When the displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position, what fraction of the total mechanical energy is kinetic energy?

Answers

Answer 1

Answer:

The ratio is  KE : TM  =  0.75

Explanation:

from the question we are told that

  The displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position

Generally the total mechanical  energy of the mass is mathematically represented as

        [tex]TM = \frac{1}{2} * k * A^2[/tex]

Here  k is the spring constant  ,  A is the total displacement of the  the mass  from maximum  compression to maximum extension of the spring

Generally this total mechanical energy is mathematically represented as

        [tex]TM = KE + PE[/tex]

=>     [tex]KE = TM - PE[/tex]

Here the potential  energy of the mass is mathematically represented as

     [tex]PE = \frac{1}{ 2} * k * [ x ]^2[/tex]

Here x is the displacement of the mass from maximum compression or extension of the spring to equilibrium position and the value is  

      [tex]x = \frac{A}{2}[/tex]

So

     [tex]PE = \frac{1}{ 2} * k * [ \frac{A}{2} ]^2[/tex]

So

      [tex]KE = \frac{1}{2} * k * A^2 - \frac{1}{2} * k * [\frac{A}{2} ]^2[/tex]

=>    [tex]KE = \frac{1}{2} * k * A^2 - \frac{1}{8} * k * A ^2[/tex]

=>    [tex]KE = 0.375 * k * A^2[/tex]

So the ratio of  [tex]KE : TM[/tex] is  mathematically represented as

       [tex]\frac{KE}{TM} = \frac{0.375 k A^2 }{0.5 k A^2}[/tex]

=>    [tex]\frac{KE}{TM} = 0.75[/tex]


Related Questions

Can someone help with my physics homework? please

A go cart engine applies a force of 888N and moves the cart forward 22m.

a) How much work is done?


b) What is doing the work?


c) If the driver wants to go further will the amount of work increase or decrease? Do you need a bigger engine to go

further?


d) We put on a bigger engine (1111N) but the cart still moves forward 22m. How much work is done now?


e) Why would you put on a bigger engine if you are still moving 22m?


f) Work requires a change in energy, which engine uses more gas to go 22m?


g) Even an empty semi truck uses much more gas than a car. Why?Find the soultions

Answers

Answer:

a) 19536 joules of work are done.

b) The work is done by the engine on the structure of the cart.

c) There are three options:  (i) Keeping the engine and changing the travelled distance, (ii) Changing the engine and keeping the travelled distance, (iii) Changing the engine and the travelled distance.

d) 24442 joules of work are done.

e) We may change for a bigger engine if it allows a greater acceleration and higher peak speed.

f) The bigger engine uses more gas to go 22 meters.

g) An empty semi truck uses more gas than a car since the first has much more mass than a car and is designed for moves big loads and for being fast.

Explanation:

a) If force applied in the cart is uniform, that is, constant in magnitude and direction and is parallel to distance travelled by the car, the work done on the cart is defined by the following equation:

[tex]W = F\cdot \Delta s[/tex] (1)

Where:

[tex]F[/tex] - Force applied by the cart, measured in newtons.

[tex]\Delta s[/tex] - Distance travelled by the car, measured in meters.

[tex]W[/tex] - Work done on the cart, measured in joules.

If we know that [tex]F = 888\,N[/tex] and [tex]\Delta s = 22\,m[/tex], then the work done on the cart is:

[tex]W =(888\,N)\cdot (22\,m)[/tex]

[tex]W = 19536\,J[/tex]

19536 joules of work are done.

b) The work is done by the engine on the structure of the cart.

c) There are three options:  (i) Keeping the engine and changing the travelled distance, (ii) Changing the engine and keeping the travelled distance, (iii) Changing the engine and the travelled distance.

d) If we know that [tex]F = 1111\,N[/tex] and [tex]\Delta s = 22\,m[/tex] , then the work on the cart is:

[tex]W = (1111\,N)\cdot (22\,m)[/tex]

[tex]W = 24442\,N[/tex]

24442 joules of work are done.

e) We may change for a bigger engine if it allows a greater acceleration and higher peak speed.

f) The gas consumption is directly proportional to the square of velocity and mass of the cart and, hence, to the work done on the cart. In consequence, we conclude that the bigger engine uses more gas to go 22 meters.

g) An empty semi truck uses more gas than a car since the first has much more mass than a car and is designed for moves big loads and for being fast.

a. The amount of work done by the go cart engine is 19,536 Nm.

b. Work is being done by the go cart engine i.e the engine installed on the go cart.

c. The amount of work will increase if the driver wants to go further because work done is directly proportional to the distance covered. No, you don't need a bigger engine to go further.

d. The amount of work done when a bigger engine is used is 24,442 Nm.

e. The reason why a bigger engine is used is, so that the engine can easily do more work in the same amount of distance.

f. Since we know that work requires a change in energy, the bigger engine would use more gas to go 22 meters.

g. An empty semi truck uses much more gas than a car because it has more weight (mass) and as such requires more energy, in accordance with the law of inertia.

