A force F = (2xî + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x-direction from the origin to x = 4.99 m. Find the work W = ∫ F · dr done by the force on the object (in J).

Answers

Answer 1

Answer:

Work done, W = 24.9001 J

Explanation:

Given that,

Force, F = (2xî + 4yĵ) Where x and y are in meters

This force acts on an object as the object moves in the x-direction from the origin to x = 4.99 m.

We need to find the work done by the force on the object. It is given by :

[tex]W=\int\limits^a_b {F dr} \\\\W=\int\limits^{4.99}_0 {(2xi+4yj)dx} \\\\W=\int\limits^{4.99}_0 {2xi\ dx} \\\\W=x^2|_0^{4.99}\\\\\text{Applying limits}\\\\W=(4.99)^2-0^2\\\\W=24.9001\ J[/tex]

So, the work done is 24.9001 J.


Related Questions

Romeo is a 68 kg astronaut. Juliet is a beautiful cosmonaut who is standing on the balcony of a 4.58 x 10^5kg space station that is at rest and out of gas. Romeo is floating 25 meters away from the space station’s center of mass, how strong is the force between Romeo and Juliet?

Answers

Answer:

F =  3.32 x 10⁻⁶ N

Explanation:

The force of attraction between two masses is given by Newton's Law of Gravitation, as follows:

F = Gm₁m₂/r²

where,

F = Force between Romeo and Juliet = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of Romeo = 68 kg

m₂ = mass of space station = 4.58 x 10⁵ kg

r = distance = 25 m

Therefore,

F = (6.67 x 10⁻¹¹ N.m²/kg²)(68 kg)(4.58 x 10⁵ kg)/(25 m)²

F =  3.32 x 10⁻⁶ N

Two identical conducting spheres each have a charge of 2 C. They have a radius of 0.1 m and are separated by 0.5 meters. If you were to increase the radius of these spheres to 0.2 meters, the electrostatic force between them would

Answers

Answer:

The electrostatic force will remain the same

Explanation:

From the question we are told that  

     The charge on the each conducting sphere is [tex]q = 2 \ C[/tex]

      The radius each sphere is [tex]r_1 = r_2 = r = 0. 1\ m[/tex]

     

Generally electrostatic force between the sphere is mathematically represented as

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

Here  k is the coulomb constant ,

         d  is the distance between the two sphere which is measured from one center of the sphere to the other center of the sphere  

Now from the question we are told that the radius of the spheres is doubled (i.e  from 0.10 m  to 0.2 m ) , this will not affect the distance between the sphere because their center are still in the same position

and given there is no change in the distance between the spheres , the electrostatic force will remain the same

ke...
11. Table salt, NaCl, is a classic binary ionic compound. (4 points)
a. What is the oxidation number of Na? Of Cl?
ave...

Answers

Answer:

+1

-1

Explanation:

The oxidation number of Na in NaCl is +1 and that of Cl is -1.

For simple ions, the oxidation number is the charge they carry.

When NaCl is oxidized we have;

        NaCl →  Na⁺  + Cl⁻

In this process, Na will lose an electron to become Na⁺ and thus isoelectronic with Ne, Cl will gain the electrons to become Cl⁻ and thus isoelectronic with Argon.

A car Excel accelerates from rest to a velocity of 5 m/s in 4 seconds. What is its average acceleration over this period of time

Answers

Answer:

1.25

Explanation:

acceleration = velocity÷time

Answer:

Its acceleration is 1.25 meters/second2

Explanation:

The car's average acceleration would be 1.25m/s^2 or 1.25meters/second/second. That looks to be the fourth one you've listed.

a ball of mass 0.5 kg is at point with initial speed 4 m/s at height 10. what is the total energy​

Answers

Answer:

The total energy is 53 Joule

Explanation:

Mechanical Energy

The mechanical energy of an object of mass m, speed v, and at a height h is:

[tex]\displaystyle E = m.g.h+\frac{mv^2}{2}[/tex]

The ball has a mass of m=0.5 Kg, a speed v = 4 m/s, and at a height of h=10 m. Thus the total energy is:

