A 25 kg block is sliding down 28o incline at a constant speed.

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Answer 1
try photo math it helps

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A student conducts three experiments to determine how certain quantities influence the centripetal force responsible for an object to spin in a horizontal circle. The student uses one end of a string to attach the object while the other end is connected to a force sensor that allows the student to change the tension on the string, as shown in the figure. The student records data from the three experiments in the table above. Which of the following experiments, if any, collected data that do not agree with the expression for the net centripetal force on the object?

A)The experiment in which mass was changed
B)The experiment in which the radius of the circular path was changed
C)The experiment in which the speed of the object was changed
D)All the data are expected.

Answers

Option C) The experiment in which the speed of the object was changed

is only statement that doesn't satisfy the given data as shown below:

The above statement can be verified using the calculation:

Formula for centripetal force(F) = [tex]\frac{mv^2}{r}[/tex]

where m is mass of object , v is speed of object and r is radius of the circular motion.

For option A) when only mass of object is changed and rest all are same.

so F = k*m where k = [tex]\frac{v^2}{r}[/tex] as both are constant

=> [tex]\frac{F_1}{F_2}[/tex] = 4.04/8.08 = 0.5

and [tex]\frac{m_1}{m_2}[/tex] = 0.1/0.2 =0.5

so [tex]\frac{F_1}{F_2} = \frac{m_1}{m_2}[/tex]

similary [tex]\frac{F_2}{F_3} = \frac{m_2}{m_3}[/tex] and hence data is correct for option A)

For option B) when only radius of object is changed and rest all are

same.

so F = k/r where k = [tex]m*v^2[/tex] as both are constant

=> [tex]\frac{F_1}{F_2}[/tex] = 4.04/8.08 = 0.5

and [tex]\frac{r_2}{r_1}[/tex] = 0.3/0.6 =0.5

so [tex]\frac{F_1}{F_2} = \frac{r_2}{r_1}[/tex]

so both are same , similary [tex]\frac{F_2}{F_3} = \frac{r_3}{r_2}[/tex] and hence data is correct for option B

For option C) when only speed of object is changed and rest all are

same.

so F = k*[tex]v^2[/tex] where k = [tex]\frac{m}{r}[/tex] as both are constant

=> [tex]\frac{F_1}{F_2}[/tex] = 4.04/9.09 = 0.44444

and [tex]\frac{v_1^2}{v_2^2}[/tex] = 4.08/9.181 =0.44439

so ,[tex]\frac{F_1}{F_2}[/tex] ≠ [tex]\frac{v_1^2}{v_2^2}[/tex]

and hence data is not correct for option C

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Complete question:

A student conducts three experiments to determine how certain quantities influence the centripetal force responsible for an object to spin in a horizontal circle. The student uses one end of a string to attach the object while the other end is connected to a force sensor that allows the student to change the tension on the string, as shown in the figure. The student records data from the three experiments in the table above. Which of the following experiments, if any, collected data that do not agree with the expression for the net centripetal force on the object?

A)The experiment in which mass was changed

B)The experiment in which the radius of the circular path was changed

C)The experiment in which the speed of the object was changed

D)All the data are expected.

FILL IN THE BLANK. the _____ theory says people are ""pulled"" by external stimuli to act in a certain way.

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The incentive theory says people are "pulled" by external stimuli to act a certain way.

Humans have both main and secondary needs that must be met in order for them to feel needed. These requirements naturally nudge a person in that direction. Hunger, thirst, and a desire for sexual activity are examples of fundamental wants. Secondary needs, on the other hand, are those that depend on advantages, with financial requirements serving as the finest illustration.

According to incentive theories, conduct is driven by the "pull" of external objectives like rewards, money, or recognition. It's simple to imagine a variety of circumstances in which a specific objective, like a job promotion, can act as an outside incentive to encourage certain actions.

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What is spectrum of thermal radiation in micro meter Mcq?

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From of the longest infrared light through the visible light spectrum to a shortest ultraviolet rays, thermal radiation spans the entire electromagnetic spectrum.

The electromagnetic spectrum is what, Mcq?

In increasing frequency and decreasing wavelength order, radio waves, microwave, infrared, visible light, ultraviolet radiation, X-rays, gamma rays, and cosmic rays make up the full electromagnetic spectrum.

