Consider a particle of mass m acted on by a force F in an inertial frame.Prove that dK=F× ( d×r), where d×r is the change in position vector of a particle in a time d×t, and d×K is the corresponding change in the kinetic energy K=1÷2(mv²)

Answers

Answer 1

From the change in the kinetic energy of the particle, the force that acted on the particle from an inertial frame is proved as F(dr) = dK.

Kinetic energy of the particle

The kinetic energy of the particle is given as;

K.E = ¹/₂mv²

dK/dv = mv

m = dK/vdv

Force on the particle

The force on the particle is given by Newton's second law of motion;

F = ma

a = dv/dt

F = m(dv/dt)

F = (dK/vdv) (dv/dt)

F = dK/vdt

F(vdt) = dK

v = dr/dt

F (dr/dt) x (dt) = dK

F(dr) = dK, proved

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Related Questions

A star is moving towards the earth with a speed at 90% the speed of light. It emits light, which moves away from the star at the speed of light. Relative to us on earth, what is the speed of the light moving toward us from the star?

Answers

Answer:

The speed of light measured in any frame is c = 3.00E8 m/s.

This is one  of Einstein's  postulates of special relativity.

Why is water often called the "universal solvent"? A. A large amount of energy is needed to raise its temperature. B. It remains a liquid over a wide range of temperatures. C. Many different substances can dissolve in it. D. Strong forces of cohesion allow it to form drops.​

Answers

Answer:

C

Explanation:

For an exponential function, y = A∙emx, what is the value of y when x = 0?

a.
A

b.
e

c.
x

d.
b

e.
zero

Answers

Answer:

a.A

Explanation:

when x=0, the power becomes 0 and the exponent becomes 1

anything to the power of 0 is 1

in addition, the exponent only applies to the 'e' term, hence the e term will become 1 and multiply A to give you A


A Studead dropped 0.25 kg box from high,
hesht of 2.3 metersit box lands on the floor.
Part A what is the potential energy of box before it fallen. part B What is Kinect energy of box before is it is dropped

Answers

Answer:

Explanation:

Potential energy is defined as the "stored" energy inside of the field, in our case the graviational field. Since the force of gravity is conservative, the reference point for our potential energy is arbitrary. This means that we can arbitrarily set where the potential energy is zero. The easiest case is setting the potential energy zero when the box is on the floor. The potential energy is defined as:

[tex]U=mgh[/tex]

We are given the mass, the height from the ground, and the graviational acceleration is 9.8m/s^2. Plugging this in gives:

[tex]U=(0.25kg)(9.8m/s^2)(2.3m)=5.64J[/tex]

Kinetic energy is defined as the energy of the configuration during motion. Before the box begins to fall, it is completely stationary. Therefore the kinetic energy is zero.

what happens to the resistance of two resistors when connected in series​ circuit

Answers

Answer:

increases as more components are added. 

Please help the due date is today.
-Don't give wrong answers
-No spam
-Correct answers will mark as brainliest​

Answers

Answer:

a the structure labelled as cell wall

Explanation:

a difference between plant cells and animal cells is the most animal cells are round whether most plant cells are rectangular. plants cells have a rigid cell wall that surrounds the cell membrane.animal cell do not have cell wall when looking under a microscope, the cell wall is an easy way to distinguish between animal and plant cells

please mark as a brainliest

hope it helps you

The graph represents velocity over time.
What is the acceleration?

Answers

Answer:

I think the answer is 0.2 m/s2

Explanation:

What happens to an object's kinetic energy as it falls from some height?

Answers

Answer:

The objects kinetic energy increases as it falls from some height.

it the satellite is put into a new circular orbit of a smaller radius, how will the Fo and the speed of the satellite change, if at all?
A Both gravitational force and speed will decrease
OB. The gravitational force will decrease and speed will increase
O c The gravitational force will increase and speed will decrease
OD. Both gravitational force and speed will increase

Answers

OD

Explanation:

both gravitational force and speed will increase

The gravitational force will increase and speed will decrease. So, the correct option is c.

What is meant by gravitational force ?

Any two objects in the universe are attracted towards each other by the gravitational force, regardless of whether their masses are equal or not.

Here,

Newton's universal law of gravitation states that the force of attraction between any two bodies is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.

So, the gravitational force of the satellite,

F ∝ 1/R²

where R is the radius of the circular orbit.

The equation for speed of the satellite is given by,

v = √Rg

where g is the acceleration due to gravity.

