# Pulley Question

#### TommyTman

5+ Year Member
I'm slightly confused with the directionality of a pulley problem from Kaplan. The problem is:

In the pulley system shown, what is the tension force in each rope?
m=10kg
Object is accelerating up at 2 m/s2.

I have attached a rough sketch below.

I began to solve it with: Sum of forces = 2T - mg = ma
My question is, is g supposed to be negative because Kaplan is giving an answer of 60N and I'm getting 4oN. This discrepancy is based on the sign given to gravity and whether to add or subtract a and g.

#### sazerac

##### rye sense of humor
5+ Year Member
You need to define a Y direction as positive.

If you define down as positive, then g=+10 and a=-2.
If you define up as positive, then g=-10 and a=+2.

You will get the same answer either way.

Since they are asking for T, and T pulls up, it would probably be easier to define up as positive in this problem.

OP
T

#### TommyTman

5+ Year Member
Right, either way the answer would be 40N then? The Kaplan book I'm looking at says the answer is 60N and assigns both g and a positive values. Is it possible that there is a flaw in the book?

#### sps27

5+ Year Member
Right, either way the answer would be 40N then? The Kaplan book I'm looking at says the answer is 60N and assigns both g and a positive values. Is it possible that there is a flaw in the book?
2T - 10*10 = 10*2 i.e., 2T = 120 , T = 60. Did I miss something.....

OP
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#### TommyTman

5+ Year Member
Ahh that was dumb...I kept inserting (-g) into the term (-mg) and getting a double negative. For some reason it looked so right, thanks for the clarification I needed a second set of eyes.