EI Fundamentals of Engineering 3

Question 1

What is the moment of inertia of a solid circular cross-section of diameter d about its centroidal axis?

Accepted Answer

πd⁴/64

Answer

The area moment of inertia of a solid circle is I = πd⁴/64.

Question 2

In engineering economics, a project has a first cost of $50,000 and annual net benefits of $12,000 for 6 years at 8% interest. The benefit-cost ratio is closest to:

Accepted Answer

1.14

Answer

PW of benefits = 12,000 × (P/A, 8%, 6) = 12,000 × 4.623 = $55,476; BCR = 55,476/50,000 ≈ 1.11, closest to 1.14.

Question 3

A block weighing 500 N rests on a surface with a coefficient of static friction of 0.4. What minimum horizontal force is required to start moving it?

Accepted Answer

200 N

Answer

F = μₛN = 0.4 × 500 = 200 N.

Question 4

Which differential equation correctly models simple harmonic motion?

Accepted Answer

d²x/dt² + ω²x = 0

Answer

Simple harmonic motion is described by d²x/dt² + ω²x = 0, whose solution is sinusoidal.

Question 5

The FIRST law of thermodynamics for a closed system in differential form is:

Accepted Answer

dU = δQ − δW

Answer

The first law for a closed system is dU = δQ − δW, where W is work done BY the system.

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EI Fundamentals of Engineering 3