Question

A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.9 m/s2. (a) If the tension in the cord is 52 N, what is the lamp's mass

Answer 1

The lamp descends with the elevator so its acceleration is also 2.9 m/s². Take downward to be the positive direction. Then the net force on the lamp is

∑ F = w - t = ma

where w = mg = weight of lamp, t = tension in the cord, m = mass of lamp, and a = acceleration. Then

mg - t = ma

mg - ma = t

m (g - a) = t

m = t / (g - a)

so that the lamp's mass is

m = (52 N) / (9.8 m/s² - 2.9 m/s²) ≈ 7.5 kg