You are designing a diving bell to withstand the pressure of seawater at a depth of 25.0 m.
a. What is the gauge pressure at this depth? (You can ignore changes in the density of the water
with depth) (2 marks)
b.
At this depth, what is the net force due to the water outside and the air inside the bell on a
circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the
pressure at the surface of the water? (You can ignore the small variation of pressure over
the surface of the window.) (3 marks)
Psw 1.03x10³ kgm³
Psw
=
-3
1.03 x 10³kgm ³
p=pgh
F = PA

Answer:

F = - K x        force is opposed to direction of extension

F = -100 N / m * .5 m = -50 N

Answer:

T = 1.4696 10⁴ years

Explanation:

For this exercise we must use Kepler's laws, specifically the third law which is the application of the universal law of gravitation to Newton's second law

               F = ma

               G m M / r² = m a_c = m v² / r

                G M / r = v²

the speed of the circular orbit is

               v = 2π r / T

we substitute

               G M / r = 4π² r² / T²

               T² = (4π² / G M)  r³

Kepler proved that this expression is the same if the radius is changed by the semi-major axis of an ellipse

               T² = (4π² /GM)  a³

the constant is worth

                (4π² / GM) = 2.97 10⁻¹⁹    s² / m³

let's reduce the distance to SI units

AU is the distance from the Earth to the Sun

               a = 600 AU = 600 AU (1.496 10¹¹ m / 1 AU)

               a = 8.976 10¹³ m

               T² = 2.97 10⁻¹⁹ (8.976 10¹³)³

               T² = 21.4786 10²²

               T = 4.63 10¹¹ s

Let's reduce to years

               T = 4.63 10¹¹s (1 h / 3600s) (1 day / 24 h) (1 year / 365 days)

               T = 1.4696 10⁴ years

The graph for velocity v/s acceleration in arbitrary path, is attached below.

Velocity and acceleration are both related to the motion of an object, but they represent different aspects of that motion.

Velocity is a vector quantity that represents the rate of change of an object's displacement over time. It is calculated as the change in position (displacement) divided by the time taken to make that change, and has both magnitude (speed) and direction.

Acceleration, on the other hand, is a vector quantity that represents the rate of change of an object's velocity over time. It is calculated as the change in velocity divided by the time taken to make that change, and also has both magnitude and direction.

The relation between velocity and acceleration is that acceleration is the rate at which an object's velocity is changing. If an object is accelerating, its velocity is changing over time. This means that if the acceleration is positive, the object's velocity is increasing, while if the acceleration is negative, the object's velocity is decreasing.

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At pH = 8, the ratio of H+ ions to OH- ions is 1:1, indicating a neutral solution. The concentration of H+ ions and OH- ions is approximately 1 x 10^(-8) mol/L. The calculated and approximated ratios should match.

To calculate the ratio of H+ ions to OH- ions at pH = 8, we need to use the relationship between pH and the concentration of H+ ions. The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution based on the concentration of H+ ions.

The formula to calculate the concentration of H+ ions (\(C_H\)+) from pH is:

\(C_H\)+ = \(10^(^-^p^H^)\)

Substituting pH = 8 into the formula:

\(C_H\)+ = \(10^(^-^8^))\)

Using the properties of logarithms, we can calculate the concentration of H+ ions:

\(C_H\)+ ≈ 1 x \(10^(^-^8^))\) mol/L

According to the concept of neutrality in water, the concentration of H+ ions is equal to the concentration of OH- ions. Therefore, the concentration of OH- ions (\(C_O_H\)-) is also approximately 1 x \(10^(^-^8^))\)mol/L.

To calculate the ratio of H+ ions to OH- ions, we divide the concentration of H+ ions by the concentration of OH- ions:

Ratio = \(C_H\)+ / \(C_O_H\)-

Ratio = (1 x \(10^(^-^8^))\) / (1 x \(10^(^-^8^))\))

Ratio = 1:1

The ratio of H+ ions to OH- ions at pH = 8 is 1:1, indicating a neutral solution. This means that the concentration of H+ ions is equal to the concentration of OH- ions, resulting in a balanced ratio.

When comparing the calculated ratio of 1:1 to the approximated ratio at pH = 8, they should be the same because the ratio of H+ ions to OH- ions is determined solely by the pH value, which is consistent and mathematically derived. Therefore, the approximated and calculated ratios should match.

