Analyze and Extend

Now that you've observed some properties of reflection and absorption of light, answer some questions based on
data from Hector's investigations.

Part A

Were the predictions you made in the beginning of this activity correct?

The 0.64 amp current flow  is in a resistor of 227 Ω if the potential difference across the resistor is 145 V.

The sum of the currents flowing through each branch represents the total current in the circuit. By dividing the total current for the circuit by the cell's potential difference, the total resistance for this circuit may be computed.

Using the equation V = E d, determine the potential difference between the two locations. Subtract the current flow rate from the resistance that exists in the circuit. The process of multiplication results in the potential difference, which is measured in volts. This formula, V = I R, is known as Ohm's Law.

The current times the resistance results in the potential difference, also known as voltage. One Joule of energy is produced when one Coulomb of charge moves between two points in a circuit with a potential difference of one Volt.

From ohm's law;

V = IR

Substitute values,

145 = I × 227

I = 0.64 Amp

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Answer & Explanation:

incident ray

|

v

----------

| diamond |

----------

^

|

refracted ray

In this diagram, the incident ray of light is represented by the line pointing downward towards the diamond. The interface between the diamond and water is shown as a horizontal line. The refracted ray of light is represented by the line pointing upward away from the diamond.

When the incident ray of light passes from diamond into water, it will refract or bend due to the change in the speed of light between the two media. The exact angle of refraction depends on the refractive indices of the diamond and water, as well as the angle of incidence.

A ray of light starting from diamond is incident on the interface separating diamond and water is as shown in the figure.

When a light is going from medium 1 to medium 2. The refractive index is defined as a ratio of velocity of light in medium 1 to velocity of light in medium 2. Refractive index is the factor which deals with the amount of bending of light. More refractive index means more it will bend in the medium 2. When it is 1 we can say that light has not been bent.

By Snell's law, Refractive index is given by,

sin (i) ÷ sin (r) = μ₂÷μ₁

where i is the the angle of incidence

r is the angle of refraction

μ₂ & μ₁ are refractive index of medium 2 and 1 resp.

Light bends as it passes from diamond to water at an angle due to Refractive index between air and glass.

white light consist of number of colors, each color has its own wavelength. Refractive index of an optical medium changes with the wavelength, therefore each color of white light get splitted from white light this phenomenon is know as dispersion of the light.

Labeled diagram is shown in the figure.

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The density of water ρ from Table 1 is [tex]1.000 * 10^{3} kg / m^{3}[/tex] . Subbing V and ρ into the expression for mass gives:m=  [tex]V=Ah=(50.0km^{2} )(40.0m)\\=[(50km^{2} ) (\frac{10^{3}m }{1km} )^2] (40.0m) = 2.00 * 10^{9} m^{3}[/tex]

We can ascertain the volume V of the supply from its aspects, and track down the density of water ρ in Table 1. Then, at that point, the mass m can be tracked down in the meaning of density.

[tex]p =\frac{m}{v}[/tex]

Tackling condition ρ = m/V for m gives m=ρV.

The volume V of the supply is its surface region Multiple times its typical profundity h:

[tex]V=Ah=(50.0km^{2} )(40.0m)\\=[(50km^{2} ) (\frac{10^{3}m }{1km} )^2] (40.0m) = 2.00 * 10^{9} m^{3}[/tex]

The density of water ρ from Table 1 is [tex]1.000 * 10^{3} kg / m^{3}[/tex] .

Subbing V and ρ into the expression for mass gives:

[tex]m= (1.00 * 10^3kg / m^3) (2.00* 10^9m^3) \\ = 2.00 * 10^{12} kg[/tex]

An enormous supply contains an extremely huge mass of water. In this model, the heaviness of the water in the repository is mg=1.96× [tex]10^{13}[/tex] N, where g is the speed increase because of the Earth's gravity (around 9.80[tex]m/s^{2}[/tex] ). It is sensible to find out if the dam should supply a power equivalent to this colossal weight. The response is no. As we will find in the accompanying segments, the power the dam should supply can be a lot more modest than the heaviness of the water it keeps down.

