Why do scientists often take several measurements of the same object, average them together, and use the average value as the measurement?

Answer:

Technician B

Explanation:

Car engine compression refers to when air and gas are mixed together in the cylinders of an engine. This process is required for the car to move and function. If there are any problems with the compression process, then you can expect to experience all kinds of car problems.

It will be easy to tell when you have a low compression problem because you may experience a misfire when you try to start the engine. Either that or the engine will offer poor performance as you’re driving the vehicle down the road. The worst-case scenario would be the car not starting if all the cylinders have no compression.

Generally speaking, if you have low compression in one(single) cylinder, the engine will start but you’ll likely experience misfires and your vehicle will run rough. If you experience no compression in ALL cylinders, your engine simply won’t start. This rule out A statement.

An engine tune-up is a exercise for engines to undergo regularly. It is a way of making a car's work at the level and standard intended by the car manufacturer when the car was first made. All manufacturers will stipulate a schedule of when a car will required an engine tune-up to ensure that a car runs at it's most efficient

Engine tune-up are imperative to ensure that all the power and efficiency that  your car is capable are being reached . This bring the answer to the question to Tech B.

Answer:

The answer is B

Explanation:

Density of the element lead (Pb) is:

[tex]d_{Pb} =11,3kg/dm^3[/tex]

Density of the element Copper (Cu) is:

[tex]d_{Cu} =7,9kg/dm^3[/tex]

First we need o find the volume of both materials:

[tex]V_{Pb}=5/11,3=440cm^3[/tex]

[tex]V_{Cu}=5/7,9=630cm^3[/tex]

And the buoyant forces on elements are:

[tex]P_{Pb}=440*1*9,81/1000=4,32N[/tex]

[tex]P_{Pb}=630*1*9,81/1000=6,18N[/tex]

Answer:

A. 200 J

Explanation:

The initial kinetic energy depends on the initial speed, while the gravitational potential energy depends on the height, both balls are thrown with the same initial speed and from the same height. Therefore, due to the law of conservation of energy, the balls must have the same mechanical energy (the sum of both energies) when both impact the ground. Since the potential energy is zero at this point, its final kinetic energy must also be the same.

The second ball, thrown vertically upward, will have kinetic energy of 200 joules when it hits the ground, making option A. the correct option.

To answer this question, let's analyze the energy transformations involved. When the ball is thrown downward, it strikes the ground with 200 joules of kinetic energy.

This energy comes from the initial throw plus the gravitational potential energy converted during its fall.

When the second ball is thrown upward, it initially gains gravitational potential energy as it rises, then this potential energy is converted back to kinetic energy as it falls back down.

The initial speed given to the ball in both scenarios is the same, meaning the total energy input into the system is identical for both throws.

Since both balls have the same initial speed and both experience the same gravitational acceleration, the second ball will also have 200 joules of kinetic energy when it hits the ground.

Therefore, the correct answer is A. 200 J.

Answer:

λ = 157 μm

Explanation:

given,

[tex]\vec{E}(y,t)=[ 3.9\times 10^5\ V/m cos(ky-(1.20\times 10^{13}\ rad/s )t)]\vec{k}[/tex]

now,

ω = 1.2 x 10¹³ rad/s

[tex]f =\dfrac{\omega}{2\pi}[/tex]

[tex]f =\dfrac{1.2\times 10^{13}}{2\pi}[/tex]

f = 1.91 x 10¹² Hz

determine the wavelength of the E M wave

 [tex]\lambda = \dfrac{c}{f}[/tex]

 [tex]\lambda = \dfrac{3\times 10^8}{1.91\times 10^{12}}[/tex]

   λ = 1.57 x 10⁻⁴ m

   λ = 157 x 10⁻⁶ m

   λ = 157 μm

hence, the wavelength of the wave is equal to λ = 157 μm

Given that,

here,

As we know,

→ [tex]f = \frac{\omega}{2 \pi}[/tex]

By substituting the values, we get

     [tex]= \frac{1.2\times 10 ^{13}}{2 \pi}[/tex]

     [tex]= 1.91\times 10^{12} \ Hz[/tex]

hence,

The wavelength will be:

→ [tex]\lambda = \frac{c}{f}[/tex]

     [tex]= \frac{3\times 10^8}{1.91\times 10^{12}}[/tex]

     [tex]=157\times 10^{-6} \ m[/tex]

     [tex]= 157 \ \mu m[/tex]

Thus the above response is correct.

