A hockey puck has a coefficient of kinetic friction of = .20. If the puck feels a normal force of 5 N, what is the frictional force that acts on the puck?

if 4 different amplitudes are used, the numbers of bits that can be transmitted with each amplitude change is 2 bits.

Distance between the wave's resting position and its highest displacement is known as amplitude. Frequency is the quantity of waves that pass by a particular place each second.

The distance between the center line (or the still position) and the top or bottom of a wave's crest or trough is known as the amplitude (). Be cautious when using this amount because a diagram may not always show the center line. Meters are used to measure amplitude ( ).

For example:

If there is 4 amplitudes, it will be: 00,01,10,11 then  2 bits

If there is 8 frequencies it will be: 000,001,010,011 ,100,101,110, 111 and then  3 bits

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See full question below

With Amplitude Shift Keying (ASK), if 4 different amplitudes are used, how many bits can be transmitted with each amplitude change?

The galaxy with a hydrogen beta absorption of 496 nm then the galaxy's distance from us in mega-light years (mly) will be equal to 277.54 Mly.

The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm).

As per the given information in the question,

The line's hydrogen laboratory wavelength, λ = 486.1 nm

The galaxy's spectrum's wavelength, λ' = 496.0 nm

Then, the change in wavelength,

Δλ = λ' - λ

Δλ = 9.9 nm

The speed of light, c = 2.998 × 10⁵ km/s

Use the equation of Doppler's effect,

v = c × Δλ/λ

v = 6,105.75 km/s

So, the radial velocity will be 6105.78 km/s.

v = H₀d

Here, v is the velocity of the galaxy, d is the distance between galaxies and H₀ is Hubble's constant.

d = v/H₀

d = 6105.75/22

d = 277.54 Mly

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Answer:

the answer is resistance

If the coefficient of kinetic friction among the tires and the street is 0. 20, 312.5m far will the truck skid before stopping.

What is kinetic friction?

Kinetic friction is defined as a force that acts between moving surfaces. A body moving on the surface experiences a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.

m =  the mass of the truck

N = normal reaction

g = 9.8 m/s²

μ = 0.2, the coefficient of kinetic friction

The resistive force on the truck is

F = μN = μmg = 0.2*(9.8)m = 1.96m N

The acceleration (actually deceleration) is

a = F/m = -1.96 m/s²

Let d =  distance for the truck to come to rest from an initial velocity of u = 35 m/s.

Then

u² + 2ad = 0

(35 m/s)² + 2(-1.96 m/s²)(d m) = 0

d = 35²/3.92 = 312.5 m

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The eye piece focal length is    fe = -0.19 m   where,   fe= focal length of eye ,

What Is Focal Length? Focal length is the distance (measured in millimeters) between the point of convergence of your lens and the sensor or film recording the image. The focal length of your film or digital camera lens dictates how much of the scene your camera will be able to capture.

Briefing :  According to the question we assume ,

let  The focal length is  F(o) =5.5 mm = -.00055m and distance between objective and eyepiece = 19 cm

This negative sign shows the the microscope is diverging light

 The  angular magnification is m=250

  The  distance between the objective and the eyepieces lenses is  z=19cm=0.19m

Generally the magnification is mathematically represented as

m={z-fe/fe}{0.25/f(o)}

Where fe is the eyepiece focal length of the microscope

 Now  making fe the subject  of the formula,

fe=z/{(1-1{M-fo)/0.25}

then : fe=0.19/([tex]1-(\frac{250+ - 0.0055}{.25} )[/tex])}

=   fe = -0.19 m

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Complete Question : The distance between the objective and eyepiece lenses in a microscope is 19 cm . The objective lens has a focal length of 5.5 mm .What eyepiece focal length will give the microscope an overall angular magnification of 250?

Answer: True

Explanation:

The shortest possible distance through which the force must be applied must be 0.83 meters.

What is force?
A force is indeed an influence that can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both magnitude and direction. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.

The shortest possible distance through which the force must be applied for each meter that the object is raised is 0.83 meters.
This is because the force needed to lift the object is 25 N,
and the mass of the object is 30 kg (30 x 9.8 = 294 N).
Therefore, the amount of work done for each meter of lifting is 25 N x 0.83 m = 20.75 Joules (J).
This means that each meter of lifting requires 20.75 J of work, and therefore the shortest possible distance through which the force must be applied must be 0.83 meters.

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The period of your heart oscillations = 60 / 67 cycles/min.

