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The concept of density allows finding that for the measured data the water temperature is 25ºC
Given parameters
- The mass m = 22.9320 gr (
) = 22.9320 10⁻³ kg
- The volume V = 23.00 cm³ (
)³ = 23.00 10⁻⁶ m³
To find
- Temperature
Density is defined by the relationship between the mass of a body and its density, it is a very useful concept.
Where ρ is the density, m the mass, and V the volume of the body.
Mass is a constant that depends on the amount of matter in a substance, therefore it does not depend on its temperature.
The volume of a body depends on the distance between the atoms or molecules that has some kind of dependence with the energy that unites them, therefore, as it has more energy (higher temperature), the volume must increase.
Let's calculate the density with of the water
ρ = 997.0 kg / m³
Water is a material where the dependence of density with temperature is tabulated, in the table we can see some values of interest
Temperature (ºC) Density (kg / m³)
0.01 999.8
4 1000
10 999.7
20 998.3
25 997.1
30 995.7
When reviewing the table we see that the water temperature for this density must be T = 25ºC
Using the concept of density we can find that the temperature of the water is 25ºC
Learn more about density here:
The maximum value of θ of such the ropes (with a maximum tension of 5,479 N) will be able to support the beam without snapping is:
We can apply the first Newton's law in x and y-direction.
If we do a free body diagram of the system we will have:
x-direction
All the forces acting in this direction are:
(1)
Where:
- T(1) is the tension due to the rope 1
- T(2) is the tension due to the rope 2
Here we just conclude that T(1) = T(2)
y-direction
The forces in this direction are:
(2)
Here W is the weight of the steel beam.
We equal it to zero because we need to find the maximum angle at which the ropes will be able to support the beam without snapping.
Knowing that T(1) = T(2) and W = mg, we have:
T(1) must be equal to 5479 N, so we have:
Therefore, the maximum angle allowed is θ = 37.01°.
You can learn more about tension here:
I hope it helps you!