In accordance with the definition of density as r = m/V, in order to determine the density of
matter, the mass and the volume of the sample must be known.
The determination of mass can be performed directly using a weighing instrument.
The determination of volume generally cannot be performed directly. Exceptions to this rule
include
· cases where the accuracy is not required to be very high, and
· measurements performed on geometric bodies, such as cubes, cuboids or cylinders, the volume
of which can easily be determined from dimensions such as length, height and diameter.
· The volume of a liquid can be measured in a graduated cylinder or in a pipette; the volume of
solids can be determined by immersing the sample in a cylinder filled with water and then
measuring the rise in the water level.
Because of the difficulty of determining volume with precision, especially when the sample has a
highly irregular shape, a "detour" is often taken when determining the density, by making use of the
Archimedean Principle, which describes the relation between forces (or masses), volumes and
densities of solid samples immersed in liquid:
From everyday experience, everyone is familiar with the effect that an object or body appears to
be lighter than in air – just like your own body in a swimming pool.
Figure 3: The force exerted by a body on a spring scale in air (left) and in water (right)
Answer:
C_{y} = 4.96 and θ' = 104,5º
Explanation:
To add several vectors we can decompose each one of them, perform the sum on each axis, to find the components of the resultant and then find the module and direction.
Let's start by decomposing the two vectors.
Vector A
sin θ =
/ A
cos θ = Aₓ / A
A_{y} = A sin θ
Ax = A cos θ
A_{y} = 4.9 sin 31 = 2.52
Ax = 4.9 cos 31 = 4.20
Vector B
B_{y} = B sin θ
Bx = B cos θ
B_{y} = 6 sin 156 = 2.44
Bx = 6 cos 156 = -5.48
The components of the resulting vector are
X axis
Cx = Ax + B x
Cx = 4.20 -5.48
Cx = -1.28
Axis y
C_{y} = Ay + By
C_{y} = 2.52 + 2.44
C_{y} = 4.96
Let's use the Pythagorean theorem to find modulo
C = √ (Cₙ²x2 + Cy2)
C = Ra (1.28 2 + 4.96 2)
C = 5.12
We use trigonemetry to find the angle
tan θ = C_{y} / Cₓ
θ’ = tan⁻¹ (4.96 / (1.28))
θ’ = 75.5
como el valor de Cy es positivo y Cx es negativo el angulo este en el segundo cuadrante, por lo cual el angulo medido respecto de eje x positivo es
θ’ = 180 – tes
θ‘= 180 – 75,5
θ' = 104,5º
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