[tex]\displaystyle E = 0.5\cdot 9.8\cdot 10+\frac{0.5\cdot 4^2}{2}[/tex]

E = 49 J + 4 J = 53 J

The total energy is 53 Joule

A 3.0 kg object moving 8.0 m/s in the positive x-direction has a one-dimensional elastic collision with an object of mass, M, initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M

Answers

Answer:

1kg

Explanation:

According to law of conservation of momentum

m1u1+ m2u2 = (m1+m2)v

m1 and m2 are the masses of the object

u1 and u2 are their initial velocities

v is their common velocity

Given

m1 = 3kg

m2 = M

u1 = 8m/s

u2 = 0m/s (object at rest)

v = 6.0m/s

Substitute and get M

3(8) + M(0) = (3+M)6

24 = 18+6M

24-18 = 6M

6 = 6M

M = 1kg

Hence the mass M is 1kg

Please help! ASAP. I'm going to have a panic attack.

Answers

Answer:

dont die bro

Explanation:

When were Earth’s landmasses first recognizable as the continents we know today? 10 million years ago 135 million years ago 180 million years ago 300 million years ago

Answers

Answer:

b

Explanation:

i took the test

Earth’s landmasses were first recognized as the continents we know today

135 million years ago.

Landmass is defines as a large area of land. It can also be referred to as the

continents we have today. There are seven types of earth landmasses and

they are

Asia, Africa, North America, South America, Antarctica, Europe, and Australia.

They were first discovered around 135 million years ago by the early

dwellers of the earth.

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A concave mirror produces a real image 1cm tall of an object 2.5mm tall placed 5cm from the mirror. Find the position of the image and the focal length of the mirror.​

Answers

Answer:

the focal length is 4cm

Explanation:

use the formula 1+1/m = f

it is obtained from the mirror formula

m is the magnification and is the ratio of the image height to the object height

however they should have the same unit . that means you would have to do a little conversion from cm to mm or vice versa .

Our school needs to offer healthier options in the lunchroom. Elever High School has recently updated its cafeteria menu to include whole wheat pasta and breads, a fresh salad bar, and other healthy menu items. Students there claim that they have more energy and focus throughout their school day. Let's encourage healthier menus in our lunchroom!

What type of evidence does the writer of this passage use to support her claim?


statistics
statistics

an expert's opinion
an expert's opinion

examples
examples

the writer's opinion

Answers

Answer:

b

Explanation:

A ball has a diameter of 3.77 cm and average density of 0.0839 g/cm3. What force is required to hold it completely submerged under water?

magnitude _________ N

Answers

The force required to hold it completely submerged under water is 0.252 N

As a result of the low density (ρ1 = 0.0839 g/cm3 = 83.9 kg/m3)of the ball compared to that of water (ρ2 =1000 kg/m3), the buoyant force that is acting on the ball is greater than its weight.

Therefore, the minimum force required to hold the ball submerged under water can be calculated using the relation

F = Buoyant force - weight of sphere

 

Radius = 3.77/2 cm = 0.0377/2 m = 0.01885 m

Volume of sphere = 4/3 π r³ = 4/3 * 3.142 * 0.01885³ = 2.805 e-5 m³

Mass of sphere = 4/3 π r³ ρ1 = 4/3 * 3.142 * 0.01885³ * 83.9 = 0.0023 kg

Weight of sphere = 4/3 π r³ ρ1 g = 4/3 * 3.142 * 0.01885³ * 83.9 * 9.8 = 0.023 N

 

Volume of water displaced = 4/3 π r³ = 2.805 e-5

Buoyant force = weight of water displaced = 4/3 π r³ ρ2 g = 4/3 π r³ = 4/3 * 3.142 * 0.01885³ * 1000 * 9.8 = 0.275 N

F = 0.275 - 0.023 = 0.252 N

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The force required to hold it completely submerged under water is 0.25 N

