A 5.0-kg object is suspended by a string from the ceiling of an elevator that is accelerating downward at a rate of 2.6 m/s2. What is the tension in the string (in N)?

36N

Explanation:

First draw a diagram so you can see which forces act in which direction.

Then define which is your positive direction. I chose the direction of accelleration (downward) to be positive. This means that the weight of the object is also acting in the positive direction but Tension is acting in the negative direction.

If the elevator which contains the object within is accellerating at 2.6 ms^-2 then the object and string system is also accellerating at the same rate.

F = ma where F is the resultant force.

Resultant for is Weight + Tension but tension is in the negative direction so

F = mg -T

F = 5g - T

F = ma so F = 5 x 2.6

13 = 5g-T

T = 5g - 13

T = 36N

(I've taken g = 9.8ms^-2 but if this is for a physics class I'd take it to be 9.81ms^-2)