EIT Dynamics and Vibrations 3

Question 1

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?

Accepted Answer

11 m/s

Answer

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

Question 2

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

Accepted Answer

490.5 J

Answer

W = mgh = 5 × 9.81 × 10 = 490.5 J.

Question 3

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?

Accepted Answer

2 m/s

Answer

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

Question 4

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

Accepted Answer

0.50 kg·m²

Answer

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

Question 5

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

Accepted Answer

4 kg·m²

Answer

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

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