3. A 1.23 kg object slides down a 1.25 m incline of 35º. Use the data table to construct a graph for force due to gravity vs. distance. Trial 1 Trial 2 Trial 3 Averages Distance (m) 1.25 1.32 1.28

4. Based on the graph in #3, calculate the work done by gravity. Assume work is constant for this data.

5. Using the data from #3, construct a free body diagram and calculate work done by gravity. Explain how this value compare to the value determined graphically in #4.
Remember that this object is on an angle. You'll need to multiply the value for work by cos0
Keep in mind that you'll need to use the angle that forms between the force of gravity and distance. ​

The stretching force acting on the second wire, given the data is 588 N

F₁ / r₁ = F₂ / r₂

450 / 3.9×10⁻³ = F₂ / 5.1×10⁻³

cross multiply

3.9×10⁻³ × F₂ = 450 × 5.1×10⁻³

Divide both side by 3.9×10⁻³

F₂ = (450 × 5.1×10⁻³) / 3.9×10⁻³

F₂ = 588 N

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The vertical weight carried by the builder at the rear is 240.89N. The weight he must now carry is 352.26N

We have w = 1.8

Then we have L as 3.30

θ = 24.0

FC = 147

We have to find FB

147 (3.3 + 1.8 tan24)/(3.3 - 1.8 tan24)

= 240.896

The vertical weight carried by the builder is 240.896

2. 240.896 + 147

= 387.896

387.896/[1 + (1.8 + 3.3 tan24) /(1.8 - 3.3 tan24)]

= 387.896/10.885

= 35.64

387.896 - 35.64

= 352.26N

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The heat energy that will be converted into mechanical energy is 1.83 kJ.

The heat energy that will be converted into mechanical energy is calculated as follows;

Q = mcΔθ

where;

at 20 ⁰C = 293 K, C = 0.915 kJ/kg K

Q = (0.1 kg)(0.915)(20 )

Q = 1.83 kJ

Thus, the heat energy that will be converted into mechanical energy is 1.83 kJ.

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The average force exerted by the ball on the glove is 480 N.

The average force exerted on the glove by the ball is equal in magnitude to the force on the ball.

mass = 145 g = 0.145 kg

Acceleration of the baseball, a = (v² - u²)/2s

where:

v is final velocity = 0

u is initial velocity = 39 m/s

s is distance = -23 cm = 0.23 m

a = (0 - 39²)/2(-0.23)

a = 3306.52 m/s²

Force = 0.145 * 3306.52

Force = 479.4 N

Average force = 480 N

In conclusion, force is derived from the product of mass and acceleration.

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There is no A in the vector, so I assume you mean λ.

The magnitude of any unit vector is 1, so

[tex]\|0.4\,\vec\imath + 0.8\,\vec\jmath + \lambda \,\vec k\| = \sqrt{0.4^2 + 0.8^2 + \lambda^2} = 1[/tex]

Square both sides and solve.

[tex]0.4^2 + 0.8^2 + \lambda^2 = 1^2 \implies \lambda = \boxed{\pm \sqrt{0.2}}[/tex]

The maximum speed with which a 1200- kg car can make a turn is 22.02 m/s.

v(max) = √μrg

where;

v(max) = √(0.55 x 90 x 9.8)

v(max) = 22.02 m/s

Thus, the maximum speed with which a 1200- kg car can make a turn is 22.02 m/s.

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The vertical component of the force being applied to the beam by the high-tension cable is 36.37 N.

Calculation of the cable's tension-

Utilizing the moment principle, determine the cable's tension:

Torque clockwise = TL sin∅

Counterclockwise torque = 1/2WL

TL sin∅ = 1/2WL

⇒T sin∅ = 1/2W

⇒T = W/2sin∅

⇒T = (29* 9.8)/ (2*sin57)

⇒T = 169.43 N

Calculation of the vertical component of the force-

Forces that operate perpendicular to the surface vertical plane are called the vertical force. Gravity always pulls objects straight down to the earth's core.

