when the first artificial satilite was launched into orbit by the former soviet union in 1957 us president asked his scientific advisors to calculate the mass of the satilite would they have been able to make this calculation?

Answer:

Magnitude of resultant vector will be 4.643 N

Explanation:

We have given x-component of the force vector is given [tex]F_{X}=2.16N[/tex]

And y component of the force vector is given [tex]F_{y}=4.11N[/tex]

We have to find the magnitude of resultant force F

Resultant force will be equal to vector sum of magnitude of x competent and y component of force vector

So F = [tex]\sqrt{F_X^2+F_Y^2}=\sqrt{2.16^2+4.11^2}=4.643N[/tex]

So magnitude of resultant vector will be 4.643 N

Answer:

Average speed =t-2t

Explanation:

Equation given for Average speed = Total distance/Elapsed time

Given: Total distance=d=t^2-2t

Elapsed time= t

Substituting into the equation

Average speed = t^2-2t/t

Dividing both numerator an denomination with t

Average speed=t-2t

Answer:

There are 5.98 electrons are missing from each ions.

Explanation:

Given that,

The electric force between two identical charges is, [tex]F=33\times 10^{-9}\ N[/tex]  

The distance between the charges, [tex]d=0.5\ nm=0.5\times 10^{-9}\ m[/tex]

The electric force between charges is given by :

[tex]F=\dfrac{kq^2}{d^2}[/tex]

[tex]q=\sqrt{\dfrac{Fd^2}{k}}[/tex]

[tex]q=\sqrt{\dfrac{33\times 10^{-9}\times (0.5\times 10^{-9})^2}{9\times 10^9}}[/tex]

[tex]q=9.57\times 10^{-19}\ C[/tex]

Let there are n number of electrons are missing from each ions. It is given by :

[tex]n=\dfrac{q}{e}[/tex]

[tex]n=\dfrac{9.57\times 10^{-19}}{1.6\times 10^{-19}}[/tex]

n = 5.98 electrons

So, there are 5.98 electrons are missing from each ions. Hence, this is the required solution.

As the period of an electromagnetic wave increases, the wavelength of the wave also increases. However, the frequency of the wave remains the same. The energy carried by the wave is inversely proportional to its wavelength, so as the wavelength increases, the energy of the wave decreases.

Electromagnetic waves have properties such as wavelength and frequency. As the period of an electromagnetic wave increases, the wavelength of the wave also increases. This means that the distance between successive crests or troughs of the wave becomes larger. However, the frequency of the wave remains the same. The energy carried by the wave is inversely proportional to its wavelength, so as the wavelength increases, the energy of the wave decreases.

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To solve this problem we will apply the concepts related to the conversion of units for which we will have that 1 slug is equal to 14.59kg. At the same time we will use Newton's second law for which weight is defined as the product between mass and acceleration (Due to gravity). This is then

A: Using the conversion ratio of slug to kilogram we have to,

[tex]1 slug = 14.59kg[/tex]

Then

[tex]m = 280*10^3 slugs (\frac{14.59kg}{1slug})[/tex]

[tex]m = 4.09*10^6kg[/tex]

B: Using Newton's second law we have to,

[tex]W = mg[/tex]

[tex]W = (4.09*10^6)(9.8)[/tex]

[tex]W = 40034960N\approx 4*10^7N[/tex]

The net torque on the circular object, considering the three forces acting on it, is calculated to be 1.46 N × m in an anti-clockwise direction.

To find the net torque on the circular object about its axle, we will first consider each of the three forces acting on it separately and determine the torque produced by each force. Torque (Τ) is defined by the equation Τ = r  ×  F  × sin(θ), where r is the radius at which the force is applied, F is the magnitude of the force, and θ is the angle between the force and the direction of the radius.

The 12 N force acts on the outer radius, so r = 0.26 m (26 cm converted to meters). Since the force is perpendicular to the radius, θ = 90 degrees, and the sin(90) = 1. Therefore, the torque from this force is Τ = 0.26 m × 12 N × 1 = 3.12 N × m.

The 16 N force also acts on the outer radius at 90 degrees to the radius, so its torque is Τ = 0.26 m × 16 N × 1 = 4.16 N   × m.

The 26 N force acts at an angle 30 degrees below the horizontal, so it makes an angle of 60 degrees with the radius. Hence, the torque from this force is Τ = 0.26 m × 26 N  × sin(60) = 5.82 N × m (rounded to two decimal places).

