A human hair has a thickness of about 60 um. What is this in millimeters

Answer:

The focal length of the concave mirror is -15.5 cm

Explanation:

Given that,

Height of the object, h = 20 cm

Radius of curvature of the mirror, R = -31 cm (direction is opposite)

Object distance, u = -94 cm

We need to find the focal length of the mirror. The relation between the focal length and the radius of curvature of the mirror is as follows :

R = 2f

f is the focal length

[tex]f=\dfrac{R}{2}[/tex]

[tex]f=\dfrac{-31}{2}[/tex]

f = -15.5 cm

So, the focal length of the concave mirror is -15.5 cm. Hence, this is the required solution.

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:

Electric field, E = 45833.33 N/C

Explanation:

Given that,

Separation between the plates, d = 4.8 mm = 0.0048 m

The potential difference between the plates, V = 220 volts

We need to find the electric field between two parallel plates. The relation between the electric field and electric potential is given by :

[tex]V=E\times d[/tex]

[tex]E=\dfrac{V}{d}[/tex]

[tex]E=\dfrac{220}{0.0048}[/tex]

E = 45833.33 N/C

So, the electric field between two parallel plates is 45833.33 N/C. Hence, this is the required solution.

The electric field between the plates is 45833.33 N/C.

Given that the separation d between the plates is 4.8 mm and the potential difference V between the plates is 220 V.

The electric field E between the plates can be calculated by the formula given below.

[tex]E =\dfrac {V}{d}[/tex]

Substituting the values in the above equation, we get

[tex]E = \dfrac {220}{0.0048}[/tex]

[tex]E = 45833.33 \;\rm N/C[/tex]

Hence we can conclude that the electric field between the plates is 45833.33 N/C.

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Answer:

A) v = 1.885 m/s

B) v = 0.39 m/s

C) E = 0.03 J

D) [tex]x(t) = (0.15m)\cos(2\pi (2.0Hz)t)[/tex]

Explanation:

Part A

We will use the conservation of energy to find the speed at equilibrium.

[tex]K_{eq} + U_{eq} = K_A + U_A\\

\frac{1}{2}mv^2 + 0 = 0 + \frac{1}{2}kA^2\\

v = \sqrt{\frac{k}{m}}A[/tex]

where [tex]\omega = \sqrt{k/m}[/tex] and [tex]\omega = 2\pi f[/tex]

Therefore,

[tex] v = 2\pi f A = 2(3.14)(2)(0.15) = 1.885~m/s[/tex]

Part B

The conservation of energy will be used again.

[tex]K_1 + U_1 = K_2 + U_2\\

\frac{1}{2}mv^2 + \frac{1}{2}kx^2 = \frac{1}{2}kA^2\\

mv^2 + kx^2 = kA^2\\

(0.23)v^2 + k(0.10)^2 = k(0.15)^2\\

v^2 = \frac{k(0.15)^2-(0.10)^2}{0.23}\\

v = \sqrt{0.054k}[/tex]

where [tex]k = \omega^2 m = (2\pi f)^2 m = 2(3.14)(2)(0.23) = 2.89[/tex]

Therefore, v = 0.39 m/s.

Part C

Total energy of the system is equal to the potential energy at amplitude.

[tex]E = \frac{1}{2}kA^2 = \frac{1}{2}(2.89)(0.15)^2 = 0.03~J[/tex]

Part D

The general equation of motion in simple harmonic motion is

[tex]x(t) = A\cos(\omega t + \phi)\\

x(t) = (0.15m)\cos(2\pi (2.0Hz)t + \phi)[/tex]

where [tex]\phi[/tex] is the phase angle to be determined by the initial conditions. In this case, the initial condition is that at t = 0, x is maximum. Therefore,

[tex]x(t) = (0.15m)\cos(2\pi (2.0Hz)t)[/tex]

The speed of the mass when passing the equilibrium point is approximately 1.88 m/s, and when it is 0.10 m from equilibrium, the speed is approximately 1.26 m/s. The equation describing the motion of the mass when x was a maximum at t=0 is x(t) = (0.15 m)cos[2π(2.0 Hz)t].

Part A: To determine the speed when the mass passes the equilibrium point, we can use the formula for the velocity of an object in simple harmonic motion, which is v = ωA, where ω is the angular frequency and A is the amplitude. In this case, the angular frequency is given by ω = 2πf, where f is the frequency. So, ω = 2π(2.0 Hz) = 4π rad/s. The amplitude is 0.15 m. Substituting these values into the formula, we get v = (4π rad/s)(0.15 m) ≈ 1.88 m/s.

Part B: To determine the speed when the mass is 0.10 m from equilibrium, we can again use the formula for velocity. Using the same angular frequency ω, we find that v = (4π rad/s)(0.10 m) ≈ 1.26 m/s.