Given the following data:

Force A = 888 NewtonDistance = 22 meterForce B = 1111 Newton

a. To determine the amount of work done by the go cart engine:

Mathematically, the work done by an object is given by the formula;

[tex]Work\;done = Force \times distance[/tex]

Substituting the given parameters into the formula, we have;

[tex]Work\;done = 888 \times 22[/tex]

Work done = 19,536 Nm.

b. Work is being done by the go cart engine i.e the engine installed on the go cart.

c. The amount of work will increase if the driver wants to go further because work done is directly proportional to the distance covered. No, you don't need a bigger engine to go further.

d. To determine the amount of work done when a bigger engine is used:

[tex]Work\;done = Force \times distance[/tex]

[tex]Work\;done = 1111 \times 22[/tex]

Work done = 24,442 Nm.

e. The reason why a bigger engine is used is, so that the engine can easily do more work in the same amount of distance.

f. Since we know that work requires a change in energy, the bigger engine would use more gas to go 22 meters.

g. An empty semi truck uses much more gas than a car because it has more weight (mass) and as such requires more energy, in accordance with the law of inertia.

Read more: https://brainly.com/question/22599382

A 1430 kg is moving at 25.6 m/s when a force is applied, in the direction of the cars motion. The car speeds up to 31.3 m/s. If the force is applied for 5.4 s what is the magnitude of the force

Answers

The car accelerates with magnitude a such that

31.3 m/s = 25.6 m/s + a (5.4 s)

→   a = (31.3 m/s - 25.6 m/s) / (5.4 s) ≈ 1.056 m/s²

Then the applied force has a magnitude F of

F = (1430 kg) a1500 N

If the magnitude of the electric field of an electromagnetic wave is 3x10^3 V/m, what is the the magntude of the magnetic field?
a. 1.1 x 10^-12 T
b. 9 x 10^11 T
c. 10^5 T
d. 10^-5 T
e. 3 x 10^3 T

Answers

Answer:

The value of the  magnetic field is [tex]B = 1.0*10^{-5} \ T[/tex]

The correct option is d

Explanation:

From the question we are told that  

    The magnitude of the electric field is  [tex]E = 3*10^{3} \ V/m[/tex]

     Generally the magnitude of  the magnetic field is mathematically represented as

        [tex]B = \frac{E}{c}[/tex]

Here  c is the speed of  light [tex]c = 3.0*10^{8} \ m/s[/tex]

=>     [tex]B = \frac{E}{c}[/tex]

=>      [tex]B = \frac{3.0*10^{3}}{ 3.0*10^{8}}[/tex]

=>      [tex]B = 1.0*10^{-5} \ T[/tex]

A 12 N net force is applied to an object as it moves a distance of 3.0 m: Use the
Work-Kinetic Energy Theorem to determine the object's change in kinetic energy.
Enter your answer in Joules.

Answers

Answer:

4 joules

Explanation:

a cannon has a mass 2500. it fires a cannon-Ball during a routine exercise. the cannon is 1000 times heavier than the cannon ball. the cannon ball leaves the barrel at a horizontal velocity of 160 m/s. the cannon comes to rest 2 seconds after the cannon ball was fired. calculate the magnitude of average net force that causes the cannon to rest​

Answers

Answer:

F = 200 [N]

Explanation:

To solve this problem we must use the principle of conservation of linear momentum, which can be calculated by means of the following equation.

[tex]P=m*v[/tex]

where:

P = lineal momentum [kg*m/s]

m = mass [kg]

v = velocity [m/s]

Now we must understand that the momentum is conserved before and after the firing of the cannon. Before firing the cannon we have the mass of the cannon and mass of the cannonball together at rest (speed = 0). After firing the cannon the cannonball moves forward with positive speed, while the cannon moves back (negative), in this way knowing the masses of each one we can determine the speed of the cannon.

