquaduct that need to be constructed (aquaducts are much more expensive
to build than canals).
Following is a marking guide.
                    Canal has constant grade (inc aquaduct) 6
                                                Grade correct 2
                                                         Neat 2
                        Bonus: minimize length of aquaduct 1
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