The Sierra Madre Oriental is located at number _____ on the map above; this is easy to remember because “oriental” is the Spanish word for “__________.”

Answer:

Q1)  -15 cm/s  and Q2)  2.143 kg

Explanation:

Q1)  mass of the first ball: M1 = 200 g

      initial velocity of the first ball: U1 = 30 cm/s

      mass of the second ball: M2 = 400 g

      initial velocity of the second ball: U2 = X cm/s

      final velocity of the first ball: V1 = 0 cm/s

      final velocity of the second ball: V2 = 0 cm/s

By using the law of conservation of momentum that states:

initial momentum = final momentum

(M1 x U1) + (M2 x U2) = (M1 x V1) + (M2 x V2)

however as after collision both the bass stick together their masses combine and the move together in the same direction with the same speed.

therefore;

(M1 x U1) + (M2 x U2) = (M1 + M2)(V)

(200 x 30) + (400 x X) = (400 + 200) (0)

6000 + 400X = 800 x 0

6000 + 400X = 0

X = -6000/400

X = -15 cm/s

( the minus sign indicates the opposite direction i.e. left)

Q2) M1 = 5 kg

M2 = X kg

U1 = 10m/s

U2 = -10 m/s ( as its the opposite direction)

V1 = 4 m/s

V2 = 4m/s

using the law of conservation of momentum:

(M1 x U1) + (M2 x U2) = (M1 x V1) + (M2 x V2)

( 5 x 10) + ( X x (-10)) = (5 x 4) + (X x 4)

50 - 10X = 20 + 4X

50 - 20 = 4X + 10X

30 = 14X

30/14 = X

2.143 kg = X

(a) The scalar x- and y-components of the displacement 300cm at 127⁰ are 259.9cm and 150.8cm respectively.
(b) The scalar x- and y-components of the displacement 500cm at 220⁰ are -400cm and -309.3cm respectively.

Displacement is a physical concept referring to the distance an object moves in a certain direction. It is a vector quantity, meaning it has both magnitude and direction. Displacement is not the same as distance, as distance is the total length traveled, while displacement is the change in position. Displacement can be measured in any unit of length, such as meters, feet, or kilometers.

(a) The scalar x-component of the displacement is 257.7 cm and the scalar y-component of the displacement is 213.3 cm.

(b) The scalar x-component of the displacement is -403.3 cm and the scalar y-component of the displacement is -281.3 cm.

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The scalar x- and y-components of the following displacements in the xy plane (a)300cm at 127⁰ is  -202.46 cm and -236.98 cm respectively, (b) 500cm at 220⁰​ is -417.51 cm and -132.96 cm respectively.

It is the difference between the initial and final position of an object and is usually measured in meters or other units of length. It can be calculated by subtracting the initial position vector from the final position vector. In physics, displacement is often used to describe the motion of an object in one dimension, such as along a straight line.

To find the scalar x- and y-components of a displacement in the xy plane, we can use trigonometry. The x-component of the displacement is given by:

x = r * cos(θ)

where r is the magnitude of the displacement and θ is the angle the displacement makes with the x-axis (measured in radians). The y-component of the displacement is given by:

y = r * sin(θ)

where r is the magnitude of the displacement and θ is the angle the displacement makes with the y-axis (measured in radians).

(a) For a displacement of 300 cm at an angle of 127°:

x = r * cos(θ) = 300 cm * cos(127°) = -202.46 cm

y = r * sin(θ) = 300 cm * sin(127°) = -236.98 cm

(b) For a displacement of 500 cm at an angle of 220°:

x = r * cos(θ) = 500 cm * cos(220°) = -417.51 cm

y = r * sin(θ) = 500 cm * sin(220°) = -132.96 cm

Note that in the above examples, the angles are converted from degrees to radians before using them in the trigonometric functions.

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The object is pulled by the gravitate attraction, which causes it to curve away from a straight line of motion and nearly towards to the center of earth 2.0 х 10-7 n.a.

8. The Force of Gravity What gravitational force exists between two parcels weighing 15 kg and spaced 35 cm apart? What percentage of the volume of one package does this make up? The gravitational pull is 8.210 10 and 0.82 components per million of the mass since the weight is milligrams 147 N.

The Earth has a stronger gravitational force than the moon, thus to start answering your question merely because Earth is a larger planet. The rising and lowering of the tides is a result of the moon's gravity, which also has an impact on Earth. But the story doesn't end there.

