Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (b) Draw a free-body diagram, including all forces acting on the system. (c) Calculate the acceleration. (d) What would the acceleration be if friction were 15.0 N?

Answer:

9 ft/s²

Explanation:

1)

d²s/dt² = -k

Integrate once:

ds/dt = -kt + C

At t=0, ds/dt = 66:

66 = -k(0) + C

C = 66

ds/dt = -kt + 66

Integrate again:

s = -½ kt² + 66t + D

At t=0, s = 0:

0 = -½ k (0)² + 66 (0) + D

D = 0

s = -½ kt² + 66t

2)

Setting ds/dt = 0:

0 = -kt + 66

t = 66/k

3)

Setting s = 242:

242 = -½ kt² + 66t

242 = -½ k (66/k)² + 66 (66/k)

242 = -2178/k + 4356/k

242 = 2178/k

k = 9

The driver must decelerate at 9 ft/s².

When half of one of the charges of equal magnitude is transferred to the other, the electric force between them reduces to 75% of the original force while maintaining the same distance.

In this scenario, you're dealing with the concept of electric forces between charged particles. The force between two charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be represented by the equation F = k * Q1 * Q2 / r^2

Initially, we have two charges both of magnitude Q, the force is F_initial = k * Q * Q / r^2. Half of one of the charges is transferred to the other, the charges become 1.5Q and 0.5Q. The new force is F_final = k * 1.5Q * 0.5Q / r^2 = 0.75 k * Q * Q / r^2.

So, the force between the charges reduces to 75% of the original force when half of one of the charges is transferred to the other while the distance remains the same.

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Answer:

12 J

Explanation:

The amount of energy stored in a spring stretched by a distance x is:

E = 1/2 k x², where k is the stiffness of the spring.

So the spring has 4J of energy when it is stretched 10 cm:

4 J = 1/2 k (0.10 m)²

k = 800 N/m

When the stretched to 20 cm, the amount of energy is:

E = 1/2 (800 N/m) (0.20 m)²

E = 16 J

So it takes an additional 12 J to stretch the spring an additional 10 cm.

The nuclear fission consists of dividing a heavy nucleus into two or more lighter or smaller nuclei, by means of the bombardment with neutrons to make it unstable.

Then, with this division a great release of energy occurs and the emission of two or three neutrons, other particles and gamma rays.

It should be noted that in the process, the emitted neutrons can interact with new fissionable nuclei that will emit new neutrons and so on. Effect better known as chain reaction.

Nuclear fission is the process of splitting heavy atomic nuclei into smaller ones, releasing energy due to the mass difference. It can produce a chain reaction that is critical for nuclear power plants and nuclear weapons.

Nuclear fission is the process of creating energy by splitting heavy atomic nuclei into smaller, medium-mass nuclei. This occurs when a neutron collides with a nucleus causing it to split into two isotopes. The mass of the products is less than the mass of the reactants, and the difference in mass is released as a tremendous amount of energy. A notable characteristic of fission is the release of additional neutrons, which can induce further fissions, leading to a chain reaction. This principle is harnessed in both nuclear power plants and nuclear weapons. To sustain a chain reaction, a certain amount, known as the critical mass, is required. The reaction can be represented as: n+AX → FF₁ + FF2 + xn, where FF₁ and FF₂ are the fission fragments, and x is the number of neutrons produced.

Answer:

Earth

Explanation:

"Light travels at a speed of 299,792 kilometers per second; 186,287 miles per second. It takes 499.0 seconds for light to travel from the Sun to the Earth, a distance called 1 Astronomical Unit."

Source : https://image.gsfc.nasa.gov/poetry/venus/q89.html

Answer:

C. It is converted into another form, mainly kinetic energy

Explanation:

Potential energy is energy available to be used in an object that isn't currently moving. When an object begins moving, potential energy becomes kinetic energy.

Answer:

The answer is: C. It becomes another form, mainly kinetic energy.

Explanation:

Potential energy is that which has a body due to the height at which it is.

For example, a pot placed in a window at a certain height has potential energy.