So, the speed is directly proportional to the square root of the radius of the orbit.

v ∝ √R

Therefore, as a result of the decrease in the radius of the orbit, the gravitational force of the satellite will increase, and its speed will decrease.

Hence,

The gravitational force will increase and speed will decrease.

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pls help thank youuuu

1. A fluorescent light bulb produces just as much light in the same electrical circuit as an incandescent bulb , but requires much less energy to produce it. Which of the following is the most logical explanation for this?

A. The incandescent bulb produces more forms of energy than just light, like heat.
B. The fluorescent light bulb produces more light than any other bulb.
C. The incandescent bulb has to be connected to another circuit.
D. The fluorescent light bulb generates more current than any other type.

Answers

The most logical explanation is the incandescent bulb produces more forms of energy than just light, like heat.

Conservation of energy

The principle of conservation of energy can be used to explain to reason behind the more energy required for an incandescent bulb to produce the same light as a fluorescent light bulb.

Some part of the energy required by the incandescent bulb is used to produce light while some is used to generate heat.

For fluorescent light bulb, all the energy are used to produce light, leading to a better efficiency and less energy required to produce same amout light as  incandescent bulb.

Thus, the most logical explanation is the incandescent bulb produces more forms of energy than just light, like heat.

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A skier at the bottom of a hill has 900J of kinetic energy. After sliding a ways along the flat, the kinetic energy is 300J. How much energy was lost due to friction?

Answers

Answer:

600 J

Explanation:

900 j = 300j = 600 j lost due to friction

Energy lost due to friction is 600 J.

The kinetic energy before and after friction is given as 900J and 300J.

What is friction?

   The force that resists the sliding or rolling over one object with another is called friction. The energy which possess in virtue of being in motion is said to be Kinetic Energy.

                                   f = μN

                      Energy lost = 900J - 300J

                                          =  600J

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Is this circuit parallel or inseries ​

Answers

Answer:

parallel circuit, hopefully I wasn't late in sending the answer

Entropy can only be decreased in a system if ?

Answers

Answer:

heat is removed.

Explanation:

hope this helps.

Answer:

energy is removed.

Because entropy is a dynamicquality realting to the system being unavaliable to do conversions because of the energy measures being low.

Using Newton's Second Law of Motion how does the difference in mass and force affect acceleration?
400kg Force 40kg MASS C Force​

Answers

Explanation:

Let & mean "is proportional to"

F & [m(V - Vo)]/∆t

We can see that increase in the applied force equals increase in the change in momentum (increase in change of velocity).

Also,

An increase in the mass of the object requires more force to be applied for work to be done.

What kinetic energy would the bicycle have if it had one-half the mass and was moving with twice the speed?

Answers

kinetic energy would beeeeeeeeeeeee 248 J

Find the focal length of a concave mirror that produces four times larger real image of an object held at 5cm from the mirror.

Answers

Answer:

6.67 cm

Explanation:

Given

h (image) = 4 x h (object)

Finding magnification

m = h (image) / h (object)m = 4 x h (object) / h (object)m = + 4.0

Finding image distance

m = - (image distance / object distance)4 = - (v / 5)4 = -v/5v = -20v = -20 cm

Mirror formula

1/f = 1/v + 1/u

Solving

1/f = 1/-20 + 1/51/f = -1 + 4/201/f = 3/20f = 20/3 cmf = 6.67 cm

How is intelligence generally defined? Based on your reading, what do you think about the concept of intelligence and the ability to both define and measure it?

Answers

Intelligence is generally defined by the Individual IQ tests. Individual IQ tests are often administered by psychologists and take an hour to an hour and a half to complete.

What is intelligence ?

The capacity for abstraction, logic, comprehension, emotional knowledge, reasoning, organization, creativity, rational reasoning, are all examples of intelligence.

Personal intellect or Intelligence quotient, given one-on-one by a psychotherapist, are the preferred process of measuring intellect.

Individual IQ tests are often administered by psychologists and take an hour to an hour and a half to complete.

Hence Intelligence is generally defined by the Individual IQ tests

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PLEASE HELP!! WORTH A TOTAL OF 100 POINTS!!
The three blocks shown are released from rest and are observed to move at a distance of 0.5m with an acceleration of magnitude of 1.5 m/s^2. answer the following assuming M=2.0kg and ignoring the pulley masses and any friction in the pulleys.

