Mathematics: The rate of change of the mass A

The rate of change of the mass A, №14323938, 03.10.2020 16:06

Physics

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. df dr = − 2gmm r3 what is the meaning of df/dr? df/dr represents the rate of change of the mass with respect to the distance between the bodies. df/dr represents the amount of force per distance. df/dr represents the rate of change of the mass with respect to the force. df/dr represents the rate of change of the distance between

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Answers:Answer 1 (a):

According to Newton's Law of Gravitation, the Gravity Force is:

$F=\frac{GMm}{{r}^{2}}$ (1)

This expression can also be written as:

$F=GMm{r}^{-2}$ (2)

If we derive this force respect to the distance between the two masses:

$\frac{dF}{dr}dFdr=\frac{d}{dr}(GMm{r}^{-2})dr$ (3)

Taking into account GMm are constants:

$\frac{dF}{dr}dFdr=-2GMm{r}^{-3}$ (4)

Or

$\frac{dF}{dr}dFdr=-2\frac{GMm}{{r}^{3}}$ (5)

Answer 2 (a): dF/dr represents the rate of change of the force with respect to the distance between the bodies.

In other words, this means how much does the Gravity Force changes with the distance between the two bodies.

More precisely this change is inversely proportional to the distance elevated to the cubic exponent.

As the distance increases, the Force decreases.

Answer 3 (a): The minus sign indicates that the bodies are being forced in the negative direction.

This is because Gravity is an attractive force, as well as, a central conservative force.

This means it does not depend on time, and both bodies are mutually attracted to each other.

Answer 4 (b): X=-32N/km

In the first answer we already found the decrease rate of the Gravity force respect to the distance, being its unit N/km :

$\frac{dF}{dr}dFdr=-2\frac{GMm}{{r}^{3}}$ (5)

We have a force that decreases with a rate 1 $\frac{dF_{1}}{dr}dFdr=4N/km$ when r=20000km :

$4N/km=-2\frac{GMm}{{(20000km)}^{3}}$ (6)

Isolating -2GMm :

$-2GMm=(4N/km)({(20000km)}^{3})$ (7)

In addition, we have another force that decreases with a rate 2 $\frac{dF_{2}}{dr}dFdr=X$ when r=10000km :

$XN/km=-2\frac{GMm}{{(10000km)}^{3}}$ (8)

Isolating -2GMm :

$-2GMm=X({(10000km)}^{3})$ (9)

Making (7)=(9):

$(4N/km)({(20000km)}^{3})=X({(10000km)}^{3}$ (10)

Then isolating :

$X=\frac{4N/km)({(20000km)}^{3}}{{(10000km)}^{3}}$

Solving and taking into account the units, we finally have:

X=-32N/km >>>>This is how fast this force changes when r=10000 km

Chemistry

Asap ! will mark brainliest, only answer if you re sure if you ever bounced a ball, you have experienced the conservation of energy or at least nearly the complete conservation of energy. when you drop a ball onto the ground, it bounces back up, nearly to your hand. the mass of the ball hasn t changed, remember that mass is conserved in any physical or chemical change. a simple change of position would conserve mass as well. the same can be said for the ball s energy, although this conservation is harder to observe. explore the behavior of energy

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1. As you drops a ball, its potential energy is converted into kinetic energy during its fall. It moves faster and faster as more PE is converted into KE until the ball hits the ground.

2. The conversion from PE to KE is due to the work done by gravity acceleration. As the ball is accelerated by gravity towards ground, its PE is converted to KE.

3. Total energy of the ball is conserved. Its position changes as it gets closer to the ground. Its PE decreases as its speed and hence KE increases until it hits the ground.

Chemistry

Asap ! will mark brainliest, only answer if you re sure if you ever bounced a ball, you have experienced the conservation of energy or at least nearly the complete conservation of energy. when you drop a ball onto the ground, it bounces back up, nearly to your hand. the mass of the ball hasn t changed, remember that mass is conserved in any physical or chemical change. a simple change of position would conserve mass as well. the same can be said for the ball s energy, although this conservation is harder to observe. explore the behavior of energy

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P Answered by PhD

1. As you drops a ball, its potential energy is converted into kinetic energy during its fall. It moves faster and faster as more PE is converted into KE until the ball hits the ground.

2. The conversion from PE to KE is due to the work done by gravity acceleration. As the ball is accelerated by gravity towards ground, its PE is converted to KE.

3. Total energy of the ball is conserved. Its position changes as it gets closer to the ground. Its PE decreases as its speed and hence KE increases until it hits the ground.