Given data :

Time taken for 67 heart beats = 1 min = 1* 60 seconds =60 s The time taken for 1 heart beat = 60 / 67

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0.84 m is the distance the painter walk before the plank starts to fall.

Torque is a measure of the force that rotates an object about an axis. A force accelerates an object with linear kinematics. Similarly, torque causes angular acceleration. Therefore, torque can be defined as the rotational equivalent of a linear force. The straight line around which an object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to twist or twist. Various terms such as moment and moment of force are used interchangeably to describe torque. The distance from the point of force application to the axis of rotation is sometimes called the moment arm or lever arm.

Mass of the painter (m₁) = 79 kg

Weight of painter (w₁) = 79 × 9.8

= 774.2 N

Mass of bucket (m₂) = 74 kg

Weight of bucket (w₂) = 23 × 9.8

= 225.4 N

Distance between them (L) = 2.9 m

Let d be the distance at which the painter can walk before the plank starts to fall.

At distance d, the torque due to painter and bucket is equal to each other:    

T₁ = T₂

w₁d = w₂L

d = (w₂L)/w₁

d = (225.4 × 2.9)/774.2

d = 0.84 m

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Answer:

Heat in = 715 K

Heat out = 250 K

Heat converted to work = 715 - 250 = 465 K

Efficiency = 465 / 715 = .65

(a)    Maximum efficiency = 65%

The fraction of the person submerged when floating gently on the freshwater is 0.973.

The average density of the human body = 973 kg/m³.

According to the Archimedes' principle, when a body floats in a fluid it experience is an upward force on it which is called buoyancy the buoyancy on an object is equal to the weight of the fluid that is displaced by the body.

If a body floats than the buoyancy must be equal to the weight of the body.

therefore buoyancy B can be given as

B = Vρg

V is the volume of the body,

ρ is the density of the body.

Also

B = V'xg

V' is the portion of the body submerged in fresh water,

x is the density of the fresh water.

Density of fresh water is 1000kg/m³.

Equating both the equations of 'B'

Vρ = V'x

ρ/x = V'/V

V'/V = 973/1000

So, the fraction of the human body submerged in freshwater is 0.973.

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Answer:

C. Artificial Resevoirs

Explanation:

For two main reasons; the first is the capacity of water of water they contain, and the second one is for mainteinance purpouse.

For a long straight wire carrying conductor the magnitude of the magnetic field produced around it  is proportional to I/r, and the direction is out of the page at P.

A magnetic field is produced by moving charges. Charges are constantly moving in a conductor carrying current; as a result, magnetic fields are created all around the conductor.

The right-hand thumb rule indicates the direction of this magnetic field. The thumb of the right hand is used in this rule to indicate the current's direction. The direction of the magnetic field surrounding the wire is indicated by the curled fingers.

The magnitude of the magnetic field produced by the current carrying conductor depends on the following factors:

The magnitude of the current flowing through the conductor

The distance to the point where the field value is calculating.

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The tension in string 1 is lesser than to the tension in string 2.

What is meant by tension in a string?

It is possible to refer to tension as the action-reaction pair of forces acting at each end of the aforementioned elements. Tension is defined as the pulling force transmitted axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other comparable three-dimensional object.

The tension in the string has a square root relationship with wave speed, while the linear density of the wire has a square root relationship with wave speed. v=sqrt(T/u)

A larger thickness suggests a higher linear density (mass per length. Thus, the speed would be slower. The wave in string 1 moves slower than the wave in string 2, and vice versa.

According to a thick string, there is a lot of mass per length and the wave speed is slow.

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The first quarter moon rises in the East. Option (c) is the right answer.

The first quarter moon occurs halfway between the new moon and the full moon. One-quarter of the moon is visible from Earth, meaning that you see half the daylit side of the moon.

Just like the Sun and the nighttime stars, the Moon's apparent rising in the east and set in the west each day is not from the Moon's orbit around the Earth, it's from the Earth spinning. The lunar orbit is slower and harder to see but you can still spot it.

The moon rises in the east and sets in the west, every day. It has to. The rising and setting of all celestial objects are due to Earth's continuous daily spin beneath the sky.

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Here we have to calculate horizontal distance and vertical displacement of a ball thrown at a particular angle and a particular speed.

How to calculate horizontal distance and vertical displacement？

The ball is thrown at an angle, θ=30o.

