# Determine acceleration given work done and vertical distance

1. A body, whose mass is 10kg, is vertically raised upwards h=2 m . 230J work was done. Find the acceleration.

W = Fh
F = ma

## The Attempt at a Solution

W = Fh

F = A/h = 230J / 2m = 115J

F = ma

a = F/m = 115J/10kg = 11.5 m/s^2

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Orodruin
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Homework Helper
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The question is incomplete. The work done on what by what force?

If it is the work done by the lifting force on the mass, the acceleration of the mass is not only dependent on this force.

So, what's the solution then?

jbriggs444
Homework Helper
2019 Award
When a problem is (or even appears to be) incompletely specified, you should point that out, make some reasonable assumptions and state those assumptions along with your solution.

For instance you might assume that the work in question is that done by the external lifting force, excluding gravity.

You need to solve it with the information given, which means you need to make some assumptions.

It could be useful to turn around the problem and think about what would have been the work done if there were no acceleration. With that clear, it could be easier to see how to solve the original situation.

OK, I think now it's correct:

A = Fh

F = A/h = 230J/2m = 115N

F1 - mg = F

F1 = F + mg = 115N + 10kg*10m/s2 = 215 N

F1 = ma

a = F1/m = 215N / 10kg = 21.5 m/s2

Orodruin
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Well, except that the lifting force and gravity are working in different directions ...

Hey, I have found another solution, but the answer is different:

A = Ek = mv2/2

V2 = 2A/m = 46 (m/s)2

V2 = vo2+2as

a = v2/ 2h = 11.5 m/s

So why is that?

Orodruin
Staff Emeritus