What is thermal radiation, exactly?

Thermal radiation is the process of transferring heat through electromagnetic radiation that is produced by thermal motion of matter particles.This electromagnetic radiation is located in the infrared portion of the spectrum, which is invisible to most Earthly bodies.

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Why does magnesium bromide have a 2?

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There are two bromide ions are required for every magnesium ion, so, magnesium bromide has a 2.

The chemical formula of magnesium bromide is [tex]MgBr_2[/tex]

As we know, the atomic number of magnesium is 12, while the atomic number of bromine is 35.

So, the electron distribution of Mg will be - 2,8,2

So, Mg needs to release its 2 electrons to complete its octet.

The electronic configuration of Br will be [tex]1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^5.[/tex]

Here, the valence electrons are in the 4s and 4p orbitals giving Bromine 7 valence electrons.

So, bromine needs one electron to complete its octet.

From above we can conclude that,

For compensating 2 electrons of Mg, 2 atoms of Bromine is required.

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The greater efficiency achieved with the curved blades of a pelton wheel is due to

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Answer:

bouncing

Explanation:

The greater efficiency achieved with the curved blades of a pelton wheel is due to bouncing.

I need help in this question

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The only true statement about the toy car is " the toy does not approach the spring".

option A is the correct answer.

What is the acceleration of the toy car?

The acceleration of the car is calculated by applying Newton's second law of motion, which states that the force applied to an object is directly proportional to the product of mass and acceleration of the object.

F - Ff = 0

F = Ff

ma = μmg

a = μg

where;

a is the acceleration of the carμ is the coefficient of frictiong is acceleration due to gravity

a = 0.14 x 9.8 m/s².

a = 1.37 m/s²

The distance traveled by the car before stopping is calculated as follows;

v² = u² - 2as

where;

v is the final velocity of the caru is the initial velocitys is the distance travelled

when the car stop's the final velocity, v = 0

0 = u² - 2as

2as = u²

s = u²/2a

s = ( 2² ) / ( 2 x 1.37 )

s = 1.5 m

Thus, the final distance travelled by the car is less than 3 m, hence the car did not come in contact with spring.

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if you could see stars during the day, the drawing above shows what the sky would look like at noon on a given day. the sun is at the highest point that it will reach on this day and is near the stars of the constellation gemini. what is the name of the constellation that will be closest to the sun at sunset on this day?

Answers

The constellation that will be closest to the sun at sunset on this day is called Taurus.

Is there a constellation of the Sun?

But have you ever questioned whether the Sun is a part of any of these constellations. The short answer is that the Sun officially has no constellation, according to both contemporary astronomy and old astrological tradition.

What constellations does the Sun travel through?

After passing through each sign in turn—Scorpius the Scorpion, Ophiuchus the Serpent Charmer, Sagittarius the Archer, Capricornus the Seagoat, Aquarius the Water Bearer, Pisces the Fish, Aries the Ram, Taurus the Bull, Gemini the Twins, Leo the Lion—the Sun returns to Virgo the Maiden, where the cycle starts over again.

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a wooden block of mass 1200g, which moves on a horizontal surface, is subjected to a frictional force of 3 N. How much frictional force will act on the block if we put a 500g weight on it?​

Answers

Answer:

Approximately [tex]4.25\; {\rm N}[/tex] as long as the wooden block continues moving.

Explanation:

Since the wooden block is moving, the friction on the block will be kinetic friction. This friction will be proportional to the magnitude of the normal force on the block. Specifically:

[tex]\begin{aligned}& (\text{kinetic friction}) \\ =\; & (\text{normal force})\, (\text{kinetic friction coefficient $\mu_{k}$}) \end{aligned}[/tex].

In this question, since the surface is horizontal, the only vertical forces on this block will be:

Weight of the block [tex](\text{weight}) = (\text{mass})\, g[/tex] where [tex]g[/tex] is the gravitational field strength, andNormal force on the block.

These two forces will balance each other. Thus, [tex](\text{normal force}) = (\text{weight})[/tex].

[tex]\begin{aligned}(\text{normal force}) &= (\text{weight}) \\ &= (\text{mass})\, g\end{aligned}[/tex].