T+F = W

⇒F = W-T

⇒F = (21*9.8)-169.43

⇒F = 36.37 N

So, the force on the beam has a vertical component of 36.37 N.

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Answer:

C. The atom loses 1 electron to have a total of 36

Explanation:

The number of electrons in a Rubidium atom is 37. Since the atom loses 1 electron, it has 36 left.

The magnitude of the tension in the string marked A is 52.5 N.

Given that the magnitude of the tension in the string labeled C is 56.3 N.

The angle at A is

tan θ = [tex]\frac{3}{8}[/tex]

below the negative x

B= tan Φ

tan Φ = [tex]\frac{5}{4}[/tex]

C = tan ρ

tan ρ = [tex]\frac{1}{6}[/tex]

Considering the Horizontal components only

74.9cos(9.46) = A*cos(20.6) + B*cos(51.3)

A = 78.9 - 0.668B

Considering the Vertical components only

74.9*Sin(9.46) + ASin(20.6) = BSin(51.3)

40.07 = 1.015B

B = 39.5 N

By substituting the value of B in the equation of A

Since, A = 78.9 - 0.668B

A = 78.9 - 0.668( 39.5 N)

A = 52.5 N

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The total electric potential energy is [tex]\frac{kq_{1} q_{3} }{r_{13} } + \frac{kq_{2} q_{3} }{r_{23} } + \frac{kq_{1} q_{2} }{r_{12} }[/tex].

Electric Potential Energy of a System of Charges :

The system's electric potential energy is equal to the amount of work necessary to create a system of charges by guiding them toward their designated locations from infinity against the electrostatic force without accelerating them. The symbol for it is U.U=W=qV. Electrostatic fields are conservative, therefore the work is independent of the path.

Assume three charges q₁ , q₂ and q₃ bring from infinity to point P.

To bring  q₁ no work is done,

[tex]V_{p} = \frac{kq_{1} }{r_{1} }[/tex]

where, V = electric potential energy.

            q = point charge.

            r = distance between any point around the charge to the point charge.

           k = Coulomb constant; k = 9.0 × 109 N.

Now bring q₂,

[tex]V_{2} = \frac{kq_{2} }{r_{2} }[/tex]

Work done by q₁ ;

[tex]W_{1} = V_{p} q_{2} = \frac{kq_{1}q_{2} }{r_{12} }[/tex]

Now bring  q₃,

[tex]V_{3} = \frac{kq_{3} }{r_{3} }[/tex]

Work done on q₃ by q₁ and q₂

[tex]W= q_{3} [ V_{1} + V_{2} ][/tex]

    [tex]=\frac{kq_{1} q_{3} }{r_{13} }[/tex][tex]+ \frac{kq_{2} q_{3} }{r_{23} } + \frac{kq_{1}q_{3} }{r_{12} }[/tex]

This work done is stored in the form of potential energy.

∴U=W= potential energy of three systems.

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The total electric potential energy is [tex]\frac{kq1q3}{r13} + \frac{kq2q3}{r23} + \frac{kq1q2}{r12}[/tex]

Electric Potential Energy of a System of Charges

The labor required to establish a system of charges by guiding them toward their intended positions from infinity against the electrostatic force without accelerating them is equal to the electric potential energy of the system. Its identifier is U.U=W=qV. Due to the conservatism of electrostatic fields, the work is independent of the path.

Consider having three charges. Q1, Q2, and Q3 bring point P from infinity.

No work has been done to bring q1,

[tex]V_{1} = \frac{kq1}{r1}[/tex]

where, V = electric potential energy.

           q = point charge.

           r = distance between any point around the charge to the point charge.

          k = Coulomb constant; k = 9.0 × 109 N.