Initial velocity of the ball, u=15 m/s

Horizontal range of the ball, R=12.3 m

We know that, R=u cosθ t,

where t is the time of flight

⟹t=53​17.3​=2 secs

using equation of motion we get:-

−h=ut−1/2gt²

=15×2−1/2×9.8×2²=−10.4

⟹ Height at which the ball reaches, h=10.4 m

The vertical distance fallen during each consecutive second will increase. (i.e., there is a vertical acceleration).

The vertical displacement follows the equation above (y = 0.5 • g • t2).

Furthermore, since there is no horizontal acceleration, the horizontal distance traveled by the projectile each second is a constant value -

Formula for horizontal distance is

x= vix × t=20 m/s

Thus, the initial horizontal velocity of 20 m/s. Thus, the horizontal displacement is 20 m at 1 second, 40 meters at 2 seconds, 60 meters at 3 seconds, etc. We can tabulate it as shown in the attachment.

TIME HORIZONTAL DISPLACEMENT

0 s          0 m

1 s          30 m

2 s          60 m

3 s          90 m

4 s          120m

5 s           150 m

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The velocity of this wave is 253.8 m/s.

Wavelength is the distance of the starting point of a wave till its ending point. The length of the wave is known as wavelength. The waves will interact via constructive interference, which is possible only when the wavelength and phase of the waves are the same.

Frequency is the number of waves that pass a fixed point.

Given,

Wavelength = 4.7 m

Frequency = 54 Hz

Velocity of any wave is given by a formula,

Velocity = wavelength * frequency

Velocity = 4.7 * 54

Velocity = 253.8 m/s

Therefore, the velocity of this wave is 253.8 m/s

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The elastic potential energy in the spring at this elongation is 45J.

What is elastic potential energy?

The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy. Until the force is released and the item bounces back to its original shape, doing labor in the process, the energy is retained. The item may be compressed, stretched, or twisted during the deformation.

To solve this problem we need to use the equations related to Elastic Potential Energy, which allows us to know the Energy stored in a spring based on its elastic constant and its respective compression. By definition it is described as

[tex]P E=\frac{1}{2} k x^2[/tex]

Where,

k = Spring constant

x = Displacement

Our values are given as

[tex]x_1=0.08 \mathrm{~m}[/tex]

As we do not know the spring constant but if the energy stored at the compression given then,

[tex]\begin{aligned}& P E=\frac{1}{2} k x^2 \\& 20=\frac{1}{2} k(0.08)^2 \\& k=6250 \mathrm{~N} / \mathrm{m}\end{aligned}[/tex]

In the case of the second compression and understanding that the spring constant is intrinsic to the internal force of the spring, then

[tex]x_2=0.12 m$$[/tex]

Replacing,

[tex]$$\begin{aligned}& P E=\frac{1}{2}(6250)(0.12)^2 \\& P E=45 . J\end{aligned}$$[/tex]

Therefore the elastic potential energy in the spring at this elongation is 45J.

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The following relationship is true T1 < T2.

An ideal gas is defined as a gas in which all collisions between atoms or molecules are perfectly elastic and no intermolecular attractive forces occur. It can be thought of as a collection of perfectly rigid spheres that collide but do not interact.

The volume of gas particles is negligible. Gas particles are the same size and have no intermolecular forces as other gas particles. Gas particles move randomly according to Newton's laws of motion. Gas particles undergo perfectly elastic collisions without losing energy. This is the relationship between four variables and describes the state of the gas.

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The energy (in Joules) of a single photon of blue light =  [tex]4.83 * 10^-^1^9 J[/tex]

What is the energy of photon?

The energy that a single photon carries is known as photon energy. Energy is inversely correlated with electromagnetic frequency of the photon.

The energy of a photon is given by the formula

E = h*v

where,

h = planks constant

v = frequency

Given,

h =  [tex]6.626 * 10^-^3^4 J s[/tex]

v = 7.30 × [tex]10^1^4[/tex] Hz

1 Hz = 1 [tex]s^-1[/tex]

v = 7.30 × [tex]10^1^4 s^-1[/tex]

E = [tex]6.626 * 10^-34 * 7.30 * 10^1^4[/tex]

E = [tex]48.36 *10^-^2^0 J[/tex]

E = [tex]4.83 * 10-19 J[/tex]

The energy (in Joules) of a single photon of blue light = [tex]4.83 * 10^-^1^9 J[/tex]

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In an explosion a 6 g piece comes out of the right end and a 4 g piece comes out of the left end at twice the speed of the 6 g piece and the third piece comes out of the right end.

