An ultracentrifuge is spinning at a speed of 80,000 rpm. The rotor that spins with
the sample can be roughly approximated as a uniform cylinder of 10 cm radius
and 8 kg mass, spinning about its symmetry axis). In order to stop the rotor in
under 30 s from when the motor is turned off, find the minimum braking torque
that must be applied.
O-19.2 Nm
-17.2 Nm
O -15.2 Nm
O-11.2 Nm
O None of the above

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

We would calculate the magnitude by applying pythagorean theorem:

[tex]\longrightarrow \sf{Magnitude= \sqrt{(-14)^2 } + 30^2}[/tex]

[tex]\longrightarrow \sf{Magnitude = 33.12}[/tex]

[tex]\longrightarrow \sf{The \: vector \: is \: (- 14, 30)}[/tex]

The angle between two vectors is given by the formula:

[tex]\sf{\longrightarrow \small \cos \emptyset = \dfrac{(a1b1 + a2b2)}{ \sqrt{(a1)^2 + (a2)^2√(b1)^2 + (b2)^2} } }[/tex]

In two dimensional, the x axis of vector form is:

[tex]\small\sf{\longrightarrow (b1, b2) = (1, 0) }[/tex]

[tex]\sf{\longrightarrow \small \cos \: \emptyset = \dfrac{(14 * 1 + 30 x 0)}{( \sqrt{(-14)^2 + (30)^2)(√(1)^2 + (0)^2)} } }[/tex]

[tex]\small\longrightarrow \sf{ \dfrac{14}{33.12} }[/tex]

[tex]\small\longrightarrow \sf{\emptyset \: = arcCos (\dfrac{ - 14}{33.12} )}[/tex]

[tex]\small\longrightarrow \sf{\emptyset= 115^\circ}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \small\bm{The \: angle \: between \: the \: vector \: }[/tex]

[tex]\small\bm{and \: \: the \: \: positive \: \: x \: \: axis \: \: is \: \: \: 115^\circ .}[/tex]

yes electrons will be emitted with the kinetic energy of

[tex]30.87 \times 10 { }^{ - 19} j[/tex]

what is photoelectric effect?

In photoelectric effect, the electrically charged particles are released from or within a material when it absorbs electromagnetic radiation.

what is kinetic energy?

It is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.

Given:

wavelength,λ

[tex] = 5.32 \times 10 {}^{ - 8} m[/tex]

Frequency

[tex] = 9.7 \times {10}^{14} [/tex]

Einstein's photoelectric equation

€= w + KE

€ = hc/ λ

[tex] = \frac{6.63 \times {10}^{ - 34} \times 3 \times {10}^{8} } {5.32 \times 10 {}^{ - 8} } [/tex]

[tex]€= 3.73 \times {10}^{ - 18} [/tex]

w=h.f

[tex] = 6.63 \times {10}^{ - 34} \times 9.7 \times {10}^{14} [/tex]

[tex] = 6.43 {10}^{ - 19} j[/tex]

KE = € - W

[tex]37.3 \times {10}^{ - 19} - 6.43 \times {10}^{ - 19} [/tex]

[tex]kE = 30.87 \times {10}^{ - 19} [/tex]

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The magnitude of the electric force that one particle exerts on the other is 8.59 x [tex]10^{-8}[/tex] N and the force is attractive.

Coulomb law states that the attractive or repulsive force between two point charges is proportional to the product of the charges and inversely proportional to square of the distance between them. That is,

F = KQq / r²

Given that two charged particles are a distance of 1.72 m from each other. One of the particles has a charge of 7.03 nC, and the other has a charge of 4.02 nC.

Where

(A) The magnitude of the electric force that one particle exerts on the other will be

F = (9 x [tex]10^{9}[/tex] x 7.03 x [tex]10^{-9}[/tex] x 4.02 x [tex]10^{-9}[/tex]) / 1.72²

F = 2.54 x [tex]10^{-7}[/tex] / 2.96

F = 8.59 x [tex]10^{-8}[/tex] N

(B) Since our answer is positive, the force is therefore attractive.

Therefore, the magnitude of the electric force that one particle exerts on the other is 8.59 x [tex]10^{-8}[/tex] N and the force is attractive.

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A. The magnitude (in N) of the electric force that one particle exerts on the other is 8.60×10⁻⁸ N

B. The force is repulsive

From the question given above, the following data were obtained:

The magnitude of the electric force can be obtained by using the Coulomb's law equation as shown below:

F = Kq₁q₂ / r²

F = (9×10⁹ × 7.03×10¯⁹ × 4.02×10¯⁹) / (1.72)²

F = 8.60×10⁻⁸ N

From the question given, we were told that:

Since both charge are positive, then the force attraction between them is repulsive as like charges repels and unlike charges attracts

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The values of the required solutions are

What is Force?

