Newton's law of gravitation says that the magnitude f of the force exerted by a body of mass m on a body of mass m is f = gmm r2 where g is the gravitational constant and r is the distance between the bodies. (a) find df/dr.

Answer: Option (D) is the correct answer.

Explanation:

The given elements Li, C and F are all second period elements. So, when we move from left to right across a period then there occurs increase in number of valence electrons as there occurs increase in total number of electrons.

So, it means more electrons are added to the same energy level.

Thus, we can conclude that a property of valence electrons for each element is located in the same energy level is common in the given elements.

Answer:

the answer is d

Explanation:

i did the usa test prep

Final answer:

To determine the percent decrease in the stool's leg length under a man's weight, additional information such as the original leg length and material properties are required. Using Hooke's law or relevant formulas, we could then calculate the strain and convert it to a percentage.

Explanation:

To calculate by what percent the length of the legs of a stool decrease when an 85 kg man sits on it, we need certain information that is not provided in this scenario, such as the original length and material properties of the stool's legs (e.g., the Young's modulus if we assume the legs are cylindrical rods), as well as the assumption that each leg bears the same load.

Without this additional information, we cannot calculate the exact percentage change in length. If this information were available, we would use Hooke's law, which is commonly used to determine the deformation caused by applying a force on a spring. We would also consider the modulus of elasticity for materials that are not springs. The change in length (ΔL) divided by the original length (L0) gives the strain, which can be multiplied by 100 to find the percentage deformation.

The length of the stool's legs decreases by approximately 0.00083% when a 85 kg man sits on it.

Calculating Deformation of Stool Legs

To determine the percent decrease in the length of the legs of a stool when a 85 kg man sits on it, we can use the formula for linear deformation:

[tex]\Delta L = (F \times L) / (A \times Y)[/tex]

Where:

Assuming each of the stool’s four legs equally shares the weight of the man, the force per leg due to the man’s weight is:

[tex]F = (85 kg \times 9.81 m/s^2) / 4 = 208.42 N[/tex]

Let’s assume the original length (L) of the legs is 0.5 meters and the radius of the legs is 0.02 meters. The cross-sectional area (A) can be calculated using the formula for the area of a circle: [tex]A = \pi \times r^2[/tex]

Thus, the cross-sectional area is:

[tex]A = \pi \times (0.02 m)^2 = 1.2566 \times 10^{-3} m^2[/tex]

Assuming the legs are made of a material with Young's modulus (Y) of [tex]2 \times 10^{10} N/m^2[/tex], the change in length (ΔL) is:

[tex]\Delta L = (208.42 N \times 0.5 m) / (1.2566 \times 10^{-3} m^2 \times 2 \times 10^{10} N/m^2) = 4.15 \times 10^{-6} meters[/tex]

To find the percent decrease in length:

[tex]\text{Percent Decrease} = (\Delta L / L) \times 100 = (4.15 \times 10^{-6} m / 0.5 m) \times 100 = 0.00083\%[/tex]

Therefore, the length of the stool's legs decreases by approximately 0.00083% when the 85 kg man sits on it.

Your most reliable answer my friend would be 1. Wind 2. All of the above 3. The expense of large tracts of land in populated areas

The statement is not correct because the velocity of the car in a free fall after 3 seconds is 29.4 m/s while the assumed velocity of the friend is 26.82 m/s.

The given information;

The velocity of an object under the influence of gravity;

v = u + gt

where;

g is acceleration due to gravity = 9.8 m/s²

Convert the given final velocity in mph to m/s;

[tex]v = 60 \ \frac{miles}{hour} \times \frac{1609.34 \ m}{1 \ mile} \times \frac{1 \ hour}{3600 \ s} = 26.82 \ m/s[/tex]

Determine if the assumed final velocity will be equal to actual velocity in 3 seconds after the motion.

v = 0 + (3 x 9.8)

v = 29.4 m/s

Thus, the statement is not correct because the velocity of the car in a free fall after 3 seconds is 29.4 m/s while the assumed velocity of the friend is 26.82 m/s.

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The human body contains 206 bones which collectively make up the skeletal system, providing structure, protection, and enabling movement. Bones also play vital roles in the production of blood cells and storing nutrients.

