forces and newton’s laws 3.1 Essential Questions How are force and motion related?

double the luminous flux of the light source is a way to exactly double the illuminance on an object.

The electromagnetic radiation that the human eye perceives as light, or visible light, is found in the region of the electromagnetic spectrum. Typically, visible light is characterized as having wavelengths between 400 and 700 nanometers (nm), or frequencies between 750 and 420 terahertz, which are intermediate between the infrared and ultraviolet (with longer wavelengths) (with shorter wavelengths).

The term "light" can be used more generally in physics to refer to electromagnetic radiation of any wavelength, whether or not it is visible.

This makes gamma rays, X-rays, microwaves, and radio waves also constitute light. Intensity, the direction of propagation, frequency or wavelength spectrum, and polarization make up the fundamental characteristics of light. One of the basic constants of nature is its speed in a vacuum, 299 792 458 meters per second (m/s).

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A rock is tossed straight up from a height of 1.20 m above the ground with an initial speed of 7.54 m/s. It will take 0.15 seconds to hit the rock ground

height = displacement = 1.20 m

initial speed = u = 7.54 m/s

final speed = v = 0

time = ?

Using kinematic equation

s = u*t + 1/2 * g * [tex]t^{2}[/tex]

1.20 = 7.54 t + 1/2 * 9.8 *  [tex]t^{2}[/tex]

= 4.9  [tex]t^{2}[/tex] + 7.54 t  - 1.20

t = 0.15 seconds

It will take 0.15 seconds to hit the rock ground

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The common speed in mph of the combined piece right after the collision was 30 mph. The cars move towards the lighter car.

An inelastic collision is a collision in which there is no internet loss in kinetic energy within the gadget because of the collision. each momentum and kinetic electricity are conserved portions in elastic collisions.

Calculation:-

50 mph = (50 × 0.477)

    = 22.35

   Applying the law of conservation of momentum.

we get the:-

m₁u₁ + m₂u₂ = (m₁ + m₂)V

V = m₁u₁ + m₂u₂/(m₁ + m₂)

   = 4000 × 22.35 + 1000 × (-22.35) / 4000 +1000

V = 13.41 m/s

 = 13.41/0.447

= 30 mph

Hence, the common speed of the car is 30mpH.

An inelastic collision is a come between two bodies in which the full kinetic energy of the two bodies remains equal. In an ideal, perfectly elastic collision, there may be no internet conversion of kinetic strength into other kinds which includes heat, noise, or capacity electricity.

Elastic collisions arise whilst both the momentum and kinetic energy are conserved, just like how billiard balls bounce off each different and move at the same speeds as earlier. Inelastic collisions appear whilst simplest the momentum is conserved but not the kinetic power.

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Two projectiles of mass and are fired at the same speed but in opposite directions from two launch sites separated by a distance, will land at a place x = D/2 [ 1+{ (m₁ - m₂) / m₁ + m₂)}

This is calculated using the conservation of linear momentum in the horizontal direction as ,

(vm₁vₓ₁ - m₂vₓ₁ ) ₓî = (m₁ + m₂) vₓ₂ ₓî

vₓ₂ = {(m₁ - m₂) / m₁ + m₂)} × vₓ₁

vₓ₂ = {(m₁ - m₂) / m₁ + m₂)} × v Cos Θ

t max = vₓ₁ / g

=  v Sin Θ / g

x =(D / 2) + vₓ₂t max

= (D / 2) { {(m₁ - m₂) / m₁ + m₂)} × v² Sin Cos Θ / g } ------ (1)

now,

D = 2 vₓ₁vₓ₂ / g

D / 2 = v² Sin Cos Θ / g

From equation (1) we get,

x = D/2 [ 1+{ (m₁ - m₂) / m₁ + m₂)}

Hence , D/2 [ 1+{ (m₁ - m₂) / m₁ + m₂)} is the place they will land.

