Math Is Fun Forum

P.S. I've edited the mistake in the first example in my original post, so's not to confuse any newcomers to the thread!

Multiply the a term by the c term (3 x 8 = 24). Then take the pair of factors of 24 that give the b term (14), which would be 2 and 12. Then put the 2 in one bracket, and the 12 in the other. Then cancel the 3x+12 to make it x + 4. And you'll have your factors; (3x+2)(x+4), which equal 3x^2 + 14x + 8.

Here's the comments on the video;

The normal force and its relation to weight, has nothing to do with Newton's third law. It is a coincidence that it is equal and opposite, but it is not the third law counterpart to weight. Its existence has a lot more to do with Newton's second law, as a constraint force to stop the object from accelerating through the surface beneath it. The third law counterpart to your weight, is the weight of Earth in your own gravitational field. The fact that gravity is a two way street, where both the small and large object pull on each other with equal and opposite forces.
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Careful with invoking 3rd law and saying the normal force is the reaction force to gravity. The 3rd law reaction force to the earth pulling on a mass is the mass pulling on the earth. The normal force is often equal to gravity when a=0 because of Newton's 2nd law
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Normal force is fun fact a type of elastic force. Normal force is the opposite of pressure force(the F in pressure equation, p=F/A), they are both caused by objects don’t elastic deformation, which our eyes can’t see. So pressure force is caused by your contacting area doing elastic deformation ever so slightly which caused an elastic force and normal force is caused by the other contacting object like the wall doing elastic deformation ever so slightly which also caused an elastic force. If you are wondering, elastic deformation is the cause of elastic force, it is basically a change in an object’s shape caused by a constant force, but will turn back into how it was with the force is not present, example of that is a spring or a rubber band. And elastic force is just a force caused by that. However it also can be explained in energy, it is caused by elastic potential energy turning into kinetic energy.

Thanks, Bob.

“If you put a bag of sugar on some kitchen scales you'll get a reading which may be expressed in kilograms or pounds weight, but is actually a measure of the force the bag is exerting on the scales.  It's a force because if you could repeat this test on the Moon you'd get a lower value even though the mass of sugar is unchanged.”

Is that why a person weighs less on the Moon than they do on Earth?

“As the bag isn't moving downwards there must be equilibrium at the point of contact. That means there must be two, not one, force acting here; the force of gravity downwards and what is called the reaction of the scales acting upwards on the bag.”

So for the force of gravity downwards it would be;

F=ma. F=1kgx10m/s^2. F=10N downwards?

Would the reaction force of the scales acting upwards on the bag match/mirror this?

F=ma. F=1kgx?. What would the acceleration upwards be? If you removed the 1kg bag of sugar would the top part of the scale spring up at 10m/s^2?

Nb; I’m using 10m/s^2 as an approximation for g.

“Is the door any different after you have pushed it?  I tried this and asked the door but it refused to answer.”

“If you pushed really hard you might break it. I expect every time you open and shut a door the hinge screws cut a little more into the wood until eventually you have to put in some larger ones.”

I saw a Youtube video about the normal force. There was a diagram of a box on a floor. It was given as an example of Newton’s 3rd Law but a few people in the comments said it wasn’t, that it was more about elasticity than about Newton’s 3rd Law. Is that correct? Was I incorrect in thinking that my example of me pushing on a door was an example of Newton’s 3rd Law? Is me pushing on a door different from a box resting on a floor?

“But it's just a model. At an atomic level the door is mostly open space with neutrons etc hanging about inside. Newton's laws are not consistent with Einstein's theories nor with quantum mechanics so my advice is use them when appropriate but don't get too hung up on why they work.”

By model do you mean an approximation? They are roughly correct, and work (in engineering etc), but when we look more closely they’re actually incorrect?

Thanks, Bob.
I do find looking at the inverse process helpful when checking my answer.
“But all these definitions amount to the same thing so it is up to  you which you prefer.”
One of the first Google results I got for my question was;
“Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.”
Is this answer wrong, or at least incomplete? Should it read, ‘One way of understanding division is... etc’? It’s not said that another way of looking at 15÷3 is to ask, ‘How many 3s are there in 15?’
Either way, I do find it interesting. With some questions I find it helpful to think of a physical object (often a cake) being shared amongst children. 1÷2, 1÷4, etc. With others  a different approach cab be more helpful.
What about negative numbers, when it comes to division?
If I’m faced with -10÷2 I think of a debt of £10 being split into 2 debts of £5 (-10÷2=-5) with maybe 2 people involved, each taking on a debt of £5
When faced with -5x2 I think of someone having 2 separate debts of £5 and therefore being £10 in debt (-5x2=-10)
But when it comes to, for example, -10÷-5, it seems less straightforward. I know the rule (a negative divided by a negative = a positive)so I know it goes as follows; -10÷-5=2; but I can’t think of a ‘debt’ example like above (because there is no such as, ‘-5 people’. Although could I think of it as, ‘How many -5s are there in -10, in the same way as I might think of 10÷5 as, ‘How many 5s are there in 10’? So a debt of £10 is the same as 2 debts of £5

Ha! My emoji was supposed to be a smiley face