In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.

From Doppler effect we have that the frequency observed for the relation between the velocities is equivalent to the frequency observed. That is mathematically,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

Here,

Speed of sound in water [tex]v = 1522m/s[/tex]

The Dolphin swims directly away from the observer with a velocity [tex]v_s = 8.5m/s[/tex]

Observed frequency of the clicks produced by the dolphin [tex]F_r = 2770Hz[/tex]

Replacing we have,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

[tex]F_s = \frac{v+v_s}{v}[/tex]

[tex]F_s = 2770 (\frac{1522}{1522+8.5})[/tex]

[tex]F_s = 2754.61Hz[/tex]

Therefore the frequency emitted by the dolphin is 2754.61Hz

Answer:

84%

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

[tex]y_0=1\ m[/tex]

x = 10 m

t = Time taken

[tex]v_0[/tex] = 3.5 m/s (assumed, as it is not given)

[tex]A_0=\pi 1.5^2[/tex]

We have the equation

[tex]y=y_0+ut+\dfrac{1}{2}gt^2\\\Rightarrow 0=y_0-\dfrac{1}{2}gt^2\\\Rightarrow t=\sqrt{\dfrac{2y_0}{g}}\\\Rightarrow t=\sqrt{\dfrac{2\times 1}{9.81}}\\\Rightarrow t=0.45152\ s[/tex]

[tex]x=x_0+vt\\\Rightarrow 10=0+v0.45152\\\Rightarrow v=\dfrac{10}{0.45152}\\\Rightarrow v=22.14741\ m/s[/tex]

From continuity equation we have

[tex]Av=A_0v_0\\\Rightarrow A=\dfrac{A_0v_0}{v}\\\Rightarrow A=\dfrac{\pi 1.5^2\times 3.5}{22.14741}\\\Rightarrow A=1.11706\ cm^2[/tex]

Fraction is given by

[tex]f=\dfrac{A_0-A}{A_0}\times 100\\\Rightarrow f=\dfrac{\pi 1.5^2-1.11706}{\pi 1.5^2}\times 100\\\Rightarrow f=84.196\ \%\approx 84\ \%[/tex]

The fraction is 84%

A fraction of the cross-sectional area of the hose hole that Isabella must cover is 84%.

Given the following data:

Vertical distance = 1.0 meters.

Horizontal distance = 10.0 meters.

Radius = 1.5 cm.

Vertical speed = 3.5 m/s.

The time taken to reach a maximum height is given by this formula:

[tex]H=\frac{1}{2} gt^2\\\\t=\sqrt{\frac{2H}{g} } \\\\t=\sqrt{\frac{2\times 1.0}{9.8} }[/tex]

t = 0.452 seconds.

For the velocity required, we have:

[tex]x=x_o+Vt\\\\10=0+V0.452\\\\V=\frac{10}{0.452}[/tex]

V = 22.12 m/s.

From continuity equation, we have:

[tex]A=\frac{A_0V_0}{V} \\\\A=\frac{\pi r^2V_0}{V}\\\\A=\frac{\pi1.5^2 \times 3.5}{22.12} \\\\A=\frac{24.7433}{22.12}[/tex]

A = 1.118 cm^2.

Now, an expression for the fraction of the cross-sectional area is given by:

[tex]F=\frac{A_0-A}{A_0} \times 100\\\\F=\frac{7.0695-1.118}{7.0695} \times 100\\\\F=\frac{5.9515}{7.0695} \times 100\\\\F=0.8419 \times 100[/tex]

F = 84.19 ≈ 84%.