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Answer:

a)A-B =(1,0,-3) +(2,-5,-1) =(3, -5, -4);    

b)B-C =(-2-3, 5-1, 1-1) = (-5,4,0);  

c)-A +(B –C) = (-1,0,3) +(-5,4,0) =(-6,4,3);  

d) =(3,0,-9) –(6,2,2) = (-3, -2, -11);  

e) = (-2,0,6) +(-6,15,3) +(-3,-1,-1) =

d) = (2,0,-6) –(-5*3, 4*3, 0) =  

Explanation:

1)C=k*A = (k*a1, k*a2, k*a3);

2)C=-A = -1*A;

3)C= A+B = (a1+b1, a2+b2, c2+c2);

4)C=A-B =A +(-B);  

5)A+B=B+A;  

6)A+B+C =(A+B)+C =A+(B+C

Answer:

which on a is the question

Answer:

You would weigh very slightly more at sea level than at the top of a mountain, not enough for you to notice, but a measurable amount. Weight, which really means gravitational force, is proportional to the product of the masses of two objects acting on each other, in this case the giant earth and the minuscule you.

Explanation:

Answer:Position is an object’s location in relation to a reference point.

Yes. As in the movie theater example, an object can be one unit positive from the reference point and a different object can be one unit negative from the reference point. Both objects are one unit away (the same distance), but they occupy different locations in space because they are in different directions.

Distance is the total amount an object has traveled, while displacement is the shortest distance between the object’s starting and finishing point.

Distance does not have direction. Objects can be one unit away from a point in every direction. However, displacement does have a direction. Displacement is defined as a specific distance in a specific direction.

Explanation: hope it helped

A) The net electric flux through the closed surface S₁ is given by the equation: Net electric flux = q1/4πε0
= 4.45 nC / (4π x 8.85 x 10-12 C2/Nm2)
= 0.541 x 10-3 Nm2/C .

Electricity is a form of energy that exists in nature and is created through the movement of electrons between atoms. It is the force that powers all of the electrical appliances and devices in our homes and offices.

B) The net electric flux through the closed surface S₂ is given by the equation:
Net electric flux = q1/4πε0 + q2/4πε0
= (4.45 nC + (-7.50 nC)) / (4π x 8.85 x 10-12 C2/Nm2)
= -2.05 x 10-3 Nm2/C
C) The net electric flux through the closed surface S₃ is given by the equation:
Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0
= (4.45 nC + (-7.50 nC) + 2.15 nC) / (4π x 8.85 x 10-12 C2/Nm2)
= -0.239 x 10-3 Nm2/C
D) The net electric flux through the closed surface S₄ is given by the equation:
Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0 + q1/4πε0
= (4.45 nC + (-7.50 nC) + 2.15 nC + 4.45 nC) / (4π x 8.85 x 10-12 C2/Nm2)
= 0.302 x 10-3 Nm2/C

E) The net electric flux through the closed surface S₅ is given by the equation:
Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0 + q1/4πε0 + q2/4πε0
= (4.45 nC + (-7.50 nC) + 2.15 nC + 4.45 nC + (-7.50 nC)) / (4π x 8.85 x 10-12 C2/Nm2)
= -1.75 x 10-3 Nm2/C.

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A) The net electric flux through the closed surface S₁ is given by the equation: Net electric flux = q1/4πε0

= 4.45 nC / (4π x 8.85 x 10⁻¹² C²/Nm²)

= 0.541 x 10⁻³ Nm²/C .

Electricity is a form of energy that exists in nature and is created through the movement of electrons between atoms. It is the force that powers all of the electrical appliances and devices in our homes and offices.

B) The net electric flux through the closed surface S₂ is given by the equation:

Net electric flux = q1/4πε0 + q2/4πε0

= (4.45 nC + (-7.50 nC)) / (4π x 8.85 x 10⁻¹² C²/Nm²)

= -2.05 x 10⁻³ Nm²/C

C) The net electric flux through the closed surface S₃ is given by the equation:

Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0

= (4.45 nC + (-7.50 nC) + 2.15 nC) / (4π x 8.85 x 10⁻¹² C²/Nm²)

= -0.239 x 10⁻³ Nm2/C

D) The net electric flux through the closed surface S₄ is given by the equation:

Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0 + q1/4πε0

= (4.45 nC + (-7.50 nC) + 2.15 nC + 4.45 nC) / (4π x 8.85 x 10-12 C²/Nm²)

= 0.302 x 10⁻³ Nm²/C

E) The net electric flux through the closed surface S₅ is given by the equation:

Net electric flux = q1/4πε0 + q2/4πε0 + q3/4πε0 + q1/4πε0 + q2/4πε0

= (4.45 nC + (-7.50 nC) + 2.15 nC + 4.45 nC + (-7.50 nC)) / (4π x 8.85 x 10⁻¹² C²/Nm²)

= -1.75 x 10⁻³ Nm²/C.