The density of the ball ([tex]\rho_b[/tex]) = 0.0839 g/cm³ = 83.9 kg/m³

The density of water [tex]\rho_w[/tex] = 1000 kg/m³

Diameter = 3.77 cm = 0.0377 m

radius of ball = 0.0377/2 = 0.01885 m

The volume (V) = [tex]\frac{4}{3} \pi r^3=\frac{4}{3}*\pi*0.01885^3=2.8*10^{-5}\ m^3[/tex]

Let us assume the acceleration due to gravity (g) = 9.8 m/s², Hence:

The force is required to hold it completely submerged under water (F) is:

[tex]F=\rho_w Vg-\rho_b Vg=1000*(2.8*10^{-5})*9.81-83.9*(2.8*10^{-5})*9.81\\\\[/tex]

F = 0.25 N

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A spatially challenged goldfish swims along the x-axis only. Its initial position is 7.8 m. After swimming back and forth a while, it finds itself at the position 4.4 m. Calculate the fish’s displacement (including its sign).

Answers

Answer:

The fish displacement was -3.4 m

Explanation:

Distance and Displacement

A moving object constantly travels some distance at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:

dtotal=d1+d2+d3+...+dn

This sum is obtained independently of the direction the object moves.

The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.

The displacement, when the object moves in one axis only is given by:

d = final position - initial position

We know the fist started at 7.8 m from a given reference along the x-axis.

After some undisclosed movements, it ends up at the position 4.4 m. Thus, the displacement is:

d = 4.4 m - 7.8 m = -3.4 m

This means the fish ended up to the left of the position it started from.

The fish displacement was -3.4 m

A 0.420 kg block of wood rests on a horizontal frictionless surface and is attached to a spring (also horizontal) with a 20.5 N/m force constant that is at its equilibrium length. A 0.0600 kg wad of Play-Doh is thrown horizontally at the block with a speed of 2.80 m/s and sticks to it. Determine the amount by which the Play-Doh-block system compresses the spring.

Answers

Answer:

leon

Explanation:

leom ofjfjbfbfdnns

A horizontal force of 30N is applied to a mass of 10 kg causing it to accelerate. If the coefficient of friction is 0.20 what is the frictional force?
If work is shown that would be great

Answers

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The force of friction is equal to the product of the vertical force applied by the surface to the object in the coefficient of friction.

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In this question ,

surface vertical force = Weight of the object

Thus ;

svf = ( mass ) × ( gravity acceleration )

_________________________________

If gravity acceleration is 10 :

svf = 10 × 10 = 100 N

So ;

frictional force = 100 × 0.20

frictional force = 20 N

##############################

If gravity acceleration is 9.8 :

svf = 10 × 9.8 = 98 N

So ;

frictional force = 98 × 0.20

frictional force = 19.6 N

_________________________________

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If the velocity of Homer the astronaut (mass =200 kg) is 5 m/s and he runs into and grabs his stationary pal Larry (mass = 150 kg), what is the new velocity of the astronauts after the collision?

Answers

We are given:

Homer the Astronaut:

Mass of Homer the astronaut(m1) = 200 kg

initial velocity of Homer the astronaut(u1) = 5 m/s

Larry the Pal:

Mass of Larry the Pal (m2) = 150 kg

initial velocity of Larry the Pal (u2) = 0 m/s

Since they will move together after the collision, they will have the same velocity:

v1 = v2 = V

Solving for the Final velocity:

from the law of conservation of momentum:

m1u1 + m2u2 = m1v1 + m2v2

since v1 = v2 = V:

m1u1 + m2u2 = V(m1 + m2)

replacing the variables with the given values

200 * 5 + 150 * 0 = V(200 + 150)

1000 = 350V

V  = 1000 / 350

V = 2.86 m/s

If a 25 kg lawnmower produces 347 w and does 9514 J of work, for
how much time did the lawnmower run?

Answers

Steps 1 and 2)

The variables are W = work, P = power, and t = time. In this case, W = 9514 joules and P = 347 watts.

The goal is to solve for the unknown time t.

