Dynamics and Vibrations Flashcards

A ball is launched horizontally from a 80 m cliff with a speed of 20 m/s. How long does it take to reach the ground? (g = 9.81 m/s²)

Answer: 4.04 s

Using h = ½gt², t = √(2h/g) = √(160/9.81) ≈ 4.04 s.

A particle travels in a circle of radius 2 m at a constant speed of 10 m/s. What is the centripetal acceleration?

Answer: 50 m/s²

Centripetal acceleration a = v²/r = (10)²/2 = 50 m/s².

Train A travels east at 60 mph and Train B travels west at 40 mph. What is the velocity of B relative to A?

Answer: 100 mph west

v_B/A = v_B − v_A = −40 − 60 = −100 mph, meaning 100 mph westward.

A car starts from rest and accelerates uniformly at 3 m/s². How far does it travel in 10 seconds?

Answer: 150 m

Using s = ½at², s = ½(3)(10²) = 150 m.

A flywheel starts from rest and reaches 120 rpm in 4 seconds. What is its angular acceleration?

Answer: 3.14 rad/s²

ω_f = 120 × (2π/60) = 4π rad/s; α = (4π − 0)/4 = π ≈ 3.14 rad/s².

A particle has a velocity vector v = 4i + 3j m/s. What is its speed?

Answer: 5.0 m/s

Speed = |v| = √(4² + 3²) = √25 = 5.0 m/s.

Gear A has 20 teeth and meshes with Gear B, which has 60 teeth. If Gear A spins at 300 rpm, what is the speed of Gear B?

Answer: 100 rpm

N_A × T_A = N_B × T_B → N_B = 300 × (20/60) = 100 rpm.