Question

Hello there!

Please show your work and explain your answer. I don't just need the answer, I also want to know how to solve this kind of problems.

Thank you :)

Answer 1

In the first answer, Paul James is kind of on the right track,
but the problem is the CUBE of the way he describes it.

I thought about it for the past few hours, trying to come up with
the best way to explain it. I think I can do it, and I hope it's clear.

Look at it this way:

In the REAL bridge, the volume of a little piece is

V = (Length) x (Width) x (Height) .

Whatever that volume is, it'll have 'V' units of steel in it,
and its weight will be 'V' units of weight.

Now, the engineers come along and build a scale model of the bridge.
The scale is 1:100 .
The "scale" always means the ratio of the LINEAR DIMENSIONS.
So that same little piece of the scale model will have

length = 1/100 of the REAL length
width = 1/100 of the REAL width
height = 1/100 of the REAL height .

The volume of the little piece will be

v = (0.01 L) x (0.01 W) x (0.01 H)

That's (L · W · H) x (0.01 · 0.01 · 0.01)

= V x (0.000001) .

= one millionth of the volume of the real bridge !

The first answer said that if the scale is 1/100 , then the model
has 1/100 of the weight of the full-size bridge. That's not true.

==> If the scale is 1/100 , then the model has (1/100)³
of the weight of the full-size bridge. That's one millionth.

If the model weighs 50 Newtons, then the real full-size bridge
weighs 50 million Newtons.

Looking at it the other way ... If you scale the model down by 100,
you scale the volume and weight down by (100)³ = one million.

So the answer to ' b ' is: No! The defense is wrong. It does not hold water !

At that scale, you could probably build the model out of cardboard and Kleenex,
and it would be stronger than the full-size structure built with steel !


Here's a general rule for scale models:

... You build a model to some SCALE.

... Each dimension of the model is (1/scale) the size of the original dimension.

... The AREA of the model or any part of it is (1/scale)² the size of
the original area.

... The VOLUME of the model or any part of it is (1/scale)³ the size of
the original volume. That also goes for the weight, and the amount of
material you'll need to build them with.

Answer 2

So the bridge is 1/100 of original proportion right?
That means the original bridge will have a weight equivalent to 100 times the model bridge right?
So 50N multiplied by 100 is 50000N.

And you see the original bridge might sag because as we saw here it has a weightof 100 times greater than the model bridge.
Think of it this way if you had a model bridge made of one orange peel on two ends it might hold right?
But if we use thousands of orange peels to make a real bridge it wouldn’t hold right?

As for these kind of problems I don’t understand that,maybe you can comment and I will reply.

Hope this helps :)