Now bring q₂,

[tex]V_{2} = \frac{kq2}{r2}[/tex]

Work done by q₁ ;

W1 = [tex]V_{p} q2[/tex] = [tex]\frac{kq1q2}{r12}[/tex]

Now bring  q₃,

[tex]V_{3} = \frac{kq3}{r3}[/tex]

Work done on q₃ by q₁ and q₂

W= q3{[tex]V_{1} + V_{2}[/tex]}

W = [tex]\frac{kq1q3}{r13} + \frac{kq2q3}{r23} + \frac{kq1q2}{r12}[/tex]

This work done is stored in the form of potential energy.

∴U=W= potential energy of three systems.

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Answer:

Explanation:

——»To measure centimeters, we can use ruler.

Answer: See below

Explanation:

Given:

The potential between plates, V = 240 V

Distance between plates, d = 0.02 m

The mass of drop, m = 2x10^-11

Charge on electron, e = 1.6x10^-19

Part (a)

The free-body diagram is attached below

Part (b)

The electric field is given by,

[tex]E=\frac{V}{d}[/tex]

On applying force balance, the force on oil drop is equal to the weight of the oil,

[tex]$$\begin{aligned}F_{E} &=m g \\q E &=m g \\q \frac{V}{d} &=m g \\q &=\frac{m g d}{V}\end{aligned}$$[/tex]

Substituting the given values in the above equation,

[tex]\begin{aligned}&q=\frac{2 \times 10^{-11} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^{2} \times \frac{1 \mathrm{~N}}{1 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}^{2}} \times 0.02 \mathrm{~m}}{240 \mathrm{~V} \times \frac{1 \mathrm{~N} \cdot \mathrm{m} / \mathrm{C}}{1 \mathrm{~V}}} \\&q=1.63 \times 10^{-14} \mathrm{C}\end{aligned}[/tex]

Therefore, the charge on the oil drop is 1.63x10^-14 C

Part (c)

There will be an excess of electrons on the oil drop.

The number of electrons on oil drop can be calculated as,

[tex]\begin{aligned}q &=n e \\1.63 \times 10^{-14} \mathrm{C} &=n \times 1.6 \times 10^{-19} \mathrm{C} \\n &=1.01 \times 10^{5}\end{aligned}[/tex]

Therefore, the number of excess electrons is 1.01x10^5

Big bang happened about 13.7 billion years ago in our universe.

According to the big bang theory, about 13.7 billion years ago, an explosive expansion began, expanding our universe outwards faster than the speed of light.

According to the flat model, the universe is infinite and will continue to expand forever because the universe is expanding.

Cosmic background radiation is a weak radio-frequency radiation that is traveling through outer space in every direction. It is the residual radiation of the big bang, when the universe was very hot.

The Big Bang theory predicts that the early universe was a very hot place and that as it expands, the gas within it cools. Thus the universe has all over radiation which is called the “cosmic microwave background".

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Answer: The small spherical planet called "Glob" has a mass of 7.88×1018 kg and a radius of 6.32×104 m. An astronaut on the surface of Glob throws a rock straight up. The rock reaches a maximum height of 1.44×103 m, above the surface of the planet, before it falls back down.

1) the initial speed of the rock as it left the astronaut's hand is 19.46 m/s.

2) A 36.0 kg satellite is in a circular orbit with a radius of 1.45×105 m around the planet Glob. Then the speed of the satellite is 3.624km/s.

Explanation: To find the answer, we need to know about the different equations of planetary motion.

                           [tex]v=\sqrt{2gh}[/tex]

                       [tex]g_g=\frac{GM}{r^2} =\frac{6.67*10^{-11}*7.88*10^{18}}{(6.32*10^4)^2}= 0.132[/tex]

                        [tex]v=\sqrt{2*0.132*1.44*10^3} =19.46 m/s[/tex]

                       [tex]v=\sqrt{\frac{GM}{r} } =\sqrt{\frac{6.67*10^{-11}*7.88*10^{18}}{1.45*10^5} } =3.624km/s[/tex]

Thus, we can conclude that,

1) the initial speed of the rock as it left the astronaut's hand is 19.46 m/s.