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Answer:

C 30 mph

Explanation:

The speed limits in various area's can be concluded as

1. 25- 30 mph in urban residential areas and school districts.

2.55 mph on rural highways, and

3. 70 mph on rural Interstate highways.

so, the correct answer is c

Answer:

The center of mass of a cone is located along a line. This line is perpendicular to the base and reaches the apex. The center of mass is a distance 3/4 of the height of the cone with respect to the apex.

Explanation:

The center of mass of a solid cone is located one-third of the way up from the base.

The center of mass of a solid cone is located at one-third of its height from the base. In this case, the cone is 10 cm high, so the center of mass is located 10 cm * (1/3) = 3.33 cm from the base.

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Answer:

Explanation:

Laws of  refraction:

(a) The incident ray, the refracted ray and the normal at the point of incident all lies in the same plane

(b) The ratio of the sine of incident  to the sine of refraction is a constant for a given pair of media, which is the refractive index of the second medium with respect to the first medium. The is also called Snell's law

from Snell's law,

Index of refraction of the glass = sini/sinr.............. Equation 1

where i = incident angle, r = angle of refraction.

given: i = 45°, r = 30°

Substituting these values into equation 1,

Index of refraction of the glass = sin45°/sin30°

Index of refraction of the glass = (1/√2)/(1/2)

Index of refraction of the glass = 2/√2

Index of refraction of the glass = √2.

Therefore, The Index of refraction of the glass = √2.

Final answer:

To calculate the index of refraction of the glass, we apply Snell's Law, resulting in an index of refraction of approximately 1.41.

Explanation:

To find the index of refraction of the glass, we can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media. Snell's Law states:

n1 * sin(θ1) = n2 * sin(θ2),

where n1 and n2 are the indices of refraction of the first and second media (air and glass, respectively), and θ1 and θ2 are the angles of incidence and refraction. Given that the index of refraction of air is approximately 1 (since it's very close to a vacuum) and using the provided angles (45° and 30°), the calculation will look like this:

1 * sin(45°) = n2 * sin(30°)

Which simplifies to:

1 * √2/2 = n2 * 1/2

After calculating, we find:

n2 = √2

Thus, the index of refraction of the glass is √2, which is approximately 1.41.

Answer: 14.62 Earth days

Explanation:

This problem can be solved by Kepler’s Third Law of Planetary motion:

[tex]T=2 \pi \sqrt{\frac{a^{3}}{GM}}[/tex]

Where:

[tex]T[/tex] is the period of the probe

[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant

[tex]M=1(10)^{13} kg[/tex] is the mass of the comet Churyumov–Gerasimenko

[tex]a=30 km \frac{1000 m}{1 km}=30000 m[/tex] is the semimajor axis of the orbit the probe described around the comet (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit)

[tex]T=2 \pi \sqrt{\frac{(30000 m)^{3}}{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(1(10)^{13} kg)}}[/tex]

[tex]T=1,263,771.768 s \frac{1 h}{3600 s} \frac{1 Earth-day}{24 h}=14.62 Earth-days[/tex]

Hence, the orbital period of the probe is 14.62 Earth days.

The orbital period of the Rosetta space probe, in orbit around the comet Churyumov–Gerasimenko in 2014, is calculated to be approximately 0.178 Earth days using Kepler's Third Law of Planetary Motion and given values.

This question pertains to the calculation of the orbital period of the Rosetta space probe when it entered orbit around the comet Churyumov–Gerasimenko in 2014. First, we establish the gravitational constant (G) as approximately 6.674 × 10^-11 m^3 kg^-1 s^-2. To calculate the orbital period of an object in orbit around a celestial body, we can use Kepler's Third Law of Planetary Motion which states the square of the orbital period T is proportional to the cube of the semi-major axis a. Rearranging this law and substituting, we get T = 2π sqrt(a^3/(G*M)). Applying the given values, we get T = 2π sqrt((30*10^3 m)^3/(6.674 × 10^-11 m^3 kg^-1 s^-2*1.0*10^13 kg)) = 15378 seconds or approximately 0.178 days.

