How does slope on this graph indicate the amount of density?

Density comparison

Question 3 options:

A higher density is indicated by a slope that is not steep (yellow line)

The line in the middle (red line) has the highest density

The steeper slope (green line) indicates a higher density

a) The line with the highest slope represents the highest density values

b) False, the higher density is indicated by the green line.

c) False, the higher density is indicated by the green line, not the red line.

d) True, the higher density is indicated by the green line

Explanation:

This problem can be solved simply by using the definition of density, which stipulates that density is the relation between mass and volume.

d = m / V

where:

d = density [g/ml]

m = mass [g]

V = volume [ml]

For practical purposes we will compare the line with the lowest slope (Green Line) and the line with the highest slope (yellow line).

On the horizontal axis we will see the volume value of 40 [ml].

V = 40 [ml]

Then we climb up to cut with the yellow line and see that the mass is equal to:

m = 65 [g]

So the density is:

density yellow = 65 / 40

density yellow = 1.625 [g/ml]

Then we climb up to cut with the green line and see that the mass is equal to:

m = 155 [g]

So the density is:

density yellow = 155 / 40

density yellow = 3.875 [g/ml]

We can see that the green line, that is the line with the highest slope represents the highest density values.

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2