F=ma Confusion about answer given for F

King

Hi,

I'm reading a book and one of the questions asks: how much force is required to give an object weighing 3000lb an acceleration of 12ft/sec²?

I calculated this as F=3000x12=36,000pdl. The answer given is "1125 force" (36,000/32). Why is this? Why isn't it just 36,000pdl?

SteamKing

If an object weighs 3000 lbs, that 3000 lbs is not the same as its mass.

TheAbsoluTurk

I think you need to find the mass. They give you the weight.

The acceleration on earth due to gravity is 32.174 ft/s^2. Divide the weight of the object by the acceleration on earth due to gravity and that will be the mass in pounds.

I have not worked in imperial units that much but I think the pound has two definitions; mass pounds and force pounds. In the metric system the unit for mass is the gram and the unit for weight is the newton. Weight is simply force exerted by an object with a field of gravity on an object.

After when you have the mass you multiply the mass by the acceleration given.

I'm on my phone so I can't write it out but I calculated it and it works out.

King

Thanks TheAbsoluTurk! I was so confused by the fact that the book states that pounds is the mass and poundals is the weight, such that when he stated pounds of weight I was unsure which of the two he meant.

This makes sense now: I find out the mass of the automobile on earth and then find the force required to make it reach an acceleration of 12ft/sec² in the horizontal direction.

PhanthomJay

The United States of America, and to some extent Myanmar, are the last of the world's countries to stick with the non-SI units of measurements, where force and weight is measured in pounds, and mass is measured in slugs. Forget about concepts of poundals and pound mass, as they are no longer used, and inconsistent with Newton's 2nd law. An objects mass in slugs is its weight on earth in pounds divided by 32. Mass is independent of the planet it is located on. Weight is very much dependent on the planet. Just as, by definition, a 1 N force will accelerate a 1 kg mass at 1m/sec^2, a 1 pound force will acelerate a 1 slug mass at 1 ft/sec^2. For your problem , the objects mass is 3000/32 = 93.75 slugs, and the net force required to accelerate it at 12 ft/sec^2 is 93.75(12) = 1125 pounds (1125 lb), per newton 2. I'd personally toss out any text that uses poundals or pound mass as a unit of measure. As uncomfortable an unorthodox the USA units may be, they are here to stay in the USA for a long long long time.

TheAbsoluTurk

Thank you for the information. I had no knowledge of the slug.

Here in Canada we're sort of in the middle; no one gives weight or height in kilograms or centimeters but our traffic signs are in km/h. Giving weight in kilograms would be wrong but the newton I'm assuming is either unknown or completely unintuitive to most people.

PhanthomJay

Out of curiosity, in Canada, when a kid's height and weight are measured in school, his/her height is given in _____ and weight in ____. Please fill in the blanks.

TheAbsoluTurk

I've never had my weight or height measured in school.

Just to give you an idea of how far along I am in the 'metrification' process, I graduated from high school this year.

mfb

But probably somewhere else?

The CIA factbook adds Liberia to that list. Both Liberia and Myanmar are switching to SI-units. It is ridiculous, but the US will be the last country to adopt SI-units.

"I weight x kg" is common in europe, too, with the true meaning "I have a mass of kg" (which has correct units). After all, weight changes when you change your location, mass does not. Well ... at least not purely based on the changed location.

Whovian

Laughed when I read the last bit. I'm assuming you're referring to special relativistic effects?

PhanthomJay

30 or 40 years ago here in the States, metric was trying to be introduced into the schools, and the kids were given their weight in pounds but their height in centimeters. But when Johnny was asked his height, he'd respond "I'm 3 feet-4 centimeters tall". That pretty much ended the experiment with SI, and now most kids through high school don't know what a kg or meter is. Conversion is a very slow process.

King

I'm actually reading a book by a 20th century American, hence the use of pounds and poundals. It truly is confusing, I'm most certain he sometimes refers to mass when he uses the word "weighs" so it is almost impossible for me to know what he is truly saying/asking. His section on Newton is the most confusing of all sections because of this, but I understand what he means by mass and force/weight.

I've not heard the term "slugs" used before :D. In Europe grams and Newtons are used.

mfb

If you climb a mountain or travel by bike, you actually lose mass. But that belongs to the biology forum.

Would be interesting to compare this to the knowledge about miles, feet and pounds in Europe.

Whovian

Oh! That's what you meant. I assumed you meant that in an arbitrary reference frame, stuff "traveling quickly" will have more mass than they would at rest.

gmax137

The "confusing" part is this: If you push a one-pound mass (1 lbm) with a one-pound force (1 lbf) the object will accelerate at 32 ft/sec2, NOT 1 ft/sec^2. This is because the 1 lbm object weighs 1 lbf here on the surface of the earth, yet when you drop it, it falls with an acceleration of 32 ft/sec/sec. Slugs and poundals were invented to disguise this fact and avoid confusion. For me, I think they cause more problems then they solve.

This doesn't come up in SI where, if you push 1 kg with a force of 1 N, it accelerates at 1 m/sec2.

I'm also curious about this, does anyone anywhere say "I weigh 690 newtons" or does everyone say "...70 kilos" ?

Apparently the reasons for converting aren't strong enough to overcome the obstacles. I learned physics with "the metric system" but I work in engineering in the US. At first I thought the units were funny (pounds per hour, gallons per minute, etc.) but soon they became familiar. As long as you understand what is going on, any system of units "works" and you may see the advantages of one or the other, depending on the given situation.

jetwaterluffy

Km/h isn't SI derived either (although a lot better than mph). The SI version of speed is m/s.

TheAbsoluTurk

This is true. I should've referred to it as a metric unit.