An object has a mass of 100 kg moving at 5 m/s. What is the linear momentum of the object?.

6.25 s does the car come to a stop and 78.125 m distance travelled before stopping.

Solution:

Given:

Initial velocity, v0 = 25 m/s

Acceleration, a = -4m/s2

Final velocity, vf = 0

Put these values in the formula,

To find time,

vf = v0 + a*t

0 = 25 - 4t

t = 25/4

t = 6.25 s

To find distance travelled,

d = ((vf + v0)/2)*t

d = 25/2 * 6.25

d = 12.5 * 6.25

d = 78.125 m

Hence,  6.25 s does the car come to a stop and 78.125 m distance travelled before stopping.

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A cart speed will often increase on a downhill slope while decreasing on an uphill section. A steeper gradient portion has a more pronounced impact on the acceleration or slowdown of a vehicle's speed.

The cart speed/velocity will progressively rise by the same amount each second. The rate of acceleration of the car increases with the slope's steepness (or the ramp's greater angle of inclination). This is so because the slope's angle determines how much gravity is felt.

Therefore, the more gravitational potential energy that can be turned into kinetic energy, the higher the ramp will be, and the more kinetic energy there is, the faster the car will move.

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The maximum speed she can tolerate at the low point of her swing is 10.78 m/s.

Given that,

Mass of the carpenter = 61.7 kg

Length of the rope = 11.5 m

Capable force = 1229 N

Centripetal force acting on the body, F = mv²/r = 61.7* v²/11.5 = 5.37 v²

Gravitational force acting on her is

F = mg = 61.7* 9.81 = 605.28 N

Equating the summation of centripetal force and gravitational force with total capable force,

5.37 v² + 605.28 = 1229

5.37 v² = 623.72

v² = 116.15

v = 10.78 m/s

Thus, the maximum speed she can tolerate at the low point of her swing is 10.78 m/s.

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By utilizing the idea of parallax, we can decide how cosmologists decide distances to stars.

Presently, we perceive how parallax estimations can be utilized to decide the distances, one of the realities we know is that if we have any desire to gauge the distance of divine bodies, we are familiar with the parallax, first and foremost, point. That's what it intends assuming we can quantify tiny parallax points, we can gauge enormous distances moreover.

The purpose for why we can not make precise estimations of parallax past a specific distance is that as the distance of the star from earth builds the parallax point turns out to be tiny.

Subsequently, presently we comprehend how parallax estimations are utilized.

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The height the block reachs when launched by the spring 0.917 m.

Simply said, a spring-mass system is a spring system with a block hanging or fastened to the free end of the spring. The period of any item moving in a simple harmonic motion may often be determined using the spring-mass system. There are several other uses for the spring-mass system. For instance, the spring-mass system may be used to replicate foot skin deformation and the action of human tendons using computer images. There are two ways to arrange spring mass systems. These consist of: The parallel arrangement of springs , a series of springs combined.

m = 0.5 kg , K = 100 N/m , ∆x = 0.3 m

By conservation of energy :-

KEi + PEg + PEelastic = KEf + PEg + PEelastic

0 + 0 + 0.5*K*∆x^2 = 0 + mgh + 0

0.5*100*(0.3)^2 = 0.5*9.81*h

h = 0.917 m

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The change in internal energy when heat is released is 14000J.

W=12000J

Q=2000J

Q=U+W

U=Q-W

U=14000J or 14kJ

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The time takes for the green ball to reach the ground is equal to 0.78 s. As both balls are thrown from the same height they will take the same time to reach the ground irrespective of their velocity.

The equations of motion can be described as the equations which establish the relationship between the time, velocity, acceleration, and displacement of a moving object.

The equations of motions as the mathematical expressions:

[tex]v = u +at\\S = ut +(1/2)at^2\\v^2-u^2= 2aS[/tex]

Given, the height from which the ball is thrown, h = 3

From the 2nd equation of motion, calculate the time taken by the ball reach to the ground:

H = ut + (1/2)gt²

3 = 0 + (1/2)× 9.8×t²

t = 0.78 s

As the time is independent of the velocity of a ball so both balls take the same time to reach the ground as they are thrown from the same height.

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Answer:

the mass of the car is very big

Explanation:

its heavy

The image height of the given converging lens is  6.67 cm.  

The focal length of an optical gadget is a degree of the way strongly the gadget converges or diverges light; it's miles the inverse of the gadget's optical energy. A effective focal length suggests that a system converges light, while a poor focal period shows that the gadget diverges mild.

The focal length is half of the radius of curvature and is as f=R2 f = R 2 , where f is the focal period, and R is the radius of curvature.

