Finding acceleration given mass and tension

1. Oct 21, 2015

Rionic

If there is a 70N tension in a rope attached to a 4.0 kg bucket, what will be the vertical acceleration of the bucket?

I'm not really sure how to do this. I can find tension but not acceleration. I think I'm missing something simple. I'm also confused about the direction because it doesn't state whether it is going up or down.

For the formula I got a=Ft-g and m+mg-Ft=a. Idk either are right

2. Oct 21, 2015

Staff: Mentor

Where do those formulas come from? Their units do not match.

Did you draw a diagram with all relevant forces in it? That should always be the first step if you are unsure how to proceed.

3. Oct 21, 2015

Rionic

I drew an FBD with Fg downwards and Ft upwards

4. Oct 21, 2015

jbriggs444

If those are the only two forces on the bucket, what is the net force on the bucket?

5. Oct 21, 2015

Mister T

What did your equation look like before you got this equation from it? It looks like you started out with the right equation but then made mistakes rearranging it.

You know, for example, that Ft = 70 N and g = 9.8 m/s2, but subtracting them doesn't make sense because they have different units.

6. Oct 21, 2015

Rionic

Fnet=Ft-Fg then I turned fnet into ma and Fg into mg so it looked like
Ma=Ft-mg then rearranged it to a=Ft-g by dividing m on both sides

7. Oct 21, 2015

jbriggs444

That should be a lower case m on the left $ma = F_t - mg$
Now, when you divide the right hand side by m, what do you get again?

8. Oct 21, 2015

Mister T

You mean,

$ma=F_t-mg$,

right?

Then dividing the left side by $m$ does give you $a$, but you got the wrong result when you divided the right side by $m$.

9. Oct 21, 2015

Staff: Mentor

Who says that the rope is pulling upward on the bucket? How do we know that the rope isn't pulling downward on the bucket?

Chet

10. Oct 21, 2015

Rionic

Doesn't the m on the right side cancel?
And maybe this question doesn't require a direction because it doesn't tell me if it's going upwards or downwards

11. Oct 21, 2015

Mister T

Plug the numbers in and find out! Tell us the magnitude of each force, subtract them, and see if you get a net force that's equal to the mass times the acceleration.

12. Oct 21, 2015

jbriggs444

There are two terms on the right hand side.

13. Oct 21, 2015

Rionic

Ohh so it's a=Ft/m - g?

14. Oct 21, 2015

Yes!