If the work done to move a toy car by a force of 20N is 60J how far did the car move?​

Part A: The angular momentum of each particle about the origin

Part B: The total angular momentum of the four-particle system is 0.95 kg.m²/s.

The expression used to calculate angular momentum L is:

                             L = r x mv

Here, r is the position vector of the object m is the mass and v is the velocity vector.

According to the superposition principle, the resultant angular momentum due to many particles is the vector sum of the individual angular momentum.

L = L₁ + L₂ + L₃ + ...

Here, L₁ is the angular momentum of a particle, L₂ is the angular momentum of the particle, and so on.

In the question

Mass of a particle = 5.0 kg

vector r = (2.0i - 3.0j) m

vector v = (3.0i) m/s

Part A (seen in the picture for instruction)

For particle 1

The position vector is 2.0j m

Substitute 0.10 kg from m₁, 2.0j from r, and 2.0i m/s for v₁ in the expression of angular momentum

L = r x mv

L₁ = (2.0jm) x [(0.10 kg)( 2.0i m/s)]

L₁ = -4.0 kg.m²/s

The angular momentum for the first particle is -4.0 kg.m²/s.

For particle 2

Position vector is (2.0i - 2.0j) m

Substitute 0.20 kg from m₂, (2.0i - 2.0j) m from r, and (3.0i - 3.0j)m/s for v₂ in the expression of angular momentum

L₂ = (2.0i - 2.0j) m x [ (0.20 kg) (3.0i - 3.0j) m/s]

L₂ = 0

The angular momentum for the second particle is 0

For particle 3

The position vector is (-3.0i + 1.0j) m.

Substitute 0.30 kg from m₃,  (-3.0i + 1.0j) m from r, and  -5.0j m/s for v₃ in the expression of angular momentum

L₃ = (-3.0i + 1.0j) m x [((-3.0i + 1.0j) m) ( -5.0j m/s)]

L₃ = 1.35 kg.m²/s

The angular momentum for three particles is 1.35 kg.m²/s.

For particle 4

The position vector is 4.01i m.

Substitute 0.40 kg from m₄, 4.0i m from r, and -4.0i m/s for v₄ in the expression of angular momentum

L₄ = (4.0i m) x [(0.40 kg) (-4.0i m/s)

L₄ = 0

The angular momentum for four particles is 0.

Part B

Formula used: L = L₁ + L₂ + L₃ + L₄

The total angular momentum of the four-particle system is calculated as follows:

By superposition principle

L = L₁ + L₂ + L₃ + L₄

L = -4.0 kg.m²/s + 0 + 1.35 kg.m²/s + 0

L = 0.95 kg.m²/s

Hence, the total angular momentum of the four-particle system is 0.95 kg.m²/s.

Your question is incomplete but most probably your full question was:

Suppose the particles in the preceding problem have masses m₁ =0.10 kg, m₂=0.20 kg, m₃ = 0.30 kg, m₄ = 0.40 kg. The velocities of the particel are  v₁= 2.0i m/s,v₂= (3.0i - 3.0j) m/s,  v₃= - 1.5j m/s,  v₄= -4i m/s.

(a) Calculate the angular momentum of each particle about the origin.

(b) What is the total angular momentum of the four-particle system about the origin?

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Example of erosion: Wind carries small pieces of rock away from the side of a mountain.

Erosion is the procedure by which the surface of the Earth gets worn down. Erosion can be created by natural elements such as erosion as wind and glacial ice. But everyone who has ever seen a picture of the Grand Canyon knows that nothing strikes the erosion slow steady movement of the water when it comes to commuting the Earth

Rain, rivers, floods, lakes, and the ocean convey away bits of soil and sand and slowly wash away the deposit. Rainfall produces four types of soil erosion: splash erosion, sheet erosion, rill erosion, and ravine erosion.

So we can conclude that Erosion is a ruinous force that wears away land features.

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The length of nylon rope from which a mountain climber is suspended has a force constant of 1.15 ✕ 104 N/m.