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Answer:

[tex]1.9\times 10^5\ J[/tex]

[tex]1.8\times 10^{2}\ kcal[/tex]

[tex]1.3\times 10^{2}\ kcal[/tex]

[tex]1.2\times 10^{3}\ W[/tex]

Explanation:

m = Mass of person = 60 kg

g = Acceleration due to gravity = 9.81 m/s²

t = Time taken = 10 min and 49 s

Total height

[tex]h=3.7\times 86\\\Rightarrow h=318.2\ m[/tex]

Potential energy is given by

[tex]U=mgh\\\Rightarrow U=60\times 9.81\times 318.2\\\Rightarrow U=187292.52\ J[/tex]

The gravitational potential energy is [tex]1.9\times 10^5\ J[/tex]

The energy in the climb

[tex]\dfrac{187292.52}{0.25}=749170.08\ J[/tex]

Converting to kcal or Cal

[tex]\dfrac{749170.08}{4184}=179.05594\ kcal[/tex]

The amount of energy used to climb [tex]1.8\times 10^{2}\ kcal[/tex]

Amount gone to heat

[tex]179.05594\times 0.75=134.291955\ kcal[/tex]

The amount burned [tex]1.3\times 10^{2}\ kcal[/tex]

Power is given by

[tex]P=\dfrac{E}{t}\\\Rightarrow P=\dfrac{749170.08}{10\times 60+49}\\\Rightarrow P=1154.34526\ W[/tex]

The power is [tex]1.2\times 10^{3}\ W[/tex]

A) Intensity: [tex]4.8 W/m^2[/tex]

B) Intensity: [tex]2.1 W/m^2[/tex]

C) Total intensity: [tex]13.8 W/m^2[/tex]

D) Distance: [tex]1.38\cdot 10^5 m[/tex]

Explanation:

A)

The relationship between intensity of a sound and power emitted is given by

[tex]I=\frac{P}{A}[/tex]

where

I is the intensity

P is the power

A is the surface area at the distance considered

For the speaker in this problem:

P = 60 W

The distance is r = 1.0 m, so the area to consider is the surface of a sphere with this radius:

[tex]A=4\pi r^2 = 4\pi(1.0)^2=12.6 m^2[/tex]

Therefore, the intensity is

[tex]I=\frac{60}{12.6}=4.8 W/m^2[/tex]

B)

For this problem, we can use the same equation we used before:

[tex]I=\frac{P}{A}[/tex]

where in this case, we have:

P = 60 W is the power of the speaker

r = 1.5 m is the distance considered

Therefore, the area of the spherical surface is

[tex]A=4\pi r^2 = 4\pi(1.5)^2=28.3 m^2[/tex]

And so, the intensity here is

[tex]I=\frac{60}{28.3}=2.1 W/m^2[/tex]

C)

In this problem, we have to consider 4 speakers. In order to find the total intensity, we have to add the intensity of each speakers.

For the two front speakers, we have

[tex]P=60 W[/tex]

r = 1.0 m

So we have already calculated their intensity in part A), and it is

[tex]I_1 = I_2 = 4.8 W/m^2[/tex]

For the two rear speakers, we have

[tex]P=60 W[/tex]

r = 1.5 m

So their intensity has been calculated in part B),

[tex]I_3 = I_4 = 2.1 W/m^2[/tex]

Therefore, the total intensity is

[tex]I=I_1 + I_2 + I_3 + I_4 = 4.8+4.8+2.1+2.1=13.8 W/m^2[/tex]

D)

In this case, we want to find the distance r at which the intensity is

[tex]I=10^{-12} W/m^2[/tex]

Using four speakers with power

P = 0.06 W

Since we have 4 speakers, the intensity due to each speaker at the location considered must be

[tex]I'=\frac{I}{4}=\frac{10^{-12}}{4}=2.5\cdot 10^{-13} W/m^2[/tex]

Using the usual equation, we find the area:

[tex]A=\frac{P}{I'}=\frac{0.06}{2.5\cdot 10^{-13}}=2.4\cdot 10^{11} m^2[/tex]

And so, we can find what is the corresponding distance:

[tex]A=4\pi r^2\\r=\sqrt{\frac{A}{4\pi}}=\sqrt{\frac{2.4\cdot 10^{11}}{4\pi}}=1.38\cdot 10^5 m[/tex]

So, the person must be at 138 km.

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The intensity of sound waves can be computed by using the equation I = P / (4πr²). For the minimum discernible intensity, we employ a rearranged version of the same formula to calculate the distance from the car stereo at the threshold of hearing.