Substitute to obtain:

[tex]\begin{aligned}& (\text{kinetic friction}) \\ =\; & (\text{normal force})\, (\text{kinetic friction coefficient $\mu_{k}$}) \\ =\; & (\text{mass})\, (\text{kinetic friction coefficient $\mu_{k}$})\, g\end{aligned}[/tex].

In other words, the kinetic friction on the block is proportional to the mass. As long as the block continues moving, increasing mass from [tex]1200\; {\rm g}[/tex] to [tex](1200 + 500)\; {\rm g} = 1700\; {\rm g}[/tex] will increase friction to [tex](1700 / 1200) = (17/12)[/tex] the initial value, [tex](17/12)\, (3\; {\rm N}) \approx 4.25\; {\rm N}[/tex].

A parallel-plate capacitor has a voltage v = 6.0 v between its plates. each plate carries a surface charge density σ = 7.0 nc/m2. what is the separation of the plates?

Answers

The separation of the plates in this parallel-plate capacitor is approximately 6.49 micrometers.

The separation of the plates in a parallel-plate capacitor can be calculated using the equation:

d = ε0 * ∆V/σ

where d is the separation of the plates, ε0 is the electric constant (also known as the permittivity of free space), ∆V is the potential difference between the plates, and σ is the surface charge density on the plates.

In this case, the potential difference between the plates is given as v = 6.0 V, and the surface charge density on the plates is given as σ = 7.0 nC/m^2. Plugging these values into the equation above, we get:

d = (8.85 x 10^-12 C^2/N*m^2) * (6.0 V) / (7.0 nC/m^2)

This simplifies to:

d = 6.49 x 10^-6 m

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After the core of a massive star becomes a neutron star, the rest of the star’s material

a. Continues regular fusion and returns to the main sequence
b. Is vaporized by the incredible heat of the dying star and is ejected outward
c. Falls inward and gets compressed to incredible densities.
d. Makes a planetary nebula, which gently moves outward from the center

Answers

After the core of a massive star becomes a neutron star, the rest of the star’s material falls inward and gets compressed to incredible densities.

The correct option is C.

What is considered a massive star?

Star which is larger than eight solar masses during its regular main sequence lifetime is considered a massive star.

Massive stars typically have a quick main sequence phase, a short red supergiant phase, and a spectacular death via a supernova explosion.

If the core of a massive star becomes a neutron star, the rest of the star’s material is known be be compressed to incredible densities.

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What are some of the safety procedures to follow when refueling?

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The safety procedures to follow when refueling includes emptying the vehicle and turning of the engine.

Some certain safety procedures has to be followed while refueling the vehicle.

1. We have to make sure that we turn off the engine while refueling because keeping the engine on while refueling can give price to an unexpected explosion.

2. There are certain vehicles that have the gas cylinders in them as a fuel tank, in these cases we have to make sure that there is no one sitting inside the car while refueling. Doing this is not an economical thing and also it can give rise to certain unexpected accidents.

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What is the relationship between wavelength and frequency Mcq?

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The relationship between wavelength and frequency is λ=c/f. According to the equation, v = f λ, frequency and wavelength are inversely proportional to each other.

It is measured in the wave's direction. The frequency decreases as the wavelength lengthens In a similar vein, A wave's wavelength and frequency are inversely related. The quantity of wave crests passing a specific place in a second is known as frequency. In order for this to occur, the wavelengths must be short; at higher frequencies, more wave crests will pass the site each second. The relationship between frequency and wavelength is inversely proportional. Less frequency corresponds to a longer wavelength and vice versa. A wave's wavelength and frequency are inversely proportional. This translates to a small wavelength for waves with a high frequency.

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solid wooden sphere of volume 0.0100 m3 floats freely exactly one-half submerged in a liquid of density 800 kg/m3. a lightweight cord is now tied to the sphere and is used to pull the sphere under the surface and hold it completely submerged. what is the tension in the cord?

Answers

The tension in the cord is 39.2 N.

What is tension in the cord?

The tension in the cord used in pulling down the solid wooden sphere  is equal to the weight of the solid wooden sphere .

The weight of the sphere is calculated from the density of the solid wooden sphere.