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The mass of the lifted object, given the height the heavy load was elevated to and average power is 1, 013.85 kg.

To calculate the mass of the lifted object, we can use the work-energy principle, which states that the work done on an object is equal to its change in gravitational potential energy.

Calculate the work done by the lifter:

Power (P) = 1.2 kW = 1200 W (converting from kilowatts to watts)

Time (t) = 25 seconds

Work (W) = Power × Time = 1200 W × 25 s = 30,000 J (joules)

Calculate the change in gravitational potential energy:

Height (h) = 12 in = 12 × 0.0254 m = 0.3048 m (converting from inches to meters)

Gravitational acceleration (g) = 9.81 m/s²

Solve for mass (m):

Since the work done is equal to the change in gravitational potential energy, we have:

30,000 J = m × 9.81 m/s² × 0.3048 m

Now, we can solve for the mass:

m = 30,000 J / (9.81 m/s² × 0.3048 m) = 1, 013.85 kg

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The angle to the horizontal the ball was launched at can be determined using trigonometry. Once you have the initial horizontal and vertical velocities, you can use the tangent function to calculate the launch angle.

Velocity is a physical quantity that describes the rate at which an object changes its position. It is a vector quantity, which means it has both magnitude and direction. The magnitude of velocity is the speed of the object, while its direction is the direction of motion.

Time is a concept that refers to the sequence of events that occur in a continuous progression, from the past, through the present, and into the future. It is a way to measure the duration or the length of events or periods, and it is a fundamental aspect of our experience and understanding of the world.

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Answer:

0.667 cm

Explanation:

|F_1on3| = |F_2on3|

k×q1×q3/x^2 = k×q2×q3/(d-x)^2

q1/x^2 = q2/(d-x)^2

(d-x)^2/x^2 = q2/q1

(d-x)/x = sqrt(q2/q1)

(2 - x)/x = sqrt(4×q/q)

(2 - x)/x = 2

2 - x = 2x

2 = 3x

x = 2/3

x= 0.667 cm

Answer:

because they have opposite charges

Explanation:

If you're talking about magnetism and electricity, the laws are that like charges attact and and unlike charges repel.

Charged particles interact with each other because they have opposite charges.

When charged particles are close to each other, their electric fields interact. So particles with opposite charges attract each other whereas particles with similar charges repel each other.

So we can conclude that Charged particles interact with each other because they have opposite charges.

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9\(\^{i}\)+8\(\^{j}\)/\(\sqrt{136}\)

F=(9.00i-8.00j)N

we are now to find the unit vector

according to formula

unit vector = \(\frac{vector of F}{Magnitude of F}\)

Now :

vector form of F = 9\(\^{i}\)+8\(\^{j}\)

magnitude of F =\(\sqrt{9^2+8^2}\)

magnitude of F=\(\sqrt{136}\)

now put that in formual

unit vector = 9\(\^{i}\)+8\(\^{j}\)/\(\sqrt{136}\)

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Answer:

the particle is at coordinates (18,15/2)

Explanation:

To find the acceleration of the particle, we can use the formula for velocity: v = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is the time. Since we know the initial and final velocities, as well as the time interval, we can solve for the acceleration:

a = (v - v0)/t = [(9i + 7j) - (3i - 2j)]/3 = (6i + 9j)/3 = 2i + 3j

So the acceleration of the particle is a = 2i + 3j m/s².

To find the coordinates of the particle at t=3s, we can use the formula for position: r = r0 + v0t + 1/2at², where r0 is the initial position. Since the particle starts at the origin, r0 = 0. Plugging in the values we have:

r = 0 + (3i - 2j)(3) + 1/2(2i + 3j)(3)² = 9i - 6j + 9i + 27/2 j = 18i + 15/2 j

We can use the kinematic equations of motion to solve this problem.

Let the acceleration of the particle be a = axî + ayj.

(a) Using the equation of motion v = u + at, where u is the initial velocity:

f = v = u + at

Substituting the given values, we get:

(91+7j) = (3î-2j) + a(3î + 3j)

Equating the real and imaginary parts, we get:

91 = 3a + 3a (coefficients of î are equated)

7 = -2a + 3a (coefficients of j are equated)

Solving these equations simultaneously, we get:

a = î(23/6) + j(1/2)

So the acceleration of the particle is a = (23/6)î + (1/2)j.