Spring constant is the common name for the force constant. Hooke's law states that F=-kx. k=N/m is used to replace units in the equation where F is force, x is displacement, and k is force constant (spring constant) to determine the SI unit of force constant (spring constant).

The slope (gradient) of the graph equals the force constant. The proportionality constant, or k, is also known as the force constant in physics. A spring that is more rigid will have a higher value for k. The graph is no longer a straight line beyond point A since the gradient has changed and the formula F = Kx is no longer valid.

Maximum speed is at equilibrium where:

F = kx ⇒x =F/k

Now, F x=1/2mv²+1/2kx²

Solving we get,

V=F/√mk=Vmax

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Torque is one of the key ideas to comprehend in order to solve problems with rotational motion. Torque is the tendency of a force to produce or change rotational motion.

Torque is a measure of an engine's capacity to control a load and generate a certain level of power to turn the engine on its axis. which is an important part of an automobile engine's power-generating process. Per foot (ft) of rotation about a single point, the force is expressed in pounds (lb).

The force that can cause an object to revolve around an axis is measured in torque. In linear kinematics, force causes an item to accelerate, and torque causes an object to produces the angular acceleration of an object. A vector quantity is a torque.

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Answer:

False

Explanation:

The centripetal force is the force that points towards the center and is responsible for keeping an object in a curved path. This force is provided by the tension in the string, not the mass of the object.

The piston's position, velocity, and acceleration at t = 1.15 s are :

Position: 3.45 m

Velocity: 3 m/s

Acceleration: 0 m/s^2

To calculate the piston's position, velocity, and acceleration at t = 1.15 s, we need to know the angular position, velocity, and acceleration of the wheel.

The angular position of the wheel at t = 1.15 s is given by

θ = ωt + [tex]A_{0}[/tex]

where ω is the angular frequency, t is the time, and [tex]A_{0}[/tex] is the initial angular position.

Since the angular frequency is given as 12 rad/s and the initial angular position is 0, the angular position of the wheel at t = 1.15 s is

θ = 12 x 1.15 = 13.8 radians

The piston's position is given by

r = Rθ

where R is the radius of the wheel.

Substituting the value of R and θ,

r = 0.25 x 13.8 = 3.45 m

The velocity of the piston is given by

v = r' = Rθ' = Rω

Substituting the values

v = Rω = 0.25 x 12 = 3 m/s

Acceleration of the piston is given by

a = v' = Rθ'' = Rω' = R(ω^2)θ

As the angular frequency is constant, the angular acceleration is 0 so the linear acceleration is also 0.

Note: Linear acceleration is not equal to the derivative of linear velocity, it is equal to the derivative of velocity with respect to time, which is zero in this case.

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Answer:

1) -5 N, Left

2) 14 N, Up

3) 13, Right

4) 10, Right

5) 22, Down

6) 9, Left

Explanation:

IF: Left or Down, then Negative

1) 15+15=30

Left= 30

Right= 25

30-25=5

30>25

2) 60+10=70

Down= 70

84-70= 14

70<84

3) Left= 62

75-62= 13

Answer:

27s

Explanation:

Time = distance/speed

Time = 219/8

Time = 27.375 s

The frequency of Sound A is 440.3 Hz.

The resultant frequency of the sound A and sound B is calculated as follows;

Mathematically, the relationship between period and frequency of a wave is given as;

F = 1 / T

where;

The resultant frequency from the given graph is calculated as;

The period of the sound in the image = 0.3 s

F = 1 / T

F = 1 / 0.3 s

F = 3.3 Hz

If sound B = 437 Hz, the frequency of sound A which is greater is calculated as;

F ( A ) = 437 Hz  +  3.3 Hz

F ( A ) = 440.3 Hz

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The E = -kλo/xo is the magnitude of the electric field at the origin, negative sign the direction is towards the origin.

What is electric field ?

The force per unit charge imposed on a positive test charge that is at rest at a given position is mathematically defined as the electric field, which is a vector field that can be associated with any point in space.

What is magnitude ?

