particle a and particle b, each of mass m, move along the x-axis exerting a force on each other. the potential energy of the system of two particles associated with the force is given by the equation u

100 watt light bulb glows brighter than a 50 watt light bulb and  50 watt light bulb is higher resistance than 100 watt bulb.

A circuit's opposition to current flow is measured by its resistance. Resistance is the degree to which a substance obstructs or opposes an electric current. Electron flow is referred to as electric current. To better understand resistance, imagine how difficult it would be for a person to move from one shop to another in a crowded market. Resistors are used in heaters, toasters, microwaves, electric stoves, and a variety of other heating appliances due to their inherent ability to generate heat when conducting current. When electricity is passed through a metal filament in a light bulb, a very high temperature is created from the resistance, which causes the metal filament to glow white-hot. The ohm (), which represents resistance, is denoted by the letter R.

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The velocity of the ball is obtained as  6.26 m/s.

We know that the kinetic energy is the energy that is possessed by a body by virtue of the fact that it is in motion while the potential energy is the energy that is possessed by a body that is at rest.

Now we have that;

Mass of the ball = 350g or 0.35 Kg

Height of the ball =  12m

The energy of the ball at this height is potential energy. The total energy before the ball hits the ground is; 0.35 * 12 * 9.8 m/s^2 = 41.2 J and this energy is kinetic energy.

If the ball is 2m above the ground its potential energy is 2 * 2 * 9.8 m/s^2 = 39.2 m/s and the kinetic energy of the ball is zero m/s.

The velocity with which the ball hits the ground is;

mgh = 1/2mv^2

gh = 1/2v^2

v = √2gh

v = √2 * 9.8 * 2

v = 6.26 m/s

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Copernicus influenced Newton as the Copernican Revolution was brought to a close by Sir Isaac Newton's Philosophiae Naturalis Principia Mathematica.

Copernicus, the father of modern astronomy, was a Polish astronomer and mathematician. He was the first European scientist to propose the heliocentric theory of the solar system, which states that Earth and other planets revolve around the sun.

By developing the heliocentric theory of Earth's relationship to our Sun, Nicolaus Copernicus altered how educated people saw the world. The heliocentric theory, which is now widely accepted, states that Earth and the other planets revolve around the Sun.

His laws of planetary motion and universal gravitation were developed to explain the presumed motion of the heavens by asserting a gravitational force of attraction between two objects.

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0.072 J is the work would the spring take to set the object into an oscillation with amplitude 0.02 m

A periodic variable's amplitude is a gauge of its change over a single period. A non-periodic signal's magnitude in relation to a standard value is its amplitude. There are several ways to define amplitude, and they are all dependent on how much the extreme values of the variable deviate from one another.

The stiffness of the spring is how we determine spring constant. In other words, we can define the spring constant as the force used to produce the specified displacement when the spring's displacement is one unit. It follows that a spring's spring constant will increase with increasing spring stiffness.

Now to calculate the work done by spring we use the Hookes’s law

F=kx

Where F is the force required

K is the spring constant

X is the amplitude or distance

So F=kx

F=180x0.02

F=3.6 N

Now to calculate work :

Work = Force × Distance.

Work=3.6 N x0.02m

Work =0.072 J

Hence, 0.072 J is the work would the spring take to set the object into an oscillation with amplitude 0.02 m

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The buoyant force exerted on the rock is 2 N.

Buoyancy is the upward force exerted by a liquid that opposes the weight of a partially or fully submerged object. In a liquid column, the pressure increases with depth due to the weight of the liquid above. Buoyancy exists whether an object is floating or submerged. The SI unit of buoyancy is Newton. The factors on which buoyancy depends are:

For the given case,

Weight of the rock out of water (W₀) = 5N

Weight of the rock when submerged in water (Wₙ) = 3N

Now what decreases the weight of rock in water? It is the buoyant force exerted by water, which can be can be calculated as:

Fᵇ = W₀ - Wₙ

Fᵇ = 5N - 3N

Fᵇ = 2N

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The minimum energy input necessary to place this satellite in orbit is

[tex]\frac{1}{2} m(v^{2} - v_{e} ^{2} ) +GM_{E} m(\frac{1}{r} -\frac{1}{R_{E} } )[/tex]

The mass of the satellite = m

Altitude = h = r

The radius of the Earth = [tex]R_{E}[/tex]

The Mass of the Earth = [tex]M_{E}[/tex]

Speed of the satellite = v

Speed of the Earth = [tex]v_{e}[/tex]

Gravitational Constant = G

The energy at the surface of the Earth will be the sum of the kinetic and potential Energy,

So,

[tex]E_{i} = K.E. +P.E.\\\\ E_{i} = \frac{1}{2} mv_{e} ^{2} -\frac{GM_{E} m}{r}[/tex]

Also, Energy in orbit,

[tex]E_{i} = K.E. +P.E.\\\\ E_{i} = \frac{1}{2} mv^{2} -\frac{GM_{E} m}{R_{E} }[/tex]

Now, The change in energy is the minimum energy required to place this satellite in orbit,

Then, the Change in Energy =

∆E [tex]= \frac{1}{2} m(v^{2} - v_{e} ^{2} ) +GM_{E} m(\frac{1}{r} -\frac{1}{R_{E} } )[/tex]

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Using the concepts of momentum, we got that 150i-60j is the momentum vector and 162.3Kg-m/sec is the magnitude of the momentum of a 30 kg object.