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Answer:

[tex]1.73553\times 10^{-10}\ m[/tex]

Explanation:

h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]

K = Potential difference = 50 V

m = Mass of electron = [tex]9.11\times 10^{-31}\ kg[/tex]

The de broglie wavelength is given by

[tex]\lambda=\dfrac{h}{\sqrt{2mK}}\\\Rightarrow \lambda=\dfrac{6.626\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-31}\times 50\times 1.6\times 10^{-19}}}\\\Rightarrow \lambda=1.73553\times 10^{-10}\ m[/tex]

The wavelength is [tex]1.73553\times 10^{-10}\ m[/tex]

Answer:

Tm = 1,728.38 °C

Explanation:

mass of metal forging (Mm) = 67.2 kg

specific heat capacity of metal forging (Cm) = 438 J/kg°C

initial temperature of metal forging (Tm) = ?

final equilibrium temperature (Te) = 58.3 °C

mass of oil (Mo) = 786 kg

specific heat capacity of oil (Co) = 2950 J/kg°C

temperature of oil (To) = 37.1 °C

Mm × Cf × (Tm - Te) = Mo × Co × (Te - To)

Tm = [tex]\frac{Mo x Co x (Te - To) }{Mm x Cf}[/tex] + Te

Tm = [tex]\frac{786 x 2950 x (58.3 - 37.1) }{67.2 x 438}[/tex] + 58.3

Tm = 1,728.38 °C

Answer:

0.1

Explanation:

mass, m = 5 kg

θ = 60°

Force, F = 10 N

velocity is constant , it means the net force is zero.

So, the component of force along the surface is equal to the friction force

FCosθ = friction force

10 x cos 60 = μ x m x g

where, μ is the coefficient of friction

5 = μ x 5 x 9.8

μ = 0.1

Thus, the coefficient of friction is 0.1

Answer:

The frequency of the standing wave in the second case is higher than that in the first case

Explanation:

The frequency and wavelength of a wave are related.

The moment you sliced the bottle, you've reduced the wavelength of the bottle.

When wavelength decreases, frequency increases and vice versa.

So, When frequency increases in the second case, more wave crests pass a fixed point each second. That means the wavelength shortens. So, as frequency increases, wavelength decreases. The opposite is also true—as frequency decreases, wavelength increases.

Answer:

equal loudness curve

Explanation:

The curves of equal loudness, first established by Munson and Fletcher in 1930 and subsequently recalculated by Robinson and Dadson, show the relationship that must exist between the frequencies and intensities (or sound pressure) of two sine sounds to be perceived equally loudly. , that is, with the same loudness.

The sinusoidal sounds contained along each curve have the same loudness. This frequency dependence would be mainly due to the transfer characteristics of the external and middle ear. It should also be noted that as the sound pressure level increases, the curves become flatter, that is, the frequency dependence is smaller as the sound pressure level increases.

The loudness level of any sound (complex) is determined by comparing its loudness with that of a sinusoidal sound.

A curve plotted as a function of frequency defining the sound pressure level required to give equal loudness is known as an equal-loudness curve. These curves use the phon unit to illustrate how different sound pressure levels are needed at various frequencies for a sound to be perceived as equally loud.

The curve plotted as a function of frequency defining the sound pressure level required to give equal loudness is known as an equal-loudness curve. These curves are critical for understanding how the human ear perceives sound at different frequencies and intensity levels, using a unit called a phon to express loudness numerically. Phons and decibels are defined to be the same at 1000 Hz, which serves as a standardized point of reference. The equal-loudness curves show that at different frequencies, different sound pressure levels are required for a sound to be perceived as equally loud. This phenomenon underlines the non-linear nature of human hearing across the frequency spectrum.

Large numbers of people have compared the loudness of sounds at different frequencies and sound intensity levels to determine these curves. Each curve is labeled with its loudness in phons, and all sounds on a given curve are perceived as equally loud. This concept is vital for various applications, including the design of audio equipment, hearing aids, and soundproofing materials, to ensure sound is produced or mitigated in a manner consistent with human loudness perception.

Answer:

400-450 nm and 670-680 nm

Explanation:

Which wavelengths of light drive the highest rates of photosynthesis?

400-450 nm and 670-680 nm

Light in the violet-blue and red portions of the spectrum is most effective in driving photosynthesis

photosynthesis is the process through which green plant manufacture there food through sunlight, they synthesize nutrient in the this process through chlorophyll thereby releasing oxygen as a bye-product. a spectrum contains 7 colours combined . the violet-blue and red portions of the spectrum is most effective

Answer:

option C

Explanation:

The correct answer is option C

An orange triangular sign on the rear of the vehicle will show that the vehicle will move at a slow speed.

Warning Sign is an important method of conveying the message. Warning sign helps for the smooth movement of the traffic.