When a body falls from a certain height, and if we despise friction with the air, what happens is that its potential energy is transformed into kinetic energy.

The answer is: C. It becomes another form, mainly kinetic energy.

Answer:

Predicting the size, location, and timing of natural hazards is virtually impossible, but now, earth scientists are able to forecast hurricanes, floods, earthquakes, volcanic eruptions, wildfires, and landslides using fractals.

Explanation:

Answer:

Of longitudinal waves

Explanation:

Depending on the direction of the oscillation, there are two types of waves:

- Transverse waves: in a transverse wave, the oscillations occur perpendicularly to the direction of propagation of the wave. Examples are electromagnetic waves.

- Longitudinal waves: in a longitudinal wave, the oscillations occur parallel to the direction of propagation of the wave. In such a wave, the oscillations are produced by alternating regions of higher density of particles, called compressions, and regions of lower density of particles, called rarefactions. Examples of longitudinal waves are sound waves.

Compressions and rarefactions are characteristic of sound waves, which are longitudinal waves. Compressions are regions of high pressure, while rarefactions are regions of low pressure, both created by the vibrating motion of the sound source.

Compressions and rarefactions are characteristic features of a sound wave, which is a type of longitudinal wave. When a sound source vibrates, it causes fluctuations in the pressure of the medium through which it travels, typically air. These fluctuations manifest as alternating regions of higher pressure, known as compressions, and lower pressure, known as rarefactions. Sound waves consist of these repeating patterns of compressions and rarefactions, moving away from the source of the sound in the form of a wave.

During compression, air molecules are pushed closer together, leading to a higher pressure region. Conversely, during rarefaction, air molecules are spread out, creating a lower pressure region. For example, when a speaker cone moves forward, it compresses the air in front of it, and when it moves backward, it creates a rarefaction. These disturbances travel through the air, causing our eardrums to vibrate and enabling us to perceive sound.

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(a) -15.2 cm

We can solve the problem by using the lens equation:

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where

f = -22.8 cm is the focal length of the lens (negative because it is a diverging lens)

p = 45.6 cm is the distance of the object from the lens

q is the distance of the image from the lens

Solving the equation for q, we find the position of the image:

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-22.8 cm}-\frac{1}{45.6 cm}=-0.066 cm^{-1}[/tex]

[tex]q=\frac{1}{-0.066 cm^{-1}}=-15.2 cm[/tex]

and the negative sign means that the image is virtual.

(b) -11.4 cm

In this case, the distance of the object from the lens is

p = 22.8 cm

Substituting into the lens equation, we can find the new image distance, q:

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-22.8 cm}-\frac{1}{22.8 cm}=-\frac{2}{22.8 cm}[/tex]

[tex]q=\frac{-22.8 cm}{2}=-11.4 cm[/tex]

and the negative sign means that the image is virtual.

(c) -7.6 cm

In this case, the distance of the object from the lens is

p = 11.4 cm

Substituting into the lens equation, we can find the new image distance, q:

[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-22.8 cm}-\frac{1}{11.4 cm}=-0.132 cm^{-1}[/tex]

[tex]q=\frac{1}{0.132 cm^{-1}}=-7.6 cm[/tex]

and again, the negative sign means that the image is virtual.

Final answer:

To locate the images for a diverging lens with a focal length of -22.8 cm, the lens formula is used, yielding image distances of approximately -45.6 cm for an object 45.6 cm away, undefined (at infinity) for an object 22.8 cm away, and -15.2 cm for an object 11.4 cm away.

Explanation:

To locate the images formed by a diverging lens with a negative focal length, we use the lens formula:

[tex]\( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \)[/tex]

Where  f is the focal length, [tex]\( d_o \)[/tex] is the object distance, and [tex]\( d_i \)[/tex] is the image distance. Since the lens is diverging, f  is negative.

Given a focal length (f) of -22.8 cm for the diverging lens, we can solve for the image distance [tex](\( d_i \))[/tex] for the following object distances [tex](\( d_o \))[/tex] :

The negative sign for [tex]\( d_i \)[/tex] means that the image is virtual and located on the same side as the object.

