How to Calculate Work Done by Tension in a Vertical Rope for a Moving Mass

[NasuSama]

Sorry for the second post, but I want to know how to solve such problem when it comes to this situation.

Homework Statement

A vertical rope is used to lower a block of mass M = 48.3 kg at a constant acceleration of magnitude a = 1.54 m/s2. Find WT, the work done by the tension in the cord if the mass moves down distance s = 2.47 m.

Homework Equations

→W = mad

The Attempt at a Solution

Hm... Tried to use this form:

W = m(g - a)d

But I'm not sure if I'm at the right path.

 

[cheahchungyin]

It seems correct to me :)
m(g-a) is the force used to reduce the block acceleration.
then m(g-a)d is the work done..nothing else to be considered anymore from here

 

[tiny-tim]

Hi NasuSama!

→W = mad

No.

The definition of work done is W = F "dot" d

Hm... Tried to use this form:

W = m(g - a)d

But I'm not sure if I'm at the right path.

How did you get that equation? Did you use F = ma?

If so, your F is correct, your d is correct, but your "dot" isn't.

 

[NasuSama]

Hi NasuSama! No.

The definition of work done is W = F "dot" dHow did you get that equation? Did you use F = ma?

If so, your F is correct, your d is correct, but your "dot" isn't.

So W = F * d [Can't do the dot].

I used F = ma to get the equation. What about the answer? Is it correct. You said F is correct and d is correct, right?

My answer is around 987 J, but it's incorrect.

 

[NasuSama]

W = m(g - a) [dot] d doesn't seem quite right.

 

[NasuSama]

Never mind. I got the solution!