Formulas:
T₁ - m*g = m₁*a --- (1)
T₂ - T₁ - F = m₂*a --- (2)
m₃*g - T₂ = m₃*a --- (3)
m₁ = M
m₂ = 2M
m₃ = 2M

Questions solved:
The magnitude of the friction force: 4.6 N
The coefficient of friction: 0.12
The tension in the left string: 22.6 N
The work done by gravity: 9.8 J
The work done by friction: -2.3 J
The velocity of the blocks after they moved the 0.5 m distance from rest: 1.22 m/s

Needed:
What is the tension in the string on the left?

Answers

The last equation gives you the tension in the string on the right:

[tex]T_2 = 2Mg - 2Ma = 2M (g-a) = \boxed{33.2 \, \mathrm N}[/tex]

Calculate the wavelength (in m) of a 589 Hz sound in air at room temperature and pressure where the velocity of sound is 344 m/s.

Answers

Answer:

just use the formula λ = v/f

Explanation:

v = velocity

f = frequency

A 82.9 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 670 (food) calories. How high must the person climb? The acceleration due to gravity is 9.8 m/s2 and 1 food calorie is 10^3 calories.

Answers

The weight watcher must climb : 3.45 km to work off the equivalent of a large piece of chocolate cake rated at 670 calories.

Determine how high the weight-watcher must climb

First step : convert the energy to joules

670 calories to Joules

E = 670 * 10³ * 4.184

  = 2803280 J

Next step : Equate energy to gravitational potential energy

2803280 J = mgh

2803280 = 82.9 * 9.8 * h

Therefore :

h = 2803280 / ( 812.42 )

  = 3451 m  = 3.45 Km

Hence we can conclude that The weight watcher must climb : 3.45 km

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Write down the advantage and disadvantage of using mercury as thermometric liquid..

Answers

Answer:

Advantage: Mercury has a lower freezing point (-1140 degree Celsius)

Disadvantage: Mercury has a lower boiling point

why do some motor vehicles contain graphite

Answers

Answer:

Some motor tyre contain Graphite to contain friction.

Answer:

to contain friction

Explanation:

If it takes a wave on the ocean 95.2 seconds to pass by the point of a rock, what is the frequency with which the waves are passing by to the nearest two decimal places?

Answers

Answer:

.01 Hz

Explanation:

f = 1/period

 = 1 / 95.2 = .01 Hz

A 43 kg object is hanging from a rope. If it has the potential to do 3160 J of work, how high is it above the ground?

Answers

the answer is 78 kg because that

What do chemical symbols and formulas represent, respectively? elements and compounds compounds and mixtures atoms and mixtures

Answers

Answer:

They represent compounds and mixtures

Explanation:

If a measurement is 4.2 cm and its possible error is 0.04 cm, the relative error is?​

Answers

Given the value of possible error, the relative error of the measurement is 0.0095.

Given the data in the question;

Measurement taken; [tex]m = 4.2cm[/tex]Absolute or possible erorr; [tex]e = 0.04m[/tex]Relative error; [tex]RE = \ ?[/tex]

Relative Error

Relative error is simply the ratio of the absolute or possible error of a measurement to the measurement its self.

Relative error is expressed as;

[tex]RE = \frac{e}{m}[/tex]

Where e is the absolute or possible error and m is the measurement being taken.

To determine the relative error, we substitute our given values into the expression above.

[tex]RE = \frac{0.04cm}{4.2cm} \\\\RE = 0.0095[/tex]%

Therefore, given the possible error, the relative error of the measurement is 0.0095.

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Cells store waste in ________.
A
DNA

B
vacuoles

C
chloroplasts

D
ribosomes

Answers

Answer:

B vacuoles

Explanation:

if relative density is equal to 1 then the substance would sink in water ..true or false​

Answers

relative density is equal to 1 then the substance would sink in water

How many grams of C are in
1.7 x 10^24 atoms of C?

Answers

1 mol = 6.022 × 10^23  atoms

1.7 x 10^24   x   1/(6.022 × 10^23) = 2.823 mol

Carbon has an atomic weight of 12.011 (grams per mol)

2.823 x 12.011 = 33.907053 g

Hope I'm right!

Why do you not want to stand still when on offense?

Question 2 options:

It makes you very easy to cover.


Your coach will take you out of the game.


Its lazy.


It makes it harder for the defense to cover you.

Answers

It makes it harder for the defense to cover you.

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