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