Force vs Torque vs Power

[Apocalypse]

This is a subject which confuses many.

A friend asked me to explain the difference between power and torque and ?I explained that really, in vehcile terms, it's all about how much force you can apply.

As he is Welsh, he was even more confused because he thought that force was something you used on unwilling sheep.


Anyway.....

I think the biggest obstacle to people understanding the difference between the three concepts is that , when metrication occurred, some idiot start teaching people that they 'weigh' a certain number of kg.

and this is WRONG.

Weight is a force - the force we exert upon the surface that resists against us falling - and force is measured in Newtons, NOT in kg.

MASS is measured in kg.

In imperial terms, pounds is actually a Force and is used correctly, and the imperial term for mass is a 'slug'

so, no , 1 kg does not equal 2,2lbs as we've always been taught - it can't as Force and mass are 2 totally different things.

In fact, to further confuse matters, because of the confusion, many technical journals started using kgf as a force - kilograms of Force - because it kind of makes more sense to people.

the relationship is pretty simple - F=ma , so ON EARTH where Gravitaional acceleration (g) is approx 9,81m/s/s a mass of 100kg will exert a force of 981N.m kgf is simply Force in Newtons x 9,81

Mass is mass.

in metric terms mass is defined as 1kg = 1 litre of pure water at 20degrees C = i litre is a volume of 1 cubic decimetre 1 decimetre = 10cm or 0,1m so 1dm^3 = 1 dm x 1 dm x 1dm

apparently this was decided by someone French. What can I say.

So - to understand the concepts - you have a MASS of a certain number of kg which means that you WEIGH that number of kg x 9,81 and the unit if measurement is in N - Newtons.

for the purposes of this lot, we will use 1kg = 10N (on earth) because it's just easier.

obviously people like Manny exert a far larger force upon the planet than others - this is because of their larger mass, not because they are fat.

so, anywhere in the universe you have a mass of, say, 100kg.

on Earth you will WEIGH 1000N, on the moon , with 1/6th of earths gravity, you will WEIGH 166,66N , on Mars with 1/4 of earths gravity you will WEIGH 250N - in orbit with neutral gravity - you weigh nothing.

but if you've got a mass of 150kg you are still a fat bastard despite your lower weight.

capiche?

so, all objects have a mass. even the smallest ones.

the only thing that can cause a mass to accelerate is Force.

the relationship between Force, mass and acceleration is F=ma

Force is measured in Newtons - from the formula 1N = 1kg.m/s^2


so, if you apply a Force of 100Newtons to a mass of 100kg, it must accelerate at 1m/s/s (there may be counter forces (drag) applicable so ACTUALLY we are talking about Nett Force)

NB - Drag is not dressing in women's clothing in terms of this discussion.

and it doesn't matter whether you are in a zero gravity environment or on jupiter - that is how much nett force it will take to accelerate that mass ANYWHERE.

the bigger the mass the more Force you need to accelerate it at a given rate. it takes twice as much force to accurate an object with a mass of 2000kg than to accelerate a mass of 1000kg.

If you apply the same force to an object of twice the weight, it will accelerate at half the rate. etc.


now, the next problem with how we think about things is that we would consider someone capable of exerting a great force on an object as 'powerful' - but actually, thats not power. thats just force. It's measured in Newtons. A weightlifter might be able to lift a great weight (measured in Newtons) but he might not be able to do it a lot.

The weight lifter can apply a Force of (say) 2000N to an object and lift it 2m. so on earth he can lift a mass of 200kg above his head. On Mars he could still lift 2000N above his head but that would be a mass of 800kg.

now, Mr. Forceful there might be able to do that once an hour. he picks up 200kg and puts it on a shelf 2m high.

but, the little gym bunny in aerobics class next door is lifting 3kg above her head 10 times a minute to the beat of some dodgy song.

so, she could lift 30kg a minute onto the same shelf, or 1800kg in the hour that the weightlifter puts 200kg on the shelf.

now... both energy and work measured in Joules. a Joule is defined as the energy released when exerting an effort (Force) of 1N on an object for 1m

this means Joules are technically measured in N.m.... the same as Torque. Energy is a little different to torque, even though they have the same units.. they aren't the same, although they are very related - just take my word for it for this conversation. effectively and simply by lifting an object that weighs 100N by 1m you would imbue it with a potential Energy of 1 Joule (1N.m) - if you drop it, you release this energy and it becomes kinetic energy. Do not confuse Joules with Newton metres of Torque.

so, the gym bunny is using WAY more energy and doing way more WORK than the weight lifter. hence the high energy name for aerobics.

now...