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The speed of the aircraft would decrease as force is exerted on it.

We know that according to the Newton second law, the rate of change of the momentum of the body is directly proportional to the impressed force.

Given that there was a burst of gunfire from their jet fighter, the speed of their aircraft decrease from 265 to 250 km per h, we can see that there was a decrease in the velocity because of the force that has been exerted on the jet by the fire of the bullet.

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Change in the momentum of the object with mass 4.9 kg on which force of 6.36 N acts for 20.4 s is 31.164kgm/s and change in velocity is 6.36m/s

As we know Force acting on any object is

F = m.a...........(1)

where m ⇒ mass

and a ⇒ acceleration

Also [tex]a=\frac{v}{t}[/tex]..........(2)

where v ⇒ velocity

t ⇒ time

so equation (1) can be written as:

[tex]F=\frac{m.v}{t}[/tex]..........(3)

Change in Momentum is equal to

p=m.v.......(4)

where m ⇒ mass

v ⇒ velocity

Now as per the question:

Force, F = 6.36 N

Mass, m = 4.9 kg

Time, t = 20.4s

putting the values in equation (3),

we get [tex]6.36=\frac{4.9*v}{20.4}[/tex]

by solving this we get a value of v=6.36m/s

putting the values in equation (4)

we get, Change in momentum

[tex]p=4.9*6.36\\p=31.164kg m/s[/tex]

so the change in velocity is 6.36m/s and change in momentum is 31.164kgm/s

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The change in kinetic energy = 212.50 J - 197.458 J = 15.042 J.

Kinetic energy is the energy possessed by an object due to its motion. It is the energy that an object has because of its motion. Kinetic energy is the energy of motion and is equal to one half of the mass of the object times the square of its velocity. Kinetic energy can be converted into other forms of energy, such as electrical, thermal, or chemical energy.

The kinetic energy of the two fish before the collision can be calculated by using the equation K = 1/2mv^2. For the first fish, K = 1/2 (0.650 kg)(15.0 m/s)^2 = 113.125 J. For the second fish, K = 1/2 (0.950 kg)(13.5 m/s)^2 = 99.375 J.

The total kinetic energy of the two fish before the collision is 212.50 J.

To calculate the change in kinetic energy, we first need to calculate the velocity of the two fish after the collision. To do this, we can use the equation for the conservation of momentum for an inelastic collision, p = m1v1 + m2v2. We know the masses and initial velocities, so solving for the final velocities, we get:

For the first fish, v1 = (0.950 kg)(13.5 m/s) + (0.650 kg)(15.0 m/s) / (0.650 kg + 0.950 kg) = 14.3 m/s.

For the second fish, v2 = (0.650 kg)(15.0 m/s) + (0.950 kg)(13.5 m/s) / (0.650 kg + 0.950 kg) = 13.2 m/s.

Now that we have the final velocities of the two fish, we can calculate the change in kinetic energy by plugging the final velocities into the equation K = 1/2mv^2.
For the first fish, K = 1/2 (0.650 kg)(14.3 m/s)^2 = 105.938 J.
For the second fish, K = 1/2 (0.950 kg)(13.2 m/s)^2 = 91.520 J.

The total kinetic energy of the two fish after the collision is 197.458 J.

Therefore, the change in kinetic energy = 212.50 J - 197.458 J = 15.042 J.

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The value of acceleration due to gravity on that planet is -2.2/t m/s.

The net acceleration that objects get as a result of the combined action of gravity and centrifugal force is known as the Earth's gravity, or g. It is a vector quantity whose direction is determined by the strength of a plumb bob.

The net acceleration that objects get as a result of the combined action of gravity and centrifugal force is known as the Earth's gravity, or g. It is a vector quantity whose direction is determined by the strength of a plumb bob.

using the equation of motion,

v - v0 = a. t

we know that the velocity at the height where it stops is zero, and time needed to get there is half the time of the whole movement, t' = t/2

⇒ - v0 = a. t/2

⇒ a = -v0.2/t

putting values in the above equation,

⇒ a = - 11 m/s . 2/t

⇒a =  -2.2/t m/s

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The fact that the charge rises as the number of capacitors is increased is proof. Option B is right, so.

Can the addition of the capacitors in series or parallel be determined using evidence from the data?