2) A 36.0 kg satellite is in a circular orbit with a radius of 1.45×105 m around the planet Glob. Then the speed of the satellite is 3.624km/s.

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The tiny planet known as "Glob" has a radius of 6.32× 10^4 meters and a mass of 7.88× 10^18 kg. On Glob's surface, an astronaut launches a rock straight upward. Before falling back down, the rock rises to a maximum height of 1.44×10^3 m above the planet's surface.

1) The rock was moving at 19.46 m/s when it first left the astronaut's palm.

2) A 36.0 kg spacecraft is orbiting the planet Glob in a sphere with a radius of 1.45 105 meters. The satellite is moving at 3.624 km/s at that point.

Understanding the planetary motion equations is necessary in order to determine the solution.

                                [tex]V=\sqrt{2gh}[/tex]

                     [tex]a=\frac{GM}{r^2} =\frac{6.67*10^{-11}*7.88*10^{18}}{(6.32*10^4)^2} \\a=0.132m/s^2[/tex]

                   [tex]V=\sqrt{2*0.132*1.44*10^3} =19.46m/s[/tex]

                         [tex]v=\sqrt{\frac{GM}{r} } =3,624km/s\\where,\\M=7.88*10^{18}kg[/tex]

Consequently, we can say that

1) The rock was moving at 19.46 m/s when it first left the astronaut's palm.

2) A 36.0 kg spacecraft is orbiting the planet Glob in a sphere with a radius of 1.45 105 meters. The satellite is moving at 3.624 km/s at that point.

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Answer:

When the same amount of heat is added to cold sand and cold water, the temperature change of sand will be higher because of its lower specific heat capacity.

What is specific heat capacity?

Specific heat capacity is the quantity

of heat required to raise a unit mass of

a substance by 1 kelvin.

Specific heat capacity of water and sand

{refer to the above attachment}

Δθ = Q/mc

Thus, for an equal mass of water and sand, when the same amount of heat is added to cold sand and cold water, the temperature change of sand will be higher because of its lower specific heat capacity.

The minimum value of the coefficient of static friction is equal to 0.92.

First of all, we would derive an expression for the horizontal and vertical component of forces acting acting on the car.

For the vertical component, we have:

∑Fy = 0

Fn + Fg = 0

Fn - mg = 0

Fn = mg     .....equation 1.

For the horizontal component, we have:

∑Fx = mAc

uFn = m(V²/r)    .....equation 2.

Substituting eqn. 1 into eqn. 2, we have:

umg = m(V²/r)

u = 1/g(V²/r)

u = (V²/gr)

u = (30²/9.8 × 100)

u = 900/980

u = 0.92.

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Answer:

80 kgm/s

Explanation:

Momentum = Mass x Velocity

It can be expressed as [tex]\displaystyle{p = mv}[/tex] where p is momentum, m is mass and v is velocity.

We know that mass is 10 kg and velocity is 8 m/s - therefore, substitute the given information in formula:

[tex]\displaystyle{p=10 \ \times \ 8}\\\\\displaystyle{p=80 \ \ kgm/s}[/tex]

Hence, the momentum is 80 kgm/s.

288.51 N is  the magnitude of the force that the beam exerts on the hi.nge.

Given

Mass 0f beam = 40 Kg

The horizontal component of the force exerted by the hi_nge on the beam is 86.62 N

Angle between the beam and cable is = 90°

Angle between beam and the horizontal component = 31°

As the system of the beam, hi_nge and cable are in equilibrium.

The magnitude of the force that the beam exerts on the hi_nge can be calculated by -

F =The  horizontal component of force + the vertical component of force  

F = 86.62 N + 40 × 9.8 × sin 31°

F =86.62 N + 201.89 N

F = 288.51 N

Hence, the magnitude of the force that the beam exerts on the hi_nge is 288.51  N.