We know very well that momentum is given by the product of mass and velocity of the object.

In other words P=M. v

But, here velocity is given in 2-D form, means momentum is possible in two different directions.

Therefore, for momentum we just need to multiply the mass of the object with velocity

=>Momentum of the object=M×(5i-2j)

=>                                       p=30×(5i-2j)

=>                                       p=150i-60j

Now, talking about the magnitude we know that magnitude is given by

√(x-component)² + (y-component)²

Therefore, magnitude of momentum (|p|)=√(150)²+(--60)²

=>                                                     |p|=√22500+3600

=>                                                     |p|=√26100

=>                                                     |p|=162.3Kg-m/sec

Hence, for  30 kg object is moving along with the velocity given, the momentum vector is 150i-60j, as well as the magnitude of the momentum for v=5i-2j is 162.3kg-m/sec.

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Other forms of electromagnetic radiation you think could be ionizing are x-rays and gamma rays.

Ionizing radiation, including nuclear radiation, consists of subatomic debris or electromagnetic waves which have sufficient strength to ionize atoms or molecules by using detaching electrons from them.

Ionizing radiation is a shape of power that acts by using casting off electrons from atoms and molecules of materials that include air, water, and dwelling tissue. Ionizing radiation can journey unseen and bypass these materials. whilst ionizing radiation interacts with cells, it is able to purpose damage to the cells and genetic fabric (i.e., deoxyribonucleic acid, or DNA). If now not properly repaired, this damage can result in the death of the mobile or probably dangerous adjustments in the DNA (i.e., mutations.

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As the angle of inclination increases, the normal force A) increases.

What is normal force ?

In mechanics, the normal force is the component of the contact force normal to the surface in contact with the object. Because normal in this case is used in the geometric sense to mean perpendicular, as opposed to its usual usage meaning "usually" or "usually". A person standing still on the platform would be subject to the gravitational pull toward the core of the Earth, if not for the reaction force from the drag forces of the platform's molecules. This force is called the "normal force".

Normal force is a type of ground reaction force. If a person is standing on a slope and not sinking to the ground or sliding down the slope, the total ground reaction force can be divided into two components:

Vertical forces perpendicular to the ground and frictional forces parallel to the ground.

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which best describes the field of physics the study of matter and energy

physics, science that deals with the structure of matter and the interactions between the elemental constituents of the observable universe. the scope of study envelops not as it were the conduct of objects beneath the activity of given forces but the nature and root of gravitational, electromagnetic, and nuclear force fields. In simple words, physics is characterized as the science of matter, movement, and energy. Its laws are regularly expressed with economy and accuracy within the language of science.

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As a shot putter in track,  if you want to throw far then throw it fast and at angle approximately 45 degrees.

As a thrower spins, his body acts as an axis of rotation and therefore, farther the object is from the axis of rotation, larger is its moment of inertia.

The angle of release in the shot-put event is of great importance. The estimation of the optimum angle of release such that the distance thrown is maximized is a  key. Theory has shown that the optimum angle of release is between 41 to 43 degrees.

Release velocity is also a important factor in determining the distance of a throw. Release velocities of about 13 m/s are necessary for elite-level throws.

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14 m is the displacement for a trip from the math classroom in Figure 2.4 to the music classroom and then to the library

Displacement= final position-initial position

Displacement=14m-0

Displacement=14m

distance= total route= 14m

Distance is all covered distance but displacement is shortest distance. Being a vector quantity, displacement has both a magnitude and a direction. The vector (or straight line) distance between an initial and final position is what is meant by this term. Knowing these two places is consequently all that is necessary to determine the resultant displacement.

Calculate the inverse tangent of the ratio of the displacement components in the y- and x-directions to determine the direction of the displacement vector.

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Answer:

0.0003945 kg / m6

Explanation:

center of mass of a solid hemisphere of radius R is 3R / 8 and the Mass of the solid is M.

An elemental disc at a height of h from the base of the hemisphere is taken.

The mass of the elemental disc is taken dM

and the width is taken dy.

et the solid hemisphere be of mass M and has the radius R.

The center of mass will lie vertically which passes through the center of the hemisphere.

