Units of measurement (1 Viewer)

KingOfActing · Dec 31, 2015

I don't really know how to ask this so I'll show an example first:

$A train of mass 80 tonnes is moving in a circle of radius 320m at a speed of 48 km/hr. What force must be exerted by the rails towards the centre?$

The way I would solve this, would just be $F = \frac{mv^2}{r} = \frac{80 \text{ tonnes} \times (48\frac{\text{km}}{\text{h}})^2}{320\text{m}} = 576\frac{\text{tonnes} \times \text{km}^2}{\text{m} \times \text{h}^2} = 576 \frac{10^3\text{kg}\times10^6\text{m}^2}{\text{m} \times 60^4\text{s}^2} = ~ 44,444\frac{\text{kg} \times \text{m}}{\text{s}^2} = 44,444\text{N}$

My teacher told me that I should change the units to base units first before doing the calculations, though I find it easier manipulating the units afterwards. Is this something I could get marked down for in an exam?

InteGrand · Dec 31, 2015

KingOfActing said:
I don't really know how to ask this so I'll show an example first:

$A train of mass 80 tonnes is moving in a circle of radius 320m at a speed of 48 km/hr. What force must be exerted by the rails towards the centre?$

The way I would solve this, would just be $F = \frac{mv^2}{r} = \frac{80 \text{ tonnes} \times (48\frac{\text{km}}{\text{h}})^2}{320\text{m}} = 576\frac{\text{tonnes} \times \text{km}^2}{\text{m} \times \text{h}^2} = 576 \frac{10^3\text{kg}\times10^6\text{m}^2}{\text{m} \times 60^4\text{s}^2} = ~ 44,444\frac{\text{kg} \times \text{m}}{\text{s}^2} = 44,444\text{N}$

My teacher told me that I should change the units to base units first before doing the calculations, though I find it easier manipulating the units afterwards. Is this something I could get marked down for in an exam?

$It's probably easier just to convert everything to SI units at the start and then just do the question without needing to worry about units till the very end, when you know it'll be in newtons. This is because if everything is in SI units to start with, the end of a calculation is also in SI units, and so the final units must be newtons, since the calculation was for a force. I.e. We'd say at the start that$

$$m=80000\text{ kg}, v = 48\times \frac{1000}{3600} \text{ m/s} = \frac{40}{3} \text{ m/s}$ (and $r$ is already in SI units), and then just plug the numbers into the formula \textsl{without} their units, only putting in newtons once the calculation is fully simplified. This is especially nicer to do if the formula for the required quantity is relatively complicated.$

$That being said, I don't see why you'd lose marks for your method, since it's equally valid, and they don't seem to be too fussy about units in HSC 4U.$

KingOfActing · Dec 31, 2015

InteGrand said:
$It's probably easier just to convert everything to SI units at the start and then just do the question without needing to worry about units till the very end, when you know it'll be in newtons. This is because if everything is in SI units to start with, the end of a calculation is also in SI units, and so the final units must be newtons, since the calculation was for a force. I.e. We'd say at the start that$

$$m=80000\text{ kg}, v = 48\times \frac{1000}{3600} \text{ m/s} = \frac{40}{3} \text{ m/s}$ (and $r$ is already in SI units), and then just plug the numbers into the formula \textsl{without} their units, only putting in newtons once the calculation is fully simplified. This is especially nicer to do if the formula for the required quantity is relatively complicated.$

$That being said, I don't see why you'd lose marks for your method, since it's equally valid, and they don't seem to be too fussy about units in HSC 4U.$

Alright, thank you. I like keeping the units in the equations as it helps me make sure I'm applying all the formulas correctly. That way I can always check that the units on both sides of the equation match up and that I didn't use an incorrect variable somewhere.

leehuan · Dec 31, 2015

KingOfActing said:
Alright, thank you. I like keeping the units in the equations as it helps me make sure I'm applying all the formulas correctly. That way I can always check that the units on both sides of the equation match up and that I didn't use an incorrect variable somewhere.

In the exam you could just bring a highlighter with you and mark every time you make a substitution on the question booklet.

Or you can do what my physics teacher recommended - Actually write out a conversion first (which is basically what IG did). You can't apply a formula incorrectly if you have all the variables written out in front of you, and the formula rewritten. (This means, actually write F=mv^2/r instead of just substitute immediately.)

KingOfActing · Dec 31, 2015

leehuan said:
In the exam you could just bring a highlighter with you and mark every time you make a substitution on the question booklet.

Or you can do what my physics teacher recommended - Actually write out a conversion first (which is basically what IG did). You can't apply a formula incorrectly if you have all the variables written out in front of you, and the formula rewritten. (This means, actually write F=mv^2/r instead of just substitute immediately.)

Yeah, I always write the formula first, but I'm still very prone to making silly mistakes.

Units of measurement (1 Viewer)

KingOfActing

lukewarm mess

InteGrand

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KingOfActing

lukewarm mess

leehuan

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KingOfActing

lukewarm mess

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