Mathematics

Alex heated water in a pan until the entire water changed in to vapor. the mass of the total vapor formed was 150g. what was most likely the mass of the water alex headted and why? 175 g, water vapor formed is lighter then water 150 g, mass of the water remains the same when it changes state 175 g, some water molecules are destroyed during phase change 150 g, mass remains same during chemical change of water into vapor

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B) 150 g, mass of the water remains the same when it changes state

Physics

You re the first person to visit mars and you ve just met a group of martian schoolchildren. they are playing street hockey with parts from the mars polar lander and, after years of watching star trek reruns, they are fluent in english. one of them asks you how your weight and mass have changed since you left earth. you take a moment to measure both and reply correctly that (a) your weight is essentially unchanged but your mass is less than on earth. (b) your mass is essentially unchanged but your weight is less than on earth. (c) your weight and

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(B) your mass is essentially unchanged but your weight is less than on Earth.

Explanation:

Well, firstly we have to explain the difference between the concepts of mass and weight:

-Mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

-Weight is a measure of the gravitational force acting on an object and is directly proportional to the product of the mass of the body by the acceleration due gravity in that place and is mathematically expressed as:

W=m.g

So, according to this explanation and since the Earth and Mars have different values of acceleration due gravity (in fact, Mar's is less than Earth's), your weight has changed, but not your mass.

Physics

Why does the equilibrium position of the spring change when a mass is added to the spring? will the mass oscillate around the new equilibrium position of the spring or the previous position without a mass attached to the spring? if the equilibrium position of the spring changes by 20 cm (assuming no initial mass) when a mass is added to the spring with constant 4.9 kg/s^2, what is the mass of the object attached to the spring?

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whenever a new mass is added to spring the equilibrium state of the spring will change and then the mas will start oscillating about the new equilibrium position.

So here we can say that mass will always oscillate about its new equilibrium position if it is changed

Now in next situation it is given that

spring constant(k) = 4.9 kg/s^2

displacement of mass after suspending through spring = 20 cm

now we have the formula of spring force as

F = kx

here applied force is due to gravity so we have

mg = kx

m(9.8) = (4.9)(0.20)

m = 0.10 kg

so mass of object will be 100 g or 0.10 kg

Physics

You re the first person to visit mars and you ve just met a group of martian schoolchildren. they are playing street hockey with parts from the mars polar lander and, after years of watching star trek reruns, they are fluent in english. one of them asks you how your weight and mass have changed since you left earth. you take a moment to measure both and reply correctly that (a) your weight is essentially unchanged but your mass is less than on earth. (b) your mass is essentially unchanged but your weight is less than on earth. (c) your weight and

Step-by-step answer

P Answered by PhD

(B) your mass is essentially unchanged but your weight is less than on Earth.

Explanation:

Well, firstly we have to explain the difference between the concepts of mass and weight:

-Mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

-Weight is a measure of the gravitational force acting on an object and is directly proportional to the product of the mass of the body by the acceleration due gravity in that place and is mathematically expressed as:

W=m.g

So, according to this explanation and since the Earth and Mars have different values of acceleration due gravity (in fact, Mar's is less than Earth's), your weight has changed, but not your mass.

Physics

Why does the equilibrium position of the spring change when a mass is added to the spring? will the mass oscillate around the new equilibrium position of the spring or the previous position without a mass attached to the spring? if the equilibrium position of the spring changes by 20 cm (assuming no initial mass) when a mass is added to the spring with constant 4.9 kg/s^2, what is the mass of the object attached to the spring?

Step-by-step answer

P Answered by PhD

1

whenever a new mass is added to spring the equilibrium state of the spring will change and then the mas will start oscillating about the new equilibrium position.

So here we can say that mass will always oscillate about its new equilibrium position if it is changed

Now in next situation it is given that

spring constant(k) = 4.9 kg/s^2

displacement of mass after suspending through spring = 20 cm

now we have the formula of spring force as

F = kx

here applied force is due to gravity so we have

mg = kx

m(9.8) = (4.9)(0.20)

m = 0.10 kg

so mass of object will be 100 g or 0.10 kg

Physics

Which property of physical changes explains why matter is conserved in a physical change? the arrangements of particles do not change, and the bonds between atoms do not break. mass, not energy, changes in a physical change. energy and mass change in a physical change. the bonds between atoms do not break; it is only the arrangement that changes.

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P Answered by Specialist

115

Option (d) is the correct answer.

Explanation:

Physical change is defined as a change in which no new product is formed, that is, there is no change in chemical composition of a substance.

For example, when ice melt then solid state of water changes into liquid state.

That is, arrangement of atoms changes and bond between the atoms do no break during a physical change.

Thus, we can conclude that the property bonds between atoms do not break; it is only the arrangement that changes explains why matter is conserved in a physical change.

Physics

Which property of physical changes explains why matter is conserved in a physical change? the arrangements of particles do not change, and the bonds between atoms do not break. mass, not energy, changes in a physical change. energy and mass change in a physical change. the bonds between atoms do not break; it is only the arrangement that changes.

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P Answered by PhD

61

The property of physical changes that explains why matter is conserved in a physical change is - the bonds between atoms do not break; it is only the arrangement that changes.

The rate of change of the mass A

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