(b) Using the equation of motion s = ut + (1/2)at^2, where s is the displacement and u is the initial velocity:

At t = 3s, the displacement of the particle is:

s = ut + (1/2)at^2

Substituting the given values, we get:

s = (3î-2j)(3) + (1/2)(23/6)î(3)^2 + (1/2)(1/2)j(3)^2

Simplifying, we get:

s = 9î + (17/2)j

So the coordinates of the particle at t=3s are (9, 17/2).

Answer:

-12.1

Explanation:

i’m almost sure this is it, i’m checking my old answers

if not let me know and i’ll give you some more answers

The angular velocity to nearest degree per second, gives:

A) 21584°/s

B) 79217°/s

C) 215848°/s

D) 551180°/s

The formula to convert frequency (f) in Hertz (Hz) to angular velocity (ω) in radians per second is:

ω = 2πf

To convert the result to degrees per second, we can multiply by 180/π, which is the conversion factor between radians and degrees.

Using this formula, we get:

A) ω = 2π × 60 = 376.99 rad/s ≈ 21584°/s

B) ω = 2π × 220 = 1382.94 rad/s ≈ 79217°/s

C) ω = 2π × 600 = 3769.91 rad/s ≈ 215848°/s

D) ω = 2π × 1.53 × 10^3 = 9621.89 rad/s ≈ 551180°/s

Rounding these results to the nearest degree per second, we get:

A) 21584°/s

B) 79217°/s

C) 215848°/s

D) 551180°/s

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Answer: Negative

Explanation: The acceleration along the y-axis for any projectile motion will always be -9.8m/s^2.

Answer: the answer is d

Explanation:

The final angular velocity of Dhabitah is 16 rad/s.

The principle of conservation of angular momentum states the total angular momentum of an isolated system is constant.

The final angular velocity of Dhabitah is calculated by applying the principle of conservation of angular momentum as follows;

\(I_1 \omega _1 = I_2 \omega _2\\\\(Mr_1^2 )\omega _1 = (Mr_2^2) \omega_2\\\\r_1^2 \omega_1 = r_2^2 \omega_2 \\\\\omega _2 = \frac{r_1^2\omega _1}{r_2^2}\\\\ \omega _2 = \frac{0.5^2 \times 4}{0.25^2} \\\\\omega_2 = 16 \ rad/s\)

The diver applied the conservation of angular momentum to perform the somersault because he understood that the initial angular momentum is equal to final angular momentum.

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Explanation:

You want  N/m

 N = 66 * 9.81

 m = 2.3 x 10^-2 m

66* 9.81 / 2.3 x 10^-2  = 28150 =  28 000 N/m    to two S D

The final velocity of the 25.8 g marble after the collision is 16.15 cm/s.

The velocity of the 25.8 g marble after the collision is calculated as follows;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where;

The final velocity of the 25.8 g marble after the collision is calculated as;

( 25.8 x 21 ) + ( 12.4 x 13.8 ) = ( 12.4 x 23.9 ) + ( 25.8v )

712.92 = 296.36 + 25.8v

25.8v = 416.56

v = 416.56 / 25.8

v = 16.15 cm/s

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The tax rate you will pay is displayed in tax brackets for each category of taxable income.

Thus, For instance, in 2022, the first $10,275 of your taxable income is subject to the lowest tax rate of 10% if you are single.

Up until the maximum amount of your taxable income, the following portion of your income is taxed at a rate of 12%.

As taxable income rises, the tax rate rises under the progressive tax system. Overall, this has the result that taxpayers with higher incomes often pay a greater rate of income tax than taxpayers with lower incomes.

Thus, The tax rate you will pay is displayed in tax brackets for each category of taxable income.

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1,000 J of energy are needed to melt 10 g of a solid substance that is already at its melting point ,  the heat of fusion of the substance is 548 joules .

Heat of fusion, also known as enthalpy of fusion or latent heat of fusion, is the amount of energy required to melt or freeze a substance under constant pressure conditions. When it comes to chemistry, "fusion" is basically synonymous with "melting." In the classroom, heat of fusion is typically used when a substance is at its melting or freezing point. In such instances, most people consider heat of fusion to be a constant.

Water, for example, has a heat of fusion of 334 J/g at its melting point of 0°C. At 0°C, one grams  of liquid water requires 334 Joules of energy to completely freeze into ice. In addition, one grams of ice requires 334 Joules of energy to melt entirely.

q = m×∆Hf

q: Total change in heat energy (in Joules)

∆Hf: Heat of fusion of substance (in Joules per gram)

m: Mass of substance (in grams)

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Answer:

B. 120 kgm/s

Explanation:

The initial momentum of the system is zero since the boy and the girl are at rest. When they push each other apart, the total momentum of the system remains conserved. Since the girl moves in a negative direction, the boy must move in the positive direction with the same momentum to keep the total momentum of the system zero.