S.G = density of solid wooden sphere / density of liquid

where;

S.G is specific gravity of the solid wooden sphere

¹/₂ = ρ / (800 kg/m³)

ρ  = ¹/₂ x 800 kg/m³

ρ  = 400 kg/m³

The mass of the solid wooden sphere is calculated as;

m = density x volume

m = 400 kg/m³  x  0.01 m³

m = 4 kg

The tension in the cord is calculated as follows;

T = W = mg

T = 4 kg  x  9.8 m/s²

T = 39.2 N

Thus, the tension in cord is equal to the weight of the solid wooden sphere submerged in the liquid.

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a ball is swung in a vertical circle such that at one point along its circular path the forces exerted on the ball can be represented by the free body diagram. the magnitude of the tension force exerted on the ball, t, is twice that of the force due to gravity exerted on the ball from earth, fg. what is the location of the ball, and what is the magnitude of the centripetal acceleration of the ball?

Answers

Location of the ball is top of the circle and acceleration is 3g.

Since tension force is more, surely ball is having net force upward and hence, the location of the ball in this case is top of the circle.

Any object that moves in a circle has an acceleration vector towards the center of that circle. This is known as Centripetal acceleration.

total force/ net force when ball is top of the circle is sum of tension force and gravity force.

[tex]F_{net[/tex] = T + mg

Because of this net force, there is centripetal acceleration towards the center.

so, T + mg = ma

2mg + mg = ma

3mg = ma

a = 3 × force of gravity

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What happens to waves when they pass through a narrow opening?

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The act of waves spreading out after passing through a tight opening happens when they cross the edge of a surface, as they are twisted around an object, and as they pass through the aperture's narrow opening. phenomenon where the amplitudes of two or more waves combine.

What happens when a wave enters a narrow passageway?

When a wave runs into a minor obstruction or an opening, it may bend to get around it or pass through it before spreading out. The term "diffraction" refers to this bending or spreading out.

What occurs to waves when they pass through a barrier with a small opening?

A wave that runs into a minor obstruction will typically bend around it. Diffraction is the name given to this wavefront bending.

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How much does CO2 contribute to global warming?

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Co2 alone was responsible for roughly two-thirds of the overall heating effect of all life form greenhouse gases in 2021, according to observations even by NOAA Global Monitoring Lab.

What portion of climate change is CO2 responsible for?

About 76 percent of all greenhouse gas emissions are made up of CO2.Nitrous oxide generates 6 percent of global emissions, while methane, which is mostly produced in agriculture, accounts for 16% of greenhouse gas emissions.

What is the primary cause of global warming?

Fossil fuels, which include coal, oil, and gas, are by far the biggest cause of climate change, contributing more than 75% of all emissions of greenhouse gases and almost 90% of all emission of carbon dioxide.

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This is finance literacy help me ASAP!!!!

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Your marital status, health information, shopping patterns, financial transactions, income, account balances, criminal history, and level of education are not included in your credit report. Thus, option C is correct.

What are the item are found in credit report?

Your credit report contains personal information, credit account history, credit queries, and public records. These details will be provided to the credit reporting agencies by your creditors and lenders. A significant portion of information is utilized to determine your Scores, which tell prospective lenders how creditworthy you are.

All credit reports contain essentially the same types of information, even if Experian, Equifax, and TransUnion format and publish your information differently.

Therefore, The amount of money in your checking account.

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a 700 kg elevator starts from rest. it moves upward for 2.50 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. (a) what is the average power of the elevator motor during this period? correct: your answer is correct. w (b) how does this power compare with the motor power when the elevator moves at its cruising speed? pcruising

Answers

(a) The average power of the elevator motor during this period will be 6431.25 W

(b) Power delivered by the motor during Constant speed motion. is greater than power delivered during moving at a Constant acceleration

Mass of elevator. m=700 kg

Initial velocity.u =0 m/ s

Final velocity v=1.75 m/ s

time [tex]\Delta t[/tex] =2.5 sec

(a) Average power of elevator motor the this during Period [tex]P{avg =\frac{w}{\Delta t}[/tex]

We know [tex]W=F\cdot d \cos \theta[/tex]

[tex]W_{motor }=F_{motor } d \cos 0^{\circ}[/tex]