Taking the elemental disc at a height h from the base of the hemisphere’s base. The DM is the mass of the elemental disc and the width is dy.

the radius of the disc is:

R = R²- y²

Mass of the disc dM

= (3 M/ 2π R³) × ( πr² dy )                                   …..(2)

eq.(1)   in    eq.(2)..................

 dM = ( 3M  /  2 π  R³ ) ×  π (  R²  –   y²  )   dy)

Y - coordinate  of Centre of mass,

 Yc  =   (1 / M)  ഽ y  dM

Here y is the y - coordinate representing the height of the elemental disc from the base.

Putting the dM and calculating the center of mass, we get

yc= (1/M) ഽ  y(3M  /2 R^3) × ( R^2  -  y^2) dy)

Integrating between    0⟶R

yc = (1/M)   ഽ y  (3M / 2 R^3) × (R^2  -  y^2) dy)

yc = (  3/2r^3  )  ഽ × (R^3 y-  y^3 ) dy

   = (  3/  2R2)[ (R4 / 2 ) – ( R4 /  4)] = 3R / 8

yc =  3 R /8

Centre of Mass of solid hemisphere (yc) = 3 R / 8.

Mass of solid  =  M

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The velocity of the bowling ball is 4 m/s when mass of the bowling ball is 3.5 kg and  momentum given is 14kgm/s.

As we know that,

Momentum= Mass* Velocity

p=mv

Here, Mass of the Bowling Ball(m)= 3.5 Kg

Momentum(p)= 14kgm/s

Velocity= Momentum/Mass

=14/3.5 = 4m/s

The definition of momentum is "mass in motion." Since every item has mass, if it is moving, it must have momentum since its mass is in motion. The quantity of motion and the speed of the motion are the two factors that determine how much momentum an item possesses. The factors mass and velocity affect momentum. According to an equation, an object's momentum is determined by multiplying its mass by its velocity.

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To answer this question, we need to use the formula for momentum, which is:

momentum = mass * velocity

We can rearrange this formula to solve for velocity, which is:

velocity = momentum/mass

We are given the momentum and the mass of the bowling ball, so we can plug them into the formula:

velocity = 14 / 3.5

We can simplify this expression by dividing both numbers by 0.5:

velocity = 28 / 7

We can convert this fraction into a decimal by dividing the numerator by the denominator:

velocity = 4

Therefore, the bowling ball is travelling at 4 m/s.

The answer is Aerodynamic Shaping.

Aerodynamic Shaping can reduce the drag force of an automobile and hence Increase the car's gas mileage. Integrated into the overall shape of an aerodynamic car are the wheel arches and headlights that reduce drag while also reducing wind resistance.

AeroDynamics is basically the study of how air move arround the things which deal with lift, drag, thurst and weight.

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Scope quality is it most accurate to say that einstein's theory has based on this brief description.

According to Einstein's theory of relativity, the curvature of space and time is what causes what we experience as the gravitational force. This is the fundamental tenet of Einstein's theory of general relativity, which is frequently encapsulated in the sentence: "Matter instructs spacetime to curve, and curled spacetime instructs matter to move." Based on Einstein's astounding discovery that light always moves at a constant speed, regardless of how fast you're moving when you measure it, the theory, which revolutionized our understanding of time and space, was developed. Light in the quantum realm. The photons that make up light, or photons, are tiny energy packets with wavelike characteristics, as demonstrated by Einstein's quantum theory of light. In this theory, Einstein also described the process by which electrons are released from metals after being struck by lightning.

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Answer:

c) It has more nitrogen than oxygen.

Explanation:

Our Earth’s atmosphere has more nitrogen (78%) than oxygen (21%). Hence, the option (c) is the correct answer.

Answer:

C. It has more nitrogen than oxygen.

Explanation:

Earth's atmosphere is composed of about 78% nitrogen, 21% oxygen, and one percent other gases. These gases are found in layers (troposphere, stratosphere, mesosphere, thermosphere, and exosphere).

If it takes an object 3.5 seconds to make one revolution,  its frequency is 0.286 Hz.

The number of vibrations counted per second is called frequency. A wave is a group of vibrations that are referred to as energy. The bottom node is known as the crest, and the top node is known as the trough.

The frequency of an alternating current is the number of full cycles per second. The hertz, also known as Hz, is the accepted unit of frequency. The frequency of a current is 1 Hz if one cycle is completed per second; 60 cycles per second equals 60 Hz.

Frequency = 1/t

Frequency = 1/3.5

Frequency = 0.286 Hz

If it takes an object 3.5 seconds to make one revolution,  its frequency is 0.286 Hz

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The volume of the gas at the given conditions will be 26.6 ML.