[tex](m_{cannon}+m_{ball})*v_{1}=-(m_{cannon}*v_{2})+(m_{ball}*v_{3})[/tex]

where:

m_cannon = 2500 [kg]

m_ball = 2.5 [kg]

v₁ = 0 (velocity of the group before firing)

v₂ = velocity of the cannon after firing [m/s]

v₃ =  160 [m/s] (velocity of the cannonball after firing)

[tex](2500+2.5)*0 = -(2500*v_{2})+(2.5*160)\\v_{2}=0.16[m/s][/tex]

Now using the following equation of kinematics, we can calculate the acceleration.

[tex]v_{f}=v_{o}-a*t[/tex]

where:

Vf = final velocity = 0 (cannon comes to rest)

Vo = initial velocity = 0.16 [m/s]

a = acceleration [m/s²]

t = time = 2 [s]

[tex]0 = 0.16 - a*2\\2*a=0.16\\a = 0.08 [m/s^{2}][/tex]

With the value of acceleration, we can use Newton's second law which tells us that the forces acting on a body is equal to the product of mass by acceleration.

ΣF = m*a

where:

F = force [N] (units of Newtons)

m = mass = 2500 [kg]

a = acceleration = 0.08 [m/s²]

[tex]F = 2500*0.08\\F = 200 [N][/tex]

When you heat water on a stove, how does its energy change?
A. Its electromagnetic energy decreases.
B. Its thermal energy decreases. c. Its thermal energy increases.
D. Its electromagnetic energy increases.

Answers

Answer:

C. its thermal energy increases

Answer:

Explanation:

C

How long does it take a plane, traveling at a constant speed of 123 m/s, to fly once around a circle whose radius is 4330 m?

Answers

Answer:

3.7 min

Explanation:

Step one:

given data

speed = 123m/s

radius of circle= 4330m

Step two:

We need to find the circumference of the circle, it represents the distance traveled

C=2πr

C= 2*3.142*4330

C= 27209.72m

Step three:

We know that velocity= distance/time

time= distance/velocity

time= 27209.72/123

time=221.2 seconds

in minute = 221.2/60

time= 3.7 min

Galaxy B moves away from galaxy A at 0.577 times the speed of light. Galaxy C moves away from galaxy B in the same direction at 0.731 times the speed of light. How fast does galaxy C recede from galaxy A?

Answers

Answer:

The value is  [tex]p = 0.7556 c[/tex]

Explanation:

From the question we are told that

   The speed at which galaxy B moves away from galaxy A is  [tex]v = 0.577c[/tex]

Here c is the speed of light with value  [tex]c = 3.0 *10^{8} \ m/s[/tex]

     The speed at which galaxy C moves away from galaxy B is  [tex]u = 0.731 c[/tex]

Generally from the equation of  relative speed we have that  

     [tex]u = \frac{p - v}{ 1 - \frac{ p * v}{c^2} }[/tex]

Here p is the velocity at which galaxy C recede from galaxy A so

     [tex]0.731c = \frac{p - 0.577c }{ 1 - \frac{ p * 0.577c}{c^2} }[/tex]

=>   [tex]0.731c [1 - \frac{ p * 0.577}{c}] = p - 0.577c[/tex]

=>   [tex]0.731c - 0.4218 p = p - 0.577c[/tex]

=>   [tex]0.731c + 0.577c = p + 0.4218 p[/tex]

=>   [tex]1.308 c = 1.731 p[/tex]

=>    [tex]p = 0.7556 c[/tex]

Which two things occur when electric charges move through a conductor?

A. The field is perpendicular to the electron flow.

B. The field is parallel to the electron flow.

C. An electric field forms.

D. A magnetic field forms.

The two correct answers are A and D ap3x approved!

Answers

A C and D

C because ofc when electric charge flow electric field is produced

Answer:

A & D

Explanation:

A 1369.4 kg car is traveling at 28.9 m/s when the driver takes his foot off the gas pedal. It takes 5.1 s for the car to slow down to 20 m/s. How large is the net force slowing the car

Answers

Answer:

F = 2389.603 N

Explanation:

Given:

Mass m = 1,369.4 kg

Initial velocity u = 28.9 m/s

Final velocity v = 20 m/s

Time t = 5.1 s

Find:

Net force

Computation:

a = (v - u)/t

a = (20 - 28.9)/5.1

a = -1.745 m/s²

F = ma

F = (1369.4)(1.745)

F = 2389.603 N

A cicada produces a sound of roughly 5000 Hz frequency. What category would that sound fall into?