In the field of physics, an influence that can alter the motion of an object is referred to as a force. An object having mass can experience a change in its velocity, often known as an acceleration, when subjected to a force. Intuitively, force can also be conceptualized as either a push or a pull. Because it may be measured in both magnitude and direction, a force is considered a vector quantity.

What is atmospheric pressure?

The pressure that is exerted within the atmosphere of the Earth is referred to as barometric pressure as well as atmospheric pressure. As a unit of pressure, the standard atmosphere is defined as having a value of 101,325 Pa. This value is equivalent to 1013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi.

In most situations, the equation for force can be expressed numerically as

Force = pressure * A

Therefore

[tex]F= (970 - 15 B)(\pi * (0.430 )^2)[/tex]

F= 53731 N

In conclusion, If each horse can pull with a force of 1450N

The number of horses required is

[tex]N=\frac{60754 }{1450}[/tex]

N=37.05

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False, their national space organization receives a significant amount of funding if they lead the mission.

The team typically sends about 30,000 remote control commands from the ground to the space station to manage the platform. Highly interactive, hands-on, tactile, and highly rewarding.

A mission control center (MCC, sometimes called a flight control center or operations center) is a facility that typically manages spaceflight from the launch point to landing or the end of the mission. This is part of the ground segment of spacecraft operations.

The station serves as a microgravity and space laboratory where scientific research in fields such as astrobiology, astronomy, meteorology, and physics is conducted.

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The work done by this gravitational force during a fast time interval in which the Earth drives through a displacement in its orbital path is (a) zero.

Gravitational Force

The kilogram force (kgf) is a gravitational unit of force. The force exercised by the earth on a body of mass 1 kg is regarded as 1 kgf. Force = Mass × Acceleration. 1 kgf = 9.8 N.

The gravitation force and perpendicular to the path of movement

hence angle between gravitational force [ F ]and displacement (d)=90°

work done (W)= F d cos 90°

           = 0

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A sine bar is used to get the angular measurement of a part feature. The angle of the part feature is 18.24°

From the question

Given that,

Length of the sine bar, L = 8.000 in

Diameter of the rolls = 1.000 in

Height under the roll, H = 2.0000 + 0.5000 + 0.0050

                                     = 2.505 in

From sine bar formula,

we know that,

H = sin A x L

sin A = H ÷ L  

where,

A ⇒ angle of part feature

H ⇒ height under the roll

L ⇒ length of the sine bar

Substituting values in the above equation,

sin A = H / L

A = sin⁻¹ ( 2.505 ÷ 8 )

A = sin⁻¹ (0.3131)

A = 18.24⁰

Hence the angle of the part feature = 18.24°

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The distance of an object from the mirror's vertex if the image is real and has the same height as the object is 39 cm.

A concave mirror has a reflective surface that is curved inward and away from the light source.

Concave mirrors reflect light inward to one focal point and it usually form real and virtual images.

Apply mirrors formula as shown below;

1/f = 1/v + 1/u

where;

when image height = object height, magnification = 1

u/v = 1

v = u

Substitute the given parameters and solve for the distance of the object from the mirror's vertex

1/f = 1/v + 1/v

1/f = 2/v

v = 2f

v = 2(19.5 cm)

v = 39 cm

Thus, the distance of an object from the mirror's vertex if the image is real and has the same height as the object is 39 cm.

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Answer: A

Explanation: We know that f=p*n

f=50*300=15000 Hz = 15kHz.

Have a great day! <3

If the number of revolutions is 300 and the paired poles are 50 , then the frequency would be 15 kHz, therefore the correct answer is option A.

It can be defined as the number of cycles completed per second. It is represented in hertz and inversely proportional to the wavelength.

The frequency of a pendulum is the reciprocal of the time period can be given by the following relation,

F = 1 / T

As given in the problem, we have to calculate frequency if the number of revolutions is 300 and the paired poles are 50.

F = 300 × 50

  = 1500 kHz

Thus, If the number of revolutions is 300 and the paired poles are 50, then the frequency would be 15 kHz, therefore the correct answer is option A.

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The information is missing here but data that may support the existence of life in an exoplanet may include the discovery of atmospheric biological gases.

An exoplanet is any planet that surrounds another star beyond the sun, and therefore they are discovered by analyzing other galaxies in the Universe.

The existence of life in these exoplanets can be indirectly supported by the presence of gases that are only produced by organisms, which are detected by suitable telescopes that analyze emission spectra.