Power (or work) is measured in Watts. a Watt is 1Joule per second, or 1 N.m.s

Obviously, the imperial term, horsepower was based around how much work a machine could do compared to a horse. so if a machine could do the work of 3 horses, it was 3 hp. It's worth noting that some people had much lazier horses than others back in the old days, notably the Italians.

so.

Work is Force * Distance = N.m = Joule
Power is work / time = Joule / second or N.m/s


Our Gym Bunny has lifted 1200kg by 2m - she's used 24000Joules of Energy in 3600 seconds - 12000N*2m/3600seconds = 6,66N.m/s = 6,66 Watts
Our Weightlifter has lifted only 200kg by 2m in 3600 seconds - thats 4000Joules of energy in the same hour so - 2000N*2m/3600seconds = 1,11 N.m/s = 1,11 Watts.

(actually we need to add in the mass of body thats moved, air thats pumped in and out and blood thats pumped to their actual total work done so thats why the figures look low if you have ever been on a treadmill or whatever, but we are simplifying things somewhat here)

so technically, even though the weight lifter can exert 6 times the Force, he's way down on work rate (Power) compared to the gym bunny. He's NOT more powerful.

He can't improve his work rate (Power) unless he makes major changes to his body. he's stuck with 0,28W
She too can't improve her DIRECT force without major changes to her body and is stuck with being able to apply a force of only 30N at a time.




BUT....

there is the world's simplest machine to hand. It's called the lever.

now, lets say our gym bunny constructs a slightly complicated lever. Instead of putting a stick on a rock she arranges a lever around an axle shaft on bearings.

so, on one side of the shaft is a 6m long lever, on the other side is a 0,5m long lever.

on the short side is a weight of 360N and she applies her maximum capability of force of 30N to the 6m side.

so - at the axle shaft, she has a TORQUE of 30N*6m = 180N.m

at the outer end of the short lever the force applied is 180N.m/0,5m = 360N

so, she can now lift 36kg. but.... her 2m of motion on the long lever is reduced on the short side of the lever by a factor of 12, so she's only lifted it 0,166m to get it up to 2m she's going to have to lift it 12 times.

but , she can still perform the task 10 times a minute / 600times an hour.

Now, the weightlifter can also build himself a lever system and pick up ever bigger weights - but he's still limited to that one big push every hour.

If gym bunny were to create a complicated multiple lever system she could eventually pick up more than the weight lifter. and she'd still be doing more work because she can perform the task more often than the weightlifter.

but she'd be lifting less and less distance per stroke.

This is basically what a gearbox does - it multiplies torque as much as you like but power remains constant.

to bring this back to engines - effectively, an engine creates a constant torque on the axle shaft (crank shaft) - the crank is the one side of the lever arm.

you can't define that 'force' in Newtons because the output depends on the length of the output lever arm (a gear or a tyre or whatever)

so it's in N.m. your actual force is simply the Torque divided by the length on the output lever arm.

so, if you had an engine pushing 400N.m and acting directly on the wheel of (say) 500mm diameter, you'd get 400N.m/0,5m = 800N of force.

which is actually not a lot (80kgf)

so, it's run through other 'lever' systems - gears. so, an input gear of (say) 17 teeth with an effective radius of 17mm is acting against a gear of 68 teeth with an effective radius of 68mm

so, we increase the lever ratio by 4 times and thus inscrease the torque on the output shaft by 4 times, but also decrease the rpm by 4 times - thus, while Torque ('work') is increased by 4 times, the work is done 4 times less often. thus Power remains constant (Power = Work/time = 4/4 = 1)


so, we can now (hopefully) easily comprehend torque

The short version is that if we attach a 1m long lever parallel to the ground to an axle and get a person with a mass of 150kg and weighing 1500N on earth (we'll call this person 'Manny' for the sake of the discussion - disclaimer: there is no intention that the fictional Manny bears any resemblance to anyone I know living or dead)

anyway. Manny stands on the end of the 1m lever.