Supersonic

Normal range

Infrasonic

Ultrasonic

Answers

It’s ultrasonic 100% not much help but I knew the answer

An object with a mass of 32 kg has an initial energy of 500). At the end of the experimentthe velocity of the object is recorded as 5.1 m/s . the object travelled 50 m to get to this point, what was the average force of friction on object during the tripAssume no potential energy Show all work

Answers

Answer:

 F = 1.68 N

Explanation:

Let's solve this exercise in parts.

Let's use the concept of conservation of the mechanical nerve

initial

    Em₀ = 500 J

The energy is totally kinetic

     Em₀ = K = ½ m v₀²

     v₀ = [tex]\sqrt{\frac{2 Em_{o} }{m} }[/tex]

     v₀ = √ (2 500/32)

     v₀ = 5.59 m / s

now with kinematics we can find a space

      v² = v₀² - 2 a x

the negative sign is because the body is stopping

       a =[tex]( \frac{v_{o}^{2} - v^{2} }{2x} )[/tex]  

let's calculate

       a = (5.59² - 5.1²) / 2 50  

       a = 0.0524 m / s²

Finally let's use Newton's second law

     F = ma

     F = 32 0.0524

     F = 1.68 N

if A=3i +2j+3k ,find the magnitude of A+B and A-B​

Answers

Since vector B was not specified, I'll assume one at random. You can later answer your own question.

Answer:

[tex]\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}[/tex]

[tex]\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}[/tex]

Explanation:

Given:

[tex]\vec A=3\hat i +2\hat j+3\hat k[/tex]

And (assumed):

[tex]\vec B=-5\hat i +8\hat j-4\hat k[/tex]

Find the magnitude of

[tex]\vec A+\vec B[/tex]

[tex]\vec A-\vec B[/tex]

Given a vector

[tex]\vec P=x\hat i +y\hat j+z\hat k[/tex]

The magnitude of the vector is:

[tex]\mid\mid \vec P\mid \mid=\sqrt{x^2+y^2+z^2}[/tex]

First part:

[tex]\vec A+\vec B =3\hat i +2\hat j+3\hat k-5\hat i +8\hat j-4\hat k[/tex]

[tex]\vec A+\vec B =-2\hat i +10\hat j-\hat k[/tex]

The magnitude of the sum is:

[tex]\mid\mid \vec A+\vec B \mid \mid=\sqrt{(-2)^2+10^2+(-1)^2}=\sqrt{4+100+1}[/tex]

[tex]\mathbf{\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}}[/tex]

Second part:

[tex]\vec A-\vec B =3\hat i +2\hat j+3\hat k-(-5\hat i +8\hat j-4\hat k)[/tex]

[tex]\vec A-\vec B =3\hat i +2\hat j+3\hat k+5\hat i -8\hat j+4\hat k[/tex]

[tex]\vec A-\vec B =8\hat i -6\hat j+7\hat k[/tex]

The magnitude of the difference is:

[tex]\mid\mid \vec A-\vec B \mid \mid=\sqrt{8^2+(-6)^2+7^2}=\sqrt{64+36+49}[/tex]

[tex]\mathbf{\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}}[/tex]

A 12 kg coyote runs towards a rabbit in the Ortega Mountains
with a velocity of 8 m/s. Determine the momentum of the
coyote.
What is "given" in the word problem?
A) mass and velocity
B) momentum
C) momentum and mass
D) momentum and velocity

Answers

Given :

A 12 kg coyote runs towards a rabbit in the Ortega Mountains  with a velocity of 8 m/s.

To Find :

The momentum of the  coyote.

Solution :

The given in the question is mass of coyote which is 12 kg and velocity which is 8 m/s .

Momentum is given by :

M = mass × velocity

M = 12 × 8 kg m/s

M = 96 kg m/s

Hence, this is the required solution.

The force of gravity between any two ordinary objects on the earth is.......
A) stronger when closer to the earth
B) stronger if the objects are closer to each other C) always downward
D) stronger than the force of gravity from the earth​

Answers

Answer:

c

Explanation: beacuse newtons law of phisics says ''what goes up must come down''

The force of gravity between any two ordinary objects on the earth is stronger if the objects are closer to each other.

The force of gravity between two object on the earth surface is given Newton's law of universal gravitation;

[tex]F= \frac{Gm_1m_2}{r^2}[/tex]

where;

G is gravitational constantm₁ and m₂ are the masses of the two objectsr is the distance between the two objects

The distance between the object is inversely proportional to the force of gravity between the objects. The smaller the distance between the two objects, the greater the force of gravity and vice versa.