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Answer:

The speed of light is constant for all observers

Explanation:

As per general postulate of relativity

So

light speed c is independent of States of matter

The tension in the cable is 169.43 N and the vertical component of the force exerted by the hi.nge on the beam is 114.77 N.

Apply the principle of moment and calculate the tension in the cable;

Clockwise torque = TL sinθ

Anticlockwise torque = ¹/₂WL

TL sinθ  =  ¹/₂WL

T sinθ  =  ¹/₂W

T = (W)/(2 sinθ)

T = (29 x 9.8)/(2 x sin57)

T = 169.43 N

T + F = W

F = W - T

F = (9.8 x 29) - 169.43

F = 114.77 N

Thus, the tension in the cable is 169.43 N and the vertical component of the force exerted by the hi.nge on the beam is 114.77 N.

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Answer:

The density of this object is approximately [tex]1.36\; {\rm kg \cdot L^{-1}}[/tex].

The density of the oil in this question is approximately [tex]0.600\; {\rm kg \cdot L^{-1}}[/tex].

(Assumption: the gravitational field strength is [tex]g =9.806\; {\rm N \cdot kg^{-1}}[/tex])

Explanation:

When the gravitational field strength is [tex]g[/tex], the weight [tex](\text{weight})[/tex] of an object of mass [tex]m[/tex] would be [tex]m\, g[/tex].

Conversely, if the weight of an object is [tex](\text{weight})[/tex] in a gravitational field of strength [tex]g[/tex], the mass [tex]m[/tex] of that object would be [tex]m = (\text{weight}) / g[/tex].

Assuming that [tex]g =9.806\; {\rm N \cdot kg^{-1}}[/tex]. The mass of this [tex]63.8\; {\rm N}[/tex]-object would be:

[tex]\begin{aligned} \text{mass} &= \frac{\text{weight}}{g} \\ &= \frac{63.8\; {\rm N}}{9.806\; {\rm N \cdot kg^{-1}}} \\ &\approx 6.506\; {\rm kg}\end{aligned}[/tex].

When an object is immersed in a liquid, the buoyancy force on that object would be equal to the weight of the liquid that was displaced. For instance, since the object in this question was fully immersed in water, the volume of water displaced would be equal to the volume of this object.

When this object was suspended in water, the buoyancy force on this object was [tex](63.8\; {\rm N} - 16.8\; {\rm N}) = 47.0\; {\rm N}[/tex]. Hence, the weight of water that this object displaced would be [tex]47.0 \; {\rm N}[/tex].

The mass of water displaced would be:

[tex]\begin{aligned}\text{mass} &= \frac{\text{weight}}{g} \\ &= \frac{47.0\: {\rm N}}{9.806\; {\rm N \cdot kg^{-1}}} \\ &\approx 4.793\; {\rm kg}\end{aligned}[/tex].

The volume of that much water (which this object had displaced) would be:

[tex]\begin{aligned}\text{volume} &= \frac{\text{mass}}{\text{density}} \\ &\approx \frac{4.793\; {\rm kg}}{1.00\; {\rm kg \cdot L^{-1}}} \\ &\approx 4.793\; {\rm L}\end{aligned}[/tex].

Since this object was fully immersed in water, the volume of this object would be equal to the volume of water displaced. Hence, the volume of this object is approximately [tex]4.793\; {\rm L}[/tex].

The mass of this object is [tex]6.50\; {\rm kg}[/tex]. Hence, the density of this object would be:

[tex]\begin{aligned} \text{density} &= \frac{\text{mass}}{\text{volume}} \\ &\approx \frac{6.506\; {\rm kg}}{4.793\; {\rm L}} \\ &\approx 1.36\; {\rm kg \cdot L^{-1}} \end{aligned}[/tex].