Answer:

About 4-10cm/yr

Explanation:

Plates have different motion due to the tectonic settings and the properties of the plates.

Tectonic plates typically move very slowly over the weak asthenosphere in the mantle. This accounts for the wide range of about 4-10cm/yr. Some plates moves slower than this. It is difficult to perceive plate movement using our observational senses.

Scientists use GPS units and satellites to monitor the rate of movement of plates in a year to as to forecast a whole lot of environmental event that might  result from that.

Answer:

216.31 (the work done by gravity is -216.31) positive for going up.

Explanation:

We look at this question first by getting the right equation for work.

Which should be... W = F x D.

From this, we can do everything, we need the Force (F) first - the question tells us that Joe is lying on his back and moves his arms upward to raise the barbell. This means that he is countering the force of graving on the object.

What is the formula for the force of gravity on an object near the earth?

Right here --- [tex]F_{grav}[/tex] = mg

m = the mass and...

g  =  the acceleration due to gravity which is 9.81 m/s2

Before we plug things in though, we need to convert everything to SI units,

the weight is in kg - so we're good to go there, but the length of Joe's arms are in "cm" we need m or meters. Converting 70 cm to m = .7 m.

Now, we just put it all together - (31.5kg)(9.81m/s2)(.7m) =  216.31 J or 216.31 N m.

Answer:

On balance, near the equator, but I would say it really depends on the environment you were looking in. On land, relatively little lives near the south pole as it is an ice sheet, and there is no land at the north pole. Marine environments are less clear cut. Tropical reefs have high biodiversity (probably more so than any other marine environment), but generally everywhere life is sparser in the deep ocean. Some polar marine environments also contain abundant life though as the cold increases oxygen solubility in the water and also means most organisms have a slow metabolism. Glacial activity grinding up rocks also means polar water can have more available nutrients.

Greater biodiversity is found near the equator.

One would expect to find greater biodiversity near the equator compared to Earth's poles. This phenomenon, recognized as one of the oldest patterns in ecology, demonstrates that biodiversity significantly increases as latitude declines. Near the equator, especially in tropical rainforests, the species richness is the highest. In contrast, near the poles, the species richness markedly decreases due to factors like lower temperatures, which limit year-round growth and reduce the number and complexity of available ecological niches.

Several hypotheses have been proposed to explain why biodiversity is greater near the equator. These include the greater age of tropical ecosystems, which allows more time for speciation; the higher energy input from the sun; the complexity of tropical ecosystems providing a wider variety of ecological niches; and the relative stability of the climate in tropical regions promoting speciation. Regardless of the specific mechanisms, it's clear that the equator hosts a much richer biodiversity compared to the poles.

Answer:

B

Explanation:

Judging from the shape of the lens, you already know that the lenses are concave rather than convex. This eliminates C and D. Concave lens produce a smaller and virtual image at any specified distance.

Hope this helped!

During convection of air currents,  cool air sinks. (b)

Answer:

Cool air sinks

Explanation:

In this type of heat transfer, warm air rises and cool air sinks, making a current. Which is convection

Answer:

-3.4 eV ([tex]-5.4\cdot 10^{-19} J[/tex])

Explanation:

In a hydrogen atom, the energy of an electron is given by:

[tex]E_n = - 13.6 eV \frac{1}{n^2}[/tex]

where

n is the principal quantum number

For an electron in the 2s orbital,

n = 2

So substituting this value into the formula, we find

[tex]E_2 = -13.6 eV \frac{1}{2^2}=-3.4 eV[/tex]

And converting this into Joules, we have

[tex]E_2 = -3.4 eV \cdot 1.6\cdot 10^{-19} J/eV=-5.4\cdot 10^{-19} J[/tex]

Req = 30.0Ω.

When two or more resistors are in series, the intensity of current that passes through each of them is the same. Therefore, if you notice, you can observe that the three previous series resistors are equivalent to a single resistance whose value is the sum of each one.

Req = R1 + R2 + R3 = 10.0Ω + 10.0Ω + 10.0Ω = 30.0Ω

The equivalent resistance if you connect three 10.0 Ω resistors in series will be 30 ohms.