In conclusion, the information is missing here but data that may support the existence of life in an exoplanet include biological gases.

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The correct answer is Self-critical.

Why is self-improvement?

Self-critical:

Self-critical causes them to always strive for self-improvement and never to see accomplishing a goal as good enough.

The characteristic of a turbulent person causes them to always strive for self-improvement and to never see accomplishing a goal as good enough is Self-critical.

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The radius of the Sun is approximately 654497.9 kilometers.

A subtended angle in geometry is an angle created by a common point (in this case, the Earth) that crosses two points of a nearby circular arc (the Sun in this case). Below is a visual illustration of the subtended angle.

The law of cosine can be used to calculate the sun's radius, which is 654497.950 kilometers in kilometers.

The Sun's radius is nearly 109 times bigger than the Earth's. The Earth's radius is 6378 kilometers. Or to put it another way, both dimensions are 1: 109 ratios.

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Answer:

4 m/s

Explanation:

Conservation of momentum ,  mv

Before collision  80 kg * 6 m/s  = 480  kg-m/s  

   after the collision,

         the momentum is the same but the mass is 80+40 kg =120 kg

 mv = 480

120 * v = 480

v = 4 m/s

By Bernoulli's equation as well as the Equation of continuity the relation between pressure and velocities at different points are,

To find the answer, we need to know about the Bernoulli's equation as well as the Equation of continuity.

1) We have to find the relation between pressure at U and Q.

                  [tex]P+\frac{1}{2}dV^2+dgh=constant.[/tex]

where, P is the pressure, V is the velocity, d is density, g is acceleration due to gravity and h is the height of the flow.

                       [tex]P_u+\frac{1}{2}dV_u^2+dg*0= P_q+\frac{1}{2}dV_q^2+dgh\\where,\\V_u=V_q, \\since, D_p=D_q\\Thus,\\P_u=P_q+dgh[/tex]

                       [tex]P_u > P_q[/tex]

2) We have to find the relation between velocity at U and T.

                           [tex]AV=constant\\A_1V_1=A_2V_2[/tex]

                          [tex]A_u=\pi r^2=\pi *(0.5)^2=0.25\pi *mm^2\\A_t=\pi *1=\pi mm^2\\V_u=V\\V_t=?[/tex]

                      [tex]V_t=\frac{A_uV_u}{A_t}=\frac{V}{4}[/tex]

                      [tex]2V_t=2*\frac{V}{4} =\frac{V}{2}\\V_u=V\\[/tex]

                       [tex]V_u > 2V_t[/tex]

3) We have to find the relation between pressure at R and U

                 [tex]P_u+\frac{1}{2}dV_u^2+dg*0= P_r+\frac{1}{2}dV_r^2+dg*0\\\\V_u=V , then\\V_r=V_t=\frac{V}{4}=\frac{V_u}{4} \\\\P_u=P_r+\frac{1}{16}[/tex]

                   [tex]P_u > P_r[/tex]

4)  We have to find the relation between velocity at R and S

                                     [tex]V_r=V_s[/tex]

5)  We have to find the relation between velocity at Q and U

                                    [tex]V_q=V_u[/tex]

6)  We have to find the relation between pressure at R and S

                          [tex]P_r=P_s+dgh[/tex]

                           [tex]P_r > P_s[/tex]

Thus, we can conclude that, By Bernoulli's equation as well as the Equation of continuity the relation between pressure and velocities at different points are,

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The Aster's final position from her initial position is determined as 45.3 m.

The direction that she has to head to return to her initial position is 30° west of north.

The distance traveled by the person can be determined by making a sketch of the person's journey.

From the initial distance traveled and the second distance distance the angle between the two position is calculated as;

θ = 37⁰ + 20⁰ = 57⁰

The distance opposite to the angle is resultant displacement and it is calculated as follows;

r² = (70²) + (82²)  - (2 x 70 x 82) x cos(57)

r² = 5,371.54

r = √5,371.54

r = 73.3 m

Haven walked 28 m in the same direction to her initial position, the remaining distance is calculated as follows;

d = 73. 3 m  - 28 m

d = 45.3 m

Thus, the Aster's final position from her initial position is determined as 45.3 m.

The direction that she has to head to return to her initial position is 30° west of north.

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Answer:

See below

Explanation:

I will break the legs into vertical and horizontal components then add them

Horizontal = 70 cos 37  + 82 cos 340  + 28 cos 120 =  118.96 m

Vertical  =   70 sin 37     + 82 sin 340   + 28 sin 120 =  38.33 m

Resultant distance from origin is found via pythag theorem

   d^2 = 118.96^2  + 38.33^2        d = 124.98 m

   direction FROM origin is   arctan ( 38.33/118.96) = 17.86°

       to get BACK to the origin , will have to walk 180 degrees from this = 197.86°

The Q in the enthalpy of fusion equation stands for heat energy absorbed or released.

