Answer: 1.6 N
Explanation:
The weight of an object is calculated as:
W = g*m
where:
g = gravitational acceleration = 9.8m/s^2
m = mass of the object.
We also know that:
mass = density*volume.
or:
m = d*v
Let's start:
The weight of the beaker is 0.4N
And the weight of the beaker filled with water is 1.4N
Then the weight of the water alone will be:
1.4N - 0.4N = 1N = (d*v)*9.8m/s^2
And we know that the density of the water is:
1 g/cm^3
But we are working with Newtons, then we need to rewrite this with kilograms as the mass unit, we can use that:
1000g = 1kg
Now we can rewrite the density as:
d = 1 g/cm^3 = 1*(1/1000) kg/cm^3 = 0.001 kg/cm^3
Replacing that in the above equation, we get:
With this, we can find the volume that the water occupies.
W = 1 N = v* 0.001 kg/cm^3*9.8m/s^2
1 N /( 0.001 kg/cm^3*9.8m/s^2 ) = 102.04 cm^3.
Now, when we fill it with a brine with a density of 1.2 g/cm^3, the mass of this brine in a volume of 102.04 cm^3 be:
M = (1.2 g/cm^3)*( 102.04 cm^3) = 122.448 g
Rewriting this in kg we get:
M = 122.448 g = (122.448/1000) kg = 0.122448 kg
Then the weight of this brine is:
M = 0.122448 kg*9.8m/s^2 = 1.2 N
And the beaker weighs 0.4N, then the beaker filled with this brine will weight:
1.2 N + 0.4N = 1.6 N