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the complete question is:

A reservoir has a surface area of [tex]50.0 km^{2}[/tex] and an average depth of 40.0 m. What mass of water is held behind the dam? (See Figure 2 for a view of a large reservoir—the Three Gorges Dam site on the Yangtze River in central China.)

Question

A coconut of mass m falls from its tree through a vertical distance of s and could reach ground with a velocity of v ms−1 due to air resistance. The work done by air resistance is:

A.) −m/2 (2gs−v2)

B.) −1/2 mv^2

C.) −mgs

D.) mv^2+2mgs

Solution

Correct option is A)

Here, a coconut of mass m falls from its tree through a vertical distance of s, with a velocity of v hence work done by gravity is,

Wg=mgs .......(1)

Change in velocity of coconut is,

E=1/2m(u−v)^2 = −1/2m(v)2 ........(2)

Now, total work done on coconut is equal to change in kinetic energy hence,

Wa+Wg=1/2mv^2

where, Wa is  work done by air resistance.

Using (1) and (2), we get

Wa=1/2mv^2−Wg

Wa=1/2mv^2−mgs

Wa=−m/2(2gs−v2)

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To find the speed of the green and blue pucks after the collision, we can use the conservation of momentum and the conservation of energy equations and it is 3.33 m/s and  2.78 m/s respectively.

First, let's find the mass of the blue puck. If the mass of the blue puck is 20% greater than the mass of the green one, then:

m (blue) = 1.2 * m (green)

Next, let's use the conservation of momentum equation:

m (green) * v (green), initial + m (blue) * v (blue), initial = m (green) * v (green), final + m (blue) * v (blue), final

Since the pucks approach each other with equal and opposite momenta, we can set v (blue), initial = -v (green), initial = -10 m/s. Plugging in the values we know:

m (green) * 10 + 1.2 * m (green) * (-10) = m (green) * v (green), final + 1.2 * m (green) * v (blue), final

Next, let's use the conservation of energy equation. If half the kinetic energy is lost during the collision, then:

0.5 * m (green) * v (green), initial2 + 0.5 * m (blue) * v (blue), initial2 = 0.5 * (m (green) * v (green), final2 + m (blue) * v (blue), final2)

Plugging in the values we know:

0.5 * m (green) * 102 + 0.5 * 1.2 * m (green) * (-10)2 = 0.5 * (m (green) * v (green), final2 + 1.2 * m (green) * v (blue), final2)

Now we can solve for the final velocities of the pucks using these two equations. We get:

v (green), final = -3.33 m/s
v (blue), final = 2.78 m/s

Therefore, the speed of the green puck after the collision is 3.33 m/s and the speed of the blue puck after the collision is 2.78 m/s.

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Answer:

The person sings at the same frequency as the piano wire, called the resonance frequency.

Explanation:

The person sings at a different frequency than the piano wire, called as resonance frequency. So, option d is correct.

Interference directs to a phenomenon in which two wires meet while traveling along the exact medium and they superpose to create a resulting wave that is lower, greater, or the same amplitude as each other. The soundboard is a big wooden panel that amplifies the sound of the vibrating string.

In the given scenario, a beat frequency is listened to by a player when using a tuning fork to adjust a piano wire. Thus, the piano tuner should change the strain in the wire, this decreases the frequency of the wire.

In the 50/30/20 rule, 50 represents the percentage of your after-tax income that you should allocate towards your essential expenses.

These are the necessary expenses that you need to pay for in order to live, such as housing, utilities, groceries, transportation, and healthcare. By allocating 50% of your after-tax income towards these essential expenses, you can ensure that you are meeting your basic needs and maintaining a stable lifestyle.

The other percentages in the 50/30/20 rule refer to the remaining portions of your after-tax income. 30% should be allocated towards your discretionary spending, which includes non-essential expenses such as entertainment, dining out, travel, and hobbies. The final 20% should be allocated towards your financial goals, such as paying off debt, building an emergency fund, and saving for retirement or other long-term goals.

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Shear stress is tangential tension that results from fluid moving against resistance against a solid surface.  therefore (iii) > (i)  = (ii) option  a).