According to the physics definition, magnitude is just "distance or quantity." It demonstrates how an object moves as it is moving, including whether the movement is absolute, relative, or of a particular size. It serves as a means of describing the size or scope of something. Physicists use the word "magnitude" to indicate size or distance.

a)Lets take an element dx at x distance from origin

Field due to that element of origin; E = k*((λo)dx)/x2 (E = kq/r2)

Integrating from xo to ∞

E =integral( kλo/x2 dx )(xo to ∞)

E = -kλo/xo

b)As we have negative sign the direction is towards the origin

Therefore, E = -kλo/xo is the magnitude of the electric field at the origin, negative sign the direction is towards the origin.

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The greater the mass of an object, the more particles there are in the sample and the more thermal energy it possesses at the same temperature. Assume you have some boiling hot water at 100 degrees Celsius to demonstrate this concept.

Thermal energy is shown by boiling water on a stove. Thermal energy is created when the atoms and molecules of a material vibrate faster as the temperature rises.

Mass is best defined as the quantity of matter contained in any item or body. Everything in our environment has mass. For example, a table, a chair, your bed, a football, a glass, and even air has mass. That being said, all objects are light or heavy because of their mass.

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The mass of planet is 3.886×10^25 kg. The radius of planet is 1. 2x10^7m.

Complete Resolution. If the acceleration caused by gravity on the surface of the earth is given by the formula g, then the acceleration caused by gravity on a planet with a mass half that of the earth and a radius equal to that of the earth is given by the formula g/2. Where G = 6.67 ×10^-11 N m2/kg2 (Newton's gravitational constant).

As a result, acceleration due to gravity (a) depends on the gravitational constant (G), the mass of the Earth (M), and the radius of the Earth (R), but not on the mass of the body (m).

Given:

Radius of planet (r) =  1. 2x10^7m

Acceleration due to gravity (g) = 18 m/s^2

The acceleration due to gravity at the surface of the planet is,

[tex]g=G\frac{M}{r^2}[/tex]

Where, G = Universal gravitational constant

[tex]G= 6.67*10^-11N.m^2/kg^2[/tex]

[tex]M=\frac{g*r^2}{G}[/tex]

[tex]M=\frac{18*(1.2*10^7)^2}{6.67*10^-11}[/tex]

M =3.886×10^25 kg

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Sometimes in phase and sometimes out of phase.The voltage across the resistor and generator will depend on the phase difference between the current and voltage in the circuit.

The voltage across the resistor and generator will depend on the phase difference between the current and voltage in the circuit. If the phase difference is 0°, then the voltage across the resistor and generator will be in phase. If the phase difference is 180°, then the voltage across the resistor and generator will be out of phase. In any other scenario, the voltage across the resistor and generator will be somewhere in between in phase and out of phase.

Sometimes in phase and sometimes out of phase.

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Resistance and impedance (in AC circuits) are one such pair of synonyms (DC circuits). Technically speaking, they both stand in the way of current flow, but factor ability of impedance also takes resistance into account.

Obviously all, reactance and inductance are also included in this (capacitors).

Impedance, which results from the interaction of reactance and ohmic resistance, is the active resistance to AC of an electric circuit or component. We also describe it as any restriction of an electric current's ability to move energy when voltage is applied.

The more precise meaning is the overall resistance a circuit of electricity provides to an AC current flowing at a single frequency. In conclusion, we measure reactance and resistance in ohms, and we denote this measurement with the sign Z.

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14 a, 14 b, 14 c, and 14 d are the Expressions that require renaming mixed numbers before we can subtract.