Initially all three balls are at rest so u = 0

Given m1 = 6g and m2=4g where m is the mass of balls

Let v1 be the velocity of the first ball = v(i) (denoted as (i) since the right end points to the positive X axis)

Let velocity v2 of second ball = 2(v)(-i) (denoted as (-i) since left end points negative X axis)

Mass of the third ball m3 = m and its velocity v3 = v'

By applying conservation of momentum

m1(u1) + m2(u2) + m3(u3) = m1(v1) + m2(v2) + m3(v3)

Since all balls are initially at rest u1 = u2 = u3 = u = 0

0 = (6×10⁻³)(v)(i) + (4×10⁻³)(2v)(-i) + m(v')

m(v') = (2×10⁻³)(v)(i)

v’ = (2×10⁻³)(v)(i)/(m)

So positive (i) indicates right end

So the third ball comes from the right end.

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Mutual inductance is the property by which one coil affects the current and voltage of the other coil.

Magnetic flux us the total magnetic field around both the coils.

EMF are invisible energy around the coils, which are mainly referred to as radiation.

How to find mutual inductance, magnetic flux and EMF around two coils?

We know

N = 30 turns

N¹= 310 turns

Inner solenoid length L¹= 20 CM= 0.2m long

Diameter d¹= 2.5 CM= 0.025m

Current i¹= 0.150 A

Rate of increase in current = di¹/dt= 1700A/s

Part A : magnetic flux = ∅¹= B¹A¹

B¹= ûⁿ × n¹ × i¹ = 2.92× 10↑-4T

Thus, ∅= 2.92×10↑-4× π/4×0.025²

= 1.432×10↑-7 Wb

Part B

Magnetic flux in one coil× number of turns in second coil = mutual inductance× current in the first coil

∅¹ × N² = Mi¹

= 1.432×10^-7 ×30

M × 0.150=1.432×10^-7×30

M=2.86×10^-5H

Part C

E = M di¹/dt

= 2.86×10^-5×1700 V

= 0.048 V

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In view of both the given query The inner solenoid's mean flux density per rotation is 1.43 * 10⁻⁷ Wb, or the two solenoids' mutual coupling is 2.86 x 10⁻⁴ H. The induced emf in the exterior loop is 4.86 * 10⁻¹ V.

A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core. The electromagnetic field causes the armature to move, and when it does, it opens and closing valves or switches, converting mechanical energy into electrical movements and force.

Given:

N1 = 310 revolutions in the inner solenoid.

N2 = 30 is the number of revolutions in the outer solenoid.

The inner solenoid's length is 20 cm, or 0.2 meters.

Inner solenoid radius = r = diameter/2 = 2.50/2 = 1.25 cm = 0.0125 m

The inner solenoid's current I is equal to 0.150 A.

1700 A/s is the current growth rate, di/dt.

A). Average magnetic flux across the inner solenoid's turns is equal to BA.

Include the values:

Average magnetic flux via the inner solenoid's turns:

= [4π x 10⁻⁷][310/0.2][0.150]π(0.0125)²

= 1.43 * 10⁻⁷ Wb

B). The two solenoids' mutual inductance is given by M = N2 x (average flux) / current.

= (30 x 1.43 * 10⁻⁷) / 0.150

= 2.86 x 10⁻⁴ H

C). The change in current there in inner solenoid causes an induced emf in the outer magnet that is equal to M*di/dt.

= 2.86 x 10⁻⁴ * 1700

= 4.86 * 10⁻¹ V

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The displacement and the distance traveled by the particle during the time interval  [-2, 5] are -26.83 units and 27.17 units.

Displacement is the straight path between the initial and end positions, whereas distance traveled is the actual length the body covers.

Here, the velocity is given as v(t)=(-t²)+3t-2 and the interval is [-2, 5]. By integrating the given velocity function, we will get the total distance traveled and displacement within the given interval.

The displacement is given as follows,

[tex]\begin{aligned}\int\limits^5_{-2} v(t)dt&=\int\limits^5_{-2} ((-t^2)+3t-2)dt\\&=\left[\frac{-t^3}{3}+\frac{3t^2}{2}-2t\right]^5_{-2}\\&=\left(\frac{5^3}{3}+\frac{3(5)^2}{2}-2(5)\right)-\left(-\frac{(-2)^3}{2}-2(-2)\right)\\&=-\frac{85}{6}-\left(\frac{38}{3}\right)\\&=-\frac{161}{6}\\&=-\mathrm{26.83\;units}\end{aligned}[/tex]

