APRIL 10 MEMO.pdf - PHY1015 April 2010 Test Solutions 1(a...

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PHY1015 April 2010 Test Solutions 1. (a) Separate sets of forces are said to be equivalent if they produce the same external effects of translation and rotation (or external support reactions) when applied to a given rigid body. An example of equivalent system is shown in Figure 1. Figure 1: Diagram for 1a): Examples of equivalent systems. (b) A sliding vector is one whose effect on a rigid body is the same regardless of where it is applied along its line of action. Sliding vectors obey the principle of transmissibility. Figure 2: Diagram for 1c) (c) Following the notation in Figure 2, adding up the moments due to the forces about P (taking 1
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anti-clockwise as positive) gives + M R P = X M P = F B g h × b + F B f h × e - F A sin θ × ( a - d ) + F A cos θ × ( b + c ) = 1500 N 5 13 × 2 . 5 m + 1500 N 12 13 × 2 . 0 m - 2000 N sin 25 × (3 . 5 - 2) m +2000 N cos 25 × (2 . 5 + 4) m = 14 . 7kN m 2. (a) The corresponding couple moments must be of the same magnitude and the couples must lie in the same plane or in planes parallel to one another.
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