Solving the Torque Problem: Find the Weight of Each Boy

[Equilibrium]

Torque problem!

When one boy is sitting 2.0ft from the center of a seesaw, another boy must sit on the other side 2.5ft from the center to maintain an even balance. However, when the second boy carries an additional weight of 10lbs & sits 3.5ft. from the center, the 1st boy must move to 4.0ft from the center to balance. Neglecting the weight of the seesaw, find the weight of each boy.
Im confused
There's no given weight of these boys...
< -------- 4.0ft-------------------> <-------------3.5ft------------------->
---.-----------------------------------*---------------------------------------.-----

 

[Chi Meson]

There's no given weight of these boys...

That's because weight is what you need to find!

Call the weight of the first boy "w." Call the weight of the other boy "w + 10." You have only one unknown quantity. Solve for this.

 

[BerryBoy]

Hint: Define boy one with a mass of x then boy two as (x+10).
Your answer will be in lbs.

Regards,
Sam

 

[BerryBoy]

Sorry about that repeat...
Looks like a simulaneous job :-)

I am confused, its seems that many people in this forum regard: weight = mass
Even when the standard base units ( N = kg ) do not equate.

Anyone know why?

 

[Equilibrium]

does this mean that the weight of the two boys are equal? How come..
Fw1stboy = Fw2ndboy

 

[BerryBoy]

No, the mass of the two boys are not equal...

If you regard the mass of the first boy as M. It is given that the second boy's mass is 10lbs larger. So the mass of the second boy can be written as M+10. So, if the the see-saw is balanced, then the net torque of the system is zero. From the two situations you'll end up with two equations with M to solve.

Hints:

Torque = Force x Perpendiular distance

You have a MASS of M and (M+10)

So the FORCE = WEIGHT = Mg and (M+10)g

Hope this helps (if you want a diagram just ask),
Sam

 

[BerryBoy]

Sorry, I don't want to confuse you, don't worry about the The Mg & (M+10)g.

You can just use their mass as the gs cancel anyway.

So consider: M_boy1 x distance_{from centre} = M_boy2 x distance_{other distance from centre}

;-)

Sam

 

[Chi Meson]

Sorry about that repeat...
Looks like a simulaneous job :-)
I am confused, its seems that many people in this forum regard: weight = mass
Even when the standard base units ( N = kg ) do not equate.
Anyone know why?

This is one fo the greates common misconceptions of physics. The distinction between weight and mass is the first hurdel for those who have difficulty with these problems. For some it's no problem, for others it is hard to separate "mass" from the "force of gravity."

In this particular problem, we are looking for the force, so therefore it is not even necessary to bring mass into the picture.

 

[Chi Meson]

I had mis-read the original problem. Let's start over:

Just dealing with weights (in pounds):
boy # 1 has a weight of $$w_1$$ . Boy # 2 has a weight of $$w_2$$

Set up an equation for balanced torques using the distances given in the first part.

Now the second part:
boy #1 still has weight $$w_1$$ lbs. boy #2 has weight $$w_2 + 10$$ lbs.

set up a second equation for balanced torques using these forces and the given distances.

You now have two unknowns with two equations. Can you do simultaneous?

 

[BerryBoy]

This is one fo the greates common misconceptions of physics. The distinction between weight and mass is the first hurdel for those who have difficulty with these problems. For some it's no problem, for others it is hard to separate "mass" from the "force of gravity."

I agree with this. (except that gravity isn't a force, its a field where an inertial mass is subject to a force). But...

In this particular problem, we are looking for the force, so therefore it is not even necessary to bring mass into the picture.

I disagree with this, the pound is the imperial unit of MASS so you cannot equate a force to a mass. The question has given a value in 'lbs' you must conclude that it is a mass.

I think that a question that is given which equates mass to weight is bad physics, it'll become confusing to people when they learn they are two different things.

Your thoughts...

Sam

 

[Chi Meson]

I agree with this. (except that gravity isn't a force, its a field where an inertial mass is subject to a force). But...
I disagree with this, the pound is the imperial unit of MASS so you cannot equate a force to a mass. The question has given a value in 'lbs' you must conclude that it is a mass.
I think that a question that is given which equates mass to weight is bad physics, it'll become confusing to people when they learn they are two different things.
Your thoughts...
Sam

No, pounds is not a unit of mass, it is a unit of force. The imperial unit of mass is the seldom-used 'slug, which is pounds/32.2. A slug is currently defined as 14.59 kg exactly

"gravity" is a phenomenon. Weight is the force due to gravity. In the SI units, weight is measured in Newtons. One pound of force is currently defined as 4.448 N exactly. "g" represents the strength of the gravitational field.

I agree with your statement afout equating mass with weight, but I'm afraid that you are incorrect regarding pounds as measuring mass.

 

[Equilibrium]

1st equation
Torque CClockwise + (-TorqueClockwise)= 0
W1 * 2.0ft - ( 2.5ft*W2) = 0
W1 = (2.5ft * W2) / 2.0ft
W1 = 1.25 W2 ----> equation 1

Tcc + (-Tc) = 0
4.0ft * W1 + ( - ( 3.5ft * (w2 + 10lbs) = 0
4.0ft * 1.25 W2 + (-(3.5ft*w2 + 35 ft * lbs) = 0
5ft*W2 - 3.5ft*W2 = 35 ft * lbs
W2 = (35ft*lbs) / 1.5 ft
W2 = 23.33lbs

W1 = 1.25 (23.33)
W1 = 29.16

is this correct?

