# Physics Question?

#### hrf2

Hey all,
I'm having a lot of trouble working through this physics question from coursesaver, mostly because I don't think the algebra of the solution is quite right:
A 2000kg elevator is connected to a cable. What is the tension in the cable when the elevator is accelerating downward at the rate of 1.5 m/s2? (Approximate the acceleration due to gravity as 10m/s2)
The solution is listed as:
The components of the net force, FNET, for the elevator are tension, T, and weight, W:
FNET = T  W = ma

Substitute in the weight: W = mg = (2000kg)(10m/s2) = 20,000N
* Note, the acceleration of 1.5m/s2 is negative since the acceleration is downwards.

T  20,000N = (2000kg)(-1.5m/s2)
T  20,000N = -3000N
T = -3000N + 20,000N = 17,000N

I'm not sure here if FNET = T W = ma should be T+W or T-W. I'm guessing it's T-W, as that's how the algebra works out. Can someone clarify for me? I though weight and tension would be working in the same direction?

I'm getting really discouraged because even going over physics every day doesn't seem to be helping me... argh.

#### trevithick

7+ Year Member
17000 is correct. F=ma; the net mass*acceleration of the elevator= sum of forces acting on the elevator. Since the elevator is accelerating down, you can choose that as the positive direction. There are two forces acting on the elevator; gravity pulling it down (positive) and the tension on the cable pulling it up (negative). So going back to F =ma:

1.5*2000= Gravity - Tension.
So 1.5*2000= 10* 2000 - T or T= 8.5* 2000=17000.

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