Let's assume the final momentum of the boy is p. According to the law of conservation of momentum,

(initial momentum) = (final momentum)

0 = p + (-40 kg)(-3 m/s)

0 = p + 120 kg m/s

p = -120 kg m/s

Therefore, the final momentum of the boy must be 120 kg m/s in the positive direction, which is answer choice B.

Ans

According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal. Initially, the momentum of the system is zero since the boy and the girl are at rest. When they push each other, the girl moves in the negative direction with a speed of 3 m/s. Let's assume that the boy moves in the positive direction with a speed of v m/s.

The total initial momentum of the system is:

P_initial = m_boy * 0 + m_girl * 0 = 0

The total final momentum of the system must also be zero since there are no external forces acting on the system. Therefore:

P_final = m_boy * v + m_girl * (-3) = 0

where m_boy = 60 kg, m_girl = 40 kg, and v is the final speed of the boy in m/s.

Solving for v, we get:

60v - 120 = 0

v = 2 m/s

Therefore, the total final momentum of the boy must be:

P_final = m_boy * v = 60 kg * 2 m/s = 120 kg m/s.

So, the total final momentum of the boy must be 120 kg m/s.

part a.

the total energy of Saul and the toboggan  is 70530 J

part b.

The height of the hill is  235.1 m.

part c.

Saul's velocity at the bottom of the hill will be  22.3 m/s.

part d.

Saul's height when he is moving at a velocity of 9.5 m/s is 10.5 m

The total energy of Saul and the toboggan is the addition all of potential energy and kinetic energy.

we know that the initial total energy = potential energy at top of hill

Therefore total energy is gien as

initia total energy  = mass of Saul + mass of toboggan x gravity x height

initia total energy  = (30 kg + 10 kg) x (9.81) x (20 m)

initia total energy  = 5886 J

Total energy  = potential energy + kinetic energy

Total energy = (30 kg + 10 kg) (9.81 ^2) x (20) + (30 kg + 10 kg) x (15)^2/2

= 70530 J

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Answer:   the acceleration of the masses is given by = 0, which means the angular acceleration of the pulley is zero. This implies that the masses m and 2m move with constant velocity,  they are in equilibrium.

Answer:

Therefore, the GPE of the fish from the given height is 26.19 J.

Explanation:

The gravitational potential energy (GPE) of an object at a height h is given by the formula:

GPE = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

In this case, the mass of the fish is 0.3 kg, the height from which it was dropped is 9 meters, and the acceleration due to gravity on Earth is approximately 9.81 m/s². Thus, the GPE of the fish can be calculated as:

GPE = (0.3 kg) × (9.81 m/s²) × (9 m) = 26.19 J

Therefore, the GPE of the fish from the given height is 26.19 J.

I like puffins

When a 2.5 kg sledgehammer hit a cement block with a force of 6.0 Newtons. The force the sledgehammer exerted on the cement block is greater in magnitude and opposite in direction to the force the cement block exerted on the sledgehammer.

This refers to forces that act on an object in opposite directions. The net force is gotten by solving for the difference between the two forces.

When the opposing forces are equal or balanced, the net force is zero.  The sledgehammer hits with a force and the cement block is receiving the impart as a stationary object.

Obviously, the force the sledgehammer exerted on the cement block is greater in magnitude and opposite in direction to the force the cement block exerted on the sledgehammer.

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The statement "B. Gravity exists only on Earth" and the statement "E. Gravity doesn't exist between Earth and the sun"  is not true about gravity.

Gravity is a fundamental force of nature that exists in the whole universe, not just on Earth. It is a force that acts between any two objects that have mass. This means that statement "C. Gravity is a force that pulls two objects together" and "D. Gravity exists between two objects that have mass" are both true. Gravity plays a significant role in the functioning of our solar system. The sun's gravitational force acts on the planets, including Earth, keeping them in their orbits. Similarly, Earth's gravitational force attracts objects towards its center, giving weight to objects on its surface. Gravity is the force that holds Earth in orbit around the sun and is responsible for the planets' motion in the solar system. Gravity is a universal force that exists throughout the universe, acts between objects with mass, and plays a crucial role in celestial bodies' movements, including the interaction between Earth and the sun.

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