The question is about the calculation of sound intensity produced by a car stereo featuring four speakers, each rated at 60 Watts, at various distances. To calculate the intensity (I) of the sound waves at different distances, we use the equation I = P / (4πr²) where P represents power and r is the distance.

For part D, to find the distance (d) at which sound from the stereo could still be discerned, we rearrange the intensity equation to solve for distance, d = √(P / (4πI)). We substitute P with the sound produced (0.06 W) and I with the minimum discernible intensity (10-12 W/m²). Disclaimer: Since external factors like absorption or diffusion are not taken into account, and the car stereo is not treated as a perfect point source emitter, these values serve as approximation.

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To solve this problem we will apply the concepts related to balance. Since the force applied is 3 times the weight, and the weight is defined as the multiplication between mass and gravity, we will have that the dynamic equilibrium ratio would be given by the relation,

[tex]\sum F = ma[/tex]

[tex]3mg-mg = ma[/tex]

Rearranging to find a,

[tex]a = 2g[/tex]

Using the linear motion kinematic equations, which express that the final velocity of the body, and in the absence of initial velocity, is equivalent to the product between 2 times the acceleration by the distance traveled, that is

[tex]v^2 = 2as[/tex]

[tex]v^2 = 2(2g)(0.18)[/tex]

[tex]v^2 = 2(2*9.8)(0.18)[/tex]

[tex]v = 2.66m/s[/tex]

Therefore the upward speed is 2.66m/s

Answer:

[tex]0.005734 s^{-1}[/tex] and 20.86 seconds are the values of the rate constant and the half-life for this process respectively..

Explanation:

Expression for rate law for first order kinetics is given by:

[tex]a_o=a\times e^{-kt}[/tex]

where,

k = rate constant  

t = age of sample

[tex]a_o[/tex] = let initial amount of the reactant  

a = amount left after decay process  

We have :

[tex]a_o=x[/tex]

[tex]a=58\%\times x=0.58x[/tex]

t = 95 s

[tex]0.58x=x\times e^{-k\times 95 s}[/tex]

[tex]\k= 0.005734 s^{-1}[/tex]

Half life is given by for first order kinetics::

[tex]t_{1/2}=\frac{0.693}{k}[/tex]

[tex]=\frac{0.693}{0.005734 s^{-1}}=120.86 s[/tex]

[tex]0.005734 s^{-1}[/tex] and 20.86 seconds are the values of the rate constant and the half-life for this process respectively..

Answer:

318K

113°F

Explanation:

45°C = 45 + 273K = 318K

45°C = (45 × 9/5) + 32 = 81 + 32 = 113°F

Answer:

156.67 m/s

0.45676 times the speed of sound

Explanation:

Distance from the ground = 23.5 km = 23500 m

Time taken by the blast waves to reach the ground = [tex]2\ minutes\ 30\ seconds=2\times 60+30=150\ s[/tex]

Spedd of the wave would be

[tex]Speed=\dfrac{Distance}{Time}\\\Rightarrow v_b=\dfrac{23500}{150}\\\Rightarrow v-b=156.67\ m/s[/tex]

The velocity of the blast wave is 156.67 m/s

v = Velocity of sound = 343 m/s

[tex]\dfrac{v_b}{v}=\dfrac{156.67}{343}\\\Rightarrow v_b=v\dfrac{156.67}{343}\\\Rightarrow v_b=0.45676v[/tex]

The blast wave is 0.45676 times the speed of sound

The average velocity of the blast wave can be calculated using the distance traveled and time taken, resulting in 156.7 m/s. This velocity is less than half the speed of sound at sea level.

The average velocity of the blast wave can be calculated by dividing the distance traveled by the time taken. The distance is the altitude where the explosion occurred, 23.5 km. Converting 2 minutes 30 seconds to seconds gives a time of 150 seconds.

So, velocity = distance / time = 23.5 km / 150 s = 0.1567 km/s = 156.7 m/s.Comparing this to the speed of sound at sea level, which is 343 m/s, the blast wave's velocity of 156.7 m/s is less than half the speed of sound.