A student didn't show up for a lab looking at how numerous capacitors behave in circuits. Students in the class supplied the student the information above, which illustrates the effect of adding more identical capacitors to a circuit on its equivalent capacitance, but they did not specify if the capacitors were increased.

Can it be determined whether the capacitors was added in parallel or series using evidence from the data?

A. As capacitors are added, the charge changes.

B. With each subsequent capacitor, the charge doubles.

C. As capacitors are added, the charge grows.

D. There is no evidence in the data to support how the capacitor were added.

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Answer:

300 km

Explanation:

Vi 10m/s

Vf = 40m/s

a= 2.5 m/s^2

Vf^2 - Vi^2 = 2as

S = (40^2 -10^2)/(2*2.5) = 300 Km

The wave speed will increase by a factor of the square root of 2, or approximately 1.41.

A quantity of any characteristic value per unit of length is defined as having a linear density. Two frequently used examples in science and engineering are linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit length).

The speed of a wave on a stretched string is directly proportional to the square root of the tension divided by the linear mass density of the string.

Therefore, if the string is replaced by another with half the linear mass density, the wave speed will increase by a factor of the square root of 2, or approximately 1.41.

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The factor of which the speed of a wave on the string change is square root of the tension divided by the mass per length, the linear density.

v = μT, where T is the string's tension and μ is the mass of the string per unit length.

The linear density of the rope a wave travels through determines its speed. The speed rises as the linear density decreases. The relationship states that the square root of linear density and speed are inversely related. Thus, a doubling or tripling of speed results from a quartering of the linear density.

Wavelength x Frequency = Speed.

Wave speed and wavelength are related by the wave speed equation (Speed = Wavelength x Frequency). The quantity of waves that move in a wave's frequency is measured in waves per second.

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We know that the work-energy theorem states that the change in energy (in this case, kinetic energy) is equal to the work done on a system.

what is energy ?

Energy is the capacity to do work. It exists in many forms, such as kinetic, potential, thermal, electrical, chemical, nuclear, and mechanical energy. Kinetic energy is energy that is in motion, such as a moving car or the wind. Potential energy is energy that is stored, such as the energy stored in a stretched rubber band or a raised weight.

Thermal energy is the energy of moving molecules, such as the energy in hot water or in the air. Electrical energy is energy associated with the movement of electrons. Chemical energy is the energy stored in the bonds of atoms and molecules. Nuclear energy is energy stored in the nucleus of an atom. Mechanical energy is energy associated with the motion and position of an object.

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When the robotic spacecraft Mars is 400 million kilometers away from Earth, we communicate with it via radio waves, which move at the speed of light.

The atmosphere, fortunately, shields life on earth. The surface is also not accessible to infrared and long wavelength radio frequencies. Light, which really is difficult for the air to absorb, close rays, and some magnetic fields make up the electromagnetic waves that we can often view on the ground.

In reality, radio waves go through space incredibly swiftly. Since radio waves are an electromagnetic wave, they travel at the speed as light. Light travels at a speed of slightly less than 300,000 km/s second. A light beam could circle the Earth's equator more than seven times in a sec at that speed.

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Energy-interaction diagrams, also known as energy level diagrams, are graphical representations of the possible energy states of a system and the transitions between them. They are used to describe the behaviour of a system in terms of its energy levels and the interactions that cause transitions between them.

There are two types of interaction diagrams- a sequence diagram and the other is a collaboration diagram.

There are stages of relational interaction in which relationships come together (initiating, experimenting, intensifying, integrating, and bonding) and come apart (differentiating, circumscribing, stagnating, avoiding, and terminating).

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The speed of the rock when it hits the ground vd is greater than the speed of the rock when it is thrown upward vu(vd>vu).

The rock will eventually reach its maximum height above the ground if thrown upward. It will fall back to the ground at the same vertical height at which it was thrown at a speed of 15 m/s. The rock's speed will increase above its initial speed of 15m/s as it continues to fall 100m below its initial vertical position.

Velocity is the rate of change in the position of an object in motion as measured by a specific time standard (e.g., 60 km/h northbound). Velocity is a key concept in kinematics, the branch of classical mechanics that studies body motion.

Velocity is a physical vector quantity that must be defined by both magnitude and direction. Speed is a coherently derived unit whose quantity is measured in the SI (metric system) as meters per second (m/s or ms1). For example, "5 m/s" is a scalar, whereas "5 m/s east" is a vector.