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Answer:

a = 6.27 m/s² - acceleration

Explanation:

Given:

F = 9 079 N

m = 1 447 kg

_________

a - ?

Acceleration:

a = F / m

a = 9 079 / 1 447 ≈ 6.27 m/s²

The dielectric constant of the wax is 2.

The dielectric constant of wax is the ratio of the capacitance of a capacitor that has wax between its plates to its capacitance when there is no wax between its plates.

This can be calculated by first finding the total capacitance of the capacitor with wax in between it:

C = 2 * pf * (0.5cm)^2

= 1.5 pf

Then, we can calculate the change in capacitance:

C' = C - C

= 2 pf * (0.5cm)^2 - 1.5 pf

= 0.5 pf

Finally, we divide 1/0.5 to find C'/C = 2, so we conclude that the dielectric constant for wax is 2, or twice as large as air's dielectric constant of 1!

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The period of the  object undergoing simple harmonic motion   is

simple harmonic motion sometime shortened as SHM may be a sort of periodic movement where the restoring drive on the moving object is straightforwardly relative to the magnitude of the displacement of the object and acts towards the object's equilibrium position. It comes about in an oscillation that proceeds inconclusively, on the off chance that uninhibited by friction or any other dissemination of energy.

we are given the time taken to complete the distance covered between two  zero velocity  points apart from the distance of   41.6 cm which is  0.12 so the period  will be  = 2T = 2 * 0.12 = 0.24 s

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Using the concepts of pressure, we find that 625m[tex]s^{-1}[/tex] is the speed of the stomp rocket rising at that moment when it is watched by students 500 meters away. after 2 seconds, when the angle of elevation is the angle is increasing at a rate of 0.4 radians per second.

We know that when an object is very far away, at the centre of that object there is an angle enclosed by the observer and that is given

angle=(length of arc)/radius of the arc.

θ=l/r

So, we are given that length of arc is 500 metres and angle is 0.4 radians/sec.

So,=>0.4=500/r

      =>r=500/0.4

       =>r=1250m

Now we are given the time when it is observed i.e. is 2 seconds.

So, we apply distance speed formula.,

which is Distance=Speed × Time

            =>1250=Speed×2

              =>Speed=1250/2

              =>Speed =625m[tex]s^{-1}[/tex].

Hence, when a stomp rocket is launched straight into the air and is being watched by students 500 meters away. after 2 seconds, and the angle of elevation is the angle is increasing at a rate of 0.4 radians per second, the speed of stomp rocket is 625m[tex]s^{-1}[/tex].

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The speed of the sled after it has travelled a distance 3.58 meter is 2.96m/s.

Mass of sled = 2.49kg

Initial speed across the horizontal surface = 4.53m/s

Coefficient of kinetic friction between the slate and surface = 0.168

Distance = 3.58m

Now to calculate the acceleration of sled we use :

F = ma

a = F/m

where

a = acceleration

m = mass

F = frictional force

a = μmg / m

a = μg

a = 0.168 x 9.8

a = 1.64m/s²

To calculate the speed of sled we use:

v² = u² - 2as

v² = (4.53)² - 2x 1.64 x 3.58

v² =  8.7785

v = 2.96m/s

The speed of the sled after it has travelled a distance 3.58 meter is 2.96m/s.

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The magnitude and direction of the sum of vectors will be 4.15 m aligned in  50° in north west direction.

Both the vectors are making angle in a way that it will add up to 90° , hence a right angles triangle will be formed .

using Pythagoras theorem

[tex]H^{2} = P^{2} + B^{2}[/tex]

sum of vector = [tex]H^{2} = P^{2} + B^{2}[/tex]

H = [tex]\sqrt{P^{2} + B^{2} }[/tex]

   = [tex]\sqrt{3.14^{2} + 2.71^{2} }[/tex]

   = 4.15  m

let theta is the angle along the base vector 2

tan (theta ) = P/B = 3.14 / 2.71 = 1.16 °

theta = [tex]tan^{-1}[/tex] ( 1.16 )

         ≈ 50°

hence , The magnitude and direction of the sum of vectors will be 4.15 m aligned in  50° in north west direction.