In the series circuit, the amount of current flowing through any component in a series circuit is the same and the sum of the individual resistances equals the overall resistance of any series circuit.

The voltage in a series circuit, the supply voltage, is equal to the total of the individual voltage drops.

[tex]\rm R_{eq}= R_1+R_2+R_3 \\\\ R_{eq}=10+10+10 \\\\ R_{eq}=30 \ ohms[/tex]

Hence, the equivalent resistance will be 30 ohms.

To learn more about the series circuit, refer to the link;

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If the lightbulb A in the circuit shown in the image burned out, the path for the  current to flow is disrupted because one of its terminals is connected direct to the source. So, there will be no current through the lightbulbs B, C, and D, and they will turn off. Similarly it will happen, if the lightbulb D burned out.

If the lightbulb B burned out the current will continue circulating through the lightbulbs A, C, and D, because lightbulb B is connected in parallel. Similarly it will happen, if the lightbulb C burned out.

In a series circuit, if one bulb burns out, it interrupts the flow of electricity, causing all other bulbs in the circuit to not light up.

Assuming the lightbulbs are in a series circuit, if lightbulb A burned out, the circuit would be interrupted and thus the other bulbs (B, C, and D) would also not light up as there would be no continuous pathway for current to flow. Similarly, if lightbulb B, C, or D burned out, it would act like a break in the circuit and just like the previous scenario, none of the other bulbs will light. The fundamental aspect of a series circuit is that the current is the same through all components, so if one pathway is interrupted (one bulb burns out), the entire circuit is affected.

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       Answer:

► 88 Earth Days

       Explanation:

It takes Mercury about 88 Earth days to complete an orbit around the sun. It also takes Mercury 59 Earth days to do one full spin on its axis. The length of one full day on Mercury would take 176 Earth days.

Mordancy.

Final answer:

Mercury's orbital period is 88 Earth days, while its rotation period is 59 days, leading to a 3:2 spin-orbit resonance. A day on Mercury lasts 176 Earth days, and the planet exhibits unique solar movement patterns due to its strange rotation.

Explanation:

Mercury's orbital period, or the length of time for one revolution around the sun, is 88 Earth days. This orbital period is known as a Mercury year. In contrast to its revolution, Mercury's spin or period of rotation is 59 Earth days. This difference in timescales leads to an interesting dynamic where a day on Mercury (defined as the Sun returning to the same position in the sky) lasts 176 Earth days. This is because Mercury has a unique 3:2 spin-orbit resonance, rotating three times on its axis for every two revolutions it completes around the Sun.

Visual studies initially suggested that Mercury had a synchronous rotation with the Sun, akin to how the Moon rotates with Earth, leading to the belief that one side was perpetually hot and the other perpetually cold. However, this was proved incorrect when it was found that Mercury's rotation and orbit are in a stable 2:3 ratio. Mercury's Strange Rotation results in extremely long days relative to the years and unusual solar movement patterns in the sky for hypothetical observers on the surface.

Answer:

Insurance is for items like cars and things health insurance is for injuries. Hope this helps!

Explanation:

Answer:

B

Explanation:

E = hf

E = (6.626×10⁻³⁴ Js) (8.0×10¹⁵ 1/s)

E = 5.3×10⁻¹⁸ J

Answer is B.

Answer:

yes answer is B

Explanation:

Answer:

[tex]\Delta E = -5.89\cdot 10^{-19} J[/tex]

Explanation:

The change in energy of the electron that undergoes the decay is equal to the energy of the photon, which is given by:

[tex]\Delta E=hf[/tex]

where

h is the Planck constant

f is the frequency of the Photon

Here we have

[tex]f=8.88\cdot 10^{14}Hz[/tex]

Substituting into the formula, we find

[tex]\Delta E=(6.63\cdot 10^{-34} Js)(8.88\cdot 10^{14}Hz)=5.89\cdot 10^{-19} J[/tex]

and since the electron decays from a higher energy level to the ground state, its change in energy will be negative:

[tex]\Delta E = -5.89\cdot 10^{-19} J[/tex]

The change in energy ΔE, that an electron undergoes when it decays to its ground state during triboluminescence can be calculated using the energy of a photon formula E=hf. By substituting the given values, we get E=(6.63 x 10^-34 JS) x (8.88 x 10^14 Hz), which results in E=5.89 x 10^-19 Joules.