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The tension in the chain for the same angle is 533.37 N.

The speed of each seat is determined by treating the system as a simple harmonic motion.

Apply the law of conservation of mechanical energy as shown below.

kinetic energy of each seat at the bottom = potential energy of each seat at the top

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √ ( 2gh )

where;

The vertical displacement of the seats is calculated from the length of the chain as follows;

h = L cos (24.4)

The speed of each seat is calculated as follows;

v = √ ( 2g L cos (24.4) )

v =  √ ( 2 x 9.8 x 2.54cos (24.4) )

v = 6.73 m/s

The tension in the chain is calculated by applying the formula for centripetal force as follows;

T = mv²/r

where;

T = ( 73.6 x 6.73² ) / ( 6.25 )

T = 533.37 N

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The complete question is below:

An amusement park ride consists of a rotating circular platform 12.5 m in diameter from which 10 kg seats are suspended at the end of 2.54 m massless chains. When the system rotates, the chains make an angle of 24.4° with the vertical. The acceleration of gravity is 9.8 m/s^2..

If a child of mass 63.6 kg sits in a seat, what is the tension in the chain (for the same angle)? Answer in units of N.

β = 1131 db is the total sound intensity level heard on the ground (in terms of db).

Total intensity heard at the pitching mound is,

I=15811×1.0×10⁻⁵ W/m²

I=15811×10⁻⁵ W/m²

I=15811×10⁻⁵ W/m²

Total intensity heard at the pitching mound is,

β= 10log(I/I₀)

β= 101og(15811×10⁻⁵ W/m² / 1.0×10⁻¹²)

β=1131 db

β = 1131 db

The power carried by sound waves per unit area in a direction perpendicular to that region is known as sound intensity or acoustic intensity. The watt per square metre (W/m2) is the SI unit of intensity, which also covers sound intensity.

The power carried by sound waves per unit area in a direction perpendicular to that region is described as sound intensity, also known as acoustic intensity. The watt per square metre (W/m2) is the SI unit of intensity, which includes sound intensity.

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The initial potential gravitational energy will be 0 joules because the height will be zero.

Potential energy is the energy that is stored in any object of reffred to its height of the base of surface of earth. The object or system is unaffected by external factors like air or height. The power of moving particles within a system or an item is referred to as kinetic energy.

Potential energy is often represented by its height from surface. Height-dependent energy is known as gravitational potential energy. Weight determines the potential energy amount (mass times gravity).

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The work done by the machine is 14000 joules if the efficiency of the machine is 70% and the 20,000 Joules work is done on it.

Efficiency of the machine is the ratio of the work done by the machine and the work done on the machine. It is a unitless quantity. In other words, efficiency of a machine is the ratio of output and input of the machine.

Work done on the machine = 20000 J

Efficiency(η%) = 70%

Efficiency(η%) = (Work done by the machine×100)/work done on the machine

70% = (100 × work done)/(work supplied)

70/100 = work done/20000

Work done = (70×20000)/100

Work done = 14000 J

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In the first frame of reference, attached to the ground with its origin at a fence post, the momentum of the truck is given by the product of its mass and velocity.

As the truck is accelerating, its velocity is changing and therefore its momentum is also changing. The rate of change of the truck's momentum in this frame is equal to the force acting on the truck.

In the second frame of reference, attached to the police car that is traveling at a constant velocity, the truck is moving at a relative velocity with respect to the police car.

The momentum of the truck in this frame is still given by the product of its mass and velocity, but now the velocity is relative to the police car. The momentum of the truck will be different in this frame of reference.

The rate of change of the truck's momentum is not the same in these two frames. In the first frame, the rate of change of momentum is equal to the force acting on the truck.

However, in the second frame, the truck is moving with a constant velocity relative to the police car, so the rate of change of momentum is zero.

In summary, in the first frame of reference attached to the ground, the truck is accelerating and its momentum is changing, while in the second frame of reference attached to the police car, the truck is moving at a constant velocity relative to the police car, so its momentum is different but the rate of change of momentum is zero.

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According to the question, 1.132887kcal energy used by a 55.0-kg woman who does 50 deep knee bends in which her center of mass is lowered and raised 0.400 m.

People have figured out how to transform energy from one format to the next and then use it to accomplish tasks, making modern civilization possible.

