Question

A lamp hangs vertically from a cord in a descending elevator that decelerates at 1.7 m/s2. (a) if the tension in the cord is 63 n, what is the lamp's mass? (b) what is the cord's tension when the elevator ascends with an upward acceleration of 1.7 m/s2?

Answer 1

(a)
The formula is:
∑ F = Weight + T = mass * acceleration

as the elevator and lamp are moving downward, I choose downward forces to be positive.
Weight is pulling down = +(9.8 * mass)
Tension is pulling up, so T = -63
Acceleration is upward = -1.7 m/s^2

(9.8 * mass) + -63 = mass * -1.7
Add +63 to both sides
Add (mass * 1.7) to both sides

(9.8 * mass) + (mass * 1.7) = 63
11.5 * mass = 63

mass = 63 / 11.5

Mass = 5.48 kg


(b)
Since the elevator and lamp are going upward, I choose upward forces to be positive.
Weight is pulling down = -(9.8 * 5.48) = -53.70
Acceleration is upward, so acceleration = +1.7


-53.70 + T = 5.48 * 1.7

T = 53.70 + 9.316 = approx 63 N

The Tension is still the same - 63 N since the same mass, 5.48 kg, is being accelerated upward at the same rate of 1.7 m/s^2