An item experiences deformation when an exterior force works upon it. if the force's orientation is parallel to the object's surface. Along that line, there will be a distortion. The item in this instance is under tensile or tangential tension.

The stress an object experiences is known as shearing stress or tangential stress when the path of the deforming force or exterior force is parallel to the cross-sectional area.

Shear stress results from forces that are parallel to and reside in the plane of the cross-sectional area, whereas normal stress results from forces that are perpendicular to a cross-sectional area of the substance.

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To find the wavelength of the wave along the string, we first need to measure the distance between two consecutive points on the wave that are in the same phase.

We can look at the graph provided by the question, whose full cycle of the wave completes in 0.1sec, i.e. demonstrating that this is a complete up and down movement of the point.

As measured in the graph, we see that the distance between two consecutive points is 0.5 cm. Then we calculate the wavelength of the wave using the following formula:

Therefore, the wavelength of the wave corresponds to 0.005m.

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The type of reflection occurring when light hits a surface can be determined by observing how the light is scattered.

Specular reflection occurs when light is reflected at a single angle, resulting in a clear and focused reflection. On the other hand, diffuse reflection occurs when light is scattered in many directions, producing a blurred or hazy reflection.

In the case of water reflecting light, it is likely that the reflection is a combination of both specular and diffuse reflection. When the water surface is smooth and still, light is reflected at a specific angle, resulting in a clear and focused reflection.

This is specular reflection. However, when the surface of the water is disturbed, the reflection becomes scattered and blurred, which is characteristic of diffuse reflection.

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The minimum antenna length for efficient radiation if it is to be broadcast without the benefit of modulation is 2000 meters and  broadcast after it is amplitude-modulated with a sinusoidal carrier having a frequency that is 100 times the bandwidth of the message signal is 9.87 meters.

To determine the minimum antenna length for efficient radiation, we need to calculate the wavelength of the transmitted signal first.

(a) The given bandwidth of the signal is 30 kHz, which means that the signal occupies a frequency range from f - 15 kHz to f + 15 kHz,

where f is the center frequency of the signal.

Since the signal is broadcast without modulation, its bandwidth is equal to its frequency, so the center frequency is 15 kHz.

The minimum antenna length for efficient radiation is given by: Antenna Length = (1/10) x Wavelength

where Wavelength = Speed of light / Frequency

The speed of light is approximately 3 x 10⁸ meters per second.

Therefore, the wavelength of the signal is:

Wavelength = Speed of light / Frequency = 3 x 10⁸ / 15,000 = 20,000 meters

The minimum antenna length for efficient radiation is then:

Antenna Length = (1/10) x Wavelength = (1/10) x 20,000 = 2000 meters

Therefore, the minimum antenna length for efficient radiation without modulation is 2000 meters.

(b) The message signal is amplitude-modulated with a sinusoidal carrier having a frequency that is 100 times the bandwidth of the message signal.

This means that the carrier frequency is 100 x 30 kHz = 3 MHz.

The bandwidth of the transmitted signal is then the sum of the carrier frequency and the message signal bandwidth, which is 3 MHz + 30 kHz = 3.03 MHz.

Using the same formula as in part (a), we can calculate the wavelength of the transmitted signal:

Wavelength = Speed of light / Frequency = 3 x 10⁸ / 3.03 x 10⁶ = 98.68 meters

The minimum antenna length for efficient radiation is then:

Antenna Length = (1/10) x Wavelength = (1/10) x 98.68 = 9.87 meters

Therefore, the minimum antenna length for efficient radiation after modulation with a sinusoidal carrier is 9.87 meters.

The minimum antenna length for efficient radiation without modulation is 2000 meters and  the minimum antenna length for efficient radiation after modulation with a sinusoidal carrier is 9.87 meters.

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As the distance between the objects increases, the size of the electric force decreases.

Electricity is a form of energy that results from the movement of charged particles, such as electrons or ions. It is the flow of electric charge through a conductor, which can be used to power devices and machines. Electric phenomena occur naturally, such as in lightning strikes, but can also be harnessed and controlled for practical applications, including lighting, heating, and communication.