(Rounded to [tex]\text{$3$ sig. fig.}[/tex])

Similarly, since this object was fully immersed in oil, the volume of oil displaced would be equal to the volume of this object: approximately [tex]4.793\; {\rm L}[/tex].

The weight of oil displaced would be equal to the magnitude of the buoyancy force: [tex]63.8\; {\rm N} - 35.6\; {\rm N} = 28.2\; {\rm N}[/tex].

The mass of that much oil would be:

[tex]\begin{aligned}\text{mass} &= \frac{\text{weight}}{g} \\ &= \frac{28.2\: {\rm N}}{9.806\; {\rm N \cdot kg^{-1}}} \\ &\approx 2.876\; {\rm kg}\end{aligned}[/tex].

Hence, the density of the oil in this question would be:

[tex]\begin{aligned} \text{density} &= \frac{\text{mass}}{\text{volume}} \\ &\approx \frac{2.876\; {\rm kg}}{4.793\; {\rm L}} \\ &\approx 0.600\; {\rm kg \cdot L^{-1}} \end{aligned}[/tex].

(Rounded to [tex]\text{$3$ sig. fig.}[/tex])

The results of the calculation are;

a) The feet spends 0.41 s in air

b) The highest point above board is 2.62 m

c) The velocity when her feet hit the water is  7.2 m/s

From the data presented;

v = u + at

But v = 0 m/s at the maximum height thus;

0 = 4 - (9.8 * t)

4 = 9.8 * t

t = 4/9.8

t = 0.41 s

b) from;

h = ut - 1/2gt^2

h = (4 * 0.41) - (0.5 * 9.8 * (0.41)^2)

h = 1.64 - 0.82

h = 0.82 m

The total height above board = 0.82 m + 1.8 m = 2.62 m

c) The total time in air is obtained from;

h = ut + 1/2gt^2

u = 0m/s because she dropped off the board

h = 1/2gt^2

2.62 = 0.5  * 9.8 * t^2

t = √2.62/0.5  * 9.8

t = 0.73 seconds

Hence, the velocity when her feet hit the water is obtained from;

v = u + gt

when u = 0 m/s

v = gt

v = 9.8 *  0.73 s

v = 7.2 m/s

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The behavior of water when subjected to temperature change is that the volume of water will increase if cooled from 3° to 2°C.

The chemical compound water, which can exist in the gaseous, liquid, and solid phases, is made up of the elements hydrogen and oxygen in the ratio 2: 1 i.e. 2 atoms of hydrogen and 1 atom of oxygen.

In general

Volume of water depends on the temperature and is directly proportional to it.

Thus, as the temperature rises, the molecules of water gain energy and move more quickly, which causes the molecules to spread apart and increase the volume of the liquid.

When water cools, it initially contracts (decreases in volume) until a temperature of about four degrees Celsius (4°C).

But at temperatures below 4.0° C, water undergoes an abnormal expansion that causes its volume to start to rise.

This ability is related to the formation of hexagonal structures, which take up a lot of room and increase the volume of the water, as a result of strong hydrogen bonding between water molecules at a lower temperature.

Hence, the volume of water will increase if cooled from 3° to 2°C

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Answer:

You would weigh the same.

Explanation:

At the moment, since Earth is not a perfect sphere, the Earth "bulges out" at the equator, so you're further from the centre of the Earth. Since gravity acts through a body's center of mass, the further you are from the centre the weaker the gravitational acceleration you will feel, because gravity weakens over distance.

So, you're actually lighter at the equator than you'd be at the poles.

However, if the Earth was a perfect sphere, this "bulge" at the equator would not happen, and so you would weigh the same at the poles and at the equator.

Hope this makes sense.

Answer:

The mass of Sun doesn't change with respective to the conditions.

Michael has 4 Apples, which may increase his own mass or weight but not the Sun's .

His train is 7 minutes, but this doesn't mean the Sun has been made to change. The train coming late affects the time management and delays work.

So, As the per the question, It is evident that Sun's Mass is still the same irrespective of conditions .

