Ask question

Ask question

All categories

Marta_Voda [28]

2 years ago

7

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.50 x 105 P

a. Assuming that the top and bottom surfaces of the cap each have an area of 4.40 x 10-4 m2, obtain the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle. The air pressure outside the bottle is one atmosphere

1 answer:

MArishka [77]2 years ago

4 0

Answer:

$F \approx 19.5 N$

Explanation:

From the question we are told that:

Pressure of $P_{CO_2}=1.50 * 105 Pa.$

Bottle cap area $A_b= 4.40 * 10-4 m^2$

Generally the equation for Resultant pressure $P_r$ is give as is mathematically given by

$P_r=P_{CO_2}-P_a$

Where

$P_a=atmospheric\ pressure = 1.013*10^5 pa$

$P_r=1.50 * 105 Pa-1.013*10^5 pa$

$P_r=0.487*10^5 pa$

Generally the equation for Force exerted by screw F is give as is mathematically given by

$F = P*A\\F = 0.487*10^5*4.00*10^-4\\ F = 19.48 N$

$F \approx 19.5 N$

You might be interested in

A single-turn square loop carries a current of 16 A . The loop is 15 cm on a side and has a mass of 3.8×10^−2kg . Initially the

DiKsa [7]

Answer:

The minimum magnetic field is 0.078 T.

Explanation:

Given that,

Current = 16 A

Side = 15 cm

Mass $m= 3.8\times10^{-2}\ kg$

Mass each segment in given square loop is

$m=\dfrac{3.8\times10^{-2}}{4}$

We need to calculate the torque due to gravity

Using formula of torque

$\tau_{g}=2mg(\dfrac{L}{2})+mgL$

$\tau_{g}=2mgL$

The torque due to magnetic field

$\tau_{B}=FL$

$\tau_{B}=BIL^2$

The equilibrium condition

$\tau_{B}=\tau_{g}$

Put the value into the formula

$BIL^2=2mgL$

$B=\dfrac{2mgL}{IL^2}$

$B=\dfrac{2mg}{IL}$

Put the value into the formula

$B=\dfrac{2\times\dfrac{3.8\times10^{-2}}{4}\times9.8}{16\times15\times10^{-2}}$

$B=0.078\ T$

Hence, The minimum magnetic field is 0.078 T.

7 0

3 years ago

State and prove bessel inequality

maria [59]

Statement :- We assume the orthagonal sequence ${{\{\phi\}}_{1}^{\infty}}$ in Hilbert space, now ${\forall \sf \:v\in \mathbb{V}}$ , the Fourier coefficients are given by:

${\quad \qquad \longrightarrow \sf a_{i}=(v,{\phi}_{i})}$

Then Bessel's inequality give us:

${\boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Proof :- We assume the following equation is true

${\quad \qquad \longrightarrow \displaystyle \sf v_{n}=\sum_{i=1}^{n}a_{i}{\phi}_{i}}$

So that, ${\bf v_n}$ is projection of ${\bf v}$ onto the surface by the first ${\bf n}$ of the ${\bf \phi_{i}}$ . For any event, ${\sf (v-v_{n})\perp v_{n}}$

Now, by Pythagoras theorem:

${:\implies \quad \sf \Vert v\Vert^{2}=\Vert v-v_{n}\Vert^{2}+\Vert v_{n}\Vert^{2}}$

${:\implies \quad \displaystyle \sf ||v||^{2}=\Vert v-v_{n}\Vert^{2}+\sum_{i=1}^{n}\vert a_{i}\vert^{2}}$

Now, we can deduce that from the above equation that;

${:\implies \quad \displaystyle \sf \sum_{i=1}^{n}\vert a_{i} \vert^{2}\leqslant \Vert v\Vert^{2}}$

For ${\sf n\to \infty}$ , we have

${:\implies \quad \boxed{\displaystyle \bf \sum_{1}^{\infty}\vert a_{i}\vert^{2}\leqslant \Vert v\Vert^{2}}}$

Hence, Proved

5 0

2 years ago

Read 2 more answers

A runner completes the 200-meter dash with a time of 19.80 seconds. What was the runner's average speed in miles per hour?

andriy [413]

Answer:

v = 22.54 mph.

Explanation:

Given that,

Distance moved, d = 200 m

Time, t = 19.8 s

We need to find the runner's average speed.

We know that,

1 mile = 1609.34 m

200 m = 0.124 miles

19.8 seconds = 0.0055 h

So,

Speed = distance/time

$v=\dfrac{0.124}{0.0055}\\\\v=22.54\ mph$

So, the runner's average speed is 22.54 mph.

4 0

3 years ago

Part 1: Use complete sentences to explain why solar winds occur. Part 2: Give two examples in which solar winds impact Earth.

Troyanec [42]

Part 1

When the solar atmosphere accumulates a lot of magnetic energy to a point that cannot accumulate more, all that magnetic energy is suddenly released, and with it, a lot of radiation. So much, that in fact it covers all of the electromagnetic spectrum; from radio waves to gamma rays. That burst of radiation is called a solar flare. In a single solar flare the amount of radiation released is millions of times greater than all the nuclear bombs in the face if the earth exploding together. Lucky for us, most of the high-energy radiation dissipates before reaching the Earth, and the radiation that do reach us, is deflected by the Earth’s magnetic field.

Part 2

1. Not all the radiation of solar flares that reach the Earth is deflected by its magnetic field; some of them reach us and charges the upper atmosphere with ionized particles. Those particles react with the gases in the atmosphere and produce a light; that light is what we call Auroras borealis or southern nights; One the most beautiful natural spectacles in earth, who thought Auroras begin their lives as deadly solar flares.

2. Solar flares contain a lot of high-energy radiation that is extremely dangerous for our electronic devices; when they reach the Earth, they can damage sensible electronics like satellites. A very powerful solar flare could even damage all the electronic devices on the surface of the Earth.

4 0

3 years ago

A water gun fires 5 squirts per second. The speed of the squirts is 15 m/s.

stira [4]

Answer: 3.75 m

Explanation:

5 squirts in 1 second

So, 1 squirt in 1/5 second which is 0.2 second.

The difference in timing of two consecutive squirt is 0.2 second, so

time (t) = 0.2 s.

speed (s) = 15 m/s

Distance of separation (d) = ?

Now, formula for distance is

d = s × t

d = 15 × 0.2

d = 3.75 m

4 0

3 years ago