Question 1
Two control rods are attached at A to lever AB. Using trigonometry and knowing that the force in the right-hand rod is F2 = 80 N, determine (1) the required force F1 in the left-hand rod if the resultant R of the forces exerted by the rods on the lever is to be vertical. (2) The corresponding magnitude of R. (25 points)
a) Draw the force vectors (F1 and F2) and the resultant vector R according to the parallelogram law. Label all forces and known quantities. (4 points)
b) Draw the force vectors (F1 and F2) and the resultant vector R according to the triangle rule. Label all forces and known quantities. (4 points)
c) For each vector (F1, F2, R), identify whether the magnitude and direction are known or unknown. (2 points)
d) Identify which of the following could be used to solve the unknown values in the problem: (2 points)
Cosine law: a^2 = b^2 + c^2 - 2bc cos A
Sine law: sin A / a = sin B / b = sin C / c
e) Using either the parallelogram law or the triangle rule, solve for the unknown values. (6 points)
f) Find the components of forces F1 and F2 in the x and y axes. (4 points)
g) Write each force (F1, F2, and R) in Cartesian vector form. (3 points)