In the phenomenon of triboluminescence, the change in energy denoted by ΔE that an electron undergoes to decay to its ground state can be found using the formula for the energy of a photon: E = hf, where h is Planck's constant (6.63 x 10^-34 Joule seconds) and f is the frequency of the photon. Given that the frequency of the photon emitted when the decay occurs is 8.88 x 10^14 Hz, we multiply this frequency by Planck's constant to find the change in energy.

E = hf = (6.63 x 10^-34 JS) x (8.88 x 10^14 Hz) = 5.89 x 10^-19 Joules. This value is the change in energy that the electron undergoes as it decays to its ground state, a phenomenon evidenced by the sparks observed when wintergreen candies are chewed.

Triboluminescence, while intriguing and visible in the dark, is the result of energetic electrons reacting with nitrogen molecules and releasing energy in the form of visible light. This physical phenomenon can be explained and calculated using basic principles of photon energy.

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Answer:

5.03 m

Explanation:

The wavelength of a wave is given by

[tex]\lambda=\frac{v}{f}[/tex]

where

v is the speed of the wave

f is the frequency of the wave

For the sonar signal in this problem,

[tex]f=288 Hz[/tex]

[tex]v=1.45\cdot 10^3 m/s[/tex]

Substituting into the equation, we find the wavelength:

[tex]\lambda=\frac{1.45\cdot 10^3 m/s}{288 Hz}=5.03 m[/tex]

Taking into account the definition of wavelength, frecuency and propagation speed, the correct answer is the third option: The wavelength of the sonar signal is 5.03 m.

In first place, wavelength (λ) is one of the parameters used to physically define a wave. This parameter can be defined for any periodic wave, that is, for the type of wave that repeats itself with exactly the same shape every given interval of time.

In a periodic wave the wavelength is the physical distance between two points from which the wave repeats itself. It is expressed in units of length (m).

On the other side, frequency (f) is the number of vibrations that occur in a unit of time, that is, a measure of the number of cycles or repetitions of the wave per unit of time. Its unit is s⁻¹ or hertz (Hz).

Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave's disturbance propagates along its displacement.

Relate the wavelength and the frequency inversely proportional using the following equation:

v = f × λ

In this case, you know:

Replacing:

1.45×10³ m/s= 288 Hz× λ

Solving:

λ= 1.45×10³ m/s÷ 288 Hz

λ= 5.03 m

Finally, the correct answer is the third option: The wavelength of the sonar signal is 5.03 m.

Learn more:

Explanation:

This described situation is known as Refraction, a phenomenon in which the light bends or changes it direction when passing through a medium with a index of refraction different from the other medium.  

In this context, the index of refraction is a number that describes how fast light propagates through a medium or material.  

According to Snell’s Law:  

[tex]n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})[/tex] (1)  

Where:  

[tex]n_{1}=1[/tex] is the first medium index of refraction  (air)

[tex]n_{2}[/tex] is the second medium index of refraction (the value we want to know)

[tex]\theta_{1}=27\°[/tex] is the angle of the incident ray  

[tex]\theta_{2}=11\°[/tex] is the angle of the refracted ray

Now, let's find [tex]n_{2}[/tex] from (1):

[tex]n_{2}=n_{1}\frac{sin(\theta_{1}}{sin(\theta_{2}}[/tex] (2)  

Substituting the known values:

[tex]n_{2}=(1)\frac{sin(27\°)}{sin(11\°)}}[/tex]

Finally:

[tex]n_{2}=2.379\approx 2.4[/tex]

If we compare this result with the given table, the index of refraction value that is close to this number is diamond's index of refraction.

Therefore, the correct option is A: the material is diamond.