-----------------------

Step 3)

Since we want to solve for the time, and we have known W and P values, we use the equation t = W/P

-----------------------

Step 4)

t = W/P

t = 9514/347

t = 27.4178674351586

t = 27.4 seconds

-----------------------

Step 5)

The lawn mower ran for about 27.4 seconds. I rounded to three sig figs because this was the lower amount of sig figs when comparing 9514 and 347.

-----------------------

Note: we don't use the mass at all

uses of atmospheric pressure​

Answers

Atmospheric pressure is an indicator of weather. When a low-pressure system moves into an area, it usually leads to cloudiness, wind, and precipitation.

A shell traveling with speed, v0 , exactly horizontally and due north explodes into two equal mass fragments. It is observed that just after the explosion one fragment is traveling vertically up with speed v0 . What is the velocity of the other fragment? Hint: Velocity has both magnitude and direction.

Answers

Answer:

yeah

Explanation:

yeah yeah yeah yeah

what is Force and Preasure ??

Answers

Answer:

Definition: Pressure:- Force per unit area surface is called pressure. P = F/ A Pressure = Force /Area Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. 

Answer:

A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force.

Pressure is defined to be the amount of force exerted per area.

Formula of pressure = P = F÷A

Where, P = Pressure,

            F = Force applied and,

            A = Unit area.

Examples of Pressure is Air pressure.

           

HELP ASAP !!! !!!!!!!

Answers

the second option - B

Answer:

they are cooler than the rest if the sun

Two balls collide in a head-on elastic collision and rebound in opposite directions. One ball has velocity 1.2 m/s before the collision, and −2.3 m/s after. The other ball has a mass of 1.1 kg and a velocity of −4.2 m/s before the collision. (a) What is the mass of the first ball? (b) What is the velocity of the second ball after the collision?

Answers

Answer:

If two particles are involved in an elastic collision, the velocity of the second particle after collision can be expressed as: v2f=2⋅m1(m2+m1)v1i+(m2−m1)(m2+m1)v2i v 2 f = 2 ⋅ m 1 ( m 2 + m 1 ) v 1 i + ( m 2 − m 1 ) ( m 2 + m 1 ) v 2 i .

Explanation:

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The diagram shows the four primary steps in the production of work in a four-stroke heat engine.

What is the correct order in which these steps occur?
A. Y, W, X, z
B. X, Z, W. Y
C. W, X, Y, Z
D. Z, X, Y, W

Answers

Answer:

D- Z, X, Y, W

Explanation:

Correct on edge

HELP ASAP !!!!!!!!!!!!!!

Answers

The Big Bang theory supports that belief. If everything exploded from one point, then it is continuing to expand outward now

Answer:

big bang theory

Explanation:

Edwin Hubble is credited for the initial development of the Big Bang theory, an idea which helps to explain the formation of the universe over 15 billion years ago.

what is environment​

Answers

Answer:

Explanation:

all biotic and abiotic factors around a living organism is its environment

Answer: An environment is the surroundings or conditions in which a person, animal, or plant lives or operates. the natural world, as a whole or in a particular geographical area, especially as affected by human activity. The best synonym for environment would be nature.

Explanation: Environment is a place where different things are such as a swampy or hot environment. They constantly interact with it and adapt themselves to conditions in their environment. In the environment there are different interactions between animals, plants, soil, water, and other living and non-living things. Environment plays an important role in healthy living and the existence of life on planet earth. Earth is a home for different living species and we all are dependent on the environment for food, air, water, and other needs. Therefore, it is important for every individual to save and protect our environment. To divide environments' sorts we can mention 3 kinds of environments Natural, industrial, and social environment. Natural environment: Include water, light, land, air and all organisms that live in nature.

What happens to the mechanical advantage of a machine if the output force is less than the input force? What must happen to output distance? Give an example of a machine that does this?

Answers

a machine that put in force is a Mechanical

How does the abundance of hydrogen and helium support the Big Bang Theory?

Answers

It is the proportion predicted to be present in the early universe.

The hydrogen and helium abundance helps us to model the expansion rate of the early universe.

In the abundance of hydrogen and helium, we can say that they account for nearly all the nuclear matter in today's universe.

In big Bang model, the universe is mostly light or protons.