W_{motor}=F_{motor } d

Net force = F_{net}=F_{motor}mg

As per Newton's Second Law ma =F_ {motor }-mg

Now applying the equation of motion: v=u+at

1.75=0+a*2.5 =>a=0.7 m/s^2

[tex]F_ {motor}=Ma+g=700(0.7+9.8) \\\Rightarrow F_ {motor}=7350 ~N\\d=ut+\frac{1}{2} \times a \times t}^2\\\Rightarrow d=0 t+\frac{1}{2} \times 0.7(2.5)^2\\d}=2.1875 m[/tex]

[tex]W_{motor}=F_{motor} \times d=7350 \times 2.1875=16078.125 J\\P_ {avg }=\frac{W_{motor }}\Delta t}=\frac{16078.125}{2.5}=6431.25 W[/tex]

B) if the elevator is Constant with moving up speed

F_{net}=F_{motor }-mg

But a =0

So, F_motor=mg = 700*9.8=6860 N

So, the value of the distance moved will be:

[tex]\triangle \mathrm{x}=\mathrm{vt}=1.75 \times 2.5=4.375 \mathrm{~m}\\\\\mathrm{~W}_{\text {motor }}=\mathrm{F}_{\text {motor }} \Delta \mathrm{x}=7350 \times 4.375=32156.25 \mathrm{~J}\\\\\mathrm{P}_{\text {avg }}=\frac{32156.25}{2.5}=12865.5\mathrm{w}\\\\[/tex]

[tex]\frac{\left(\mathrm{p}_{\text {avg }}\right) \mathrm{a}}{\left(\mathrm{p}a_{\text {avg }}\right) \mathrm{b}}=\frac{6431.25}{12865.5},\left(\mathrm{p}_{\text {avg }}\right) \mathrm{a}=0.499 \times\left(\mathrm{p}_{\mathrm{avg}}\right) \mathrm{b}[/tex]

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Suppoe that the electric field part of an electromagnetic wave in vacuum i 5 E-3. 1 Co (18 5. 4x101)
(a) What i the direction of propagation?
(b) What i the wavelength ?
(c) What i the frequency?
(d) What i the amplitude of the magnetic field part of the wave?
(e) Write an expreion for the magnetic field part of the wave

Answers

The given question is incomplete, and hence, can not be answered. Still, adding some relevant information for your reference.

What are electromagnetic waves?

Electromagnetic waves, or EM waves, are waves produced by oscillations between electric and magnetic fields. In other words, EM waves consist of oscillating magnetic and electric fields.

Electromagnetic waves are produced when an electric field contacts a magnetic field. Therefore, they are called "electromagnetic waves". The electric and magnetic fields of electromagnetic waves are perpendicular (right angles) to each other. They are also perpendicular to the EM wave direction. The

EM wave propagates in vacuum with a constant velocity of 3.00 x 108 ms-1. They are not deflected by electric or magnetic fields. However, they can exhibit interference or diffraction. Electromagnetic waves penetrate everything, including air, solids, and vacuums. No medium is required to diffuse or move from one place to another.

The given question is incomplete, and hence, can not be answered. Still, adding some relevant information for your reference.

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Why 3 define the term frequency?

Answers

Frequency, in physics, the number of waves that pass fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

What is frequency?

The definition of frequency says that it is the number of complete cycles of a wave passing through a point per unit time.The SI unit of the frequency is Hertz (Hz).Frequency of a sine wave as the number of complete oscillations made by any wave element per unit time.A frequency is in periodic motion, it has gone through one cycle after passing through a series of events or positions and returning to its original state.

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a flat coil of wire consisting of 240 turns, each with an area of 40 cm, is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 0.27 t to -0.77 t in 5.3 s. if the coil has a total resistance of 22 , what is the magnitude of the induced current when the field is -0.25 t?

Answers

magnitude of the induced current        

where  I = 0.5A

 Briefing

Knowing that the formula for magnetic flux is = NBA

Here, N is the number of turns,

B is the magnetic field,

and A is the area of the loop.

Knowing that the coil's EMF will be induced by the rate of change in magnetic flux,

we may calculate it as EMF = NA db/dt.

To find the induced EMF,

we now plug in all values.EMF = 0.2

voltageTherefore, according to Ohm's rule,

Current = EMF/Resistance I = 0.2/0.40.

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if an object is placed beyond the the focal length of a converging lens (s>f) the image will be

Answers

if an object is placed beyond the focal length of a converging len, the image will be real smaller image or real and bigger image depending on the position.