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The GPE that the barbells have at max height is ,

3680.h j=11,000 units

where h= maximum height the barbells were lifted

work done by the championship lifter ,W = 11,000 units

weight of the barbells, N = 3680 N

The gravitational potential energy, P.E., the barbells had at their maximum height of lift is given as follows;

P.E. = m × g × h

Where;

m = The mass of the barbells;

g = The acceleration due to gravity = 9.8 m/s^2

h = The maximum height to which the barbells are lifted

m × g = The weight of the barbells = 3680 N

∴ P.E. = 3680 N × h = 3680·h J

we know the law of conservation of energy, according to this the work done by the weight lifter is equals to the maximum gravitational potential energy gained by the barbell is equal to energy at maximium height i.e P.E

therefore, GPE = 3680.h j = W = 11,000j is your answer.

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The wavelength of the radiation is 2.93×10⁻⁷ m

Given,

The energy of photon E=6.78×10⁻¹⁹

now, E=hc/λ

λ=hc/E

=6.626×10⁻³⁴×3×10⁸/6.78×10⁻¹⁹

=2.93×10⁻⁷ m

Radiation is the emission or transmission of energy through a material medium or across space in the form of waves or particles.

According to the energy of the radiated particles, radiation is frequently classified as either ionizing or non-ionizing. Ionizing radiation has an energy level of more than 10 eV, which is sufficient to ionize atoms and molecules as well as rupture chemical bonds. Due to the significant difference in how destructive it is to living things, this is a crucial distinction. Ionizing radiation is frequently produced by radioactive substances that release radiation in the form of helium nuclei, electrons or positrons, or photons, respectively.

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Yes, a spectrophotometer can be used to measure the absorption of a particular wavelength of light that is not visible to a normal human eye.

Even though we can't directly perceive this light's absorption, it can be quantified. We may calculate concentration by using a spectrophotometer, which detects the absorption of light at particular wavelengths (whether visible or not) by a solution. The number of chemicals in a solution or the amount of light absorption may be measured using the common and affordable method of spectrophotometry.

Each substance in the solution either absorbs or transmits light over a certain wavelength when a light beam is directed through the sample. Combining them with colored derivatives that are visible and measurable. Another is that colorless substances typically absorb light from the part of the spectrum that is invisible to the unaided eye, as measured by a spectrophotometer.

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Newton's first law states that an object at rest will remain at rest, and an object in motion won't change its velocity while the equilibrium condition is met.

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The phase angle between the voltages of the inductor and capacitor in a RLC series circuit is 180 degrees.

RLC circuit contains resistor , capacitor and inductor. Resistor doesn't store energy but capacitor and inductor stores energy and that is the reason resistor is called a passive element and inductor and capacitors are called active element.

Inductor leads the current by a phase angle of 90 degrees and the voltage across the capacitor lags the current by 90 degrees, so the phase difference between the voltages of the inductor and the capacitor is 180 degrees in an LCR circuit.

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The weight of box 2 and box 3 is 33.72N and 15.32N

According to Lami's Theorem, if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces. The magnitudes of concurrent, coplanar, and non-collinear forces that keep an object in static equilibrium are all related to Lami's Theorem. This theorem also aids in the analysis of most mechanical and structural systems. For all three forces used in Lami's Theorem, the proportionality constant is the same.

Given box1 weighs 31N

Given two angles 63 and 24

So the third angle will be

180 – 87

= 93

By using Lamis theorem

T_2/(SIN 93)=T_3/(SIN (90+63))=T_1/(SIN (90+24))

Here T1 = 31N

Weight of box 2 = w2 = 31/cos24 x sin 93

= 33.72

Weight of box 3 = w3 = 31/cos24 x cos 63

= 15.32

Therefore the weight of box 2 and box 3 is 33.72N and 15.32N

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Answer: an upward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the X-axis

just took the test

an upward-sloping line drawn on a graph with acceleration shown on the y-axis and force shown on the X-axis best describes a graph that would represent the relationship shown in the table

A graph is represented as pictorial form  the of data or numeric values in an organized manner which enables user to represent large amount of data in visual form.