A car with an orange sign on the rear will inform the fellow driver that the vehicle is slow and they can overtake it.

Explanation:

The relation between angular frequency and frequency is directly proportional:

[tex]\omega=2\pi f[/tex]

So, if the angular frequency decreases, the frequency also decreases.

The relation between angular frequency and period is inversely proportional:

[tex]\omega=\frac{2\pi}{T}[/tex]

So, if the angular frequency decreases, the period increases.

When the angular frequency of an object in simple harmonic motion decreases, the period increases and the frequency decreases.

When the angular frequency of an object in simple harmonic motion decreases, the effect on the period and frequency is as follows:

Answer:

a) 4.40 s

b) 2.20 s

Explanation:

Given parameters are:

At constant power  ,

initial speed of the car, [tex]v_0=0[/tex]

final speed of the car, [tex]v=32[/tex] mph

At full power,

initial speed of the car, [tex]v_0=0[/tex]

final speed of the car, [tex]v=64[/tex] mph

a)

At constant power, [tex]KE = \frac{1}{2} mv^2[/tex]

At full power, [tex]KE = \frac{1}{2} m(2v)^2[/tex]

So [tex]KE_f = 4KE_i[/tex]

So, time to reach 64 mph speed is 4 times more than the initial time

[tex]t = 4*1.10 =4.40[/tex] s

b)

[tex]v=v_0+at\\a=\frac{v-v_0}{t}=\frac{32-0}{1.1/3600}=104727.27[/tex] [tex]miles/hours^2[/tex]

For final 64 mph speed,

[tex]v=v_0+at\\t=\frac{v-v_0}{a}=\frac{64-0}{104727.27} = 6.111*10^{-4}[/tex] [tex]hours[/tex] = [tex]6.111*10^{-4}*3600=2.20[/tex] s

Answer:

Dermatome. (Ans. C).

Explanation:

Dermatome is defined as the area of the human anatomy skin which is supplied by single spinal sensory nerve root. At the spinal cord these spinal sensory nerve enter the nerve root, and the branches of spinal sensory reach to the periphery of the body.

The sensory nerve which is present in the periphery of the body are the type of nerve which helps to transmit signals from sensation such as pain, temperature, etc. to the spinal cord from some specific area of the anatomy.

Answer:

L= 1.06 m

Explanation:

frequency of a wave in a pipe closed at one end is given by

[tex]f= \frac{v}{4L}[/tex]

L= length of the pipe

v= velocity of wave

therefore, the length of the pipe

[tex]L= \frac{v}{4f}[/tex]

[tex]L= \frac{340}{4\times80}[/tex]

L= 1.06 m

L= 1.06 m far from the wall must you move to find the first quiet spot.

The distance from the wall(i.e the pipe length) you need to move to find the first quiet spot is 1.06 m.

The smallest standing wave pattern, i.e the first fundamental frequency or harmonic for a closed pipe usually consists of one node and an antinode. When the wavelength of a closed pipe of length L is 4 L, the basic standing wave is formed.

The frequency of a sound wave for a closed pipe at one end may thus be represented using the following formula:

[tex]\mathbf{f = \dfrac{v}{4L}}[/tex]

where;

Thus, the length of the pipe can be computed as:
[tex]\mathbf{L = \dfrac{340 \ m/s}{4\times 80 \ Hz}}[/tex]

L = 1.06 m

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Answer:

Resistance of order of 10Kiloohms

Explanation:

Pull up resistors are essential in every microcontroller devices or digital circuits. Which helps prevent floating ( a process of not being able to determine the state of a pin) It works by allowing the state of a pin to be in either a high state or low state. A resistor is connected between the Vcc and the pin.

When the switch is open, the entire voltage flows through the resistor (V=IR). When the switch is closed the pull up resistor and the internal impedance of the pin form a voltage divider to limit the current flow.

The maximum value of a pull-up resistor to avoid floating when the switch is open is typically between 1KΩ to 10KΩ. This helps to prevent excessive current flow and quickly pulls the input pin high to avoid a floating state. Extremely high resistance values, like 1 megaohm, may cause brief floating, potentially leading to incorrect readings.

The maximum value of the pull-up resistor, in order to avoid a floating condition when the switch is open, depends on several factors including the characteristics of the microcontroller's input pin and the voltage level of the system. However, a moderately high resistance value is often chosen in the range of 1KΩ to 10KΩ to prevent excessive current flow when the switch is closed while still pulling the input pin high quickly enough to avoid a floating state when the switch is open. Remember that a pull-up resistor's purpose is to define a state of a digital input pin when it is not otherwise driven by an external component or system.

