Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 22 minutes. Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m2 and the density of air is 1.2 kg/m3.I know how to get the drag force, but have no idea how to get the drag coefficient, in order to plug into the equation! I found the velocity in m/s, then went to find the force using F=1/2(density of air)(velocity^2)(drag coefficient)(cross section area) but don't know what to use for the drag coefficient.

Answer:

Bottle                 =               .04

Bottle + Bearing    =            .20

Bottle + Bearing + Water = .24

Bottle + Water =                   .1

Full bottle of water weighs  =  .06

Weight of bearing    =           .16

What volume  of water does the bearing replace????

It takes .14 of bottle to replace bearing leaving .06 of water

Density = 16 / 6 = 2.67

Check:     probably should use volumes

The Planck constant is 1.41 x 10-34 Js, the work function Φ for sodium is 2.39 eV, and the cutoff wavelength λ₀​ for sodium is 590 nm.

Using the data, we can calculate the Planck constant, work function, and cutoff wavelength for sodium.

To start, we use the formula E = hc/λ, where E is the stopping potential, h is the Planck constant, c is the speed of light, and λ is the wavelength.

To find the Planck constant, we rearrange the equation to get h = Eλ/c.

Plugging in the values from the data, we get

h = (1.85 V)(300 nm)/(3 x 108 m/s)

= 1.41 x 10-34 Js.

Now to find the work function Φ for sodium, we use the equation Φ = hc/λ - E.

Plugging in the values from the data, we get

Φ = (1.41 x 10-34 Js)(3 x 108 m/s)/(400 nm) - 0.82 V = 2.39 eV.

Finally, to find the cutoff wavelength λ₀ for sodium, we use the equation λ₀​ = hc/Φ.

Plugging in the values from the data, we get

λ₀​ = (1.41 x 10-34 Js)(3 x 108 m/s)/2.39 eV = 590 nm.

Therefore, the Planck constant is 1.41 x 10-34 Js, the work function Φ for sodium is 2.39 eV, and the cutoff wavelength λ₀ for sodium is 590 nm.

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The power dissipation in the ion channel is 4.9 mW given that the potential difference across the ion channel is 70 mv

The power dissipated by a resistor is given by the formula:P = V² / RwhereP = PowerV = VoltageR = Resistance

The power dissipated in the ion channel is unknown. However, we can consider the ion channel to have a resistance of 1 Ω. This is because the resistance of an ion channel is very small and close to zero. So, we can assume the resistance of the ion channel as 1 Ω.As we know the potential difference across the ion channel, we can use the above formula to find the power dissipated in the ion channel.P = (70 mV)² / 1 ΩP = 0.0049 W = 4.9 mW

Therefore, the power dissipation in the ion channel is 4.9 mW.

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Biomass is created through the conversion of chemical energy into kinetic energy, which can then be used to generate electricity. In contrast, tidal energy involves the conversion of kinetic energy into electricity.

Thus, the correct option is C.

Biomаss energy is the energy creаted from the decomposition of orgаnic mаtter, such аs wood, crops, аnd аnimаl wаste. It is а renewаble source of energy, аnd unlike fossil fuels, it is sustаinаble in nаture.

Biomаss energy cаn be generаted through the conversion of chemicаl energy into kinetic energy, which cаn be hаrnessed to creаte electricity. Biomаss energy cаn аlso be used to produce heаt аnd fuel, mаking it а versаtile аnd environmentаlly friendly energy source.

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All of the following statements are true about studying spectrum from a star except the statement that "The total amount of light in the spectrum tells us the star's radius."

It is possible to identify chemical elements present in the star by recognizing patterns of spectral lines that correspond to particular chemicals. In other words, we can determine which elements are present in a star by analyzing the spectrum of the light it emits. This is because every chemical element has a unique spectrum of energy that it emits.

The wavelength shifts of spectral lines compared to the wavelengths of those same lines measured in a laboratory on Earth can tell us the star's speed toward or away from us. This is known as the Doppler effect, and it enables astronomers to calculate how fast a star is moving relative to Earth. For example, if the spectral lines are shifted towards the blue end of the spectrum, it means that the star is moving towards us.

On the other hand, if the spectral lines are shifted towards the red end of the spectrum, it means that the star is moving away from us.The peak of the star's thermal emission tells us its temperature: hotter stars peak at shorter (bluer) wavelengths. This is because the hotter an object is, the more energy it radiates, and the shorter the wavelength of that radiation. Therefore, the peak of the thermal emission spectrum provides an indication of the star's temperature.