There are 2 types of questions and the features of graphs are interpretation of given graphs or selecting a graph based on a verbal description.

The bar graphs are the most common type of graph, other graphs are dot plots, histograms, line graphs and scatterplots.

A Bar Graph is represented as the graphical display of data using rectangular bars of different parameters like heights, The structure can be represented  in the y axis contains values, and the x axis contains categories or time periods.  

A dot plot is a simple graphical representation  which shows the frequency with which items appears in a data set and present data on the x axis.

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Thus, more than 30 J of potential energy can be loosed by the ball. Thus, the gravitational potential energy of the ball is more than 30 J.

If there is no air resistance, the ball's potential energy is entirely transformed into kinetic energy. When air resistance is taken into account, a portion of the potential energy is used to overcome it. Thus, AU > AKE. In the current scenario, a ball gains 30 J of kinetic energy while falling and is treated as encountering air resistance. The energy that an object retains due to its position in relation to other objects, internal stresses, electric charge, or other factors is known as potential energy in physics. The potential energy will be transformed into kinetic energy if the stones fall. High on the tree, branches have the potential to fall, which gives them energy. Chemical potential energy exists in the food we eat.

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Kinetic energy of Corvette with a mass of 1,054 kg and a velocity of 48m/s is 12,14,208 J

Kinetic energy is a type of power that an item or particle possesses as a result of motion. An object accelerates and acquires kinetic energy when it undertakes work—the transfer of energy—by being subjected to a net force. Kinetic energy is one of the properties of a moving object or particle, which depends on both mass and speed. The type of motion can be any combination of vibration, rotation on an axis, and translation (or transit along a path from one spot to another).

A body's translational kinetic energy is equal to 1/2mv2, or one-half of the product of its mass, m, and square of its velocity, v.

Here,

m = 1,054 kg

v = 48 m/s

KE = ?

KE = 1/2 mv²

KE = [tex]\frac{1}{2}[/tex] × 1054 × 48²

KE = 0.5 × 1054 × 2304

KE = 12,14,208 J

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Suppose a car travels at a constant 10 m/s.

using d = vt

v = 10m/s.

t                                    d

1 hr= 3600s                3.6x [tex]10^{4}[/tex]m

1 min = 60s                  6.0x [tex]10^{2}[/tex]m

1s                                  10m

1ms = [tex]10^{-3}[/tex] s                 10 x[tex]10^{-3}[/tex]m = 10mm

1μs = [tex]10^{-6}[/tex]s                  10x [tex]10^{-6}[/tex]m =  10μm

1ns = [tex]10^{-9}[/tex]s                   10x [tex]10^{-9}[/tex]m = 10 nm

something immutable or unchangeable: eg; a number having a definite value in a particular situation or universally, or a characteristic of some substance or instrument. : a number that is expected not to change value in a given mathematical discussion a term with fixed notation in logic.

A constant can be defined as a fixed value used in algebraic expressions and equations. A constant does not change over time and has a fixed value. For example, the size of a shoe, fabric or any accessory does not change at any time.

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The cylinder will reach the bottom first.

In this case, the body acceleration should be applied to the incline.

Therefore, the equation listed below should be utilized.

gsin / (1 + k2 / r2) = a

Here

K is the gyrating radius.

r is the radius, and

Now

in hoop

k = r

gsin / (1 + r2 / r2) equals a.

= g / 2 x sinθ

0.5 gsinθ

as cylinder

k² = r² /2

A is equal to gsin / (1 + r2 /2 r2).

= 2 / 3 g sinθ

= .67 g sinθ

We can observe that the cylinder is more responsible for the acceleration.

