<span>Work: W = Fd. 50(distance) multiplied by 90(force) would equal 4500 J or, answer D</span>
Answer:
W = 46 J
Explanation:
We need to find the angle between the two vectors Force vector and displacement vector.
First we will find the angle α of the force vector
![tan\alpha =\frac{1}{8} \\\\\\alpha =7.125 deg\\](https://tex.z-dn.net/?f=tan%5Calpha%20%3D%5Cfrac%7B1%7D%7B8%7D%20%5C%5C%5C%5C%5C%5Calpha%20%3D7.125%20deg%5C%5C)
Then we find the angle β of the displacement vector
![tan\beta=\frac{2}{6} \\\\beta = 18.43 deg\\](https://tex.z-dn.net/?f=tan%5Cbeta%3D%5Cfrac%7B2%7D%7B6%7D%20%5C%5C%5C%5Cbeta%20%3D%2018.43%20deg%5C%5C)
With these two angles we can find the angle between the two vectors
∅ = α + β = 25.56 deg
The definition of work is given by the expression
![W=F*d*cos (theta)](https://tex.z-dn.net/?f=W%3DF%2Ad%2Acos%20%28theta%29)
The absolute value of F will be:
![F=\sqrt{8^{2}+1^{2} } \\F= 8.06 N](https://tex.z-dn.net/?f=F%3D%5Csqrt%7B8%5E%7B2%7D%2B1%5E%7B2%7D%20%20%7D%20%5C%5CF%3D%208.06%20N)
The absolute value of d will be:
![d=\sqrt{(6 )^{2}+(2)^{2} } \\d= 6.32m\\](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%286%20%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%20%20%7D%20%5C%5Cd%3D%206.32m%5C%5C)
Now we have:
![W=8.06*6.32*cos(25.56)\\W=46 J](https://tex.z-dn.net/?f=W%3D8.06%2A6.32%2Acos%2825.56%29%5C%5CW%3D46%20J)
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The height of the oil column above the water in the vessel is determined as 2 cm.
<h3>
Pressure of the vessel</h3>
The pressure of the vessel due to water, oil and silver poured into the vessel is determined from mercury column.
let level of mercury = 20 cm + 0.5 cm = 20.5 cm
20.5 cmHg = 205 mmHg
1 mmHg = 133.32 Pa
205 mmHg = 27,330.6 Pa
<h3>Height of the liquids in the vessel</h3>
P = ρgh
where;
ρ is the density of water, oil and silver respectively
ρ = 1000 kg/m³ + 881 kg/m³ + 10,800 kg/m³ = 12,681 kg/m³
h = P/(ρg)
h = (27,330.6) / (12,681 x 9.8)
h = 0.22 m
h = 22 cm
<h3>Height of oil column</h3>
Oil is less dense than water and will float on water.
Height of oil column = 22 cm - 20 cm = 2 cm
Learn more about density here: brainly.com/question/6838128
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