Actually, there are a few steps to convert normal fractions into a mixed fractions. The steps are as follows:

Solving one by one with the help of the given options:

1) 14a

[tex]5\frac{2}{5}-2\frac{1}{4} \\\\\frac{17}{5} -\frac{9}{4} \\\\\frac{68-45}{20}\\\\ \frac{23}{20} =1\frac{3}{20}[/tex]

2)14b

[tex]5-2\frac{7}{8} \\\\\frac{5}{1} -\frac{7}{8} \\\\\\\frac{40-23}{8}\\\\ \frac{17}{8} =2\frac{1}{8}[/tex]

3)14c

[tex]7\frac{2}{3} -6\frac{1}{8} \\\\\frac{23}{3} -\frac{49}{8} \\\\\frac{184-147}{8} \\\\\frac{37}{24} =1\frac{13}{24}[/tex]

4)14d

[tex]9\frac{1}{6} -5\frac{2}{3}\\\\ \frac{55}{6}-\frac{17}{3}\\\\ \frac{165-102}{18} \\\\\frac{63}{18}=3\frac{9}{18}[/tex]

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A baseball player throws a ball which has a certain change in momentum. The magnitude of the net force on the ball is 72.22 N.

Given that,

Change in momentum Δp = 6.5 kg m/s

Time t = 90 ms = 90 × 10⁻³ s

Change in momentum can be written as,

Δp = m Δv = F×t

As we need net force on the ball,

Δp = F×t

Making F as subject and putting the values we have,

F = Δp/t = 6.5/(90 × 10⁻³) = 72.22 N

Thus, the required net force on the ball is calculated to be 72.22 N.

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The interval by which the factor by which the office noise is related to the standard threshold of hearing is (100,000, 10,000,000].

The factor by which the office noise is related to the standard threshold of hearing is given by x = 10^(d/10), where d is the sound intensity in decibels. Since the decibel reading was consistently above 50 but never above 70, we can calculate the range of x using the following:

50 < d <= 70

10^(50/10) < x <= 10^(70/10)

To find the range of x, we need to calculate the 10^(50/10) and 10^(70/10)

10^(50/10) = 10^5 = 100000

10^(70/10) = 10^7 = 10000000

Therefore, the range of x, the factor by which the office noise is related to the standard threshold of hearing is (100,000, 10,000,000].

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Your question is incomplete but most probably the complete question is:

Sound intensity, in decibels, d, can be written using a comparison factor, x, that compares sound intensity to the standard threshold of hearing. d = 10log(x) A sensor measures the sound intensity, in decibels, of an office over time. The decibel reading was consistently above 50, but never above 70. On what interval is the factor by which the office noise is related to the standard threshold of hearing? (17, 18.5) (17, 18.5] (100,000, 10,000,000] (100,000, 10,000,000)

At his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.

What is velocity?

Velocity is a vector quantity that describes the rate of change of an object's position. It is a measure of how fast an object is moving and in what direction. Velocity is measured in units of meters per second (m/s) or miles per hour (mph) and is often represented by the symbol "v".

We can use the equations of motion to calculate the time for the sprinter to complete the race.

First, we can use the equation:

v = u + at

to find the final velocity of the sprinter after accelerating for 20.0 m. Here, u is the initial velocity (which is 0 m/s since the sprinter is at rest at the start of the race), a is the acceleration of 3.20 m/s^2, and t is the time it takes for the sprinter to accelerate for 20.0 m.

v = 0 + (3.20 m/s^2)(t)

We know that the sprinter accelerates for 20.0 m, so we can use the equation:

s = ut + 1/2at^2

to find the time t:

20.0 m = (0 m/s)(t) + 1/2(3.20 m/s^2)(t^2)

t^2 = (20.0 m) * 2 / (3.20 m/s^2) = 12.5

t = sqrt(12.5) = 3.53 s

So the time it takes for the sprinter to accelerate for 20.0 m is 3.53 s.

Next, we can use the equation:

v = d/t

to find the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity. Here, d is the remaining distance of 80.0 m and v is the final velocity found before.

t = d/v = 80.0 m / (3.20 m/s) = 25.0 s

So the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity is 25.0 s

So the total time for the race is the sum of the time it takes to accelerate and the time it takes to cover the remaining distance at a constant velocity:

t = 3.53 s + 25.0 s = 28.53 s

Hence, at his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.

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With a net electric flux of -3. 63 1016 N/m2/C at its surface, the planet Mars has an electric field that is somewhat similar to that of the earth. There will be 3.26 x [tex]10^{5}[/tex]  of electric charge throughout the entire earth.