The total distance traveled is given by,

[tex]\begin{aligned}\int\limits^a_b|v(t)|dt&=\int\limits^5_{-2}|(-t^2)+3t-2|dt\\&=\int\limits^1_{-2}(t^2-3t+2)dt+\int\limits^2_1(-t^2-3t+2)dt+\int\limits^5_2(t^2-3t+2)dt\\&=\left[\frac{t^3}{3}-\frac{3t^2}{2}+2t\right]^1_{-2}+\left[-\frac{t^3}{3}+\frac{3t^2}{2}-2t\right]^2_{1}+\left[\frac{t^3}{3}-\frac{3t^2}{2}+2t\right]^5_2\\&=\frac{27}{2}+\frac{1}{6}+\frac{27}{2}\\&=\frac{163}{6}\\&=\mathrm{27.17\;units}\end{aligned}[/tex]

Therefore, the displacement and distance traveled are calculated using the given time interval.

The complete question is -

The velocity function is v(t)=(-t²)+3t-2  for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2, 5].

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Reduced moment of inertia because of the frictional effects of the Moon-driven tides.

A fundamental law of chemistry and physics stating that despite internal changes, an isolated system's total power remains static. The first conservation of energy is based on this principle, which is far more commonly phrased as the fact that electricity cannot be generated or destroyed. According to the rule of conservation of energy, energy can only be transformed from one type of energy to another and cannot be created or destroyed. This indicates that unless energy is added from the outside, a system constantly has the same quantity of energy.

According to the conservation of energy principle, energy is neither created nor destroyed. It has the capacity to change types. The validity of the conservation of energy principle, like that of mass, depends on experimental observations; as a result, it is an empirical law.

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Maximum normal stress and the maximum shearing stress in the tank are 60MPa and 18.277 MPa respectively.

Define hoop stress

A "hoop stress" is a stress distribution that maintains its original shape while the stressed item is rotated around a fixed axis. Any force exerted on the cylindrical pipe wall by a pressure differential in a straight, closed pipe will eventually result in hoop stresses.

According to the definition, shearing stress is "a kind of stress that acts parallel to the cross section of the material." Shear forces result in shear stress. They are a pair of forces that have the same magnitude and are directed in the opposite direction and operate on opposite sides of a body. A vector quantity is shear stress.

Given Data

Diameter: d = 180mm

Wall Thickness: t = 12mm

Torque: T = 12kN.m

Pressure in cylinder: p = 8MPa

Inner Radius ,c1  = d/2

                      c1  = 180/2

                      c1 = 90*10^-3 m

Outer radius, c2  = c1+ t

                      c2 = 90+12

                       c2 = 102*10^-3m

Polar moment of inertia ,J is 3.14/2*(c2^4- c1^4)

                        J ≈66.968×10^-6 m^4

The maximum torsional shear stress,  τ= Tc/J

                       τ=18.277MPa

​The normal stress due to pressure, σ1 = pr/t

                        σ1 = 60MPa

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Considering that there is a certain distance between both the student's friend as well as the camera's front, 540 cm or 5.4m

What is distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting as well as ending point. The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes. Displacement is the term used to describe this shift in an object's position.

Let d be determined by the separation between the student's friend and the camera's front.

5.0cm/15cm = 180cm/d
d = (15cm)(180cm)/5.0cm
= 540cm or 5.4m

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​

Assuming the cd is a uniform solid disk, Then the net torque acting on it is τ≈7.4×10⁻⁴ N

The product of an object's moment of inertia and angular acceleration is the torque operating on that item. We must know the CD player's moment of inertia and angular acceleration in order to calculate the torque operating on it.

Angular Acceleration:

α=ω2−ω1/t

α=22 rad/s²−0/0.91

α=24.17582rad/s²

Momemt of inertia:

I=1/2mr²

I=1/2(17×10⁻³ kg)(6.0×10⁻²m)²

I=0.0000306 kg.m²

Now, Torque:

τ=Iα

τ=(0.0000306)(24.17582)

τ=0.000739780092 kg⋅m²/s2

τ≈7.4×10⁻⁴ N

Therefore,  Torque≈7.4×10⁻⁴ N

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The maximum speed of the piston  is  8.6 m/s  and the maximum force acting on the piston when the engine is running at 3 800 rpm is   7 486 N

The given information is that the motion of a piston in an auto engine is simple harmonic. if the piston travels back and forth (side to side) over a distance of 12 cm, and the piston has a mass of 1.5 kg, The maximum speed of the piston is determined by the equation for the simple harmonic motion:

v = (2πfA)^0.5  where f is the frequency of the motion (in this case, 3 800 rpm), and A is the maximum displacement (in this case, 12 cm).  

v = (2π(3800)(0.12))^0.5   v = 8.6 m/s.