Hence, The required answer Sun's Mass is 2*10^30      kg

Explanation:

The orbital speed of an ice cube in the rings of Saturn is determined as  11,237.7 m/s.

The orbital speed of an astronomical body or object is the speed at which it orbits around the center of mass of the most massive body.

The orbital speed of ice cube in the rings of Saturn is calculated as follows;

v = √GM/r

where;

v = √(6.67 x 10⁻¹¹ x 5.68 x 10²⁶)/(3 x 10⁸)

v = 11,237.7 m/s

Thus, the orbital speed of an ice cube in the rings of Saturn is determined as  11,237.7 m/s.

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The law that relates the absolute pressure to atmospheric pressure and gauge pressure is Pascal law.

Pascal's law states that when an object is immersed in a fluid, it experiences equal pressure on all surfaces.

P = Patm + pgh

where;

Thus, the law that relates the absolute pressure to atmospheric pressure and gauge pressure is Pascal law.

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Hi there!

a)
Let's use Biot-Savart's law to derive an expression for the magnetic field produced by ONE loop.

[tex]dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} \times \hat{r}}{r^2}[/tex]

dB = Differential Magnetic field element

μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)

R = radius of loop (2.15 cm = 0.0215 m)

i = Current in loop (0.460 A)

For a circular coil, the radius vector and the differential length vector are ALWAYS perpendicular. So, for their cross-product, since sin(90) = 1, we can disregard it.

[tex]dB = \frac{\mu_0}{4\pi} \frac{id\vec{l}}{r^2}[/tex]

Now, let's write the integral, replacing 'dl' with 'ds' for an arc length:
[tex]B = \int \frac{\mu_0}{4\pi} \frac{ids}{R^2}[/tex]

Taking out constants from the integral:
[tex]B =\frac{\mu_0 i}{4\pi R^2} \int ds[/tex]

Since we are integrating around an entire circle, we are integrating from 0 to 2π.

[tex]B =\frac{\mu_0 i}{4\pi R^2} \int\limits^{2\pi R}_0 \, ds[/tex]

Evaluate:
[tex]B =\frac{\mu_0 i}{4\pi R^2} (2\pi R- 0) = \frac{\mu_0 i}{2R}[/tex]

Plugging in our givens to solve for the magnetic field strength of one loop:

[tex]B = \frac{(4\pi *10^{-7}) (0.460)}{2(0.0215)} = 1.3443 \mu T[/tex]

Multiply by the number of loops to find the total magnetic field:
[tex]B_T = N B = 0.00631 = \boxed{6.318 mT}[/tex]

b)

Now, we have an additional component of the magnetic field. Let's use Biot-Savart's Law again:
[tex]dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} \times \hat{r}}{r^2}[/tex]

In this case, we cannot disregard the cross-product. Using the angle between the differential length and radius vector 'θ' (in the diagram), we can represent the cross-product as cosθ. However, this would make integrating difficult. Using a right triangle, we can use the angle formed at the top 'φ', and represent this as sinφ.  

[tex]dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} sin\theta}{r^2}[/tex]

Using the diagram, if 'z' is the point's height from the center:

[tex]r = \sqrt{z^2 + R^2 }\\\\sin\phi = \frac{R}{\sqrt{z^2 + R^2}}[/tex]

Substituting this into our expression:
[tex]dB = \frac{\mu_0}{4\pi} \frac{id\vec{l}}{(\sqrt{z^2 + R^2})^2} }(\frac{R}{\sqrt{z^2 + R^2}})\\\\dB = \frac{\mu_0}{4\pi} \frac{iRd\vec{l}}{(z^2 + R^2)^\frac{3}{2}} }[/tex]

Now, the only thing that isn't constant is the differential length (replace with ds). We will integrate along the entire circle again:
[tex]B = \frac{\mu_0 iR}{4\pi (z^2 + R^2)^\frac{3}{2}}} \int\limits^{2\pi R}_0, ds[/tex]