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The time it takes for the wave on the string to travel from the center of the circle to the ball is 5.64 m/12 m/s = 0.47 s.

The wave on the string will take a certain amount of time to travel from the center of the circle to the ball. To calculate this time, we will use the equation:

Time = Distance/Velocity

The distance is equal to the circumference of the circle, which is equal to 2πr. In this case, the radius is (15.0 kg/9.81 m/s2)/12 rad/s = 0.90 m. Therefore, the distance is 2π(0.90 m) = 5.64 m.

The velocity is equal to the speed of the wave along the string, which is equal to the angular speed of the ball, which is 12 rad/s. Therefore, the velocity is 12 m/s.

Therefore, the time it takes for the wave on the string to travel from the center of the circle to the ball is 5.64 m/12 m/s = 0.47 s.

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Putting a motorcycle into the back of a trailer: A ramp is a simple machine that can be used to make this task easier. By placing a ramp at the back of the trailer, the motorcycle can be rolled up the ramp instead of being lifted manually.

Lifting a flag to the top of the flagpole: A pulley is a simple machine that can be used to make this task easier. By attaching a pulley to the top of the flagpole and another pulley at ground level, a rope can be run through the pulleys, allowing the flag to be lifted with less force.

Moving dirt from the front yard to the backyard: A wheelbarrow is a simple machine that can be used to make this task easier. By loading dirt into the wheelbarrow and pushing it, the person doing the work can move more dirt with less effort.

Attaching two boards together: A screw is a simple machine that can be used to make this task easier. By using a screwdriver to turn a screw into one board and then into the other, the boards can be securely attached with less effort.

Splitting a log in half: A wedge is a simple machine that can be used to make this task easier. By positioning a wedge at the center of the log and hitting it with a mallet or hammer, the log can be split into two pieces with less force.

Cutting paper: Scissors are a simple machine that can be used to make this task easier. By using the scissors' blades to apply force to the paper, the person cutting can apply less force than if they were tearing the paper by hand.

Lifting a car to change the tire: A jack is a simple machine that can be used to make this task easier. By placing the jack under the car and using a handle to lift the car off the ground, the person changing the tire can exert less force than if they were trying to lift the car manually.

Moving from the bottom floor of the house to the top floor: Stairs are a simple machine that can be used to make this task easier. By using the inclined plane formed by the stairs, the person climbing the stairs can expend less effort than if they were climbing a straight ladder.

Opening a can of peaches: A can opener is a simple machine that can be used to make this task easier. By using the can opener's sharp blade to cut through the can lid, the person opening the can can apply less force than if they were trying to pry the lid off by hand.

Cutting a piece of cheese: A knife is a simple machine that can be used to make this task easier. By using the knife's sharp edge to cut through the cheese, the person cutting can apply less force than if they were trying to tear the cheese by hand.

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A simple machine is an expression used to basically describe a tool that helps make work easier.

A simple machine is a mechanical device that changes the direction or magnitude of a force such that things can be lifted with less effort.

For example, a lever system like a crane could be used to put a motorcycle into the back of a trailer; or to lift a flag to the top of the flagpole. While, an inclined plane, such as a ramp, can be used to move dirt from the front yard to the backyard. And a screw can be used to attach two boards together.

A wedge, on the other hand, can be used to split a log in half.  A pair of scissors, which is a type of lever, can be used for cutting paper. Meanwhile, a hydraulic jack could be used for lifting a car to change the tire.

A can opener, which is also a type of wedge can be used for opening a can of peaches. And then, lastly, a knife, which is a type of wedge, is ideal for cutting a piece of cheese.

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Answer: 22.4%

Explanation: A = 49/201 0.24378109 B= 11/49 0.2244898 AxB/A I took the quiz, this is correct

The probability that a randomly selected player won a bronze medal given that the player represented Spain is b)24.4%.

To calculate this probability, we need to use conditional probability formula: P(Bronze Medal | Spain) = P(Spain and Bronze Medal) / P(Spain), where P(Spain and Bronze Medal) represents the number of players from Spain who won a bronze medal, and P(Spain) represents the total number of players who represented Spain.

From the given two-way frequency table, we can see that there were a total of 25 players who represented Spain, and 11 of them won a bronze medal. So, P(Spain and Bronze Medal) = 11/100.

Similarly, the total number of players who represented Spain is 25 + 19 + 13 = 57. So, P(Spain) = 57/100.

