How do you calculate work in a vertical rope and mass problem?

[greyradio]

[SOLVED] Work problem

A vertical rope is used to lower a mass 44.9 kg at a constant acceleration of magnitude 4.57 m/s2. Find the work done by the tension in the cord if the mass moves down distance 2.66 m.


W = F (change in X)


First, I tried to get the tension by:

-T + mg = ma
- T = ma - mg
T = -ma + mg
T = - (4.57 m/s^2)(44.9 kg) + (44.9 kg) (9.81 m/s^2)
T = 235.276 N

W = T (change of x)
W = 235.276 N (2.66 m) = 625.83416

However this seems to be wrong so my second attempt

T -mg = ma
T = ma + mg
T = 645.662 N

W = T (change of x)
W = 645.662 N (2.66 m) = 1717.46092

It seems I'm doing something wrong or overlooking a vital piece of information, I was wondering if someone could point me in the right direction.

 

[Google_Spider]

The first attempt looks good to me, except that the work done would be negative.

 

[Dick]

I can't find anything wrong with your first attempt. It looks correct. The second attempt IS wrong. It would be right if mass were accelerating 4.57m/sec^2 in an upwards direction. But it doesn't look like that's what the question is asking. Have you tried just changing the number of significant figures in the answer?

 

[greyradio]

yeah it seems i was using the incorrect direction of the tension since it is opposite of the weight then it should be negative. Thanks.