# The Naked Scientists Forum

### Author Topic: How is tension in a tow-line calculated?  (Read 6300 times)

#### RIch

• Guest
##### How is tension in a tow-line calculated?
« on: 13/09/2010 00:30:02 »

3 objects connected  by a string on a frictionless surface. You pull the string with a force of 30 newtons. What is the tension on the other two strings connecting the objects?

What do you think?
« Last Edit: 13/09/2010 00:30:02 by _system »

#### tommya300

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##### How is tension in a tow-line calculated?
« Reply #1 on: 13/09/2010 01:04:20 »

3 objects connected  by a string on a frictionless surface. You pull the string with a force of 30 newtons. What is the tension on the other two strings connecting the objects?

What do you think?
How are the blocks position relative to the pull?
What angles of force on all three strings ?
Is the pulling force parallel to the frictionless surface?

#### Geezer

• Neilep Level Member
• Posts: 8328
• "Vive la résistance!"
##### How is tension in a tow-line calculated?
« Reply #2 on: 13/09/2010 04:17:37 »
Sounds like a trick question

#### Soul Surfer

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##### How is tension in a tow-line calculated?
« Reply #3 on: 13/09/2010 12:19:22 »
An interesting problem and possibly a homework question.   I am presuming that the three objects are all connected in series with a strong at the front like this

30 newtons  <--O--O--O      no friction or air resistance so the objects just accelerate under the effect of the force

now the strings are I assume non elastic  and I am not assuming that they have equal masses so the acceleration of the whole is   force =mass x acceleration  so the acceleration is the total mass less the force  let us call the masses m1 m2 and m3 starting from the pulling end  the forces then in the strings are in proportion to the masses of the objects being pulled. so

the force in the last string is 30 newtons x  m3/(m1+m2+m3)

the force on the middle string is  30 newtons X  (m2+m3)/(m1+m2+m3)

and of course the force on the pulling string is  30 newtons x (m1+m2+m3)/(m1+m2+m3)  = 30 newtons

#### LeeE

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• Posts: 3382
##### How is tension in a tow-line calculated?
« Reply #4 on: 13/09/2010 14:40:03 »
Another way of looking at SoulSurfer's solution is to get three weights and three hanging spring scales.  Attach the first scale to the ceiling and suspend the first weight from it, then attach the second scale to the bottom of the first weight and suspend the second weight from the second scale: repeat for the remaining scale and weight.

The bottommost scale will only be suspending the mass of the third weight whilst the second scale will be suspending the mass of both the second and third weights (plus the weight of the third scale).  The first scale, being the one attached to the ceiling, will be suspending the mass of all three weights (plus the weight of the second and third scales)...

#### tommya300

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• Posts: 655
##### How is tension in a tow-line calculated?
« Reply #5 on: 13/09/2010 23:39:05 »
An Ideal condition having the coeficient of friction at zero.

"3 objects connected  by a string on a frictionless surface," implied that the coefficient of friction to be equal to zero which suggests to introduce it as part of the equation.

It is also suggested that a max force of 30 newtons was exerted on the pull.

Below...
The only time the 30 newtons can exist past (t1) is when the coefficient of friction is introduced at some fractional value.
In this case coeficient is zero, 30 newtons force will only be present in a very, very, short duration of time, if at all, at the beginning of the pull.
.

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#### Geezer

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##### How is tension in a tow-line calculated?
« Reply #6 on: 14/09/2010 04:46:18 »
Wait a minute. How many strings are there?

Anyway, assuming the objects are supported on a horizontal frictionless surface, the objects must be continuously accelerating while a force of 30N is acting on the string.

#### tommya300

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##### How is tension in a tow-line calculated?
« Reply #7 on: 14/09/2010 07:29:57 »
Wait a minute. How many strings are there?

Anyway, assuming the objects are supported on a horizontal frictionless surface, the objects must be continuously accelerating while a force of 30N is acting on the string.
3 objects at least 3 tow lines in the towing configuration.
Either they are in series or parallel, there can be a drawbar or the tow-lines can converge at some angle.
He did not mention lift nor did he emphasis up or down hill. Pick a configuration.

An object in motion will stay in motion unless some other force acts on it...
Ideally he is saying there is zero friction.

Once the initial force, given as 30 newtons, breaks the object free to move, instantaneous acceleration, and there is no friction, what opposing force is exerted to be able to even measure 30 Newtons, after the initial movement?
Ideally, no friction, no opposing forces, implies perpetual motion?
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« Last Edit: 14/09/2010 08:00:08 by tommya300 »

#### Soul Surfer

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##### How is tension in a tow-line calculated?
« Reply #8 on: 14/09/2010 09:02:59 »
Tommy you are thinking very wrongly here force= mass x acceleration in the absence of friction the presence of a force (for example a rocket motor) creates continuous acceleration.  no friction means that even the tiniest force will cause acceleration.

#### tommya300

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##### How is tension in a tow-line calculated?
« Reply #9 on: 14/09/2010 14:52:31 »
Tommy you are thinking very wrongly here force= mass x acceleration in the absence of friction the presence of a force (for example a rocket motor) creates continuous acceleration.  no friction means that even the tiniest force will cause acceleration.

Isn't the coefficient of friction directly related when incorporated into a formula?
.

http://cnx.org/content/m13781/latest/
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F=U*MA___ Mu=0 the 30 Newtons can not be calculated.

OH, I am seeing it differently, this 30 Newtons is not part of defining Mu... F=U*MG

Then that is all is to it. I see it now . Sort of like calculating the capacitance circuit of series capacitors
^^^^^^^^^^^^^^^^^^
« Last Edit: 14/09/2010 18:17:11 by tommya300 »

#### The Naked Scientists Forum

##### How is tension in a tow-line calculated?
« Reply #9 on: 14/09/2010 14:52:31 »