Calculation:-

object height  = 20 cm

object distance = 1m = 100 cm

focal length = 1.5 m = 150 cm

image height = ?

height of image/height of object = f/ f - U

20/H = 150 / 150 - 100

20/H = 150/50

20/H = 3

H = 20/3

Height of object is = 6.67 cm.

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A lunar astronaut carries a 110 kg box and a 230 kg load. The forces required to move the containers straight up on the moon are enormous compared to the forces required to hoist them on Earth.

A forces is an influence with the capacity to change the motion of an object. When an object with mass moves away from rest, for example, a force can cause it to accelerate as its velocity increases. A push or a pull are two straightforward ways to demonstrate force. Since a force has both magnitude and direction, it is a vector quantity. It is computed using the SI unit of newton (N). The letter F stands for force (formerly P). The original wording of Newton's second law states that the net force acting on an item is equal to the rate of change of its momentum over time. This law states that if an object's mass stays constant, its acceleration should be directly proportional to the net force exerted on it and inversely proportional to the object's mass. Thrust, which increases an object's velocity; drag, which decreases an object's velocity; and torque, which modifies an object's rotational speed, are all ideas connected to force. Internal mechanical stress describes how these forces are distributed within the body. The adjacent regions are frequently put under stress by each expanded body part.

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The wavelength for an electron moving at 3.00x103 m/s is 244 nm

Given, Mass of electron = 9.1093 * [tex]10^{-31}[/tex]

velocity = 3.00 * [tex]10^{3}[/tex] m/s

wavelength λ = h / mv

λ = 6.626 * [tex]10^{-34}[/tex] / [tex]9.1093 * 10^{-31}[/tex] * [tex]3.00 * 10^{3}[/tex]

λ = 244 nm

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When the train approaches you, the Doppler's effect gives the frequency  240.12 Hz

When the train moves away from you, the Doppler's effect gives the frequency  199.6 Hz

Given that,

Frequency of train horn, f = 218 Hz

Speed of train, Vt = 31.7 m/s

The speed of the sound , V = 344 m/s

When the train approaches you, the Doppler's effect gives the frequency as follows :

[tex]f^{'} = f (V/ V-V_{0} )[/tex]

[tex]f^{'}[/tex] = 218 * ( 344/ 344 - 31.7)

   = 240.12 Hz

When the train moves away from you, the Doppler's effect gives the frequency as follows :

[tex]f^{'} = f ( V / V+ Vt)[/tex]

   = 218 * ( 344/ 344 + 31.7)

   = 199.6 Hz

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The band gap energy in kilojoules per mole is 1.73×105 J.

The band gap is the distance between the valence band and the conduction band of an electron. Essentially, the bandgap represents the minimum energy required to excite an electron to a state in the conduction band where it can participate in conduction. Higher frequencies and lower wavelengths of light are absorbed.

In physics, especially for solids, the band gap is also called the energy gap. It is the range of energies that exist in solids where no other electronic state can exist. In the diagram of the electronic band structure of solids, the band gap is commonly called the energy difference.

Therefore, the band gap energy of wavelength 675 nm is 1.73×105 J.

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The Carnot engine is 40% efficient.

It's far a super reversible thermodynamic manner that includes the subsequent 4 tactics, Isothermal growth, No different heating is more efficient than this one, as there may be no finite temperature distinction between the warmth supply and warmth receiver. Therefore, it's miles the most efficient reversible system.

A Carnot engine can be notion of to include a cylinder with adiabatic lateral partitions packed with a substance which can take in and supply warmness. The cylinder is closed by way of an adiabatic piston which could move out and deliver work. The cylinder can acquire paintings by means of shifting the piston inward.

The Carnot engine is a theoretical thermodynamic cycle proposed by means of Leonard Carnot. It estimates the maximum feasible performance that a heat engine all through the conversion manner of warmth into paintings and, conversely, operating among two reservoirs can own.

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Internal energy of equipartition energy is due to kinetic energy of molecules.

There are now two possible cases:

1) Expansion occurs at the expense of the gas's internal energy, so the gas temperature decreases as it expands. Therefore U decreases.

2) As the temperature decreases, so does the velocity of the gas molecules and the K of the gas decreases continuously.

This concept often takes into account what considers heat as internal energy. Molecular kinetic energy, vibrations, rotations, electron "shell" positions, molecular bending, crystal lattice vibrations, etc.

Generally, pressure should be considered part of the internal energy. Theoretically, matter can be expanded or heat can be transferred to do work.

At absolute zero temperature and pressure we can see that there is still internal energy. This can be seen as a result of the blurring principle. Particles cannot be confined to too small a volume and velocity.