Now, we can substitute these values into the conditional probability formula to get: P(Bronze Medal | Spain) = (11/100) / (57/100) = 0.244 or 24.4%.

Therefore, the answer is B. 24.4%.

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When the skater pulls their arms in to their chest, their moment of inertia decreases, but their angular velocity remains constant.

A skater is rotating in place on an ice rink, holding their arms straight out. while still spinning, they pull their arms in to their chest the effect does this have on their angular momentum is that the pulling the arms in to the chest will decrease the skater's angular momentum. arms are pulled in to the chest, the skater's rotational inertia decreases, which results in a decrease in their angular momentum.
Angular momentum is a measure of the amount of rotational motion an object has about an axis. The axis can be any point, but it is usually the center of mass of the object. In physics, angular momentum is denoted by the letter L.

As a result, their angular momentum decreases.

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When we pull the rope hard enough to start the box moving upward, the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity is given by the equation:

Initially, the box was at rest, meaning it had no velocity. This means that the acceleration experienced by the box is constant, and hence the velocity is constant when it moves upwards.

Therefore, the force required to raise the box with a constant velocity is equal to the force of gravity acting downwards on the box (its weight).This force of gravity is given by the formula:

Weight = m x g

Where:

Hence the upward force f required to raise the box with constant velocity is:

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Answer: Noble Gases (Blue)

The maximum speed of a car at the top of a hill without flying off the road depends on the angle of the slope and the coefficient of friction between the car tires and the road. Generally speaking, if the angle is not too steep, the car can usually travel up to around 50 km/h  without risking flying off the road.

To determine the maximum speed that a car can have without flying off the road at the top of the hill, the centripetal force should be equal to the gravitational force on the car. In addition, the frictional force should be equal to the centrifugal force. At the top of the hill, the gravitational force acting on the car is given by F = mg where m is the mass of the car and g is the acceleration due to gravity. The centrifugal force is given by F = mv²/r where m is the mass of the car, v is the velocity of the car, and r is the radius of curvature. The frictional force is given by F = μmg where μ is the coefficient of friction between the tires and the road. Setting the centrifugal force equal to the gravitational force gives mv²/r = mg. Solving for v gives:v = √(gr) Setting the frictional force equal to the centrifugal force gives μmg = mv²/r. Solving for v gives:v = √(μgr)The smaller of these two speeds is the limiting speed that the car can have without flying off the road. Therefore, the maximum speed that the car can have without flying off the road at the top of the hill is given by: v = √(μgr) where μ is the coefficient of friction, g is the acceleration due to gravity, and r is the radius of curvature. The speed should be expressed in units of meters per second.

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The electric field at a point "+P" on the y-axis 0. 800 m from the origin is  53.3 N/C.  The net force on "p" (magnitude and direction) is 5.33 x 10^-5 N.

To find the electric field at point "p" on the y-axis, we can use Coulomb's law and the principle of superposition.

First, let's find the electric field contribution at point "p" due to the charge q1 at the origin. We can use Coulomb's law for point charges to find the electric field contribution:

E = k * q / r²

where k is Coulomb's constant, q is the charge, and r is the distance from q to point "p". In this case, r is simply the distance from the origin to point "p", which is 0.8 m. Plugging in the values:

E1 = (9.0 x 10⁹ N*m²/C²) * (+4.00 x 10-⁶ C) / (0.8 m)²

E1 = 18.0 N/C (upwards on the y-axis)

Similarly, the electric field contribution at point "p" due to the charge q2 on the x-axis and at a distance r2 can be calculated Using the Pythagorean theorem, we can find this distance:

r2 = √[(0.3 m)² + (0.8 m)²] = 0.854 m

Plugging in the values:

E2 = (9.0 x 10⁹ N*m²/C²) * (-6.00 x 10-⁶ C) / (0.854 m)²

E2 = 50.6 N/C (at an angle of arctan(0.8/0.3) = 69.4 degrees below the negative x-axis)

To find the total electric field at point "p", we add the contributions from q1 and q2 using vector addition:

Etotal = E1 + E2

Using the component method, we can find the magnitude and direction of the total electric field:

|Etotal| = √[(E_total,x)² + (E_total,y)²]

= √[(-18.0 N/C)² + (50.6 N/C)²]

= 53.3 N/C

θ = arctan[(E_total,y) / (E_total,x)]

= arctan[(50.6 N/C) / (-18.0 N/C)]

= -69.2 degrees

Therefore, the magnitude of the net force on a +1.00 C test charge placed at point "p" is,

Fnet = qtest * |E_total| = (+1.00 x 10^-6 C) * (53.3 N/C) = 5.33 x 10^-5 N

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The device used through a ureteroscope to capture an intact calculus or fragments if fractured by laser is called a basket retrieval device.