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The formula for the relationship between the electric and magnetic fields is:

E = cB

As the amplitude of the electric field is precisely proportional to the magnetic field, the magnetic field will also double in size when the amplitude of the electric field doubles.

Radio waves typically operate at frequencies between 300 gigahertz and below, where the longest wavelengths of the electromagnetic spectrum are found. At 300 GHz, the corresponding wavelength is 1 mm; nevertheless, at 30 Hz, it is 10,000 kilometers.

A magnetic field, a vector field that affects an electric charge, an electric current, and magnetic materials magnetically. In a magnetic field, a moving charge experiences an external force that is perpendicular to the magnetic field and has its own velocity.

The maximum electric and magnetic field strength is known as the amplitude in electromagnetic waves. The wave amplitude determines the energy of the wave. Similar to how waves themselves move, the energy density also follows the electric and magnetic fields.

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Answer:

Explanation:

Given:

t = (1/3) min = (60/3) s = 20 s

V = 300 m

_______________________

D - ?  

Distance:

D = V·t

D = 300·20 = 6 000 m

When ray estimation of geometric optics cannot be used, wave optics—also known as physical optics—is concerned with the study of numerous phenomena like polarization, diffraction, interference, and other occurrences.

wavelength of light = 633 nm = 633*10-9 m,

the angle θ = 1.20 / 2 = 0.6

condition for diffraction minimum,

d sin θ = mλ

for first minimum n = 1

d sin θ = λ,

and as a result,

slit width d = λ / sinθ = (633*10-9 m) / sin0.6 = 6.04×10 −5m

The various wave optics kinds are:

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A 1,400 kg airplane encounters a 200 newton headwind that slows it down. if the airplane was originally traveling 230 m/s .  It take 12 minutes for the headwind to slow the airplane to 120 m/s

Force = mass * acceleration

- 200 N = 1400 * ( change in speed / time interval )

- 200= 1400 * (120 - 230 / time )

-200 = 1400 * ( -110 / time )

time = 770 seconds = 12 minutes

It take 12 minutes for the headwind to slow the airplane to 120 m/s

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Thermonuclear fusion occurs faster in massive stars so larger stars use up all their fuel in less time.

The more mass a star has the faster it will exhaust its fuel supply and the shorter its lifespan. The most massive stars could burn up and explode in a supernova after just a few million years of nuclear fusion. Massive stars are the largest, hottest, and brightest main-sequence stars and are blue, blue-white, or white in color.

Massive stars run out of hydrogen fuel very quickly and therefore have short lives. This is because the more massive the star the greater the fuel consumption. Even if a high-mass star has more fuel it uses it up very quickly so it does not live as long as a low-mass star. A main-sequence star's mass determines the fundamental properties of its luminosity surface temperature radius and lifetime.

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Option C, Since there is no refraction and light travels in almost the same direction in both the glass as well as the unknown liquid, their indexes of refraction are identical.

Moving from the atmosphere to the glass causes the light to slow down. A prism's angle is 60 degrees, and its green light refractive index is 1.5.

The many media, or matter particles, through which light passes were used to gauge both its speed and how it appears to the human eye. To discern the different light wavelengths, the speed should slow down when the white light is revealed via the prism.

The following formula is used to get the refractive index:

n₁ sinθ₁  = n₂sinθ₂  

where n₁ and n₂ represent the observed difference and represent the diffraction pattern between two liquids.

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The event horizon of a black hole, the region beyond which there is no return, is the zone from which no light of any sort, including X-rays, can escape. Black hole research telescopes operated by NASA.

Are examining the black holes' surroundings, which contain material that is quite near the event horizon. A black hole is an area of spacetime where gravity is so intense that nothing can escape from it, not even electromagnetic radiation like horizon. A sufficiently compact mass can distort spacetime to generate a black hole, according to general relativity theory.

A black hole is a compact, dense object whose gravitational attraction is so powerful that nothing can escape from it up close, not even light.

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