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Physics AS June 2021 Q3.3

The block is rectangular with an area of cross-section of 8.0 cm2 and a thickness of 3.0 cm. Figure 6 shows how the density of the block varies with depth up to its maximum thickness. Calculate the mass of the block.

The mark scheme of this question indicates to calculate the average density which I am extremely unsure why....

P.S. How do you upload photos!?! This is my first post ;D

Reply 1

Bruce Wayne59875

Average density IS the total mass / volume. So it would make sense to try and work out the average density in order to work out the total mass of the block.

For example, think of speed = distance / time. The speed used in this formula isn't really "speed" at a specific time, it's the average speed! Same applies to the p = m/v equation. The maximum density is 50kgm^-3 and the minimum density is 5kgm^-3. So if you add them together and divide it by 2 you get the mean density of the solid.

You can then use the thickness x cross-sectional area x average density to find total mass. Hope this helped! :smile:

(You could also find the area under the graph, and then multiply it by the cross-sectional area as it would give the exact same answer. Averages apply to areas as well, similar to if you wanted to work out average velocity. It's the area under graph (displacement) divided by time).