There are 206 bones in the human body that work together to form the skeletal system. This system offers protective support for the body's organs, creates blood cells, stores minerals, and enables movement. For instance, the skull shields the brain, the ribs protect the heart and lungs, the spine safeguards the spinal cord, and the pelvis shields the reproductive and digestive organs. The skeletal system and muscular system are the reasons we can move.

Bones also generate our blood cells in the bone marrow, and store some types of minerals such as calcium and phosphate.

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Final answer:

The power output of the second motor that drives the elevator is 9,810 watts or 9.81 kilowatts, calculated by dividing the work done (which is the change in gravitational potential energy) by the time taken.

Explanation:

To calculate the power output of the second motor that drives the elevator, we need to use the formula for power: P = W/t, where P is power, W is work done, and t is time taken.

Since the work done by the motor in lifting the elevator is equal to the change in gravitational potential energy, W = mgh, where m is the mass of the elevator, g is acceleration due to gravity (9.81 m/s²), and h is the height the elevator is lifted. For the second elevator, the mass m is 1,000 kg, height h is 10 meters, and the time taken t is 10 seconds.

First, calculate the work done:

Now, calculate the power:

Therefore, the power output of the second motor is 9,810 watts or 9.81 kilowatts (kW).

I believe there are two things which we asked to find here:

1. its speed just as it left the ground

2. find its maximum height

Solutions:

1. We use the formula:

ΔKE = - ΔPE

where KE is kinetic energy = ½ mv^2, and PE is potential energy = m g h, Δ = change

Therefore:

½ m (v2^2 – v1^2) = m g (h1 – h2)

at initial point, point 1: h1 = 0, v1 = ?

at final point, point 2: h2 = 15.4 m, v2 = 24.2 m/s

½ (24.2^2 – v1^2) = 9.8 (0 – 15.4)

585.64 – v1^2 = -301.84

-v1^2 = 887.48

v1 = 29.8 m/s

So the rock was travelling at 29.8 m/s as it left the ground.

2. The maximum height (hmax) reached is calculated using the formula:

v1^2 = 2 g hmax

Rewriting in terms of hmax:

hmax = v1^2 / 2 g

hmax = (29.8)^2 / (2 * 9.8)

hmax = 45.3 m

Therefore the rock reached a maximum height of 45.3 meters.

This high school physics question discusses the principles of kinematics and energy conservation. Given the speed and height of a rock thrown vertically upwards, it asks to determine the initial speed of the rock. We calculate this using the given values and the formula for kinetic energy & gravitational potential energy conservation, getting the initial velocity as approximately 16.88 m/s.

The subject of this question pertains to physics, specifically the application of the principles of kinematics and energy conservation in studying projectile motion. Neglecting air resistance, the speed of a projectile (like a rock) thrown vertically upwards at a certain height from the ground can be calculated using energy considerations. From the given, the rock is starting from ground level with a certain velocity upwards and it is observed that at a height of 15.4 m, its speed is 24.2 m/s. Let's denote the initial speed when the rock was thrown as v0.

Using the equation v = √(2gh + v0²), where g is the acceleration due to gravity (9.8 m/s²) and h is the height (15.4 m), we can find the initial velocity of the rock. Plugging in the known values, we get v0 as √[(24.2 m/s)² - 2*(9.8 m/s²)×15.4 m] = √(585.64-301.6) m/s = √284.04 m/s = 16.88 m/s.

This calculation tells us the initial speed required to achieve the observed height and speed. This information can be crucial in physical scenarios involving projectiles.

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Mitosis results in daughter cells that are in the 'Interphase' of the cell cycle. During this phase, cells prepare for division by duplicating their DNA and growing in size. This phase contains the sub-phases G1, S, and G2 during which cell growth and DNA replication occur.

The process of cell division, known as mitosis, results in daughter cells that are in the Interphase. This phase represents the period between cell divisions and is the phase in which cells typically spend the most time. During Interphase, the cell prepares for division by duplicating its DNA and increasing its volume in preparation for cell division. The nucleus is visible and contains a nucleolus. The Interphase is categorized into three sub-phases: G1 (gap 1) phase, S (synthesis) phase, and G2 (gap 2) phase. Cell growth occurs during the G1 and G2 phases, while DNA replication occurs during the S phase.

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Final answer:

Primary succession occurs when new land is formed, and pioneer species like lichens and mosses help break down the rock and create soil.