A ureteroscope is a specialized tool that is used to examine and treat the inside of the ureter and kidney. It is made up of a long, thin tube with a camera and a light source at the end, which is inserted into the patient's urinary tract through the urethra. The physician will be able to examine the lining of the bladder, ureters, and kidneys during this examination.

A basket retrieval device is a specialized tool that is used during ureteroscopy, which is a minimally invasive surgical technique used to examine the inside of the urinary tract. It is used to remove kidney stones or any fragments that have been broken down by laser lithotripsy.The basket retrieval device works by capturing the stones or fragments with its metal "basket" and then removing them from the body. The physician will then be able to extract the stones or fragments by retracting the basket into the ureteroscope's working channel. The stones will be disposed of or sent to a lab for further testing.

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The ranking of the ropes on the basis of the force each exerts on the crate immediately to its left, from largest to smallest, is as follows:

F > A > D > B > E > H > G > C

Rope F exerts the largest force on the crate immediately to its left because it is attached to the crate with the largest mass. The force exerted by each subsequent rope on the crate immediately to its left decreases because the mass of the crates to their left decreases. Therefore, rope A exerts the second-largest force, followed by D, B, E, H, G, and C.

What is force?

Force is a physical quantity that describes the interaction between two objects or systems. It is defined as any influence that can cause an object to undergo a change in motion or shape.

Force can be represented as a vector, which means that it has both magnitude and direction. The standard unit of force is the newton (N) in the International System of Units (SI).

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Porter would say that the bargaining power of suppliers goes down when a company is readily able to switch to another company in order to get the raw materials it needs to make products.

It is referred to as the ability of suppliers to control the cost, quality, and availability of raw materials or components required by businesses to manufacture their products.

It is determined by a number of factors, including

Switching costs: When switching to another supplier is expensive or difficult, suppliers' bargaining power is increased.

Cost of inputs: When the cost of raw materials is high, suppliers' bargaining power is increased and vice versa.

The number of suppliers: When there are a limited number of suppliers, each supplier has more bargaining power. Suppliers' strength: When suppliers are large and well-established, they have more bargaining power.

Product differentiation: When suppliers offer unique and high-quality inputs, their bargaining power is increased.

Thus, Porter would say that the bargaining power of suppliers goes down when a company is readily able to switch to another company in order to get the raw materials it needs to make products.

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The distance did the arrow travel over if it were in the air for 2.4 seconds is  100.8 meters.

An arrow leaves a bow with a speed of 42 m/s. Its velocity is reduced to 34 m/s by the time it hits its target. And the arrow traveled in the air for 2.4 seconds.

To find the distance traveled by the arrow, we can use the following formula:

S = v₀t + 1/2at²

where, S = distance traveled v₀ = initial velocity = 42 m/s, t = time taken = 2.4 s, a = acceleration = ? u = final velocity = 34 m/s.

As per the question, the arrow is traveling through the air, so the acceleration is due to gravity, which is equal to 9.8 m/s².So, a = 9.8 m/s². Now, we can substitute the given values in the above formula:

S = 42 m/s × 2.4 s + 1/2 × 9.8 m/s² × (2.4 s)²

S = 100.8 m.

The arrow traveled approximately 100.8 meters in the air.

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Answer:  

P-type layer (base)

N-type layer (emitter)

P-type layer (collector)

Explanation:

The rock will be 12 meters from the ground level after it has been thrown upward with a velocity of 12 meters per second from the top of the 42 meter high cliff for a total of 3.5 seconds.

The cliff is the height that generally has the highest height and it can be mountains, stones, buildings.

This is because the total time taken for the rock to fall back down will be the same as the total time taken for the rock to reach the top of the cliff. The equation used to calculate this is: time = distance / velocity. Therefore:

Time = 42 meters (cliff height) / 12 meters per second (velocity) = 3.5 seconds.

So, the rock will be 12 meters from the ground level after 3.5 seconds.

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Answer:

The weight of the 225-kg space probe on the moon is 364.5 N (newtons).