To find the net torque, we need to consider the direction of each torque. Both the 12 N and 16 N forces produce torque in the same direction (let's say clockwise), whereas the 30 degree component of the 26 N force produces torque in the opposite direction (counter-clockwise).

Net torque = Torque from 12 N + Torque from 16 N - Torque from 26 N = 3.12 N × m + 4.16 N × m - 5.82 N × m = 1.46 N   × m (anti-clockwise).

Answer:

27000 Nm

Explanation:

The boom end at A is fixed and end at B is subjected to a 3kN force. Boom AB has length of 9m. The moment about A is the product of force 3kN (3000 N) at B and the moment arm of 9m

M = FL = 3000 * 9 = 27000 Nm

So the moment about A is 27000 Nm

Answer:

[tex]1.67\times 10^{-27}kg[/tex]

Explanation:

We are given that mass of proton

[tex]1.672623\times 10^{-27}kg[/tex]

There are seven significant figures.

We have to round off.

If we round off to three  significant figures

The  thousandth place  of given mass of proton  is less than five therefore, digits on left side of  thousandth  place remains same and digits on right side of thousandth place and thousandth  replace by zero

Therefore, the mass of proton can be written as

[tex]1.67\times 10^{-27}kg[/tex]

Hence, the mass of proton is [tex]1.67\times 10^{-27}kg[/tex]

To round the mass of a proton to seven significant figures, the correct way is to round up the last significant figure if it is 5 or greater, and if it is less than 5, simply drop the remaining digits.

To round the mass of a proton, we look at the digit right after the desired number of significant figures, which in this case is the seventh significant figure. If this digit is 5 or greater, we round up the last significant figure. If it is less than 5, we simply drop the remaining digits.

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Answer:

c.)

Explanation:

Assuming no other forces acting on the charges, if as time goes on, the magnitude of the force exerted on each of the particles decreases, as the electric force is inversely proportional to the square of the distance between charges, the only explanation is that this distance is increasing, so the force on both charges is repulsive.

When the force is repulsive, all we can say, is that both charges are of the same type, so they can be both positively charged or both negatively charged, as stated by the choice c).

Answer:

Fac = 21 KN

Fad = 64.29 KN

Explanation:

Step 1: Find the unit vectors in BA , CA, and DA directions

BA = -16 i + 48 j - 12 k

CA = -16 i + 48 j + 24 k

DA = 14 i + 48 j

The following magnitudes

mag (BA) = sqrt ( 16 ^2 + 48^2 + 12^2 ) = 52

mag (CA) = sqrt ( 16 ^2 + 48^2 + 24^2 ) = 56

mag (DA) = sqrt ( 14 ^2 + 48^2 ) = 50

Now compute unit vectors

unit (BA) = (-4 / 13) i + (12 / 13) j - (3 / 13) k

unit (CA) = (-2 / 7) i + (6 / 7) j - (3 / 7) k

unit (DA) = (7 / 25) i + (24 / 25) j

Step 2: Compute Force Vectors F(ml) dot unit( ML )

Fab = (-4*Fab / 13) i + (12*Fab / 13) j - (3*Fab / 13) k

Fac =  (-2*Fac / 7) i + (6*Fac / 7) j - (3*Fac / 7) k

Fad = (7*Fad / 25) i + (24*Fad / 25) j

Step 3: Equilibrium force equations in x and z direction

Fr,x = 0 = 39*( -4 / 13 ) - Fac*( 2 / 7 ) + Fad*( 7 / 25 )

Fr,z = 0 = 39*( -3 / 13 ) + Fad*( 3 / 7 )

Step 4: Solve the above equations for Fca and Fda

Fca = 21 KN

Fda = 64.29 KN

Answer:

5.994 kgm/s

Explanation:

Momentum: This can be defined as the product of the mass of a body to the velocity of that body. The S.I unit of momentum is kgm/s.

Mathematically, momentum can be expressed as,

M = mv.................................... Equation 1

Where M = momentum of the baseball, m = mass of the baseball, v = velocity of the baseball.

Given: m = 155 g = (155/1000) kg = 0.155 kg. v = 87 miles per hour = 87(1600/3600) m/s = 38.67 m/s.

Substituting into equation 1

M = 0.155(38.67)

M = 5.994 kgm/s.

