Homework Help: Density question.

lionely · Oct 30, 2011

1. A spring balance has a maximum reading of 10N and the length of the calibrated scale is 20cm. A rectangular metal block measuring 10cm by 3cm by 2cm is hung on the balance and stretches the spring by 15cm. Calculate
i) the weight of the block;
ii) the mass of the block;
iii) the density of the metal from which the block is made.(Assume G 10m/s^2)

3. The attempt at a solution

I'm not sure how to attempt the question, but my friend tried to help me but he doesn't even know himself... I must do this question. :(

sandy.bridge · Oct 30, 2011

It's a 20 cm scale with a maximum reading of 10 N. Break this 10 N value up over the entire scale. You can use this to determine how heavy the block is.

lionely · Oct 30, 2011

So 10N/20cm?? = 0.5?

sandy.bridge · Oct 30, 2011

Okay, 0.5N/cm. If the block causes a 15cm displacement , what would that be in terms of force?

lionely · Oct 30, 2011

Oh ummm 0.5N/cm x 15cm = umm 7.5N?

sandy.bridge · Oct 30, 2011

Yes, now how do you relate the mass of a substance to its weight?

lionely · Oct 30, 2011

Hmmm F=ma umm considering a(g) = 10m/s^2, 7.5N = m x 10

m= 7.5/10= .75kg?

sandy.bridge · Oct 30, 2011

Okay, can you figure out the density now?

lionely · Oct 30, 2011

Yes density = mass/volume = .75kg/0.6m?

sandy.bridge · Oct 30, 2011

I would reconsider your volume component. Remember
[tex]V=lwh[/tex]

lionely · Oct 30, 2011

but the components 10 x 3x2?

sandy.bridge · Oct 30, 2011

Not entirely sure what units your teacher wants you to be using, but yes that is the right idea. You may be required to give your answer in cubic meters rather than cubic centimeters, though.

lionely · Oct 30, 2011

lol i'm stupid I converted wrongly i converted the cubic centimetres as it was centimetres I divided by 100 when I should divided by like 10^6?

sandy.bridge · Oct 30, 2011

Here is an easy way to do it.

V=(3/100 m)(2/100 m)(10/100 m)

lionely · Oct 30, 2011

Oh thank you, but I got it. I'll remember that way.