 

[BerryBoy]

I completely agree with your answer.
(However my rounding for W₁ equals 29.17lbs)

Sorry to drag this on.. but I still disagree that pounds is a unit of force

http://physics.nist.gov/Pubs/SP811/appenB.html" - States that pounds are unit of mass.

http://en.wikipedia.org/wiki/Pound" - I refer you to this page especially (it describes why people think that pounds are a unit of force because of the common use of the word WEIGHT).

You comments are appriciated.

Sam

 

[Chi Meson]

Yes, read the Wikipedia page, specifically:

On the other hand, pounds are always to be construed as a unit of force in contexts such as these:
Thrust of rocket or jet engines in pounds-force.
Torque in foot-pounds or pound-feet.
Pressure in pounds per square foot or pounds per square inch.
Energy in foot-pounds.

and this one:
http://scienceworld.wolfram.com/physics/Pound.html
and
http://www.physics.ucla.edu/k-6connection/Mass,w,d.htm
I'll admit to the ambiguity of the pound, especially as used by engineers, but in this problem the pound is definitely intended to be a unit of force.

 

[Pyrrhus]

I agree with Chi Meson, pound is a unit of force and like the kip is important in the british system which is a gravitational system (Force-Length-Time), unlike the international system which is an absolute system (Mass- Length- Time). Also, for pound as an unit of mass, in engineering in most cases is used as lbm to avoid confusion.

 

[lightgrav]

Also in use in Engineering, at least in the US,
is the mass unit "slug", which is given 1ft/s/s accel. by 1 lb force.

I've tried to consistently say "Force by Earth's gravity", but get lazy.
On the other hand, I NEVER say "Force OF gravity" ...

The continued confusion between "mass" and "weight" is strongly correlated
to the early teaching of g as an acceleration (where F=mg and F=ma),
rather than a field strength.
It also has close ties to the treatment of kinematics, especially free-fall, before any dynamics are encountered (with other Force sources like springs)

 

[BerryBoy]

http://en.wikipedia.org/wiki/Pound-force" - I have found a site that reference pounds as a force, but they call it the pound-force. Also there is another unit of force which is called the poundal. Can someone provide me with a site with a definition as a pound as a unit of force, I can't find one.

Regards,
Sam

 

[Chi Meson]

http://en.wikipedia.org/wiki/Pound-force" - I have found a site that reference pounds as a force, but they call it the pound-force. Also there is another unit of force which is called the poundal. Can someone provide me with a site with a definition as a pound as a unit of force, I can't find one.
Regards,
Sam

Read my last post, #14, and see the links provided there. Read the FULL wikipedia page that you noted; "pound-force" is used along with "pound-mass" to avoid the confusion that results from just using "pound." Note in this page how certain uses of "pound" imply reference specifically to "pound-force." Regarding the problem of the OP: Since the unit of torque is the "foot-pound," and torque is the cross-product of force and radius, this particular "pound" must clearly be referring to the pound of force.

One google search later:
http://www.sizes.com/units/pound_force.htm
http://www.answers.com/topic/pound
http://www.abe.iastate.edu/AE520/DimensionsandUnits.pdf
http://science.howstuffworks.com/fpte2.htm
http://www.gi.alaska.edu/ScienceForum/ASF8/882.html

I have yet to see a page that said outrightly that "pound" only means mass and never means force.

 

[Chi Meson]

I've tried to consistently say "Force by Earth's gravity", but get lazy.
On the other hand, I NEVER say "Force OF gravity" ...

The continued confusion between "mass" and "weight" is strongly correlated
to the early teaching of g as an acceleration (where F=mg and F=ma),
rather than a field strength.

I totally agree on both counts. I prefer "force due to gravity," but I think that's equivalent to your statement. "Gravitational force" and "force of gravity" are too close in feeling to "gravitational field strength" for brand new students of physics. I do try to avoid them, but bad habits...

And how do you explain to a student that weight is mass x "acceleration due to gravity" when an object is just sitting on a table, not moving?

 

[BerryBoy]

I have yet to see a page that said outrightly that "pound" only means mass and never means force.

The article I supplied, says that:

Over time, the various keepers of the standards redefined pounds in terms of the metric system (which has happened in case of the avoirdupois and troy pounds as well as the metric pounds), they were defined in terms of the kilogram, not the dyne or the Newton.

- From http://en.wikipedia.org/wiki/Pound

I understand that when you say pound-force it is a force, but when the word pound is used on its own, this article states that it is a mass. I can see now that the question specifically uses the word WEIGHT and so pounds (in this case must mean a force). But I think that this has brought on an interesting point of talk and I can now see why the S.I. units makes life a lot easier.

Its been great having this conversation with you, my apologies to Equilibrium for drowning his thread with this 'pound' topic.

Regards,
Sam

 

[Chi Meson]

I can now see why the S.I. units makes life a lot easier.

We no doubt agree on that!