Thus the momentum of the baseball = 5.994 kgm/s

The magnitude of the momentum of a baseball with a mass of 155 g thrown at 87 mph is approximately 6.03 kg·m/s after converting units and applying the momentum equation.

To calculate the magnitude of the momentum of a baseball thrown at a speed of 87 miles per hour, we use the formula p = mv, where p is the momentum, m is the mass in kilograms, and v is the velocity in meters per second. First, we need to convert the mass of the baseball from grams to kilograms (155 g to 0.155 kg) and the speed from miles per hour to meters per second (87 mph to 38.88 m/s, using the conversion factor 1 mile = 1600 meters and 1 hour = 3600 seconds).

Then, we substitute the values into the momentum equation to find the momentum: p = (0.155 kg)(38.88 m/s) = 6.0264 kg·m/s. Therefore, the magnitude of the momentum of the baseball is approximately 6.03 kg·m/s when rounded to two decimal places.

Answer:

(a) A = m/s^3, B = m/s.

(b) dx/dt = m/s.

Explanation:

(a)

[tex]x = At^3 + Bt\\m = As^3 + Bs\\m = (\frac{m}{s^3})s^3 + (\frac{m}{s})s[/tex]

Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.

(b) [tex]\frac{dx}{dt} = 3At^2 + B = 3(\frac{m}{s^3})s^2 + \frac{m}{s} = m/s[/tex]

This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.

Explanation:

We know magnetic field due to a charge q moving with a velocity v [tex]=\dfrac{\mu_oq}{4\pi r^3}(v \times r)[/tex].

Case A:

r=0.5i

Putting value of r, q and v .

We get, [tex]B=-2.34\times 10^{-5} \ k.[/tex] [tex](\ j\times i=-k)[/tex]

Case B:

r=0.5 j

B=0 [tex]( j\times j=0)[/tex]

Case C:

We get, [tex]B=2.34\times 10^{-5} \ i\ (Since\ , j \times k=i)[/tex]

Case D:

We get , [tex]B=8.28\times 10^{-6} \ T \ i[/tex].

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(a) The volume occupied by the water vapor is V = 1.08 m³.

(b) The amount of water vapor present is 277.78 gram-moles.

(c) The number of molecules is [tex]\rm\(1.67305 \times 10^{26}\)[/tex] molecules.

Given:

Specific volume (v) = 0.2160 m³/kg

Mass of water vapor (m) = 5 kg

One gram-mole of water vapor = 18 g

Avogadro's number [tex]\rm (\(N_A\))[/tex] = [tex]\rm \(6.023 \times 10^{23}\)[/tex]

(a) The volume occupied by the water vapor (V) can be calculated using the formula: [tex]\rm \[ V = m \times v \][/tex]

Substitute the values:

[tex]\rm \[ V = 5 \, \text{kg} \times 0.2160 \, \text{m³/kg} \]\\\rm V = 1.08 \, \text m\³[/tex]

(b) The amount of water vapour present in gram moles can be calculated using the formula:

[tex]\rm \[ \text{Amount of water vapor} = \frac{m}{\text{One gram-mole of water vapor}} \][/tex]

Substitute the value of one gram-mole of water vapor [tex](\(18 \, \text{g}\))[/tex]:

[tex]\[ \text{Amount of water vapor} = \frac{5 \, \text{kg} \times 1000}{18 \, \text{g}} \]\\\\\ \text{Amount of water vapor} = 277.78 \, \text{gram-moles} \][/tex]

(c) The number of molecules can be calculated using Avogadro's number:

[tex]\rm \[ \text{Number of molecules in 1 gram-mole} = N_A \\= 6.023 \times 10^{23} \, \text{molecules} \][/tex]

So, the number of molecules in 1 gram of water vapor is [tex]\rm \(\frac{N_A}{18}\)[/tex] molecules.

The number of molecules in [tex]\rm \(5 \, \text{kg}\)[/tex] of water vapor is:

[tex]\rm \[ \text{Number of molecules} = 5 \times 1000 \times \frac{N_A}{18} \, \text{molecules} \][/tex]

Now, calculate the number of molecules:

[tex]\rm \[ \text{Number of molecules} = 1.67305 \times 10^{26} \, \text{molecules} \][/tex]

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Final answer:

Type m · a to correctly enter the multiplication of m and a, ensuring clarity in expressions, especially when dealing with scientific notation which simplifies multiplication and division by manipulating coefficients and powers of ten separately.