Distance refers to the physical length between two points or objects, measured in units such as meters, kilometers, miles, or inches. It is a scalar quantity that only has magnitude and no direction. Distance can be measured using various tools and methods, such as rulers, odometers, or GPS devices.

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The formula for the frequency observed by the observer when both the source and the observer are moving toward each other is given by:

f' = f0 (v + vo)/(v + vs)

where f0 is the frequency of the source, v is the speed of sound in the medium of the source, vs is the speed of sound in the medium of the observer, vo is the speed of the observer, and f' is the apparent frequency observed by the observer.

The formula for the wavelength of a wave is :

λ = v/f

where λ is the wavelength, v is the speed of the wave, and f is the frequency.

the speed of sound is different in the two media, and the wavelength of the sound wave will also be different in the two media. Let λ0 be the wavelength of the sound wave in the medium of the source and λ be the wavelength observed by the observer.

but this, we have:

λ = v'/f'

where v' is the relative speed of the source and the observer.

Since both the source and the observer are moving towards each other, their relative speed is:

v' = v + vs + vo

Substituting the given values, we get:

f' = f0 (v + vo)/(v + 2v)

= f0 (1 + vo/v)/3

λ0 = v/f0

λ = v' / f'

= (v + vs + vo) / [f0 (1 + vo/v)/3]

= 3(v + vs + vo) λ0/(1 + vo/v)

solving this, we get:

λ = 3(v + 2V)λ0/(1 + v0/v)

Thus, the apparent wavelength seen by the observer is

3(v + 2V)λ0/(1 + v0/v).

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The angular velocity of the disc after 2.0 seconds if the disc starts from rest based on the torque rotation graph is 100 rad/s.

A torque versus rotations graph is a visual representation of the relationship between the torque applied to an object and the resulting rotations produced by that torque.

Typically, the torque is plotted on the vertical axis, while the rotations are plotted on the horizontal axis. The resulting graph usually shows a linear relationship between torque and rotation, with the slope of the line indicating the object's rotational inertia or resistance to rotation.

The graph can be used to determine the amount of torque required to produce a certain amount of rotation in an object. Based on the graph, the correct option is A.

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The maximum mass of the plate that can remain glued to the bar can be determined using the maximum force that the glue can withstand.

The wooden bar rotates in a vertical circle around an axis through its center with a constant period of 2.50 seconds. The maximum force that can be exerted on each metal plate is equal to the centrifugal force acting on it due to its rotation around the axis. The centrifugal force is given by the equation Fc = mv^2/r, where Fc is the centrifugal force, m is the mass of the metal plate, v is the velocity of the metal plate, and r is the radius of the circle. In this case, the radius of the circle is equal to half the length of the wooden bar, i.e., r = 0.75 m. The velocity of the metal plate can be calculated from the equation v = 2πr/T, where T is the period of rotation. Substituting the given values, we get: v = (2π)(0.75 m)/(2.50 s) = 4.71 m/s. The maximum force that can be exerted on each metal plate is therefore: Fc = m(4.71 m/s)^2/(0.75 m) = 29.37 mN. To ensure that the maximum force does not exceed 58.0 N, the maximum mass of each metal plate can be calculated by dividing the maximum force by the acceleration due to gravity (9.81 m/s^2): mmax = 58.0 N/(2 × 9.81 m/s^2) = 2.96 kg. Therefore, each metal plate can have a maximum mass of 2.96 kg to avoid exceeding the maximum force that the glue can withstand.

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Answer:

d. 4m/s²

Explanation:

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The correct option is A. If personal information is accidentally deleted from a computer, The information is backed up, but it is an inferior copy.

Information can be defined as a measure of the degree of uncertainty reduction obtained by receiving a message or measuring a system. It is a fundamental concept in many areas of physics, including thermodynamics, quantum mechanics, and information theory.

In thermodynamics, information is related to the entropy of a system, which quantifies the degree of disorder or randomness. The more information we have about a system, the lower its entropy and the more ordered it becomes.