This abundance of hydrogen and helium is consistent with this big bang model. The process of forming this hydrogen and helium is often called big bang nucleosynthesis.

The Schramm's model for relative abundances indicate that helium is about 25% by mass and hydrogen about 73% with all other elements constituting less than 2%.

Several proponents of big Bang theory has proposed similar relative abundance for hydrogen and helium. In all  it is clear that hydrogen and helium constitute of more than 98% of the ordinary matter in the universe.

Finally, the hydrogen and helium abundance helps us to model the expansion rate of the early universe.

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An elevator is pulled up by a cable with a force of 65,000 N. The upward acceleration of the elevator is 1.8 m/s/s. What is the mass of the elevator?
a. 1.8 kg.
b. 1700 kg.
c. 54880 kg.
d. 5600 kg.
e. 36111 kg.

Answers

Answer:

36111 kg

Explanation:

Given

Force = 65000N

Acceleration = 1.8m/s²

Required

Determine the mass of the elevator

This question will be answered using the following Force formula.

Force = Mass * Acceleration

Substitute values for Force and Acceleration

65000N = Mass * 1.8m/s²

Make Mass the subject

Mass = 65000N/1.8m/s²

Mass = 36111.11 kg

From the list of given options, option E answers the question.

What must happen to an atom of magnesium in order to become a magnesium ion Mg+2?

It must lose two neutrons and become a different isotope.
It must gain two neutrons and become a different isotope.
It must lose two electrons and become an ion.
It must gain two electrons and become an ion.

Answers

Answer:

Answer is: c. It must lose two electrons and become an ion.

Magnesium (Mg) is metal from 2. group of Periodic table of elements and has low ionisation energy and electronegativity, which means it easily lose valence electons (two valence electrons).

Magnesium has atomic number 12, which means it has 12 protons and 12 electrons. It lost two electrons to form magnesium cation (Mg²⁺) with stable electron configuration like closest noble gas neon (Ne) with 10 electrons.

Electron configuration of magnesium ion: ₁₂Mg²⁺ 1s² 2s² 2p⁶.

Explanation:

Answer:

the third option

Explanation:

Please help me with this question guys.

Answers

Answer:

The average speed is 22.2 km/h

Explanation:

Average Speed

Given an object travels a total distance d and took a total time t, then the average speed is:

[tex]\displaystyle \bar v=\frac{d}{t}[/tex]

The mailman first drives d1=7 km at v1=15 km/h. The time taken to drive is:

[tex]\displaystyle t1=\frac{d1}{v1}=\frac{7}{15}=0.467\ h[/tex]

Then he drives d2=7 km at v2=43 km/h taking a time of:

[tex]\displaystyle t2=\frac{d2}{v2}=\frac{7}{43}=0.163\ h[/tex]

The total time is

t=0.467 h + 0.163 h = 0.63 h

The total distance is

d = 7 km + 7 km = 14 km

The average speed is:

[tex]\displaystyle \bar v=\frac{14}{0.63}=22.2\ km/h[/tex]

The average speed is 22.2 km/h

A car travels at a speed of 55 km/hr and slows down to 10 km/hr in 20 seconds. What is the acceleration?

Answers

Answer:

a = 0.62 [m/s²]

Explanation:

To solve this problem we must use the following equation of kinematics. But first, we must convert speeds from kilometers per hour to meters per second.

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

[tex]55[\frac{km}{hr}]*\frac{1hr}{3600s}*\frac{1000m}{1km} =15.27[\frac{m}{s} ]\\10[\frac{km}{hr} ]*\frac{1hr}{3600s}*\frac{1000m}{1km} = 2.77[\frac{m}{s} ][/tex]

where:

Vf = final velocity = 2,77 [m/s]

Vo = initial velocity = 15.27 [m/s]

t = time = 20 [s]

a = acceleration [m/s²]

Now replacing:

[tex]2.77=15.27-a*(20)\\20*a=12.49\\a = 0.62[m/s^{2}][/tex]

Answer:

It would be 10.00

Explanation:

Hope this helps its different for everyone what was it for u it was D for me

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