Explanation:

When entering the expression m times a, you should use proper notation to differentiate between multiplication and adjacent variables or numbers. Instead of using 'x' as the multiplication symbol, as you might on paper, use the multiplication dot, represented by typing m · a with your keyboard. This avoids confusion, especially in contexts like scientific notation, where clarity is crucial. For example, 1·105 is not the same as 1 followed by 105. So, it is important to insert the multiplication dot to clarify that you are multiplying 1 by 10 raised to the 5th power.

In scientific notation, multiplication and division are simplified by separately manipulating the coefficients and the powers of ten. For instance, to multiply two numbers in scientific notation, such as (3 × 105) × (2 × 10°), you would multiply 3 by 2 to get 6, and then add the exponents (5 + 0) to get 5, resulting in an answer of 6 · 105. This simplifies calculations incredibly, especially with large numbers.

Answer:

422.36 N

Explanation:

given,

time of rotation = 4.30 s

T = 4.30 s

Assuming the diameter of the ring equal to 16 m

radius, R = 8 m

[tex]v = \dfrac{2\pi R}{T}[/tex]

[tex]v = \dfrac{2\pi\times 8}{4.30}[/tex]

  v = 11.69 m/s

now, Force does the ring push on her at the top

[tex]- N - m g = \dfrac{-mv^2}{R}[/tex]

[tex] N + m g = \dfrac{mv^2}{R}[/tex]

[tex] N = \dfrac{mv^2}{R}- m g[/tex]

[tex] N = m(\dfrac{v^2}{R}- g)[/tex]

[tex] N = 58\times (\dfrac{11.69^2}{8}- 9.8)[/tex]

N = 422.36 N

The force exerted by the ring to push her is equal to 422.36 N.

The force does the ring push on her at the top of the ride will be [tex]N=422.36\ Newton[/tex]

It is Given that

Time rotation  T= 4.30 s

Mass m= 58 kg

Now the Velocity will be calculated as

[tex]V=\dfrac{2\pi r}{T} =\dfrac{2\pi 8}{4.30} =11.69 \frac{m}{s}[/tex]

Now by balancing the forces

[tex]N=\dfrac{mv^2}{R} -mg[/tex]

[tex]N=m(\dfrac{v^2}{R} -g)[/tex]

[tex]N=58\times (\dfrac{11.69^2}{8} -9.8)[/tex]

[tex]N=422.36 \ Newton[/tex]

Thus the force does the ring push on her at the top of the ride will be [tex]N=422.36\ Newton[/tex]

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Answer: Frequency distribution helps to understand data. some complex data needs to be converted into intervals to see its frequency of occurrence. it helps to find the mean median and mode of the data. It helps in the analysis of data and its practical implementation.

Explanation:

Answer:

Explanation:

In absence of friction

Work done by force is given by change in kinetic energy of box

According work Energy theorem change in kinetic Energy of object is equal to work done by all the forces

[tex]W_1=\frac{1}{2}mv^2-0[/tex]

[tex]W_1=\frac{1}{2}mv^2[/tex]

where m=mass of object

[tex]W_2=\frac{1}{2}m(2v)^2-\frac{1}{2}mv^2[/tex]

[tex]W_2=\frac{3}{2}mv^2[/tex]

[tex]\frac{W_2}{W_1}=\frac{\frac{3}{2}mv^2}{\frac{1}{2}mv^2}[/tex]

[tex]W_2>W_1[/tex]

so work done in second case is three times of first case

(b)In Presence of friction

[tex]W_f+W_1=\frac{1}{2}mv^2[/tex]

suppose [tex]f_r[/tex] is the friction force and d is the displacement

so [tex]W_f=f_r\cdot d\cos 180[/tex]

[tex]W_f=-f_r\cdot d[/tex]

[tex]W_1=\frac{1}{2}mv^2+f_r\cdot d[/tex]

for second case when speed increases v to 2v

[tex]W_2=\frac{3}{2}mv^2+f_r\cdot d[/tex]

thus [tex]W_2>W_1[/tex] when friction is present                  

The work done to accelerate the box from zero is lesser than the work done to accelerate the box from velocity [tex]v[/tex].