In quantum mechanics, information is closely related to the concept of entanglement, where two or more particles become so strongly correlated that their states cannot be described independently. The amount of information that can be transmitted through an entangled system is limited by the laws of quantum mechanics.

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580 nm light shines on a double slit with d=0. 000125 m. the angle of the third dark interference minimum(m=3) is 0.76 degrees.

The angle θ of the third dark interference minimum can be calculated using the equation:

sin θ = (m λ) / d

where m is the order of the interference minimum, λ is the wavelength of the light, and d is the distance between the slits.

In this case, m = 3, λ = 580 nm = 5.80 × 10^−7 m, and d = 0.000125 m. Plugging in these values, we get:

sin θ = (3 × 5.80 × 10^−7 m) / 0.000125 m

solving this, we get:

sin θ = 0.0132

Taking the inverse sine of both sides, we get:

θ = sin−1 (0.0132)

Using a calculator, we find:

θ ≈ 0.76 degrees

Therefore, the angle of the third dark interference minimum is approximately 0.76 degrees.

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Explanation:

Magnets are used to make a tight seal on the doors to refrigerators and freezers. They power speakers in stereos, earphones, and televisions. Magnets are used to store data in computers, and are important in scanning machines called MRIs (magnetic resonance imagers), which doctors use to look inside people's bodies

The answer is a salt. Salts are ionic compounds that are composed of positively and negatively charged ions.

When dissolved in water, the ions separate and the salt dissolves. Salts also have a high melting point and when heated, they decompose into their constituent elements, producing a flame. This is a chemical property known as thermal decomposition.Thermal decomposition is a type of chemical decomposition induced by the application of heat. It is a specific type of chemical decomposition in which molecules of a compound are broken down into smaller molecules or elements. Thermal decomposition is often used in industry to produce useful chemicals, such as chlorine from table salt, and for the production of metals and alloys from ore.

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The pitching speed of the player to cover a horizontal distance of 20 m when the ball is thrown horizontally from a height of 5 m is 19.82 m/s.

To find the pitching speed, we need to use the kinematic equation, which relates the distance traveled by an object to its initial velocity and the time it takes to travel that distance.

Since the ball is thrown horizontally, we can assume that the initial velocity of the ball is horizontal and the acceleration of the ball is vertical due to the force of gravity.

Using the equation of motion for the horizontal motion:

distance = speed × time

Since the ball is thrown horizontally, there is no initial vertical velocity, so the initial velocity is zero.

Therefore, distance = speed × time

time = distance/speed

Using the equation of motion for the vertical motion:

[tex]distance = initial \ velocity \times time + (1/2) \times acceleration \times time^2[/tex]

Since the ball is thrown horizontally, the initial vertical velocity is zero, and the acceleration due to gravity is 9.81 m/s² (since it is acting downward).

Therefore, [tex]distance = (1/2) \times (9.81) \times time^2[/tex]

[tex]time^2 = 2 \times distance/9.81[/tex]

[tex]time = \sqrt{2 \times distance / acceleration}[/tex]

Substituting the values

[tex]time = \sqrt{2\times(5/9.81)} = 1.009 s[/tex]

Now, substituting the value of time in the horizontal motion equation:

[tex]speed = distance/time[/tex]

[tex]speed = 20/1.009 = 19.82\  m/s[/tex]

Speed = 19.82 m/s

Therefore, the player's pitching speed is 19.82 m/s.

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For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.

Q = It, where I is the current, t is the time, and Q is the total charge.

Q = N

N is the quantity of electrons.

The two equations together give us:

Ne = It,

To solve for t, we obtain:

t = Ne/I

Inputting the values provided yields:

t = (3.00× [tex]10^{20}[/tex])

(1.60× [tex]10^{-19}[/tex] C/e) / (80.0× [tex]10^{-3}[/tex] A)

t = 6.00× [tex]10^{14}[/tex] s

For a particular cross-sectional area of the wire, 3.00 x [tex]10^{20}[/tex] electrons must go through it in 6.00 x [tex]10^{14}[/tex] seconds.