As we know that-

Mass = 55kg

Knee bend = 55

Efficiency = 20%

Displacement = 0.4m

We will first determine the total Workdone.

Work done = 2n(mgh)

n = 55,

m = 55kg,

g = 9.8m/s²

h = 0.4m

Work done = 2 ×55 × 55 × 9.8 × 0.4

Work done = 23,716J

Considering that the lady completes 20% of her work efficiently;

so,

her energy = 20% of 23,716J

= 4,743.2

= 4.74KJ

Energy = 1.132887kcal

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The average force that acted on the car to bring it to rest is  1.2 × 10⁵ Newton.

The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

The average force that acted on the car to bring it to rest is = - Change in momentum of the car/time interval

= (initial momentum - final momentum)/time interval

= (1200 kg × 10 m/s)/0.10 second

= 1.2 × 10⁵ Newton

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Assuming the water is at rest, then the magnitude of the force of the water on the left side of the volume is equal to the magnitude of the force of the water on right side of the volume. Pressure at point c will be greater than that of point b.

According to the pascal's law, the pressure applied on a confined fluid will be transmitted in all the direction, at every point, and on the wall of the container, without any change in the magnitude. Moreover, the pressure applied at a particular depth will be same in all direction. So if we assume that the water is at rest, and the area of left and right walls are equals, then the force will also be equal on both the walls.

If point c is deeper than the point b then the pressure on the point c will be greater than that of point b. As pressure = ρgh, where ρ is the density of  water, h is the depth of a particular point.

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The charge stored in a 1.00-cm-long segment of the wire is 5.6 x 10^6 x 1.00 cm, or 5.6 nC.

Charge is an electrical property of matter that either attracts or repels other objects with an electrical charge. This property is due to the presence of electrons, protons and neutrons, which all have different charges. The force of attraction or repulsion between two objects with a charge is known as the Coulomb force. The charge of an object is measured in Coulombs, which is a unit of electric charge.

The charge (in nC) on a 1.00-cm-long segment of the wire depends on the type of wire and the amount of charge stored in it. If the wire is an insulated copper wire, then the charge stored in it is determined by the number of electrons per unit length of the wire. The charge stored in a 1.00-cm-long segment of wire can be calculated by multiplying the number of electrons per unit length of the wire by the length of the wire itself, which is 1.00 cm. For example, if the wire has 5.6 x 10^6 electrons per centimeter, then the charge stored in a 1.00-cm-long segment of the wire is 5.6 x 10^6 x 1.00 cm, or 5.6 nC.

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The electric field inside the cavity in terms of ρ, ε₀,  r vector, and h vector is ρh/3ε₀.

Every point in space has an electric field connected to it when charge, in any form, is present. The strength and direction of the electric field are expressed by the value of E, which is also known as the electric field strength, electric field intensity, or simply the electric field.

The electric field inside the cavity as a vector in terms of ρ, ε₀,  r vector, and h vector is,

E'' = E -E' = ρ (h-a/4)/3ε₀ - ρa/4/3ε₀

E'' = E -E' =  ρh/3ε₀.

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When a 15.0 g stray bullet traveling at 145 m/s strikes a wall, if it returns in a straight line at a speed of As a result, the as same is 4.93 N.

A line of the article is a literary device that is used to describe an item in some kind of a list. A centered dot (•), which is a common symbol for a bullet point, is just one of many other symbols and characters that can be employed in bulleted lists. Even numbers and/or letters can be used in some bulleted lists.

Calculation

We know that force F = dP/dt where dP/dt = rate of change of momentum and P = momentum = mv

Now, F = dP/dt = dmv/dt = vdm/dt + mdv/dt

Now since we have 5.6 g bullets, m = 5.6 g = 0.0056 kg, dm/dt = rate of change of mass of bullet hitting superman per second = mass of one bullet × rate of change of bullet = 0.0056 kg/bullet × 110 bullets/min = 0.0056 kg/bullet × 110 bullets/min × 1 min/60 s = 0.0103 kg/s, v = speed of bullet = 480 m/s and dv/dt = 0.

So, F = vdm/dt

= 0.01027 kg/s × 480 m/s

= 4.929 kgm/s²

= 4.929 N

≅ 4.93 N

So, the average force is 4.93 N

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According to the law of conservation of energy, the car that apply hard brakes will convert more kinetic energy to thermal energy. Hence option 'a' is correct.