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The pulse rate on a light straight string is V sqrt when a weight W is suspended from it (2V)

The correct answer is D

A distance's rate of change over time is used to calculate speed. It has a dimension of distance via time. The Vernier scales of speed is made up of the fundamental units of distance and time. The unit of speed in the metric system is meters per second.

What is considered speed? the rate at which an object's location changes in any direction. Speed is defined as the relationship between length and the time required to travel a distance. Speed is a scalar number because it has no magnitude and only a direction.

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The drift velocity of electron is 4.54 * 10⁻⁴ m/s.

Given that, Density of copper is 8.8* 10³ kg/m³

Charge of an electron is 1.6* 10⁻¹⁹ C

For the density of copper, the number of free electrons n can be calculated by

n = number of electrons per kg * ρ

⇒ (9.4776* 10²⁴ ) (8.8 * 10³ kg/ 1 m³) = 8.314 * 10²⁸ electrons per m³

Diameter of the wire is given as 2.053 mm

Let us calculate A for the provided diameter of wire

A = π * (d/2)² = π * (2.053 /2)² = 3.310* 10⁻⁶ m²

Given, I = 20 A

We know the expression for drift velocity as

Vd = I /(n* A* e) = 20 / (8.314 * 10²⁸ * 3.310* 10⁻⁶ * 1.6* 10⁻¹⁹) = 20 / (4.403 * 10⁴) = 4.54 * 10⁻⁴ m/s

Thus, the drift velocity of electron is 4.54 * 10⁻⁴ m/s.

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On the starting blocks, sprinters use their feet to push backward. The blocks respond by pressing forward with a force equal to this with their feet.

Vertical forces must be larger than the pull of gravity in order to assist the sprinter in moving forward as gravity is pushing him or her downward. The propulsive force is the force that propelled the runner forward.

An interaction diagram and a free-body diagram should be included in your explanation. The player pushes down on the ground, which pushes up against him in return. As a result of his push being stronger than gravity, the player accelerates upward.

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A high or low tide that is more extreme than usual is a(n) tide, it is stronger than usual tide.

The moon is the primary cause of high and low tides. The tidal force is produced by the moon's gravitational pull. Earth and its water protrude outward on both the side that is closest to and farthest from the moon as a result of the tidal force. These watery peaks are high tides.

Your part of the Earth spins around both of these bulges every day. You encounter a high tide while you're inside one of the bulges. The tide is low when you are not in one of the bulges. On the majority of the world's coastlines, this cycle of two high tides and two low tides occurs every day.

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The heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

Consider the diagram below, the heat flow will be

Fourier's law in radial coordinates

qr = -k.AdT/dr

Substituting the values of the area of sphere,

qr = -k (4πr²) dT/dr

Integrating we get

qr/4π∫dr/r^2 = ∫kdt

qr/4π ∫dr/r^2 = ∫kdt

qr/4π (1/r1 - 1/r2) = k(t2-t1)

qr = 4πkr1r2(t1-t2) / (r2 - r1)

The thermal resistance is expressed as

R = (r2 - r1) / 4πkr1r2)

Therefore, the heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

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Infrared Radiation lies on third place of electromagnetic spectrum in the increasing order of frequency.

In his experiments to measure temperature differences between colors in the visible spectrum, he placed a thermometer in the path of light within each color in the visible spectrum. He noticed that the temperature rose from blue to red, and found that just beyond the red end of the visible spectrum showed even higher temperatures. Within the electromagnetic spectrum, infrared waves occur at frequencies higher than those of microwaves and slightly lower than those of red visible light, hence the name "infrared".

Infrared radiation is an integral part of the electromagnetic spectrum.

It has wavelength of 700nm and has good application for earth sciences.

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The answer is true: a fault's frictional resistance is higher when it is locked than when it is moving.

Friction refers to the force that prevents two hard surfaces from rolling or sliding over each other. Although friction force, such as the traction required to walking avoid slipping, may be advantageous, they can provide a significant amount of resistance to motion.

The adhesion forces between the contact zones of a surface, which are constantly microscopic examination uneven, appear to be the main contributor to metal friction. The shearing of these "bonded" joints and the movement of the rougher surface's imperfections scrubbing against the softer surface cause friction.

When an object slide over a surface, as no surface is 100% smooth there are some microscopic irregularities are there on the surfaces of both object as well as the surface so when the sliding takes place on the surface the irregularities get interlocked and that causes friction between surfaces.

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The light travels faster in water medium with a density of 1.33 when compared to diamond medium with a density of 2.42.