Work can be defined as the change in the kinetic energy of the object.

So,

In the first Scenario,

[tex]W_1 = \dfrac 12 mv^2- 0\\\\W_1 = \dfrac 12 mv^2[/tex]

In the second scenario,

[tex]W_2 = \dfrac 12 m(2v^2) -\dfrac 12 mv^2\\\\W_2 = \dfrac 32 mv^2[/tex]

Now compare both scenarios,

[tex]\dfrac {W_1}{W_2}=\dfrac{ \dfrac 32 mv^2}{\dfrac12 mv^2}[/tex]

So, [tex]W_1 <W_2[/tex]

Therefore, the work done to accelerate the box from zero is lesser than the work done to accelerate the box from velocity [tex]v[/tex].

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Answer

Organ Pipe A has both end open.

Organ Pipe B has one end open.

speed of sound, v = 343 m/s

The fundamental frequency = 270 Hz

wavelength of the pipe when both end open

  λ = 2 L

we know,

 [tex]\lambda = \dfrac{v}{f}[/tex]

now,

 [tex]L = \dfrac{v}{2f}[/tex]

inserting all the values

 [tex]L = \dfrac{343}{2\times 270}[/tex]

  L_A = 0.635 m

length of pipe A is equal to 0.635 m

b) since third harmonic of pipe B is equal to second harmonic of pipe A

     [tex]f_B = f_A[/tex]

     [tex]\dfrac{n_BV}{4L_B} = \dfrac{n_AV}{2L_A} [/tex]

     [tex]L_B= \dfrac{2n_BL_A}{4n_A}[/tex]      

     [tex]L_B= \dfrac{2\times 3 \times 0.635}{4\times 2}[/tex]

        L_B = 0.476 m

length of pipe B is equal to 0.476 m.

Answer:

B

Explanation:

Geographically throughout this area of Mexico, Central America Caribbean is located the Cocos plate. This area is scientifically known as the Central American subduction zone.

In order for a volcano to form, there is usually a clash between the technical plates that generates the elevation of the ground and the connection with ducts that release the magma from the earth. If this entire area is a subduction area, it will also be a land stress release area where volcano lines will be formed, that is, it is a convergent plate boundary area

The relationship between the epicenters of the earthquake and the position of the volcano should be explained below.

When the Mexico area should be geographically located, so the Caribbean of central America should be located on the Cocos plate. So this area should be called as the subduction zone. At the time when the volcano should be created so there is normally clash that lies between the technical plats where it generated the ground elevation and the linked with the ducts due to this, it releases the magma from the earth.

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There are some mistakes in the question as units pressure and air density are not written correctly.The correct question is here

On a summer day in Narragansett, Rhode Island, the air temperature is 74°F and the barometric pressure is 14.5 lbf/in². Estimate the air density in kg/m³.

Answer:

p=1.175 kg/m³

Explanation:

Given data

Temperature =74 F

Barometric pressure=14.5 lbf/in²

To find

Air density

Solution

From ideal gas law

[tex]pV=mRT\\p=(m/V)RT\\[/tex]

As mass/volume is pressure So

[tex]p=\frac{P}{RT}[/tex]

First we need to convert barometric pressure lbf/in² to N/m²

So

[tex]Pressure=(14.5lbf/in^{2} )*(\frac{6894.76N/m^{2} }{lbf/in^{2} } )\\Pressure=99974.02N/m^{2}[/tex]

Now Substitute the given value and pressure to find air density

[tex]p=\frac{P}{RT}\\ p=\frac{99974.02N/m^{2} }{(287J/kg.K)(\frac{74^{o}F-32}{1.8}+273.15 )}\\ p=\frac{99974.02N/m^{2} }{(287J/kg.K)*296.48K}\\ p=1.175kg/m^{3}[/tex]  

Answer:

B and D is neutral. A and C have opposite charges.

Explanation:

Opposite charges attract each other and similar charges repel each other. Furthermore, a neutral object is attracted to a charged object whether negative or positive.

- If the balls B, C, and D is attracted to A, then their charge is either opposite to that of A or neutral.  

- If the balls B and D have no effect on each other, then both balls are neutral.

- If B is neutral and attracted to C, then ball C have opposite charges than A.

Finally, B and D is neutral. A and C have opposite charges. Whether they are positive or negative cannot be determined by the information given in the question.