Explanation:

Primary succession occurs when new land is formed, such as after a volcanic eruption. The pioneer species, like lichens and mosses, help break down the rock and create soil. As the soil develops, other plants can grow and replace the pioneer species. This process eventually leads to an equilibrium state with a diverse set of organisms.

Answer:

Average distance from Uranus to the sun, a = 2.88 billion km

Explanation:

It is given that,

Orbital period of Uranus, T = 84.07 years = 2.65 × 10⁹ s

We have to find the average distance from Uranus to the sun. It can be calculated using Kepler's third law as :

[tex]T^2\propto a^3[/tex]

or [tex]T^2=\dfrac{4\pi^2}{GM}a^3[/tex]

Where

T is orbital period

a is the average distance from Uranus to the sun

G is universal gravitational constant

M is mass of sun, [tex]m=1.98\times 10^{30}\ kg[/tex]

[tex]a^3=\dfrac{T^2GM}{4\pi^2}[/tex]

[tex]a^3=\dfrac{(2.65\times 10^9)^2\times 6.67\times 10^{-11}\times 1.98\times 10^{30}}{4\pi^2}[/tex]

[tex]a^3=2.34\times 10^{37}\ m[/tex]

[tex]a=2.86\times 10^{12}\ m[/tex]

a = 2.88 billion km

Hence, this is the required solution.

Out of

I'd say 3. Oxidation.

Answer:

A) 19.3

Explanation:

As we know that specific gravity is defined as the ratio of weight of the object and weight of the water displaced by the object

so it is given by

[tex]Specific \gravity = \frac{weight \: of \: object}{weight \: of \: water\: displaced}[/tex]

now we have

weight of the object = (density)(volume)g

weight of object = [tex](19.3 g/cm^3)(2 mL)g[/tex]

now weight of the liquid displaced is given by

weight of water displaced = [tex](1 g/cm^3)(2 mL)g[/tex]

now we have

specific gravity = [tex]\frac{(19.3)(2mL)g}{(1)(2 mL)g}[/tex]

specific gravity = 19.3

Answer: d. identify the problem

Explanation:

Identify the problem is the correct option this is because of the fact that the natural environment may experience disturbance due human intervention like burning of fossil fuels, pollution or due to natural calamity like earthquakes, landslides and volcanic eruptions. To solve these problems detection of problem should be the first step that can lead to mitigation. These problems exerts negative influence over the ecosystem hence are detectable.

The correct answer is c

[tex]50^\circ[/tex] angle above the horizontal.

Step by Step Solution :

Given :

Launch speed = 11 m/sec

Height of the ceiling = 3.6 m

[tex]\rm g = 9.8\;m/sec^2[/tex]

Calculation :

Let [tex]\theta[/tex] be the launch angle, measured above the horizontal.

Vertical component of initial speed is

[tex]\rm v = 11sin\theta[/tex]

We know that

[tex]\rm v^2 - u^2=2as[/tex]

[tex]\rm 11^2 sin^2\theta - 2\times9.8\times 3.6 =0[/tex]

[tex]\rm sin\theta = 0.7636[/tex]

[tex]\rm \theta = sin^-^10.7636[/tex]

[tex]\theta = 49.8^\circ \approx 50^\circ[/tex]

[tex]50^\circ[/tex] angle above the horizontal they launched to just graze the ceiling.

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Answer: They will have same density

Explanation:

Density is defined as the mass contained per unit volume.

[tex]Density=\frac{mass}{Volume}[/tex]

Density is characteristic of a compound and thus remains constant at fixed temperatures.

A small piece would have lesser amount and will occupy a smaller volume. Similarly a larger piece would have larger amount and will occupy a larger volume.

Thus the ratio of mass and volume will remain fixed or constant and the density will be same for smaller and larger piece.

This is mainly because the wavelength of a moving soccer ball is extremely small so it is not detectable to the naked eye. The wavelength of a moving soccer ball is much smaller than what the human eye can pick up, so it cannot be seen.

The wavelength of a moving soccer ball is too small to be detected due to the ball's large mass. This tiny wavelength is immeasurable and has no noticeable effect on the soccer ball's behavior. The de Broglie wavelength is significant only for particles with small mass or high velocity.

The concept of wavelength in matter is explained by the de Broglie wavelength, which is only noticeable for particles with very small mass and/or very high velocity.