Thus, we can conclude that the force of gravity between any two ordinary objects on the earth is stronger if the objects are closer to each other.

Learn more here:https://brainly.com/question/10609143

As the building collapses, the volume of air inside the building decreases, while the mass of the air stays the same. This means that the _____ of the air inside the building will increase.

Answers

Answer:

Density

Explanation:

A person standing a certain distance from four identical loudspeakers is hearing a sound level intensity of 125 dB. What sound level intensity would this person hear if all but one are turned off?

Answers

Answer:

[tex]\mathbf{\beta = 123.75 \ dB}[/tex]

Explanation:

From the question, using the expression:

[tex]125 \ dB = 10 \ log (\dfrac{I}{I_o})[/tex]

where;

[tex]I_o = 10^{-12} \ W/m^2[/tex]

[tex]I = 10^{12.5} \times 10^{-12} \ W/m^2[/tex]

[tex]I = 3.162 \ W/m^2[/tex]

This is a combined intensity of 4 speakers.

Thus, the intensity of 3 speakers = [tex]\dfrac{3.162\times 3}{4}[/tex]

= 2.372 W/m²

Thus;

[tex]\beta = 10 \ log ( \dfrac{2.372}{10^{-12}} ) \ W/m^2[/tex]

[tex]\mathbf{\beta = 123.75 \ dB}[/tex]

what is the potential energy of a 30kg rock that falls 15 meters

Answers

Answer:

4500 J

Explanation:

The potential energy of a body can be found by using the formula

PE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 10 m/s²

From the question we have

PE = 30 × 10 × 15

We have the final answer as

4500 J

Hope this helps you

Justify this statement "Density of the impure water is greater than of pure water.​

Answers

Explaining the concept:

To explain this, we first need to know what density actually is:

Density is the mass of a given substance per unit volume, which means, that is the amount of mass present in unit volume (1 cm³ , 1m³)

Impure water is water, but with impurities added to it

Why is the density of Impure water is greater:

When we compare the mass of equal volumes of Water and Impure water, we will find that the mass of Impure water will be more, that is because the extra mass is of the impurities

Since impure water has impurities uniformly spread in it, we will find more matter in unit volume of Impure water than in Pure water

That is why the density of Impure water is greater

E=6.63E-34J-s*4.6E14 hz

Answers

Que tipo de pregunta es esa menos ósea estas menos

A 80 kg parent and a 20 kg child meet at the center of an ice rink. They place their hands together and push. The parent pushes the child with a force of 25 N, what is the force acting on the parent?

Answers

Answer:

force acting on the parent = 25 N .

Explanation:

According to third law of Newton , there is equal and opposite reaction to every action . Here force by the parent on child is action and the force by child on parent is reaction . The former is given as 25 N so force by child on parent will also be 25 N .

Answer is 25 N .

What is the atomic number for the following Bohr model?
e
P= 8
N= 8
---
a
8
b
2
OOOO
с
6
d
16

Answers

Answer:

8

Explanation:

Atomic number in the Bohr model given is 8.

For every atom, the atomic number is the number of protons in such an atom.

The protons are the positively charged particles found in an atom. They are called the atomic number.

Protons are found in the nucleus of an atom. Together with neutrons, the occupy the tiny nucleus of the atom. By so doing and coupled with their mass, the form the mass of atom. The atomic number is used to identify every atom.

How much power is required to carry a 30 N package a vertical distance of 8 m if the work on the package is accomplished in 15 s?

58 W

630 W

21 W

16 W​

Answers

Answer:

poop bear cookie

Explanation:

name the force that help us to walk​

Answers

friction force helps us to walk.
HOPE OT HELPS!!
have a good day :)

Please help It is Anatomy and Phys

Think about the last time you had your temperature taken. Describe the circumstances that led you to have your temperature taken, including the mechanism by which your temperature was measured (oral thermometer, ear thermometer, etc.), so that given the right equipment, you could demonstrate the technique yourself to another person. What would have been considered an abnormal temperature in that situation?

Answers

Answer:

the last time i had my tempature taken was at disney prings about a week ago -_- they used one of those gun things that dont touch u and the SHOVED me forward so i guess i was fine

Explanation:

Answer:

thermometer

Explanation:

A circuit component that is a composed of a semiconductor layer sandwiched between two other semiconductor layers is a(n)?

Answers

Explanation:

It's a transistor. Hope that helps!