In some cases, the maximum value of the pull-up resistor will need to be calculated based on the specifications of your particular circuit. An extremely high resistance, like 1 megaohm, can cause the input to float for a very short time, long enough that your microcontroller might read it incorrectly.

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Answer:

D.

Explanation:

8.1X10 to the power of 6 Joules.

Answer:

7.92×10^6Joules

Explanation:

Power is defined as the rate of change in work done. Mathematically, Power = Workdone/Time

Given power = 1.1×10³watts

Time = 2.0hours = 2×60×60

= 7,200seconds

Workdone = power × time

Work done = 1.1×10³×7200

Workdone = 7,920,000Joules

= 7.92×10^6Joules

If the initial speed of the box at Point A is increased by a factor of 2, the final velocity, denoted as W, will also increase by a factor of 2.

If the initial speed of the box at Point A is increased by a factor of 2, the final velocity of the box, denoted as W, will also increase by a factor of 2.

For example, if the initial speed of the box was 10 m/s, after increasing it by a factor of 2, the new speed would be 20 m/s.

Therefore, option (a), It will increase by a factor of two, is the correct answer choice.

Answer:

Vs = 6.73 m/s or Vs = 16.3 m/s

Explanation:

frequency of the trains whistle (f) = 1.64 x 10^{2} Hz = 164 Hz

frequency of beats heard = 4 beats/s = 4 Hz

velocity of the stationary train (Vr) = 0

velocity of sound in air (V) = 343 m/s

velocity of the moving train (Vs) = ?

we can get the velocity of the moving train from the formula below

Fn = f x [tex]\frac{V + Vr}{V - Vs}[/tex] ...equation 1

where Fn = net frequency

substituting the known values into equation 1

168 =  164 x [tex]\frac{343 + 0}{343 - Vs}[/tex]

1.02 = [tex]\frac{343 + 0}{343 - Vs}[/tex]

Vs = [tex]343 - \frac{343 + 0}{1.02}[/tex]

Vs = 6.73 m/s

substituting the known values into equation 1

168 =  160 x [tex]\frac{343 + 0}{343 - Vs}[/tex]

1.05 = [tex]\frac{343 + 0}{343 - Vs}[/tex]

Vs = [tex]343 - \frac{343 + 0}{1.05}[/tex]

Vs = 16.3 m/s

Explanationhe rotational kinetic energy is

[tex]K_{r} =\frac{1}{2} Iω^{2}[/tex]

The moment of inertia  I  for a sphere is  ( 2 / 5 ) m r ^2

. Substituting this in the equation yields

Kr=1/2( ( 2 / 5 ) m r ^2 )([tex](\frac{v}{r})^{2}[/tex]

1/5mv^2

1/5*5.97 × 10 ^24 *(2[tex]\pi[/tex]*6.38*10^6/86400)^2

2.57 × 10 ^29 J

b. kinetic energy of the sun

K.E=1/2*mv^2

the distance from the earth to the sun is given as

.

Answer:

a. 7.43 × 10³⁴ J b. 3.51 × 10³⁸ J

Explanation:

a. The gravitational force of attraction of a body on the surface of the earth equals the centripetal force on it due to the earth.

So, GMm/R² = mRω²

ω = √(GM/R³) where ω = angular speed of the earth. M = mass of earth = 5.972 × 10²⁴ kg, R = radius of earth = 6.4 × 10⁶ m and G = gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg²

The rotational kinetic energy of earth K.E = 1/2Iω² where I = rotational inertia = 2/5MR²

K.E = 1/2Iω²

= 1/2 × 2/5MR² × GM/R³

= GM²/5R

= 6.67 × 10⁻¹¹ Nm²/kg² × (5.972 × 10²⁴ kg)² /(6.4 × 10⁶ m × 5)

= 7.43 × 10³⁴ J

b. Similarly, the rotational kinetic energy of the earth around the sun is

K.E = GM²/5R where M = mass of sun = 1.989 × 10³⁰ kg and R = distance of earth from sun = 1.5047 × 10¹¹ m

K.E = GM²/5R

= 6.67 × 10⁻¹¹ Nm²/kg² × (1.989 × 10³⁰ kg)² / (1.5047 × 10¹¹ m × 5)

= 3.5073 × 10³⁸ J ≅ 3.51 × 10³⁸ J

Answer:

The depth of the crater is 20[m]

Explanation:

We can solve this problem using the kinematics equations, it should be noted that the negative sign of acceleration means that the drop of the object is down.