We have four positions of object in front of a converging lens, accordingly there are three types of images formed.

1) When object is placed at infinity - image is real and tiny sized. This image is formed at the focus.

2) when object is placed beyond 2F - image is real and smaller than object.

3) When object is placed at 2F - image is real and equal in size to object.

4) when object is placed between 2F and F - image is real and bigger than object.

A converging lens is a convex lens which converges all the rays coming parallel to the principal axis at a point on the principal axis, called focus.

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What is required to start an object moving?

Answers

To start an object moving, a force must be applied to the object which must be greater than the forces that are acting to keep the object at rest.

The amount of force needed to start an object moving depends on the mass of the object, as well as the type and magnitude of the forces acting on it. For example, it may take more force to start a heavy object moving than a light object, and it may take more force to start an object moving on a rough or slippery surface than on a smooth or sticky surface.

To apply a force to an object, we can push or pull on it, use a lever or other mechanical advantage to amplify the force, or use an external force such as gravity or a motor to move the object. Once the object is moving, it will continue to move unless acted upon by another force.

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What does a capacity plate indicate safe load limit?

Answers

The capacity plate tells us about the maximum load or the maximum number  of people that can be carried by a vehicle.

In boats, the maximum load is measured by the capacity plate Quizlet. The maximum load for a particular region is issued by the authority of that region, which is strictly mandatory to follow. Any violation can lead to strict punishment. Load limit can be calculated by subtracting curb weight from GVWR.

Load limit= GVWR- curb weight

By staying within the load limit one can increase the life of a vehicle also. It is also for human safety purposes.

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Q5. A cyclist travels down a hill from rest at point X, without pedalling. He applies his brakes and the cycle stops at point Y.

Which energy changes have taken place between X and Y?

A) kinetic energy-> heat energy-> gravitational potential energy.

B) gravitational potential energy -> heat energy-> kinetic energy.

C) kinetic energy-> gravitational potential energy-> heat energy.

D) gravitational potential energy-> kinetic energy-> heat energy.​

Answers

Answer:

B

Explanation:

At highest point gravitational energy is higher. While coming down without paddle it starts to gain heat energy and once it reaches the ground the kinetic energy is higher.

I hope my answer helps you.

Object A of mass 2 kg is gravitationally attracted to object B of mass 2 kg as the two objects float in space. Frictional forces are negligible. The gravitational forces of attraction between the two objects are shown in the table above. Which of these claims about the motion of the center of mass of the two objects system is true?
A) The center of mass will not accelerate
B) The center of mass will accelerate at 0.675 x 10 m/s?
C) The center of mass will accelerate at 5.4 x 10 m/s
D) The center of mass will accelerate at 2.7 x 10 m/s

Answers

The center of mass won't accelerate .Option (A)

Center of mass could be a position outlined relative to associate degree object or system of objects. it's the common position of all the components of the system, weighted consistent with their plenty.

from the question,

[tex]a_{com} = \frac{m_1a_1+m_2a_2}{m_1+m_2}[/tex]

the mass of the primary object is M1

the mass of the second object is M2

the acceleration of the primary object is a1

the acceleration of the second object is a2

acceleration (a) = force by mass

a = F/m

a1 = F/m1                                          

where F is force                                           ( F = [tex]2.7\times 10^{-10}[/tex])

a1 = [tex]\frac{2.7 \times 10^{-10}}{2 }[/tex]

a1 = [tex]1.35 \times 10^{-10} m/s^2[/tex]        ( towards right )

a2 = [tex]\frac{2.7 \times 10^{-10}}{2 }[/tex]

a2 = [tex]1.35 \times 10^{-10} m/s^2[/tex]          ( towards left)

so by this we can say this

a1 = [tex]+1.35 \times 10^{-10} m/s^2[/tex]

a2 = [tex]-1.35 \times 10^{-10} m/s^2[/tex]

to find the acceleration of center of mass

[tex]a_{com} = \frac{m_1a_1+m_2a_2}{m_1+m_2}[/tex]

[tex]a_{com} = \frac{2 \times 1.35 \times 10^{-10} -2\times1.35 \times 10^{-10} }{2+2}[/tex]

a = 0 / 4

a = 0

so by this we can say that

The center of mass will not accelerate

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a block of mass m is launched by a spring of negligible mass along a horizontal surface of negligible friction. the spring constant of the spring is k. the spring is initially compressed a distance x0. the block is released from rest. some time after the block is released and travels in the direction shown in the figure, the spring compression is xf. which of the following mathematical calculations can a student use to determine the speed vf of the block at this new position?