Explanation:

To calculate the weight of the space probe on the moon, we can use the formula:

weight = mass x acceleration due to gravity

where mass is given as 225 kg and acceleration due to gravity on the moon is 1.62 m/s^2.

weight = 225 kg x 1.62 m/s^2

weight = 364.5 N

Therefore, the weight of the 225-kg space probe on the moon is 364.5 N (newtons).

In this case, the roller coaster starts with kinetic energy because it has an initial speed of 5 m/s.

Since the roller coaster's total energy is conserved throughout the ride, its final speed when it reaches the bottom will be the same as its initial speed of 5 m/s.

As it goes uphill, the kinetic energy is gradually converted into potential energy, so its speed decreases until it reaches the top, where it has only potential energy. When it stops, all the kinetic energy has been converted to potential energy. As the roller coaster rolls back down, the potential energy is converted back to kinetic energy, and its speed increases until it reaches the bottom, where all the potential energy has been converted back to kinetic energy.

This is because the roller coaster's potential energy at the top is equal to the sum of its initial kinetic energy and the work done by gravity as it went uphill. The roller coaster then converts all of its potential energy back into kinetic energy as it rolls back down the hill.

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The path of blood through the heart and its order blood is returned to the heart from the systemic circulation through the Superior and inferior vena cavae, and the next event is that it enters the right atrium.

After that, it passes through the tricuspid valve and into the right ventricle, which is the 3rd in order, following the first and second events. After that, it passes through the pulmonic valve and enters the pulmonary artery, which is the 4th in the order. In the lungs, the blood becomes oxygenated, and then it returns to the heart through the pulmonary veins, which is the 2nd in the order. Finally, the oxygen-rich blood enters the left atrium and passes through the bicuspid (mitral) valve to the left ventricle, which is the 1st in order.

So the order of events in the path of blood through the heart is as follows:1st in order: Oxygen-rich blood enters the left atrium and passes through the bicuspid (mitral) valve to the left ventricle.2nd in order: Oxygen-rich blood returns to the heart through the pulmonary veins.3rd in order: Blood passes through the tricuspid valve and enters the right ventricle.4th in order: Blood passes through the pulmonic valve and enters the pulmonary artery. Not all locations in the pathway are listed.

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Therefore, the specific heat capacity of the object is 0.229 J/goC. Therefore, option A is the correct answer.The specific heat capacity of a 75.0 g object that requires 995 Joules to increase its temperature by 8.0 oC is 0.229 J/goC.

Explanation:In the question, we are asked to calculate the specific heat capacity of a 75.0 g object that requires 995 Joules of energy to increase its temperature by 8.0 oC.The formula used to calculate the specific heat capacity is given by:Q = m × c × ∆Twhere,Q is the amount of heat transferred,m is the mass of the object,c is the specific heat capacity of the object, and∆T is the temperature change .In the above formula, we can calculate the specific heat capacity (c) using the following formula:c = Q/(m × ∆T)Plugging in the given values,Q = 995 Jm = 75.0 g = 0.075 kg∆T = 8.0 oCSubstituting these values into the formula, we get:c = 995 J/(0.075 kg × 8.0 oC)c = 995 J/(0.6 kg.oC)c = 1658.33 J/kg.oC (Round off the value to three significant figures)Therefore, the specific heat capacity of the object is 0.229 J/goC. Therefore, option A is the correct answer.

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If the whole picture plane is affected by aerial diffusion, it stops being an effective indicator of depth - this statement is true.

Aerial diffusion is the scattering of light by particles in the air. These particles cause distant objects to appear fainter and bluer than closer objects, leading to a decrease in visual clarity and the ability to perceive depth. Aerial diffusion can be utilized in painting and drawing to create an atmospheric perspective, which produces a sense of depth by making objects are that further away appear hazier and less distinct than those that are closer. However, if the entire picture plane is affected by aerial diffusion, this can make it difficult to distinguish between objects at different depths, which can result in a lack of clarity and depth perception in the painting or drawing.

A picture plane is a theoretical plane that corresponds to the surface of a painting or drawing. The picture plane is where the artist organizes and arranges the various elements of the composition to create a visual representation of a scene. The picture plane is where the viewer's eye interacts with the artwork, and where the illusion of depth and space is created. In this context, the picture plane is an important factor in the creation of depth and atmosphere in a painting or drawing.