Data:

a = 1.6[m/s^2]

t = 5 [s]

[tex]y=y_{0} +v_{0} *t-\frac{1}{2} *g*(t)^{2}[/tex]

v0= 0, because there is not initial veocity

y = final distance = 0 the bottom of the crater

g = a = acceleration of the crater [m/s^2]

y0= Point where the ball was dropped. = Distance from the original point to the bottom of the crater.

[tex]y_{0} =\frac{1}{2}*1.6*(5)^{2}\\  y_{0} = 20 [m][/tex]

The maximum allowable current in the cable for the experiment to be accurate, considering Earth's magnetic field is 0.5 Amps. This is calculated using the magnetic field strength formula and rearranging it to find the current.

To answer the question, we would need to use the formula to determine the magnetic field strength generated by a current carrying wire which is B = μ0 * I / 2πr, where B is the magnetic field strength generated by the wire, I is the current, r is the distance from the wire and `μ0` is the permeability of free space which is a constant equal to 4π * 10^-7 T m/A.

Let's rearrange this equation to make I the subject:

I = B * 2πr / μ0

We are told in the question that the maximum magnetic field (B) that does not adversely affect the experiment is 1.0 * 10^-4 T, and the distance (r) is 1.00 m. So substituting these numbers in:

I = 1.0 * 10^-4 T * 2π * 1.00 m / 4π * 10^-7 T m/A

This simplifies to 0.5 A. Therefore, the maximum allowable current in the wire is 0.5 Amps.

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Answer:

Option A.

Explanation:

In quantum physics there is a law to relate the position and the momentum of the particle, it says that if we know with precision where is a quantum particle, we can not know the momentum of this particle, in other words, the velocity of the particle. So, when we measure the velocity of the particle we find the correct value of the particle, but we can not determine with accuracy where is the particle. This law is known as the Heisenberg's uncertainty principle and, its expressed as follows:    

[tex] \Delta x \Delta p \geq \frac{h}{4 \pi} [/tex]

where Δx: is the position's uncertainty, Δp: is the momentum's uncertainty and h: is the Planck constant.  

Therefore, the correct answer is A: measuring the velocity of a tiny particle with an electromagnet has no effect on the velocity of the particle. It only affects the determination of the particle's position.      

I hope it helps you!

Answer:

Ķ rot = 2K rot

When the arms and weight are retracted toward the body, the energy increases by twice the initial kinetic energy because the moment of inertia has decreased coupled with the energy needed to bring the hands towards the body.

Explanation:

K rot = kinetic energy of system when hands + weight are stretched out = ½ Iw²

Where w = angular velocity when arms and weight are stretched out

I = inertia of the system = ( Ie + Ip) where Ie= moment of inertia of the extra weight carried and Ip = moment of inertia of the person.

Ķ rot = final rotational energy when arms and external weight are pulled in = ½Ìŵ² where Ì =( Ìe + Ìp)

And Ìe = inertia of weight when hands are retracted and Ìp = inertia of person when hand are retracted

Using conservation of angular momentum which is

Iw = Ìŵ

Substitute ŵ = (I/Ì)*W in Ķ rot to give

Ķ rot =½Ì *[ (I/Ì) * W ]²

Ķ rot = ½ ( I²/Ì) * w²

Since K rot = ½ I w²

So Ķ rot = K rot ( I/Ì )...eq3

From the question above system inertia reduces by a factor of 2

Ì = ½I

Sub expression into equ3

Ķ rot = 2K rot

Answer:

The greater force on the rope is exerted by:

C. both the same, interestingly enough

Explanation:

Answer:

The angular velocity when the arms are pulled is ω₂= 6.25 rad/s

Explanation:

Assuming that you want to determine the final angular velocity when is the arms are pulled, then it is calculated using the principle of conservation of angular momentum. It states that:

I₁ω₁=I₂ω₂

where I = moment of inertia , ω= angular velocity , 1 and 2 denote the skater with extended hands and pulled respectively.

Thus

I₁ω₁=I₂ω₂

ω₂= I₁ω₁/I₂

replacing values

ω₂= ω₁ *(I₁/I₂) = 5 rad/s *(2.25 kg·m2/1.80 kg·m2) = 6.25 rad/s

ω₂= 6.25 rad/s