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?

(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