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Answer:

Explanation:

Using Kirchhoff's laws, we can solve for the current i:

At the node where the 2Ω and 4Ω resistors meet, the current is split into two branches, i and i1. Applying Kirchhoff's current law (KCL), we have:

i + i1 = 12/2 = 6 A

At the loop with the 2Ω, 4Ω, and 5Ω resistors, applying Kirchhoff's voltage law (KVL), we have:

-20 + 2i + 4i1 + 5i1 = 0

-20 + 6i1 + 2i = 0

6i1 + 2i = 20

3i1 + i = 10

We can solve this system of equations by substitution, which gives:

i = 2 A

Therefore, the current through the 2Ω resistor is 2 A. The answer is (A) 2 A.

The following assertions are accurate when two particles of different masses are projected at the same projection angle and beginning velocity:

Different particle trajectories will be followed by the particles: A projectile's trajectory is determined by its beginning velocity, projection angle, and gravitational acceleration. Due to the various masses of the two particles, their gravitational forces and accelerations will be different, and as a result, so will their trajectories.

Several heights will be attained by the particles: A projectile's maximum height is influenced by its starting velocity and projection angle. The two particles will ascend to different heights since they have different masses but the same beginning velocity.

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The orbit radius is 6.225 × 10^5 km.

The x-ray pulses from Cygnus X-1, a celestial x-ray source, have been recorded during high-altitude rocket flights. The signals can be interpreted as originating when a blob of ionized matter orbits a black hole with a period of 7.84 ms. And also, it is given that the blob were in a circular orbit about a black hole whose mass is 13.5 times the mass of the Sun. We need to determine the orbit radius.

The formula to be used to find the orbit radius is given by:

G(M+m)T2/4π2= r3

Where,

G = Gravitational constant = 6.67259×10−11 N⋅m2/kg2
M = Mass of the black hole
m = Mass of the blob
T = Time period of the orbit = 7.84 ms = 7.84 × 10^-3 s
r = Orbit radius

Substitute the given values in the above formula, we get:

r3 = G(M+m)T2/4π2
r3 = 6.67259×10−11 * [13.5(1.991×10^30) + m] * (7.84×10−3)2 / 4π2
r3 = 5.7919 × 10^15 m^3
Taking cube root on both sides, we get:
r = [5.7919 × 10^15 m^3] 1/3
r = 6.225 × 10^8 m
1 km = 1000 m

Therefore, the orbit radius in km is:
r = 6.225 × 10^8 m * 1 km / 1000 m
r = 6.225 × 10^5 km

Hence, the orbit radius is 6.225 × 10^5 km.

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If you stand next to a wall on a frictionless skateboard and push the wall with a force of 30 N, the wall will push you with a force of 30 N. Here's how you can show that your acceleration is 0.5 m/s² if your mass is 60 kg:Solution:The formula for force is:

F = ma

Where:

F is the force,

m is the mass,

a is the acceleration

Rearrange the equation for acceleration:

a = F/m

Substitute the given values:

F = 30 Nm = 60 kg

Then, solve for acceleration:

a = 30 N/60 kga = 0.5 m/s²

Therefore, your acceleration is 0.5 m/s² if your mass is 60 kg.

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The work required to stop the hoop is 600 joules and the distance traveled by the hoop on the inclined surface until it comes to the rest is 20.38 m.

(a) To stop the hoop, all of its kinetic energy needs to be converted into other forms of energy, such as heat due to friction. Therefore, the work required to stop the hoop is equal to its initial kinetic energy:

[tex]KE = 1/2 mv^2+1/2(mr^2)v^2/r^2[/tex]

       [tex]= 1/2 (6.0\ kg)(10.0 \ m/s)^2+1/2(6.0\times1^2)\times 100/1[/tex]

       [tex]= 600 J[/tex]

Therefore, 600 J of work is required to stop the hoop.

(b) The initial kinetic energy of the hoop is the same as in part (a), so it is still 600 J. As the hoop rolls up the incline, some of its kinetic energy will be converted into potential energy, decreasing its speed. The work done by the force of gravity on the hoop as it rolls up the incline is equal to the change in potential energy, which is given by:

PE = mgh =600 J

[tex]h=600/(6\times9.81)\ m[/tex]

[tex]h=10.19 \ m[/tex]

Where h is the vertical height that the hoop rises.

Let the hoop rolls a distance of x m on the inclined surface.

[tex]x= h/sin30[/tex]

[tex]x=10.19\times2=20.38\ m[/tex]

Therefore the distance traveled on the inclined surface is 20.38 m.

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Explanation:

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