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We know that Velocity = delta x /delta t = [-3 -1]cm/[5-0]s    = - 0.8 cm/s answer

Velocity is the direction at which an object is moving and serves as a measure of the rate at which its location is changing as seen from a specific point of view and as determined by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of things, velocity is a basic idea.

A physical vector variable called velocity must have both a value and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of motion; it is a coherent derived unit whose amount is quantified in metres per second (m/s or m/s1) in the SI (metric system).

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The speed of sound in air at 10°C is approximately 343 meters per second. Let's use the formula:

distance = speed x time

We want to find the time it takes for the sound to travel 210 meters to the top of the mineshaft. So we can rearrange the formula to solve for time:

time = distance ÷ speed

Plugging in the values we have, we get:

time = 210 ÷ 343

time ≈ 0.612 seconds

Therefore, it takes approximately 0.612 seconds for the sound to travel from the bottom to the top of the mineshaft.

Yes, the hotter block has more energy inside. This is due to the fact that the materials of the two blocks have different heat capacities. Heat capacity is the amount of heat energy that must be added to a material to increase its temperature by 1°C. Generally speaking, materials with higher heat capacities will require more heat to raise their temperature by 1°C than materials with lower heat capacities.

For example, if two blocks, one made of iron and one made of aluminum, were both placed in a fire and given the same amount of heat energy, the block made of aluminum would be hotter than the block made of iron. This is because iron has a higher heat capacity than aluminum, meaning it takes more energy to heat it up. Therefore, the aluminum block has absorbed more heat energy and has a higher temperature than the iron block.

In conclusion, after receiving the same amount of heat energy, the two blocks have different temperatures because they have different heat capacities. The block with the higher heat capacity (iron) requires more energy to raise its temperature, resulting in a lower temperature than the block with the lower heat capacity (aluminum).

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The required wavelength is calculated to be 715 nm and it belongs to infrared region.  

The band-gap of the semiconductor cdse is given as 1.74 ev.

The equation of Planck is mathematically written as,

E = h c /λ

where,

h is planck's constant

c is speed of light

λ is wavelength

E is energy/band-gap

Converting electron volts to joules we should multiply by 1.6 × 10⁻¹⁹ J

Putting all the known values and making wavelength as subject,

λ = h c /E = (6.626 × 10⁻³⁴× 3 ×10⁸)/(1.74× 1.6 × 10⁻¹⁹) = (19.88 × 10⁻²⁶)/(2.78× 10⁻¹⁹) = 7.15 × 10⁻⁷ m = 715 × 10⁻⁹ m = 715 nm

By looking into the wavelengths of electromagnetic spectrum, we can say that this wavelength belongs to infrared.

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Answer:

Distance from center and mass

Explanation:

Gravity force is determined by the distance from the center of the object, and the mass of the object (so distance and time) speed and acceleration have no effect on the gravity

Answer:

The mass of the object and the distance between objects.

Explanation:

The weight of a 65 kg person standing on the moon with a mass of 7.348e22 kg and a radius of 1738 km would be approximately 105.3 N.

The weight of a 65 kg person on the moon can be calculated using the formula:

Weight = mass x gravitational acceleration

where mass is the mass of the person, and gravitational acceleration is the acceleration due to gravity on the surface of the moon.

The gravitational acceleration on the surface of the moon is given by:

g = G*M/R^2

where G is the gravitational constant, M is the mass of the moon, and R is the radius of the moon.

In this case, the mass of the moon is M = 7.348e22 kg, and the radius of the moon is R = 1738 km = 1.738e6 m. The gravitational constant is G = 6.6743e-11 Nm^2/kg^2.

So, the gravitational acceleration on the surface of the moon is:

g = G*M/R^2 = (6.6743e-11 Nm^2/kg^2) x (7.348e22 kg) / (1.738e6 m)^2

= 1.62 m/s^2

Now, we can calculate the weight of a 65 kg person on the moon:

Weight = mass x gravitational acceleration

= 65 kg x 1.62 m/s^2

= 105.3 N

Therefore, a 65 kg person would weight about 105.3 N on the surface of the moon.

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