Question 8

**Setting up the motion** The elevator's height is y = 8[1 + sin(2πt/T)], with T = 40π s. Angular frequency: ω = 2π/T = 2π/(40π) = 1/20 rad/s Acceleration of the elevator: a = d²y/dt² = −8ω² sin(ωt) Maximum magnitude of acceleration: a_max = 8ω² = 8 × (1/400) = 0.02 m/s² **Apparent weight** Apparent weight in the elevator = m(g + a), where a is the upward acceleration. - Maximum apparent weight: 50 × (10 + 0.02) = 501 N - Minimum apparent weight: 50 × (10 − 0.02) = 499 N **Maximum variation of weight observed** Variation = 501 − 499 = 2 N

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