The maximum force acting on the piston is determined by the equation for the simple harmonic motion:  

F = mω^2A, where m is the mass of the piston (in this case, 1.5 kg), ω is the angular velocity (in this case, 2πf = 2π(3800) = 23 883 rad/s) and A is the maximum displacement (in this case, 12 cm).  

F = (1.5)(23 883)^2(0.12)   F = 7 486 N

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(a) The work done is 1.50 x 10^-6 J

(b) The potential of the starting point with respect to the endpoint is 357.14 V.

(c) The magnitude of E is 5952.38 N/C.

Given that,

Charge = 4.20 nC

Distance = 6.00 cm

Kinetic energy K.E = 1.50 x 10^-6 J

The particle start from rest. So, the initial kinetic energy i zero.

(A) We need to calculate the work by the electric force

Using formula of work done

W = ∆K.E

W = K.Ef - K.Ei

Put the value into the formula

W = 1.50 × 10^-6 - 0

W = 1.50 x 10^-6 J

The work done is 1.50 x 10^-6 J

(B). We need to calculate the potential of the starting point with respect to the endpoint

We know that.

Change in potential energy = change in kinetic energy

∆P.E = ∆K.E

So, U = 1.50 x 10^-6

Using formula of potential

V = U/q

Put the value into the formula

V = 1.50 × 10^-6/4.20 x 10^-9

V = 357.14 V

The potential of the starting point with respect to the endpoint is 357.14 V

(C) We need to calculate the magnitude of E

Using formula of work done

W = F x r (1)

Using formula of force

F = qE

Put the value in the equation (1)

W = qE x r

E = W/q x r

Put the value into the formula

E = 1.50 x 10^-6/4.20 x 10^-9 x 6.00 x10^-2

E = 5952.38 N/C

Hence, The magnitude of E is

5952.38 N/C

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a. The period of the solar system's orbit, assuming the orbit is circular, is [tex]2.05X10^{8} years[/tex].

b. There have been 24.4 completed revolutions.

c. The star has a mass of [tex]1.87X10^{41}[/tex] kg.

d. There are [tex]9.45X10^{10}[/tex] stars in the galaxy's center.

a. Distance equals 25,000 light years.

[tex]3X10^{8}[/tex]m/s equals the speed of light (c)

230 m/s is the astronomers' speed.

Using the time period formula,

[tex]t=\frac{d}{v}[/tex]

[tex]t= \frac{2\pi r}{v}[/tex]

r = distance

t = time, and v = speed.

Fill out the formula with the value

[tex]t = \frac{2\pi * 25000 * 9.46 * 10^{15} }{230 * 10^{3} }[/tex]

[tex]t= 6.460*10^{15} sec[/tex]

Number of years

[tex]t= \frac{6.460*10^{15} }{3.15*10^{7} } \\t= 2.05*10^{8} years[/tex]

Consequently, the solar system's orbit lasts [tex]2.05*10^{8}[/tex].

b. The solar system's average age is Tn=5 billion years, or [tex]5* 10^{9}[/tex] years.

The number of completed revolutions can be computed as

[tex]N=\frac{T^{n} }{T} \\N= \frac{5*10^{9}years }{2.05*10^{8}years } \\N=24.4[/tex]

24.4 revolutions have been completed.

c. The solar system's radius, r=25000 light years

velocity = 230 km/s

We can determine the big star's mass as

[tex]M= \frac{v^2r}{G} \\[/tex]

By substituting values, we obtain

[tex]M= \frac{(230*10^{3})^2* (25000*3*10^{8}*365*24*60*60m) }{(6.67*10^{-11} N/kg^2.m^2)}[/tex]

[tex]M= 1.87*10^{41} kg[/tex]

The star has a mass of [tex]1.87*10^{41} kg[/tex].

d. The sun's mass, [tex]M_{s}[/tex], is [tex]1.99*10^{30} kg[/tex]

The star's number can be computed using

[tex]N=\frac{mass of glactic center}{mass of sun} \\N= \frac{1.88*10^{41} }{1.99*10^{30} } \\N= 9.45*10^{10}[/tex]

There are [tex]9.45*10^{10}[/tex] beginnings, or around 94.5 billion, each year.

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