Evaluate:
[tex]B = \frac{\mu_0 iR}{4\pi (z^2 + R^2)^\frac{3}{2}}} (2\pi R)\\\\B = \frac{\mu_0 iR^2}{2 (z^2 + R^2)^\frac{3}{2}}}[/tex]

Multiplying by the number of loops:
[tex]B_T= \frac{\mu_0 N iR^2}{2 (z^2 + R^2)^\frac{3}{2}}}[/tex]

Plug in the given values:
[tex]B_T= \frac{(4\pi *10^{-7}) (470) (0.460)(0.0215)^2}{2 ((0.095)^2 + (0.0215)^2)^\frac{3}{2}}} \\\\ = 0.00006795 = \boxed{67.952 \mu T}[/tex]

Answer: A thin flexible gold chain of uniform linear density has a mass of 17.1 g. It hangs between two 30.0 cm long vertical sticks (vertical axes) which are a distance of 30.0 cm apart horizontally (x-axis), as shown in the figure below which is drawn to scale. Then, the magnitude of the force on the left-hand pole will be, 0.167N.

Explanation: To find the correct answer, we have to know more about the Basic forces that acts upon a body.

                                   [tex]tan\alpha =\frac{30}{30}[/tex]

                                   [tex]\alpha =tan^{-1}(1)=45[/tex] degree.

                                  [tex]y- direction,\\T_2sin\alpha =mg\\T_2=\frac{mg}{sin \alpha } =\frac{17.1*10^{-3}kg*9.8m/s^2}{sin 45}=0.236 N[/tex]

                                  [tex]x- direction\\T_1-T_2cos\alpha =0\\T_1=0.236*cos45=0.167N[/tex]

Thus, we can conclude that, the magnitude of force on the left-hand pole will be 0.167N.

Learn more about the Basic forces that acts upon a body here:

https://brainly.com/question/28105677

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Answer:

  0.1426 N

Explanation:

A chain of uniform mass density is suspended between two poles 30 cm apart. The geometry of the problem is such that the left support only supplies a horizontal force on the chain. The right support must both balance that horizontal force and supply a vertical force that balances the weight of the chain.

For some tension T in the chain at the right support, the vertical force will be ...

  vertical force = T·sin(α) = W . . . . . matches the weight (W) of the chain

for some angle α between the horizontal and the chain at the right pole.

The corresponding horizontal force is ...

  horizontal force = T·cos(α)

This force balances the horizontal force at the left support pole. In terms of W, this force is ...

  horizontal force = W/sin(α)·cos(α) = W/tan(α)

The curve assumed by a chain of uniform mass density can be demonstrated to be a catenary. For supports 30 cm apart, its equation can be described by ...

  y = 30·cosh(x/30)

The diagram shows that y=4 for x=0, so we need to subtract 26 cm from this:

  y = 30·cosh(x/30) -26

The slope of the curve at any point is the derivative of this function:

  y' = 30(1/30)(sinh(x/30)) = sinh(x/30)

At the right support, the slope of the curve is ...

  y' = sinh(30/30) = sinh(1) ≈ 1.1752012

This is the tangent of the angle that the curve makes with the horizontal at the right support.

  tan(α) = 1.1752012

Note, you can see from the grid squares on the graph that the slope at the right support is slightly more than 1.

The weight of the chain is the product of its mass and the acceleration due to gravity:

  W = ma = (0.0171 kg)(9.8 m/s²) = 0.16758 N

Then the force on the left-side pole is ...

  horizontal force = W/tan(α) = (0.16758 N)/1.1752012

  horizontal force ≈ 0.1426 N

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Additional comment

The attached graph is a plot of the catenary curve we have assumed for the gold chain. We have attempted to match the vertical height on the left side, but we note that there seems to be a small discrepancy at the right side. The graph in the problem statement seems to show the right attach point at about y=21, not 20.3.