Dynamics and Vibrations Flashcards

A 10 kg block moving at 5 m/s receives an impulse of 60 N·s in the direction of motion. What is the final velocity?

Answer: 11 m/s

mv_f = mv_i + J → 10v_f = 10(5) + 60 = 110, so v_f = 11 m/s.

A 5 kg object is lifted 10 m vertically. How much work is done against gravity? (g = 9.81 m/s²)

Answer: 490.5 J

W = mgh = 5 × 9.81 × 10 = 490.5 J.

A 2 kg ball moving at 6 m/s undergoes a perfectly inelastic collision with a stationary 4 kg ball. What is the post-collision velocity?

Answer: 2 m/s

m₁v₁ = (m₁ + m₂)v_f → 2(6) = 6v_f, so v_f = 2 m/s.

A uniform disk has mass 4 kg and radius 0.5 m. What is its moment of inertia about its central axis?

Answer: 0.50 kg·m²

For a solid disk, I = ½mr² = ½(4)(0.5²) = 0.50 kg·m².

A uniform rod (I_cm = mL²/12) has mass 3 kg and length 2 m. What is its moment of inertia about one end?

Answer: 4 kg·m²

Using the parallel axis theorem: I_end = mL²/12 + m(L/2)² = mL²/3 = 3(4)/3 = 4 kg·m².

A motor produces 1500 W at 200 rpm. What torque does it deliver?

Answer: 71.6 N·m

T = P/ω = 1500 / (200 × 2π/60) = 1500/20.94 ≈ 71.6 N·m.

A 0.5 kg ball strikes a wall at 8 m/s and rebounds at 6 m/s. What is the magnitude of the change in momentum?

Answer: 7 kg·m/s

|Δp| = m|v_f − v_i| = 0.5 × |−6 − 8| = 0.5 × 14 = 7 kg·m/s.