Answer:

[tex]3.4\cdot 10^{-4} kg/m[/tex]

Explanation:

The order of the harmonics for standing waves in a string is equal to the number of nodes minus 1, so

n = 5 - 1 = 4

In this case, the frequency of the 4th-harmonic is

[tex]f_4=1.5 kHz = 1500 Hz[/tex]

We also know the relationship between the frequency of the nth-harmonic and the fundamental frequency:

[tex]f_4 = 4 f_1[/tex]

so we find the fundamental frequency:

[tex]f_1 = \frac{f_4}{4}=\frac{1500 Hz}{4}=375 Hz[/tex]

The fundamental frequency is given by

[tex]f_1 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}[/tex]

where

L = 1.2 m is the length of the string

T = 276 N is the tension in the string

[tex]\mu[/tex] is the linear density

Solving the equation for [tex]\mu[/tex], we find

[tex]\mu = \frac{T}{4L^2 f_1^2}=\frac{276 N}{4(1.2 m)^2(375 Hz)^2}=3.4\cdot 10^{-4} kg/m[/tex]

Answer:

Increasing the area of the plates will increase the capacitance of a parallel-plate capacitor.

Decreasing the separation between the plates will increase the capacitance of a parallel-plate capacitor.

Explanation:

The capacitance of a parallel-plate capacitor is given by

[tex]C=\frac{\epsilon_0 A}{d}[/tex]

where

[tex]\epsilon_0[/tex] is the vacuum permittivity

A is the area of the plates

d is the separation between the plates

We notice that:

- The capacitance is directly proportional to A, the area of the plates

- The capacitance is inversely proportional to d, the separation between the plates

Therefore, the correct statements are:

Increasing the area of the plates will increase the capacitance of a parallel-plate capacitor.

Decreasing the separation between the plates will increase the capacitance of a parallel-plate capacitor.

Answer:

It is NOT C. It is directly proportional, so the capacitance decreases as the distance increases.

Explanation:

Final answer:

Doubling the frequency of an AC source connected to a capacitor halves the capacitive reactance due to the inverse relationship between frequency and capacitive reactance.

Explanation:

The question seems to contain a slight error in terminology, implying a mix-up between capacitive and inductive components. However, addressing the core intent, if a capacitor is connected across an AC source and the frequency of the source is doubled, the capacitive reactance is reduced by a factor of 2. This outcome is based on the principle that capacitive reactance (XC) is inversely proportional to both the frequency of the AC source (f) and the capacitance (C). The formula for capacitive reactance is XC = 1/ (2πfC), indicating that as the frequency (f) increases, XC decreases. Therefore, doubling the frequency results in the halving of the capacitive reactance, making the correct answer 'The capacitive reactance is reduced by a factor of 2'.

The answer is false , because they move without an electromagnetic

Answer: False

Explanation:

Alkali metals alkaline earth metals and halogens and noble gases. I’m pretty sure

Answer: Alkali metals alkaline earth metals and halogens and noble gases. I’m pretty sure

Answer:

On the magnitude of the charges, on their separation and on the sign of the charges

Explanation:

The magnitude of the electric force between two charges is given by

[tex]F=k\frac{q_1 q_2}{r^2}[/tex]

where

k is the Coulomb's constant

q1, q2 are the magnitudes of the two charges

r is the separation between the charges

From the formula, we see that the magnitude of the force depends on the following factors:

- magnitude of the two charges

- separation between the charges

Moreover, the direction of the force depends on the sign of the two charges. In fact:

- if the two charges have same sign, the force is repulsive

- if the two charges have opposite signs, the force is attractive

Answer:

C. g/cm³

Explanation:

The slope is measured by calculating the variation of the Y values over the X values between two points on a line.  

So, the formula is: Slope = Δy/Δx

That means that we also take the units.

In this case, the Y-axis unit is in g, while the X-axis unit is in cm³.

Dividing a Y-variation over an X-variation will give you g/cm³.

In this case, let's assume the line passes through (10,100) (not exactly, but close enough for the example), and it passes through (0,0)

So the slope would be: (100-0) g / (10-0) cm³ = 10 g/cm³