By Ideal Gas Law we know that

[tex]\frac{P1 V1}{T1}[/tex] = [tex]\frac{P2 V2}{T2}[/tex]

In the given question here, P1 = 10 Kg ; V1 = 80 ML ; T1 = 30 ; P2 = 20 Kg ; T2 = 20 Substituting the values in the equation

[tex]\frac{10 X 80}{30\\}[/tex] = [tex]\frac{20 V2}{20}[/tex]

[tex]\frac{80}{3}[/tex] = V2

V2 = 26.6 ML .

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Magnitude of the car's acceleration is 3.5 m/s²

Given:

Mass of car = 1,000 kg

Net force applied by car = 3,500 N

How to find the acceleration of the car?

Formula:

Net force = Mass × Acceleration

So,

3,500 = 1,000 × Acceleration

Acceleration = 3,500 / 1,000

Acceleration = 3.5 m/s²

Therefore, the acceleration found from the formula is 3.5 m/s².

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Given that the time between when the marathon runner changes her velocity and the finish line is t, the acceleration of the runner approaching the finish line is 0.22/t m/s² .

The acceleration of a body is the change in the velocity of a body with time.

Acceleration is a vector quantity as it takes into account the change in velocity as well as the change in the direction of the body.

Hence, a body is accelerating if either or both of these two conditions apply:

Mathematically;

The change in velocity of a body = Final velocity - initial velocity

Change in velocity of the runner = 4.17 - 3.95

Change in velocity of the runner = 0.22 m/s

Time taken for this change = t

Hence;

acceleration = 0.22/t m/s²

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Answer:   ACCELARATION  = 0.462M/S²

Explanation: INITIAL VELOCITY (VI) = 8M/S

                      DISTANCE COVERED (S) = 744M

                         TIME (t) = 42 S

                     ACCELERATION (A)= ?

       BY APPLYING 2ND EQUATION OF MOTION

              S = VIT +1/2 AT²

            744 = 8 X 42 +1/2 A X42²

            744 - 336 = 1/2 A X 42²

               408 X 2/1764 = A

           A = 816 /1764

A = 0.462M/S²

Answer:

a) 20.65kg

b)4.7rad

Explanation:

An experiment that I could do to measure the horsepower I could develop for a long period of time can be "Riding a bike over a straight path".

What is horsepower?

Horsepower can be defined as the unit of measurement of power, or the rate at which work is done. There are many different standards and types of horsepower. In order to calculate horse power we will use the following method ;

The term Horsepower was invented by James Watt. It is a unit power that compares the power of a machine to the horse muscle power, steam engine power output compared to the power of draft horses. Now it is used in piston engines, electric motors, turbines and other machinery.

One Horsepower equals to 33,000 lb. ft/min.

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D is the correct response because, although the car's speed won't change, its direction of travel will.

The car's acceleration is zero because it is driving at a constant speed of 20 meters per second. A further definition of force is the sum of mass and acceleration. Additionally, because there is no acceleration, there is no net force acting on the vehicle. For instance, the car might be round a corner at a steady speed. The speed will remain the same, but the car will change the direction it is moving.

The complete question is- car is travelling north at a constant speed of 20 m/s. A force is applied directly east on the car. The motion of the car will be change in which of these ways? A) The speed of the car will increase. B) The speed of the car will decrease. C) The speed will increase, and the car will change the direction it is moving. D) The speed will remain the same, but the car will change the direction it is moving.

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The interval of time it takes for the team to do a work of 2.35×10⁷ J is 15000 seconds.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the time interval the work was done by the team on the wagon, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the interval of time it takes to the the work is 15000 seconds.

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Answer:

The answer is C.

When Earth is positioned precisely between the Moon and Sun, Earth's shadow falls upon the surface of the Moon, dimming it and sometimes turning the lunar surface a striking red over the course of a few hours which is how a lunar eclipse happens.

When the Moon orbits Earth, the Moon moves between the Sun and Earth. When this happens, the Moon blocks the light of the Sun from reaching Earth. This causes an eclipse of the Sun, or a solar eclipse. During a solar eclipse, the Moon casts a shadow onto Earth.

A push or pull on an object is a force. All of the forces operating on an object are added together to form a net force. When an object is subject to a net force, the object will change its speed in that direction. The acceleration of an object reveals how much it accelerates or decelerates.

We can determine what occurs with the acceleration and force while maintaining the mass constant.

A connection between the mass of the cart and its acceleration. Taking into consideration Newton's second law, which states that

force = mass × acceleration

As a result, the force will change if the acceleration does. Keeping the mass constant will allow us to determine how changing the acceleration will affect the force. Once the mass is kept constant, you can determine what will happen. Therefore, if we want to maintain the acceleration constant while also changing, we must alter the mass of the car. This means adding mass to the cart—whether it be in the form of mass blocks or larger carts—or otherwise altering its mass.

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