Answer:

2.92 x 10¹² electrons

Explanation:

given,

distance between two plastic ball, r = 17 cm

                                      r = 0.17 m

Force of attraction = F = 68 mN

                F = 0.068 N

number of electron transferred from one ball to another.

using Coulomb Force equation

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

[tex]0.068 = \dfrac{9\times 10^9\times q^2}{0.17^2}[/tex]

q² = 2.1835 x 10⁻¹³

q = 4.67 x 10⁻⁷ C

now, number of electron

 [tex]N = \dfrac{q}{e}[/tex]

e is the charge of electron which is equal to 1.6 x 10⁻¹⁹ C

  [tex]N = \dfrac{4.67\times 10^{-7}}{1.6\times 10^{-19}}[/tex]

       N = 2.92 x 10¹² electrons

electrons were transferred from one ball to the other is 2.92 x 10¹²

Field strength is directly proportional to the square of charge. The charge on the given plastic ball is [tex]4.67 \times 10^{-7} \rm \ C[/tex]

[tex]F = \dfrac {kQ^2}{r^2}[/tex]

Where,

[tex]F[/tex]- field strength = 68 mN = 0.06 N

[tex]Q[/tex]- charge

[tex]r[/tex]- distance =  17 cm =0.17 m

[tex]k[/tex]- constant = 9x10⁹

Put the values in the formula,

[tex]0.068 = \dfrac{9\times 10^9 \rimes Q^2}{0.017^2}\\\\q^2 = 2.1835 \times 10^{-13}\\\\q = 4.67 \times 10^{-7} \rm \ C[/tex]

Therefore, the charge on the given plastic ball is [tex]4.67 \times 10^{-7} \rm \ C[/tex].

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Answer:

The following are true:

A satellite's motion is independent of its mass.

The launch speed of a satellite determines the shape of its orbit around Earth.

Explanation:

A satellite's motion is independent of its mass.

The speed of a satellite can be determined by means of the Universal law of gravity:

[tex]F = G\frac{M\cdot m}{r^{2}}[/tex] (1)

Where G is the gravitational constant, M and m are masses of the two objects and r is the distance between them.

In equation 1, Newton's second law can be replaced:

[tex]F = m\cdot a[/tex]

[tex]m. a = G\frac{M\cdot m}{r^{2}}[/tex]   (2)

Since it is a circular motion, the centripetal acceleration can be used:

[tex]a = \frac{v^{2}}{r}[/tex] (3)

Then, equation 3 can be replaced in equation 2:

[tex]m\frac{v^{2}}{r} = G\frac{M\cdot m}{r^{2}}[/tex]  (4)

In this case, m is the satellite's mass and M is the Earth mass. Therefore, v can be isolated from equation 4:

[tex]v^{2} = G\frac{M\cdot m r}{mr^{2}}[/tex]

[tex]v^{2} =\frac{G M}{r}[/tex]

[tex]v = \sqrt{\frac{G M}{r}}[/tex]

Where G is the gravitational constant, M is the mass of the Earth and r is the orbital radius of the satellite.

Notice, how the speed of the satellite does not depend in its mass, only in the Earth mass and its orbital radius.

The launch speed of a satellite determines the shape of its orbit around Earth.

Depending on the launch speed the satellite can reach a lower or higher height above the surface of the Earth and, therefore, its orbital radius will be bigger or smaller according with that height.

Remember that the orbital radius for the satellite will be the sum of the Earth radius and the height above the surface.      

Key term:

Geosynchronous satellite: It is a satellite with the same orbital period as Earth rotation period (24 hours).  

