Solving Part (a) of Lamp Mass in Descending Elevator w/ Deceleration of 1.4 m/s2

AI Thread Summary
To find the mass of the lamp in a descending elevator decelerating at 1.4 m/s² with a cord tension of 56 N, the equation T = mg + ma can be rearranged to m = T / (g + a). Given that the tension (T) is 56 N, gravitational acceleration (g) is 9.8 m/s², and the elevator's deceleration (a) is 1.4 m/s², the mass can be calculated. The solution for part (b) confirms that the tension remains 56 N when the elevator ascends with the same upward acceleration. This approach clarifies the relationship between tension, mass, and acceleration in varying conditions.
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Homework Statement


A lamp hangs vertically from a cord in a descending elevator that decelerates at 1.4 m/s2. (a) If the tension in the cord is 56 N, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of 1.4 m/s2?


Homework Equations


T-mg=ma


The Attempt at a Solution


I got part (b) to be 56 N and that was correct but then I used the formula... but I don't know how to solve for mass for part (a) when there are two masses in the equation above, I know T to be 56N and g to be 9.8m/s squared also a to be 1.4m/s squared... Can anyone help me out? I'm confused.
 
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Just rearrange your initial equation:
T-mg=ma

Thus:
T = mg + ma = m(g +a)

You take it from here.
 
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