Part C: The total energy of the system can be found using the formula for the total energy of an object in simple harmonic motion, which is E = (1/2)kA², where k is the spring constant and A is the amplitude. In this case, k is not given, so we cannot determine the total energy.

Part D: The equation describing the motion of the mass, assuming that at t=0, x was a maximum, is given by x(t) = (0.15 m)cos[2π(2.0 Hz)t].

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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: 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:

3.170 miles

Explanation:

Conversion from yards to feet:

5580 yards = 5580 yard * 3 ft/yard = 16740 feet

Conversion from feet to miles:

16740 feet = 16740*(1/5280) mile/ft = 3.170 miles.

Therefore, that particular artillery piece has a range R = 3.170 miles

To solve this problem we will apply the concepts related to equilibrium, for this specific case, through the sum of torques.

[tex]\sum \tau = F*d[/tex]

If the distance in which the 600lb are applied is 6in, we will have to add the unknown Force sum, at a distance of 27in - 6in will be equivalent to that required to move the object. So,

[tex]F*(27-6)= 6*600[/tex]

[tex]F = \frac{6*600}{21}[/tex]

[tex]F= 171.42 lb[/tex]

So, Force that must be applied at the long end in order to lift a 600lb object to the short end is 171.42lb

Answer: B. The speed at the bottom is the same for both hills.

Explanation A sled which can also be called a sledge is a vehicle built with a smooth body on the side touching the ground underside which makes it easy for it to be able to slide towards the ground when on a slant hill. The velocity of the sled after it has slid down the Hill and the velocity at the bottom of the Hill will be the same because both point have the same level of steepness. Velocity of a material is directly proportional to the mass of a body and inversely proportional to the time traveled.

The speed of the sled at the bottom of both hills will be the same because the total energy, determined by the height of the hill and not its steepness, remains constant.

The best answer to this question is B. The speed at the bottom is the same for both hills. This is because the total energy of the sled (kinetic plus gravitational potential energy) must remain constant if we assume no friction or air resistance. The height of the hill, not its steepness, determines the total energy. The sled will convert all its potential energy (which depends on the height) into kinetic energy (which affects the speed) as it travels downhill. Hence, if the two hills are of the same height, the sled will have the same speed at the bottom of both hills.

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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.

When an object moves with constant velocity, its acceleration is zero. So, the hay bale's velocity is 1 ft/s, and its acceleration is 0 ft/s2. These values persist irrespective of the horse's distance from the barn.

In the case of the farmer's horse and the hay bale, the horse is moving with a constant velocity of 1 ft/s. When an object moves with constant velocity, its acceleration is zero. This principle stems from the fundamental definition of acceleration as the rate of change of velocity over time. Since the horse's velocity is not changing, acceleration is zero.

Moving on to the velocity of the hay bale: if we suppose that the horse's movement directly influences the lifting of the hay bale, the bale's velocity would also be 1 ft/s. Provided that the system of lifting the bale is suitable for the task, it does not matter how far the horse is away from the barn; the velocity and acceleration values persist. Therefore, regardless of whether the horse is 10 ft away or 100 ft away, the velocity of the hay bale remains 1 ft/s and acceleration 0 ft/s2.

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The hay bale being lifted by the farmer's horse, which is walking at a constant velocity of 1 ft/s, would have the sameconstant velocity with an acceleration of 0 m/s², because there is no change in velocity. Velocity vectors for the horse's movement would remain consistent, indicating the absence of acceleration.

The question involves determining the velocity and acceleration of a hay bale being lifted into a barn loft by a horse walking at a constant velocity. When dealing with such problems in physics, we typically look for changes in velocity over time to find acceleration. In this scenario, since the horse is moving with a constant velocity of 1 ft/s and no information is provided about forces acting on the hay bale or if there is any change in the speed of the horse, we can infer that the hay bale being lifted is moving at the same constant velocity of 1 ft/s, with an acceleration of 0 m/s² (or ft/s²) since there is no change in speed. This is because acceleration is defined as the rate of change of velocity over time, and a constant velocity means no change in velocity.

To conceptualize this, imagine sketching out a series of velocity vectors for the horse's path from one point to the next, indicating consistent motion with no alterations above or below the horizontal axis, representing that there is no acceleration occurring. An example in the given information refers to a racehorse accelerating from rest to 15.0 m/s, indicating that its acceleration can be calculated by dividing the change in velocity by the change in time, giving an average acceleration. But for the farmer's horse walking forward at a constant pace, the situation is quite different since there is no increase in speed.

