Work-energy solution for a hanging weight

[jackthehat]

Homework Statement

Problem - A 120-kg mail bag hangs by a vertical rope. A worker then displaces the bag to a position 2.0 m to the side from the original position, always keeping the rope taut.
What horizontal force is necessary to hold the bag in the new position ?

Note :- We have to use energy balance methods to solve this problem.

Homework Equations

K(1) + U(G1) + W(other) = K(2) + U(G2)
where K(1) and K(2) are kinetic energy at start and end of displacement
U(G1) and U(G2) are potential energy at start and end of displacement
W(other) is work done by horizontal force in displacing the bag.

The Attempt at a Solution

I attempted to calculate the Kinetic energy of the body at start and end of displacement.
Then rearranging above equation to ..
W(other) = K(2) + U(G2) - K(1) - U(G1)
However since the tension in the rope has to be maintained throughout the displacement
to the side I assumed that the body would move in an arc. So this means, I guess, that
the estimation of the height the body is raised to would be more complicated.
I am not sure of the geometry of the displacement and so I think my height estimate is
off somewhat. I am also confused about whether the total work involved in raising the body is just the force x distance that the worker produces or a combination of this and the work
expended in overcoming gravity + the work the worker expends (and what about the
tension in the rope) . Also my calculations give me the Work expended in raising the
weight but how then do I convert this to the Force expended .. (what is the relationship
here ... is it just W = F x distance ?).
I am afraid I am confused as what quantity or combination of quantities I should be
using in my calculations and as I said the geometry of the thing is not clear to me.
Suffice to say the correct answer is .. 740 Joules .. and I got several answers
between 200-400 Joules in my several attempts at the problem.
Can anybody help me understand this problem and the general method to use ?

 

[PhanthomJay]

What is the length of the rope?? Is it given?

 

[jackthehat]

Hi .. yes ... I must have left that vital piece of information out in my haste to get the post on to the forum ..
The length of the rope is .. 3.5 metres.
Sorry about that.
Jackthehat

 

[PhanthomJay]

Hi .. yes ... I must have left that vital piece of information out in my haste to get the post on to the forum ..
The length of the rope is .. 3.5 metres.
Sorry about that.
Jackthehat

Okay.

Homework Statement

Problem - A 120-kg mail bag hangs by a vertical rope. A worker then displaces the bag to a position 2.0 m to the side from the original position, always keeping the rope taut.
What horizontal force is necessary to hold the bag in the new position ?

Note :- We have to use energy balance methods to solve this problem.

Homework Equations

K(1) + U(G1) + W(other) = K(2) + U(G2)
where K(1) and K(2) are kinetic energy at start and end of displacement
U(G1) and U(G2) are potential energy at start and end of displacement
W(other) is work done by horizontal force in displacing the bag.

Yes, correct.

3. The Attempt at a Solution

I attempted to calculate the Kinetic energy of the body at start and end of displacement.
Then rearranging above equation to ..
W(other) = K(2) + U(G2) - K(1) - U(G1)
However since the tension in the rope has to be maintained throughout the displacement
to the side I assumed that the body would move in an arc.

Yes

So this means, I guess, that
the estimation of the height the body is raised to would be more complicated.
I am not sure of the geometry of the displacement and so I think my height estimate is
off somewhat.

Now that you know the length of the rope and the horizontal displacement, you can do some basic trig and geometry to calculate the vertical displacement of the mailbag.

I am also confused about whether the total work involved in raising the body is just the force x distance that the worker produces or a combination of this and the work
expended in overcoming gravity + the work the worker expends (and what about the
tension in the rope) .

Both gravity and the man do work , does tension do work? (think about direction of tension force and direction of displacement as the bag moves in an arc) . Your equation will give work done by 'other' forces besides gravity.

Also my calculations give me the Work expended in raising the
weight but how then do I convert this to the Force expended .. (what is the relationship
here ... is it just W = F x distance ?).

yes... distance in the direction of the force.

I am afraid I am confused as what quantity or combination of quantities I should be
using in my calculations and as I said the geometry of the thing is not clear to me.
Suffice to say the correct answer is .. 740 Joules ..

that's an answer for work but you are asked for the force required...

 

[jackthehat]

Hi PhanthomJay,
My mistake again .. I read the answer for a subsequent problem in the book .. the answer for
this particular problem is .. the value of the force required = 820 Newtons.
The solutions I obtained from several attempts .. range between 200 N - 400 N ?
Jackthehat.

 

[PhanthomJay]

Hi PhanthomJay,
My mistake again .. I read the answer for a subsequent problem in the book .. the answer for
this particular problem is .. the value of the force required = 820 Newtons.
The solutions I obtained from several attempts .. range between 200 N - 400 N ?
Jackthehat.

740 joules is the correct answer for the work done by the man, so I guess that's the answer to part b? But to determine the force required to hold the bag in place, draw a free body diagram now that you know the swing angle, and solve for the force using Newtons 1st law