Answer:

Star A is brighter than Star B by a factor of 2754.22

Explanation:

Lets assume,

the magnitude of star A = m₁ = 1

the magnitude of star B = m₂ = 9.6

the apparent brightness of star A and star B are b₁ and b₂ respectively

Then, relation between the difference of magnitudes and apparent brightness of two stars are related as give below: [tex](m_{2} - m_{1}) = 2.5\log_{10}(b_{1}/b_{2})[/tex]

The current magnitude scale followed was formalized by Sir Norman Pogson in 1856. On this scale a magnitude 1 star is 2.512 times brighter than magnitude 2 star. A magnitude 2 star is 2.512 time brighter than a magnitude 3 star. That means a magnitude 1 star is (2.512x2.512) brighter than magnitude 3 bright star.

We need to find the factor by which star A is brighter than star B. Using the equation given above,

[tex](9.6 - 1) = 2.5\log_{10}(b_{1}/b_{2})[/tex]

[tex]\frac{8.6}{2.5} = \log_{10}(b_{1}/b_{2})[/tex]

[tex]\log_{10}(b_{1}/b_{2}) = 3.44[/tex]

Thus,

[tex](b_{1}/b_{2}) = 2754.22[/tex]

It means star A is 2754.22 time brighter than Star B.

Star A is brighter than Star B by approximately 2512 times.

The brightness of stars is measured using the magnitude scale. The smaller the magnitude, the brighter the star. In this case, Star A has a magnitude of 1.0 and Star B has a magnitude of 9.6. Since Star A has a smaller magnitude, it is brighter than Star B. The difference in magnitude between the two stars can be calculated using the formula:

difference = 2.512^(m₁ - m₂)

where m₁ is the magnitude of Star A and m₂ is the magnitude of Star B. Plugging in the values, we get:

difference = 2.512^(1.0 - 9.6) ≈ 2512

Therefore, Star A is approximately 2512 times brighter than Star B.

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The speed in the second segment is 36 m/s, in the third segment is 144 m/s, and the volume flow rate through the pipe is 3.38 L/s.

A: Using the principle that the volume flow rate remains constant in an incompressible fluid, we can calculate the speed in the second segment to be 36 m/s and the speed in the third segment to be 144 m/s.

B: The volume flow rate through the pipe can be calculated by applying the equation Q = Av, where Q represents the flow rate, A is the cross-sectional area, and v is the velocity of the fluid. Given the diameter changes, the volume flow rate is 3.38 L/s.

C: The primary concept involved in this problem is the relationship between cross-sectional area and fluid velocity as the diameter changes along the pipe, affecting the flow rate.

Answer:

[tex]V=-130000x+1080000[/tex]

Explanation:

Linear Dependence

Some variables are known or assumed to have linear dependence which means the graph of the ordered pairs (x,V) is a straight line.

If we know two points of the line, we can come up with the exact equation and therefore make predictions for other values of x

The linear depreciation gives us these points (2,820000) and (5,430000)

The general equation of the line is

[tex]V=mx+b[/tex]

Where V is the machine value and x is the  number of years after purchase. We need to find the values of m and b.

Replacing the first point

[tex]820000=m(2)+b[/tex]

[tex]2m+b=820000[/tex]

Replacing the second point

[tex]5m+b=430000[/tex]

Subtracting them  

[tex]-3m=390000[/tex]

[tex]m=-130000[/tex]

Replacing in any of the equations, say, the first one

[tex]2(-130000)+b=820000[/tex]

Solving for b

[tex]b=820000+260000[/tex]

[tex]b=1080000[/tex]

The formula for the machine value V is  

[tex]\boxed{V=-130000x+1080000}[/tex]

Formula for the machine value V in x year is v = -130000(x) + 1,080,000

What information do we have?

Cost of machine after 2 year = $820,000

Cost of machine after 5 year = $430,000

Liner depreciation equation

v = mx + b

After 2 year

820,000 = m(2) + b

820,000 = 2m + b .........   Eq1

After 5 year

430,000 = m(5) + b

430,000 = 5m + b .........   Eq2

Eq2 - Eq1

3m = -390,000

m = -130,000

From Eq

430,000 = 5m + b

430,000 = 5(-130,000) + b

b = 1,080,000

Liner equation of tha cost.

