Govt. Exams
e = √(h₂/h₁) = √(h/2 ÷ h) = √(1/2) ≈ 0.707
For SHM, ωmax = ω × A where ω = √(k/m) = √(50/2) = 5 rad/s. vmax = 5 × 0.1 = 0.5 m/s
Deceleration a = g(sinθ + μcosθ) = 10(0.5 + 0.2×0.866) = 10(0.5 + 0.173) = 6.73 m/s². Using v² = u² - 2as: 0 = 100 - 2(6.73)s, s ≈ 3.2 m
Both objects have constant acceleration -g. If thrown with same initial velocity but at different times, they will have the same velocity at different times. For same velocity at same instant: vA = u - gt₁ and vB = u - gt₂. Since t₁ ≠ t₂, velocities won't be equal at the same instant.
v = u + ∫a dt = 2 + ∫₀² 3t² dt = 2 + [t³]₀² = 2 + 8 = 10 m/s
v = dx/dt = 8t - 2. At t = 1s, v = 8(1) - 2 = 6 m/s
Centripetal force is perpendicular to velocity (displacement), so W = F·s·cosθ = F·s·cos90° = 0
N - mg = ma. N = m(g+a) = 50(10+2) = 600 N
Time to max height = 2s. u = gt = 10(2) = 20 m/s
System acceleration: a = F/(m₁+m₂) = 20/5 = 4 m/s². Tension = m₂a = 2(4) = 8 N