To reiterate, if the horse maintains a constant velocity, the hay bale will have the same velocity (1 ft/s) and zero acceleration, provided that the system remains unaltered. Calculating acceleration in such cases is straightforward when there's a change in velocity; for constant velocity, the acceleration is simply zero.

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:

B

Explanation:

Answer:

0.833 m³/kg

-14.4 kJ

20 kJ/kg

Explanation:

[tex]\rho[/tex] = Density = 1.2 kg/m³

[tex]V[/tex] = Volume = 0.6 m³

t = Time taken = 1 hour

P = Power = 4 W

Mass is given by

[tex]m=\rho V\\\Rightarrow m=1.2\times 0.6\\\Rightarrow m=0.72\ kg[/tex]

As there is no change in kinetic and potential energy, the specific volume of the tank will be unaffected

[tex]V_{s}=\dfrac{0.6}{0.72}\\\Rightarrow V_s=0.833\ m^3/kg[/tex]

The specific volume at the final state is 0.833 m³/kg

Energy is given by

[tex]E=Pt\\\Rightarrow E=-4\times 1\times 3600\\\Rightarrow E=-14400\ J[/tex]

The energy transfer by work is -14.4 kJ

Change in specific internal energy is given by

[tex]E=-m\Delta u\\\Rightarrow \Delta u=-\dfrac{E}{m}\\\Rightarrow \Delta u=-\dfrac{-14.4}{0.72}\\\Rightarrow \Delta u=20\ kJ/kg[/tex]

The change in specific internal energy is 20 kJ/kg

Answers:

Wilma's average speed over the entire trip is approximately 3.71 m/s, calculated by dividing the total distance by the total time. However, as she returned to her starting point, her total displacement is zero, and thus, her average velocity is 0 m/s.

The average speed is given by the total distance divided by the total time. Since Wilma I. Ball travels the same distance twice (A to B and back), we can say the total distance is 2d. Suppose the distance between A to B is 'd' m. The time taken for the first trip is d/4.51 s, and the time taken for the return trip is d/3.15 s. Therefore, the average speed is given by (2d) / ((d/4.51) +(d/3.15)). This simplifies to approximately 3.71 m/s.

However, average velocity is the total displacement divided by total time. Since she ends at her starting point, her total displacement is zero. Thus, her average velocity over her round trip is 0 m/s.

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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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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:

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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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]

Answer:

1.5 m

Explanation:

given,

wavelength of of the standing waves

λ₁ = 2 m

λ₂ = 1.5 m

to  find wavelength corresponding to higher mode.

we know,

     [tex]wavelength\ \alpha\ \dfrac{1}{n}[/tex]

where n is the mode number.

From the above expression we can say that wavelength is inversely proportional to mode.

Hence , the wavelength corresponding to higher mode is equal to 1.5 m

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.

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

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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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:

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.

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

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.

(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]

Know more about Avogadro's number:

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Answer:

a) The population of prairie dogs after nine months is 280.

b) P(t) = 30 + 30 · t - t²/4 for 0 ≤ t ≤ 60

Explanation:

Hi there!

We have the following information:

The initial population is P(0) = 30.

The rate of growth of the population is the following:

P´(t) = 30 - t/2 where

a) Let´s find the function of the population of prairie dogs P(t). For that, let´s integrate the P´(t) function between t = 0 and t and between P = 30 and P

P(t) = ∫P´(t)

P´(t) = dP/dt = 30 - t/2

Separating variables:

dP = (30 - t/2) dt

∫dP = ∫(30 - t/2) dt

P - 30 = 30 · t - t²/4

P(t) = 30 + 30 · t - t²/4

The population of prairie dogs at t = 9 months will be equal to P(9):

P(9) = 30 + 30(9) - (9)²/ 4

P(9) = 280 prairie dogs

The population of prairie dogs after nine months is 280.

b) P(t) = 30 + 30 · t - t²/4 (it was obtained in part a).

The population of the prairie dog community 9 months later would be 294 prairie dogs, and the population equation for the entire prairie dog community for t months is P(t) = 30t - t^2 / 4 + 30 for 0 ≤ t ≤ 60.

The equation given is P'(t) = 30 - t / 2. This is a differential equation, and to get P(t), we need to find the anti-derivative or integrate P'(t) with respect to time, t. The integral of P'(t) = ∫(30 - t / 2) dt = 30t - t^2/4.

Adding the initial condition, P(0) = 30, we find P(t) = 30t - t^2 / 4 + 30 for 0 ≤ t ≤ 60. Therefore, a. The population of the prairie dog community 9 months later would be P(9) = 30*9 - (9^2) / 4 + 30 = 294 prairie dogs. b. P(t) = 30t - t^2 / 4 + 30 for 0 ≤ t ≤ 60 is the population equation for the entire prairie dog community for t months.

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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