Amount of machine = mx + b

Amount of machine = -130000(x) + 1,080,000

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Answer:

n=0.03928 moles

Moles of oxygen do the lungs contain at the end of an inflation are 0.03928 moles

Explanation:

The amount of oxygen which lung can have is 20% of 5 L which is the capacity of lungs

Volume of oxygen in lungs =V=5*20%= 1 L=[tex]1*10^{-3} m^3[/tex]

Temperature=T=[tex]37^oC=273+37=310K[/tex]

Pressure at sea level = P= 1 atm=[tex]1.0125*10^5 Pa[/tex]

R is universal Gas Constant =8.314 J/mol.K

Formula:

[tex]n=\frac{PV}{RT}\\n=\frac{(1.0125*10^5) *(1*10^{-3})}{(8.314)*310} \\n=0.03928 mol[/tex]

Moles of oxygen do the lungs contain at the end of an inflation are 0.03928 moles

Answer:

(a) 2.33 J.

(b) 1.87 m/s.

Explanation:

(a)

[tex]F(x) = (2.5 - x^2)\^i[/tex]

The force as a function of position is given above. Since the force is a function of position, we can assume that we will use work-energy theorem.

[tex]W = \Delta K = K_2 - K_1\\\int\limits^2_0 {F(x)} \, dx = \frac{1}{2}mv_2 - 0\\\int\limits^2_0 {(2.5-x^2)} \, dx = (2.5x - \frac{x^3}{3})\left \{ {{x=2} \atop {x=0}} \right. = (5 - 8/3) = 7/3[/tex]

Therefore, the kinetic energy of the block is 2.33 J.

(b) In order to find the maximum speed in this interval, we need to investigate the acceleration of the block. Since acceleration is the derivative of velocity, velocity is at its maximum when acceleration is zero.

From Newton's Second Law:

[tex]F = ma\\a(x) = F(x)/m = 1.66 - 0.66x^2[/tex]

In order this to be zero:

[tex]1.66 - 0.66x^2 = 0\\x = 1.58~m[/tex]

The velocity of the block at x = 1.58 m can be found by work-energy theorem.

[tex]\int\limits^{1.58}_0 {(2.5-x^2)} \, dx = \frac{1}{2}(1.5)v^2\\ (2.5x-\frac{x^3}{3})\left \{ {{x=1.58} \atop {x=0}} \right. = 2.63 J\\2.63 = \frac{1}{2}(1.5)v^2\\v = 1.87~m/s[/tex]

Answer:

L = 47.15 yards

∅ = 55.80°

Explanation:

Given

y = 39 yards

x = 53/2 yards

L = ?

We apply the formula

L = √(x²+y²)

L = √((53/2 yards)²+(39 yards)²)

L = 47.15 yards

The angle between the direction of the net displacement of the ball and the central line of the feild is obtained as follows

∅ = tg⁻¹(y/x)

∅ = tg⁻¹(39/(53/2)) = 55.80°

Answer:

1.962 rad / s², 1.6 s

Explanation:

Radius of the part = 1.0m / 2 = 0.5 m

angular speed = 30 rpm = 30 rpm × (2πrad / rev) × 1 minutes / 60 seconds = 3.142 rads⁻¹

μk = frictional force / normal ( mg )

normal is the force acting upward against the force of gravity

frictional force = - μk mg

since the body came to rest then

Fnet + Ff =  0

Fnet = - Ff

Fnet = ma

ma =  - μk mg

a =  - μkg where g = 9.81

a = - 0.1 × 9.81 = 0.981 m/s²

magnitude of angular acceleration = tangential acceleration / radius = 0.981 / 0.5 = 1.962 rad / s²

b) time for the train to come to rest = angular velocity  / angular angular acceleration = 3.142/ 1.962 = 1.6 s

The equation earlier derived answer this question

Fnet + Ff = 0 since the body came to a rest

Fnet = - Ff and Ff = - μk mg, Fnet = ma

ma = - μk mg

m cancel m on both side

a = - μkg since it magnitude

a = μkg

The coefficient of rolling friction multiplied by gravity gives the tangential acceleration in rolling motion due to the relationship between frictional force and the object's acceleration.

The reason why the coefficient of rolling friction multiplied by gravity gives the tangential acceleration is due to the relationship between the frictional force and the force responsible for the acceleration of the object. In the case of rolling motion, the frictional force opposes the rotation and contributes to the overall acceleration.