A denser medium will have more matter compared to rarer medium. So, the scattering of light is higher in a denser medium resulting in lesser travel speed. Slower the speed higher will be the index of refraction. So light will travel more slowly in a dense medium.

Refractive index of Diamond = 2.42

Refractive index of water = 1.33

Since, refractive index is inversely proportional to speed of the wave, speed of light in water is higher than the speed of light in diamond.

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The pendulum's new time period is T.

A bob suspended at the end of a thread that is so light as to be regarded massless makes up a simple pendulum. It serves as an example of a conservative oscillatory system. A point mass m anchored to one end of a massless rod of length L makes up this idealized representation of a pendulum.

The time period of a simple pendulum is calculated by the formula, [tex]T=2\pi\sqrt{\frac{L}{g}}[/tex] where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity. Since this formula is independent of mass, the change in the mass of the bob doesn't affect the time period. Therefore, the new time period will still be T. There is no change.

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The distance of lens from the object is 4.16 cm, so that its image is seen at the near-point distance of 25 cm.

The near-point distance of a human eye, described to be s = 25 cm, is the shortest item distance that a typical or "normal" eye is capable of accommodate, or to photo onto the retina. The some distance point of a human eye is the farthest object distance that a standard eye is able to photo onto the retina.

The human eye can see objects genuinely with none pressure on the attention while an item is placed at the least 25 cm away. This distance of 25 cm is called the close to point of the eye. while the object is positioned at a distance between 25 cm and infinity, the photo of the object is fashioned on the retina and interpreted surely.

Calculation:-

for magnifier

magnification m = 25 cm /f

5 = 25/f

f = 25/5 = 5 cm

ten using lens equation

1/f = 1/do + 1/di

1/5 = (1/do)-(1/25)

1/do = (1/5)+(1/25)

do = 4.16 cm

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Dilation doesn't always change the vertices.

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M = 2.99 kg≅ 3kg under goes fusion

Given,

P = 1000 M W = 1 x 10^9 J/s

efficiency = 33% ; E' = 208 MeV = 3.33 x 10^-11 J

Energy released in a day

E(day) = P x t

E(day) = 10^9 x 24 hrs x 60 min x 60 sec = 8.46 x 10^13 J

energy released in fission would be:

E(fission) = E(day)/0.33 = 8.46 x 10^13/0.28 = 2.56 x 10^14 J

We have Energy released per fission(E'), so the number of fission to release E(fission) would be:

N = E(fission)/E'

N = 2.56 x 10^14/3.33 x 10^-11 = 7.68 x 10^24

Number of moles = N/Avogadro's No

n = 7.68 x 10^24/6.023 x 10^23 = 12.75 moles

Mass of required 235U92 will be:

M = n x 235 g = 12.75 x 235 = 2996.25 grams = 2.99 kg≅ 3 kg

Hence, M = 2.99 kg≅ 3kg

Fission:

Nuclear fission is a response in which the nucleus of an atom splits into two or more smaller nuclei. The fission method frequently produces gamma photons, and releases a completely massive amount of power even through the lively requirements of radioactive decay.

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We need to know angular acceleration α to  give answer to this question. For completing the question, suppose the disc is spinning at 300 RPM.

Angular acceleration α = (300× 2/ 60)/2.50 = 4 m/square second

The required torque L is given by

L = I*alpha,

where,

I = the moment of inertia of the disc,

I = (1/2) M R^2

Therefore

L = (1/2) M R^2 *4 rad/s^2

The units will be Newton-meters

Once you have determined L, use

F = L/R for the required friction force, in Newtons.

Friction is the force that always resists motion of a moving object on the surface of other object.

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Work done is calculated as the scalar product of force and displacement along the force's direction, so it should be zero because there is no net force acting on the object (hence the constant velocity). Thus, W is equal to 0.

Newton's first law of motion states that any object moving at a constant speed experiences no net external forces, so the total amount of forces acting on the object must be zero. The mathematical expression for an object being under no net external force is Fnet=0 or F=0.

Acceleration equals zero when velocity stays the same. Therefore, an object moving at a constant speed does not require any force.

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The momentum of the moving car is 30000 kg m/s.

The momentum of a moving body is calculated as the product of mass and velocity. It is a vector quantity. In simple terms, it is the strength or force gained by a moving object.

Newton's second law is related to momentum. According to newton's second law, " The time rate of change of momentum is equal to force".

We have the formula for finding the momentum,

Momentum = Mass× Velocity

P = M × V

Put the value in the formula,

P = 1200 × 25 kg m/s

= 30000 kg m/s

So, the car is moving with a momentum of 30000 kg m/s.

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