The electric flux across any closed surface is proportional to the net electric charge q enclosed by the surface, according to Gauss's law of electricity, which reads as = q/0, where 0 is the electric permittivity of free space, which has a value of 8.854 10-12 square coulombs per newton per square meter.

E is the magnitude of the electric field (with units of V/m), S is the area of the surface, and is the angle between the electric field lines and the normal (perpendicular) to S. If the electric field is uniform, the electric flux (E) travelling through a surface of vector area S is: E = ES = EScos.

Ф = q/ε

⇒ 3.69 x [tex]10^{16}[/tex] x = q/ 8.85 x [tex]10^{-12}[/tex]

q = 3.26 x [tex]10^{5}[/tex]

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Make sure that software and hardware developed by various manufacturers can cooperate.

A vendor is generally anybody who buys and sells goods or services. A vendor purchases products and services to resale them to different companies or individuals. Several different vendors provide the goods that big box stores like Target buy at deep discounts and then resale at higher retail rates.

The five major types of vendors are manufacturers, wholesalers, merchants, services and maintenance providers, independent vendors, and trade show representatives. Suppliers are sometimes referred to as the first link in a supply chain because they exclusively conduct business with other businesses. Contrarily, a vendor is a business or person that purchases things from a company and then sells them to another party.

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The rocket's velocity that goes 700 km north in 25 seconds, then travels another 700km south in 25 seconds is 28,000 m/s.

Given,

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(a)The center of mass of the system has no acceleration, and remains at the same position as it was earlier.

(b)The particle P, collide at a distance 1.23m from P's original position.

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The new velocity of the object after the event is 7.99m/s.

We are given that,

Mass = m = 50kg

Initial velocity = v = 11.2m/s

Energy = E = 1539j

The kinetic energy of object can be calculated as,

K= (1/2)mv²

K = (50×125.44)/2

K = 3136J

Consequently, since both the initial kinetic energy and the total amount of energy transferred are known. The article's resulting energy is easily discernible.

Final energy = initial kinetic energy - the ending energy

Final energy  = 3136-1539= 1597 joules

Therefore, using the equation for kinetic energy derivation, the speed of the object can now be determined.

K.E = 1/2MV²

1597 = 50/2V²

3194 = 50V²

V = 7.99m/s

Therefore , the new velocity of the object after the event would be 7.99m/s.

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The balloon's helium has a mass of 2.52 KG.

The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.

The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density.

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Answer:

The net force is now 12

Explanation:

The boy is applying a force of 5 newtons + his mother is helping him to apply 7 newtons = 12 newtons.

The elasticity of the balloon's material keeps the 1particles from forcing it to expand. The material stretches as the gas particles bump against the sides, allowing the balloon to expand to a certain point before contracting again.

The elasticity of the balloon's material is an important factor in determining the balloon's shape and size. In general, the more elastic the material is, the more the balloon will be able to stretch and expand. When the material is not elastic enough, it will not be able to stretch and the balloon will remain in its original shape.

The elasticity of the material also affects the amount of air pressure within the balloon. A more elastic material will be able to hold more air pressure, while a less elastic material will not be able to hold as much pressure. This is why balloons with a higher pressure will usually be larger than balloons with a lower pressure.

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Where r is the radius, v is the tangential speed, and is the angular speed The tangential speed is 2.1 m/s as a result.

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If the cone of force is facing an observer, the impact comes from the opposite side of the observer.

Newton's third law of motion states that action and reaction force are equal and opposite. That is for every action, there is an equal and opposite reaction.

Mathematically, the formula for Newton's third law of motion is given as;

Fa = - Fb

where;

Thus, when a force is applied from a side, the observed force or reaction will be directed in opposite direction. The force exerted and the reaction force are both equal in magnitude but occurs in opposite direction.

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Answer:

The potential energy can be increased by increasing the mass of the object, by varying the distance between the two objects, decreasing the kinetic energy of the molecules, by freezing, by compressing or stretching, and so on.

Explanation:

Hope this helped !