Answers

The required speed Vf of the block at this new position 1/2KX²= 1/2KXf ² + 1/2Vf m².

What is kinetic energy?

In physics, the kinetic energy of an object is the energy it has due to its motion. It is defined as the work required to accelerate a body of specified mass from rest to a specified velocity. After the body acquires this energy during acceleration, it retains this kinetic energy as long as the velocity does not change. The same work is done when the body slows down from its current speed to rest. Formally, kinetic energy is any term in the Lagrange of a system that includes the time derivative.

According to question:

In this problem, neglecting friction force, there are two energies at work viz. Potential energy of spring and kinetic energy of spring mass system.

Initially the spring is compressed to  length from the equilibrium position, therefore, initially,

Potential energy= 1/2KX²

(Because potential energy of spring= 1/2×(spring constant)×(compression)²)

At this instance system is at rest, therefore, kinetic energy=1/2mv²=0.

So total initial energy= K.E. + P.E. = 1/2KX²   -(1)

Now in the 2nd instant, spring is compressed to  length from equilibrium, therefore, P.E.=1/2K ²

and velocity=  here,

Therefore, kinetic energy= 1/2 mv²

So total energy= 1/2K ² + 1/2 m²   -(2)

From conversation of energy theorem, (1) and (2) should be equal(Neglecting friction, remember)

Therefore, the correct answer is:  1/2KX²= 1/2KXf ² + 1/2Vf m²

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What happens during 1/2 life of a radioactive isotope?

Answers

A radioactive isotope's half-life is the length of time it takes for one half of it to decay.

What is the radioisotopes' half-life?

The duration needed for a quantity of a radioisotope to decay by half is known as its radioactive half-life. If an isotope has a half-life of only a few hours or less, the majority of the radioactivity will dissipate within a few days.

How does half-life work?

A radioactive element's half-life is the amount of time it takes for it to decay to half of its original value. It can be concluded from this that a source's activity has a half-life if it takes some time before it drops to half its starting value.

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A road undergoes a 2.3 km turn to the N. If the road is to be rated for 100 km/hr, at what angle should the road be banked?

Answers

The angle the road should be banked is determined as 2⁰.

What angle should the road be banked?

The banking angle of the road is calculated by applying the following equation.

tan ( θ ) = v² / rg

where;

θ is the banking anglev is the speed rating of the roadr is the radius of the curveg is acceleration due to gravity

The given parameters includes;

radius of the road = 2.3 km = 2,300 m

speed rating of the road = 100 km/hr = 27.78 m/s

tan ( θ ) = v² / rg

tan ( θ ) = (27.78)² / (2,300 x 9.8)

tan ( θ ) = 0.034

θ = arc tan (0.034)

θ = 2⁰

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2. A rifle can shoot a 4.00 g bullet at a speed of 998 m/s.
a. Find the kinetic energy of the bullet.
b. What work is done on the bullet if it starts from rest?
c. If the work is done over a distance of 0.75 m, what is the average
force on the bullet?
d. If the bullet comes to rest after penetrating 1.50 cm into a piece of
metal, what is the magnitude of the force bringing it to rest?
Posted Thu Oct 27, 2022 at 9:11 am

Answers

a) The kinetic energy of the bullet is 1.996 joule.

b) The total work done on it is 1.996 joule.

c)  The average force on the bullet is 2.661 N.

d) The  magnitude of the force bringing it to rest is 1.33 N.

What is speed?

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

Given that: . A rifle can shoot a 4.00 g bullet at a speed of 998 m/s.

a) the kinetic energy of the bullet = (4.00/1000)×998/2 joule = 1.996 joule.

b)  If it starts from rest, the total work done on it = kinetic energy of it = 1.996 joule.

c) If the work is done over a distance of 0.75 m, the average force on the bullet is = work done/distance =  1.996/0.75  N = 2.661 N.

d)  If the bullet comes to rest after penetrating 1.50 cm into a piece of

metal, the magnitude of the force bringing it to rest is = 1.996/1.50 N = 1.33 N.

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