Answer:

D. Transistor

Explanation:

Edge 2021

What causes Ep to be converted to Ek? (giving brainliest to right anwser)

Answers

Answer:

Energy is a quantity that can be verticality from one to another,

sum of all the energy of the system remains constant if there is no friction force.

Explanation:

The potential energy of a system is a configuration energy, that is, for a given position the energy has a value with respect to a reference point.

Kinetic energy is an energy related to the movement of bodies, that is, a body must have a speed to have kinetic energy.

Energy is a quantity that can be verticality from one to another, the gravitational potential that a body has at a given height when the body is released accelerates by action of gravity, in this case the potential energy decreases and the scientific energy increases, It is appropriate to clarify that the sum of all the energy of the system remains constant if there is no friction force.

According to the law of conservation of momentum, in an isolated system:

A. The initial and final velocities remain the same.
B. The total initial momentum is equal to the total final momentum.
C. One of the colliding objects must be at rest.
D. The final momentum is always less than the initial momentum.

Answers

Answer:

Explanation:B

Answer:
B. The total initial momentum is equal to the total final momentum.

The mass and coordinates of three objects are given below: m1 = 6.0 kg at (0.0, 0.0) m, m2 = 1.5 kg at (0.0, 4.1) m, and m3 = 4.0 kg at (1.9, 0.0) m. Determine where we should place a fourth object with a mass m4 = 7.9 kg so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m

Answers

Answer:

The location of the center of gravity of the fourth mass is [tex]\vec r_{4} = (-0.961\,m,-0.779\,m)[/tex].

Explanation:

Vectorially speaking, the center of gravity with respect to origin ([tex]\vec r_{cg}[/tex]), measured in meters, is defined by the following formula:

[tex]\vec r_{cg} = \frac{m_{1}\cdot \vec r_{1}+m_{2}\cdot \vec r_{2}+m_{3}\cdot \vec r_{3}+m_{4}\cdot \vec r_{4}}{m_{1}+m_{2}+m_{3}+m_{4}}[/tex] (1)

Where:

[tex]m_{1}[/tex], [tex]m_{2}[/tex], [tex]m_{3}[/tex], [tex]m_{4}[/tex] - Masses of the objects, measured in kilograms.

[tex]\vec r_{1}[/tex], [tex]\vec r_{2}[/tex], [tex]\vec r_{3}[/tex], [tex]\vec r_{4}[/tex] - Location of the center of mass of each object with respect to origin, measured in meters.

If we know that [tex]\vec r_{cg} = (0,0)\,[m][/tex], [tex]\vec r_{1} = (0,0)\,[m][/tex], [tex]\vec r_{2} = (0, 4.1)\,[m][/tex], [tex]\vec r_{3} = (1.9,0.0)\,[m][/tex], [tex]m_{1} = 6\,kg[/tex], [tex]m_{2} = 1.5\,kg[/tex], [tex]m_{3} = 4\,kg[/tex] and [tex]m_{4} = 7.9\,kg[/tex], then the equation is reduced into this:

[tex](0,0) = \frac{(6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4.0\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4}}{6\,kg+1.5\,kg+4\,kg+7.9\,kg}[/tex]

[tex](6\,kg)\cdot (0,0)\,[m]+(1.5\,kg)\cdot (0,4.1)\,[m]+(4\,kg)\cdot (1.9,0)\,[m]+(7.9\,kg)\cdot \vec r_{4} = (0,0)\,[kg\cdot m][/tex]

[tex](7.9\,kg)\cdot \vec r_{4} = -(6\,kg)\cdot (0,0)\,[m]-(1.5\,kg)\cdot (0,4.1)\,[m]-(4\,kg)\cdot (1.9,0)\,[m][/tex]

[tex]\vec r_{4} = -0.759\cdot (0,0)\,[m]-0.190\cdot (0,4.1)\,[m]-0.506\cdot (1.9,0)\,[m][/tex]

[tex]\vec r_{4} = (0, 0)\,[m] -(0, 0.779)\,[m]-(0.961,0)\,[m][/tex]

[tex]\vec r_{4} = (-0.961\,m,-0.779\,m)[/tex]

The location of the center of gravity of the fourth mass is [tex]\vec r_{4} = (-0.961\,m,-0.779\,m)[/tex].

How does opening a parachute slow the fall rate of a skydiver?

Answers

Answer:

the air is being stopped in the pocket of the parachutes theys why the parachute has a certain shape so that the air that gets caught inside of it as the skydiver goes down slows down the landing

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