Statics, Dynamics & Mechanics of Materials Flashcards

A projectile is launched at 45° with an initial speed of 20 m/s. Neglecting air resistance, what is the maximum height? (g = 9.81 m/s²)

Answer: 10.2 m

H = (v₀sin45°)²/(2g) = (20×0.707)²/(19.62) = 200×0.5/19.62 ≈ 10.2 m.

Shear stress in a circular shaft under torque T is maximum at the:

Answer: Outer surface

Torsional shear stress τ = Tc/J is maximum at the outermost fiber where c is maximum.

The principle of transmissibility states that a force on a rigid body can be moved along its:

Answer: Line of action without changing equilibrium

Transmissibility: a force may be applied at any point along its line of action and produce the same external effect on a rigid body.

Euler's buckling load for a pin-pin column of length L, modulus E, and moment of inertia I is:

Answer: π²EI/L²

Euler's critical load Pcr = π²EI/L² for a pin-pin column (K=1), the fundamental column buckling formula.

A material has E = 200 GPa and ν = 0.3. What is its shear modulus G?

Answer: 76.9 GPa

G = E/[2(1+ν)] = 200/[2(1.3)] = 200/2.6 ≈ 76.9 GPa.

A 10 kg block slides down a frictionless incline of 30°. What is its acceleration along the incline? (g = 9.81 m/s²)

Answer: 4.91 m/s²

Along the incline, net force = mg·sin30° = 10×9.81×0.5 = 49.05 N, so a = F/m = 49.05/10 = 4.91 m/s².

In impulse-momentum analysis, the linear impulse of a force F applied over time Δt equals:

Answer: F·Δt = m·Δv

Linear impulse-momentum: F·Δt = Δ(mv), meaning the impulse equals the change in linear momentum.