In thermodynamics, enthalpy is a measure of the heat content of a chemical or physical system.

The enthalpy of fusion is the amount of heat energy required to convert a unit mass of a solid at its melting point into a liquid without an increase in temperature.

Its units are usually Joules per gram (J/g) or calories per gram (cal/g).

The enthalpy of fusion equation is given as follows:

Q = m·ΔHf

Where;

Therefore, the Q in the enthalpy of fusion equation stands for heat energy absorbed or released.

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The  electric charge on surface is 2.66×10-⁹NC

The electric charge is the property  of subatomic particle that causes it to experience a force when placed in an electric and magnetic field.

We have given ,

Electric field= 1.5×10⁴N/C

 Radius = 4cm = 0.04m

E = k× q/ r²

 1.5×10⁴×16×10-⁴/9×10⁹=q

 q= 2.66×10-⁹C

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The edge length of the unit cell at the given atomic mass and density of the molybdenum is 314.2 pm.

V = (zm/ρN)

where;

V = (2 x 95.96) / (10.28 x 6.02 x 10²³)

V = 3.10 x 10⁻²³ cm³

a³ = V

a = (V)^¹/₃

a = ( 3.10 x 10⁻²³)^¹/₃

a = 3.142 x 10⁻⁸ cm

a = 3.142 x 10⁻¹⁰ m

a = 314.2 x 10⁻¹² m

a = 314.2 pm

Thus, the edge length of the unit cell at the given atomic mass and density of the molybdenum is 314.2 pm.

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The average power supplied to the box by friction while it slows from 13 m/s to 11.5 m/s is 3.24 W.

The acceleration of the box is calculated as follows;

vf² = vi² + 2as

a = (vf² - vi²)/2s

a = (11.5² - 13²) / (2 x 8.5)

a = -2.16 m/s²

The time taken for the box to travel is calculated as follows;

a = (vf - vi)/t

t = (vf - vi) / a

t = (11.5 - 13) / (-2.16)

t = 0.69 s

P = Fv

P = (ma)(vf - vi)

P = (1 x -2.16) x (11.5 - 13)

P = 3.24 W

Thus, the average power supplied to the box by friction while it slows from 13 m/s to 11.5 m/s is 3.24 W.

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The energy becomes 0.50 times in 6.72 s.

Let E represent the oscillator's initial energy, Et be the energy's final value at time t, where A is its beginning amplitude, At amplitude at time t, be. as the oscillator's energy increases to 0.50 times its initial value. We can replace the oscillator's total energy for the energy at time t to obtain the amplitude as shown below.

Et=0.50E

1

k(4₂)² = (0.5) - kA²

(4₂)² = (0.5) A²

At = 0.71A

So, the amplitude of the oscillator becomes 0.71 times its initial ar

0.71A = = A(0.96)¹2

log(0.71)

log(0.96)

8.4

n=

So, the time taken for n oscillation is obtained as,

t = n (0.800 s)

= (8.4) (0.800)

= 6.72 s

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Answer:

Nat gas

Explanation:

Approx:

Natural gas 38%       coal 21%       oil  19%

Four are known: s, p, d, and f.

Thank you,

Eddie

The orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s. The correct answer is option C

The speed of an object travelling around a circle depends on two quantities namely;

Given that  an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 10^26 kg, and use an orbital radius of 3.00 x 105 km. (G= 6.67 × 10-11 N·m2/kg2)

The given parameters are:

Let us first calculate the gravitational field strength on the Saturn.

g = GM/r²

Substitute all the necessary parameters and convert km to m

g = (6.67 × [tex]10^{-11}[/tex] × 5.68 × [tex]10^{26}[/tex]) ÷ (300000 × 1000)²

g = 3.79 × [tex]10^{16}[/tex] ÷ 9 × [tex]10^{16}[/tex]

g = 0.421 m/s²

The  orbital speed will be

V² = gr

V² = 0.4211 × 300000 × 1000

V² = 126333333.3

V = √126333333.3

V = 11239.8 m/s

Convert it to Km/s by dividing the answer by 1000

V = 11239.8/1000

V = 11.2 Km/s

Therefore, the orbital speed of an ice cube in the rings of Saturn is 11.2 Km/s

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The body moves at a velocity of 1.62m/s after the bullet emerges.