Kinetic energy is any energy that an object gains as a consequence of motion. To accelerate an object, some force must be supplied to it. For apply a force, we must put more effort. After work is completed, energy is transmitted to the object, which then moves at a constant speed.

Running and pacing. When moving air strikes the blades of a windmill, it creates rotation, which ultimately results in the production of energy. When moving water's kinetic energy strikes a turbine at a hydroelectric facility, it is transformed into mechanical energy.

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Kepler's law of equal areas imply that gravity varies inversely with the square of the distance. (false)

Kepler's laws of planetary motion are rules in astronomy and classical physics that describe how the planets move within the solar system. They were mostly developed by the German astronomer Johannes Kepler.

Also whose analysis of the observations of the astronomer Tycho Brαhe from the 16th century allowed him to publish his first two law in 1609 and a third law nearly ten years later, in 1618. Kepler never assigned a number to these laws or made a special distinction between them and his other discoveries.

The conservation of orbital angular momentum L is a direct result of Kepler's law of equal areas.

That law is:

[tex]\dfrac{\mathrm{d}A}{\mathrm{d}t}=\dfrac{1}{2m}L[/tex]

where, dA is the area which is swept out by the radius [tex]\vec{r}[/tex] and is the object's mass m in a time dt.

Since L is conserved, the radius vector's sweep of area A over time t is unaffected by the distance from the central object (the sun).

The gravitational force, which is the primary force and is directed toward the object, causes L to remain constant.

None of these facts imply that gravity varies inversely with distance squared, so the given statement is false.

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Velocity is the rate that an object moves in a certain direction.

According to the dictionary, direction refers to how something moves, how to get somewhere in particular, how something is taking shape, or which way you are facing. Direction can be expressed using relative vocabulary, such as up, down, in, out, left, right, forward, backward, or sideways, which compares the location of one thing to another. Velocity is the directional speed of an item in movement as a measure of the rate that its location is changing as seen from a certain view point and as determined by a specific unit of time.

The entire displacement of the object divided by the total time elapsed gives the object's average velocity.

Velocity and speed both refer to how rapidly and in what direction an object moves. Speed in a certain direction is referred to as velocity in physics. It calculates the distance an object travels in a specific length of time. The definition of velocity is the distance that an object travels in one unit of time.

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( 1) The net gravitational force between the 74.8 kg mass is  8.09 x 10⁻⁵ N.

( 2) The distance from the from the 494 kg mass where the middle mass experiences net zero force is 0.258 m.

The net gravitational force acting on the middle mass is calculated by applying Newton's law of universal gravitation as shown below.

F = ( GmM ) / ( R² )

where;

The force between the first mass and the middle mass is calculated as;

F' = ( 6.672 x 10⁻¹¹ x 141 x 74.8 ) / ( 0.198² )

F' = 1.8 x 10⁻⁵ N

The force between the third mass and the middle mass is calculated as;

F'' = ( 6.672 x 10⁻¹¹ x 494 x 74.8 ) / ( 0.198² )

F'' = 6.29 x 10⁻⁵ N

The net gravitational force on the middle mass;

F (net)  = 6.29 x 10⁻⁵ N + 1.8 x 10⁻⁵ N

F ( net ) = 8.09 x 10⁻⁵ N

Let the distance of zero net force from the 141 kg mass = d.

then the distance from the 494 kg mass = 0.396 m - d

F' = ( 6.672 x 10⁻¹¹ x 141 x 74.8 ) / ( d² )

F' = 0.704 x 10⁻⁶ / d²

F'' = ( 6.672 x 10⁻¹¹ x 494 x 74.8 ) / ( 0.396 - d )²

F'' = 2.47 x 10⁻⁶ / ( 0.396 - d )²

for zero net force, the two forces must be equal

0.704 x 10⁻⁶ / d²  = 2.47 x 10⁻⁶ / ( 0.396 - d )²

0.704 (0.396 - d )² = 2.47d²

(0.396 - d )²  = ( 2.47d² ) / ( 0.704 )

(0.396 - d )²  = 3.51d²

0.396 - d = √ ( 3.51d² )

0.396 - d = 1.87d

1.87d + d = 0.396

d (1.87 + 1) = 0.396

d (2.87) = 0.396

d = 0.396 / 2.87

d = 0.138 m

The distance from the 494 kg mass = 0.396 - 0.138 m = 0.258 m

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