Finding Tension in a Suspended Wire with a Force Applied at a Given Point

[Larz31]

Homework Statement

A steel wire 40m long is suspended between two fixed points 20m apart. A force of 375N pulls the wire down at a point 15m from one end of the wire. State the tension in each part of the wire.

Known Data
Steel wire - 40m
Two points that are holding the wire up is 20m apart
375N force down 15m from one end of the wire

I suppose it may be helpful to know that this is from the Vector Concepts of my textbook, dealing with Force as a vector.

Homework Equations

Unknown

The Attempt at a Solution

I have had trouble understanding this question. My attempt at a solution is thinking that the wire would bend into two parts, one 15m long and the other 25m long. I simply split the force into a 5:3 ratio but it was clearly wrong. The back of the book states that the answer is: 375N and 0N

I do not understand how that answer can be attained, why is it that if a force acts down 15m from one end of the wire that there can be no tension on one end and the full thing on the other?

 

[Dick]

It can be if the wire is hanging straight down from one of the support points. Draw a picture and check this. It is isn't it??

 

[Larz31]

Hmm, I believe the problem I'm having is seeing the picture. I don't really understand what being suspended between two points 20m apart means exactly. Does this mean that the wire is held in place by two things 20m apart ANYWHERE on the wire?

 

[radou]

It means that the two things are 20 m apart, which has nothing to do with the length of the wire.

 

[Larz31]

There are two things that are 20m apart. There is a 40m wire. There is a force of 375N acting down 15m from one end of the wire.

That is what I have gathered. I do not see how I can use any of this data in conjunction with each other.

 

[hage567]

The "two things" are just the points where the two ends of the wire are attached to the ceiling. The mass is hanging down between it at 15m from the one end. Basically forming a triangle. If you try solving for the angles the wires make with the ceiling, it might make a clearer picture of what is going on (you can do this using the cosine law). You'll find that the wires form a right angled triangle with the ceiling. See if that helps you out at all.

 

[Dick]

The question is whether there is enough slack in the wire that it can't support the mass in between. And there is. Barely.