Mass of bullet, [tex]m_1[/tex] = 22g

                               = 0.022 kg

Mass of the block, [tex]m_2[/tex] = 1.9 kg

Velocity of bullet , [tex]v_1[/tex] = 265 m/s

[tex]v_2 = 0[/tex]

According to the law of collision which states that the momentum of the body before the collision is equal to the momentum of the body after the collision.

After penetration;

[tex]v^{'}_1 =125 m/s[/tex]

[tex]v^{'}_2=?[/tex]

The formula for calculating the collision of a body is expressed as:

p = mv

m is the mass of the body

v is the velocity of the body

∴ Momentum before = Momentum after

Substitute the given parameters into the formula as shown:

   [tex]m_1v_1+ m_2v_2 = m_1v^{'}_1+ m_2v^{'}_2\\0.022* 265 + 0 = 0.022*125+1.9*v^{'}_2\\5.83 = 1.9 v^{'}_2\\v^{'}_2 = 1.62 m/s[/tex]

Therefore, It moves with a velocity of 1.62 m/s.

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Diameter of the ball = 11.03cm

The ball rolled by the child must cover a distance in a linear motion which will be then equal to the circumference of the ball after one complete revolution.

Linear distance = 5.2m

d = diameter of the ball =?

Total revolutions = 15

S = 2πr

S = πd

For 15 revolutions

S = 15πd

The Diameter of a ball is double the radius of the ball thus we use D instead of 2r in the formula

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(a) The amplitude of the magnetic field produced is 2.667 mV/m.

(b) The intensity of the laser is 2.832 W/m².

(c) The  power delivered by the laser is 2.22 x 10⁻⁶ W.

In electromagnetic waves, the amplitude of magnetic field is the maximum field strength of the magnetic fields.

B₀ = E₀/c

where;

B₀ = (0.8 MV/m) / (3 x 10⁸)

B₀ = (0.8  x 10⁶ V/m) / (3 x 10⁸)

B₀ = 2.667 x 10⁻³ V/m

B₀ = 2.667 mV/m

The intensity of the laser is calculated as follows;

I = ¹/₂ε₀E₀²

I = (0.5)(8.85 x 10⁻¹²)(0.8 x 10⁶)²

I = 2.832 W/m²

P = IA

where;

A = πd²/4

where;

A = π(1 x 10⁻³)²/4

A = 7.854 x 10⁻⁷ m²

Power = (2.832 W/m²) x (7.854 x 10⁻⁷ m²)

Power = 2.22 x 10⁻⁶ W

Thus, the amplitude of the magnetic field produced is 2.667 mV/m.

The intensity of the laser is 2.832 W/m².

The  power delivered by the laser is 2.22 x 10⁻⁶ W.

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Answer:

-.457 m/s^2

Explanation:

Actual weight =   60 .3 (9.81) = 591.54 N

Accel of lift changes this to    60.3 ( 9.81 - L)     where L - accel of lift

                                           60.3 ( 9.81 - L ) = 564

                                               solve for L = .457 m/s^2  DOWNWARD

                                                        so L = - .457 m/s^2

The net electric force that the two charges would exert on an electron placed at point on the x -axis is 1.68 x 10⁻¹⁶ N.

The force exerted on the electron due to the charge q1 placed at the origin is calculated as follows;

F = kq₀q₁/r²

where;

F(01) = (9 x 10⁹ x 4 x 10⁻⁹ x 1.6 x 10⁻¹⁹)/(0.2²)

F(01) = 1.44 x 10⁻¹⁶ N

The force exerted on the electron due to the charge q1 placed at the origin is calculated as follows;

F = kq1q2/r²

where;

F(12) = (9 x 10⁹ x 6 x 10⁻⁹ x 1.6 x 10⁻¹⁹)/(0.6²)

F(12) = 2.4 x 10⁻¹⁷ N

F(net) = 2.4 x 10⁻¹⁷ N +  1.44 x 10⁻¹⁶ N

F(net) = 1.68 x 10⁻¹⁶ N

Thus, the net electric force that the two charges would exert on an electron placed at point on the x -axis is 1.68 x 10⁻¹⁶ N.

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Each side has to have at least 44 horses

F61160 N. This is further explained below.

Generally, We are only interested in the component that operates horizontally since the vertical components all cancel each other out. The pressure difference works on the hemisphere to generate a normal force all over the surface, but we are only concerned with that force's horizontal component. This may be determined by supposing the hemispheres to be two flat circular plates of the same radius as the hemispheres that have been forced together.

Therefore, force is equal to pressure multiplied by area, which is

F= (970 -15 )( * (0.45 m)2)

F=60754 N for each side.

Therefore, each side has to have at least 44 horses

44* 1390 = 61160 N

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