lets presume the axle shaft is frozen - it can't turn. Manny is thus exerting a twisting force of 1500N.m on the axle shaft

(it's important to note that there must be something for the force to act against)

because it's not moving no work is being done, so zero power is generated.

now. lets say we move to an alternate reality. on the other side of the axle shaft we set up a drag (a brake say) that generates 1400N.m of drag / opposite torque in opposition to Manny's 1500N.m of torque, and he moves down.... but gravity shifts to remain directly below him at all times, so he is always exerting a force of 1500N on the end of the 1m shaft.

Manny is now an engine.

Manny starts to spin round and round exerting a constant torque on the shaft, and speeding up the rpm. at a certain rpm we set the brake to 1500N.m and the rpm remains constant.

lets call it 600 rpm or 10 revs per second. we hope Manny will keep his fish and chips down because if he upchucks we'll lose mass and thus torque - a lot like a Disco 3 crank breaking. It's just not nice and the engine will come to messy halt.

at this point - because there is movement and work is being done (the brake is generating heat to use up the power) we can calculate power.

so, first the energy. now this is important to note. the twisting force (torque) on the shaft is 1500N.m as noted.

BUT the actual Work in Joules being done is actually occurring (in this case) over the circumference of a circle with a radius of 1m = 6,28m which is why it's very very important to not confuse Torque (N.m) with Work (Joules = N.m)

so. Work = 1500x6,28 - 9420 Joules

so, Power is equal to work over time - so 9420joules 10 times per second = 94 200W = 94,2kW


does this make any sense at all to anyone ?

[Apocalypse]

It’s also worth noting that it’s a lot cheaper to replace the fish and chips in Manuel than it is to replace a crank in a TDV6 motor .

[XJ Junkie]

Gonna have to read this a few times.

......Weight is not weight. Mass is weight




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[Apocalypse]

Gonna have to read this a few times.

......Weight is not weight. Mass is weight




Sent from my iPhone using Tapatalk

No. Mass is mass

Weight Is a force. It’s measured in Newtons.

Sheep are scared in Wales.

[Prof]

Sjoe...that's a mouthful.

Like Neil said....gonna have to read a few times

[ThysleRoux]

So how many SLUGGS make up a KG ?

[Chris Stoffel]

I don't understand any of this. Can you rewrite it in Afrikaans please?

[Michael]

Thanks Apoc, that made a lot of sense, even to my simple brain, even being forced to pause several times while laughing, but you lost me right at the end:
"...the actual Work in Joules being done is actually occurring (in this case) over the circumference of a circle with a radius of 1m = 6,28m..."
Where did the 6.28 come from?

P.S. I will forever be stuck with the image of a D3 TDV6 chucking up its fish and chips

[Johannes]

I don't understand any of this. Can you rewrite it in Afrikaans please?

That will help me as well

[KurtG]

I’m going to ask the admin to limit the number of characters per post.....


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[Apocalypse]

I’m going to ask the admin to limit the number of characters per post.....


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But.. but...

I wrote it really slowly for you because I know you can’t read very fast!

Some people

No appreciation .

[Apocalypse]

Thanks Apoc, that made a lot of sense, even to my simple brain, even being forced to pause several times while laughing, but you lost me right at the end:
"...the actual Work in Joules being done is actually occurring (in this case) over the circumference of a circle with a radius of 1m = 6,28m..."
Where did the 6.28 come from?

P.S. I will forever be stuck with the image of a D3 TDV6 chucking up its fish and chips

Circumference of a circle = PI * 2 * r = 3.14*2*1 = 6.28m

Incidentally , do you know You’ll never see a Porra in a TDV6? It’s because they can’t imagine changing the oil that often!

[Apocalypse]

So how many SLUGGS make up a KG ?

Had to look it up...

https://en.m.wikipedia.org/wiki/Slug_(unit)

14,5kg.

That’s a big slug!

[Ginger]

Very well explained! Thanks Apoc!

[grips]

Nice thread.