EML 5060 Analysis in Mechanical Engineering Exam 2

1.

The truss shown below does not experience nodal forces. The weight of the bars is negligible. What can you say about the forces T_i in the bars? According to statics,

T₁ - T₂ = 0

c T₁ + c T₂ + T₄ = 0

T₂ + 2 T₃ + 2c T₅ = 0

2 T₄ - T₅ - T₆ = 0

T₅ - T₆ = 0

where $c=\cos(30)$.

2.

I have a body in my windtunnel with an outside front surface area described by

3 x² + 2 xy + 3 y² + 6 z² = 3

I also have a laser positioned at a point P, (-10,0,0). I direct the laser towards the body along the axis, so that it strikes the nose at point Q, (-1,0,0). Determine the angle of deflection of the laser beam when it strikes the surface. Hint: first find the unit normal to the surface at point Q.

3.

Describe the body of question 2. Is it finite? In what direction are its principle axes?