Answer:

[tex]13.5 rad/s^2[/tex]

Explanation:

39 revolutions = 39 * 2π = 245 rad

Let [tex]\omega_0[/tex] be the initial angular velocity of the wheel before the 10 s interval. We have the following equation of motion for angular velocity

[tex]\omega = \omega_0 + \alpha t[/tex]

where [tex]\omega = 92 rad/s[/tex] is the final angular velocity of the rotating wheel. [tex]\alpha[/tex] is the constant angular acceleration of the wheel, which we are looking for, and t = 10s is the duration time that the wheel rotates

[tex]92 = \omega_0 + 10\alpha[/tex]

[tex]\omega_0 = 92 - 10\alpha[/tex]

We also have the following equation of motion for angles

[tex]\theta = \omega_0t + \alpha t^2/2[/tex]

where [tex]\theta = 245 rad[/tex] is the total angles rotated

we can also substitute [tex]\omega_0 = 92 - 10\alpha[/tex]

[tex]245 = 10(92 - 10\alpha) + \alpha 10^2/2[/tex]

[tex]245 = 920 - 100\alpha + 50\alpha[/tex]

[tex]50\alpha = 675 [/tex]

[tex]\alpha = 675 / 50 = 13.5 rad/s^2[/tex]

The increase in the separation between the bright fringes in the diffraction pattern formed by diffraction grating occurs when there is increase in the wavelength of the light.

The equation for diffraction grating that relates the wavelength and separation of bright fringes is given as;

[tex]d sin\theta = m \lambda \\\\sin \ \theta = \frac{m \lambda}{d}[/tex]

where;

Thus, we can conclude that the increase in the separation between the bright fringes in the diffraction pattern formed by diffraction grating occurs when there is increase in the wavelength of the light.

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Increasing the wavelength of the light will increase the separation between the bright fringes in the diffraction pattern. The correct option is Option A. Immersion in water or changing slit separation do not contribute similarly.

To increase the separation between the bright fringes in a diffraction pattern, one effective approach is to increase the wavelength of the light. When the wavelength increases, the angle of diffraction becomes larger for each order of maximum, resulting in greater fringe separation. Therefore, the correct answer is Option A: INCREASE THE WAVELENGTH OF THE LIGHT.

Answer:

300000 N

Explanation:

We are given that

Mass of jumbo jet=300,000kg

Acceleration of jet=[tex]4m/s^2[/tex]

We have to find the force generated by each of its four engines.

We know that

Force,F =ma

Total force exert by four engines=4F

[tex]4F=300000\times 4[/tex]

[tex]F=\frac{300000\times 4}{4}=300000N[/tex]

Hence, the force generated by each of its four engines=300000 N

This is a complex thermodynamics problem about a steam power plant's ideal reheat Rankine cycle. It requires calculation of pressure at reheat stage, total heat input rate and thermal efficiency by using correct thermodynamic practices. Due to the complexity, expert understanding and use of steam tables is necessary.

This is a thermodynamics problem associated with the ideal reheat Rankine cycle in a steam power plant. Due to the complex nature of the problem, the aid of thermodynamics and steam table reference books is required to solve it.

Under these ideal cycle conditions, calculating assumed pressure drops and using the steam tables, we can estimate the reheat pressure during the cycle. The exact figures would be subject to critical examination and calculation based on precise cycle parameters following real-life engineering practices.

For part (b), the total rate of heat input can be calculated using the mass flow rate and specific enthalpies at different stages of the cycle. The thermal efficiency for part (c) can be obtained by dividing the net work output by the total heat input.

An actual T-s diagram for the Rankine cycle would aid in visualizing the process but cannot be drawn here. Basically, the cycle is plotted with entropy(s) on the x-axis and temperature(T) on the y-axis, showing the expansion, reheat, and condensation stages of the steam.

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The Ideal Reheat Rankine Cycle is a model for determining efficiency in steam power plants. The pressure at which reheating takes place is typically assumed to be at the midpoint of the high and low-pressure limits. The total heat rate input in the boiler and thermal efficiency cannot be determined without more detailed specification of the conditions.

This question is related to the concepts of thermodynamics in the field of Mechanical Engineering. The Ideal Reheat Rankine Cycle is a model used to predict the performance of steam turbine systems, and we will use principles from this model to answer your questions.

(a) The pressure at which reheating takes place cannot be definitively stated without more specific information like the temperature at the exit of the high-pressure turbine or the entropy at key points in the cycle. However, it’s commonly assumed in practice to occur at the mid-point of the high and low-pressure limits, which would be 7.5 MPa or 7500 kPa.

(b) The total rate of heat input in the boiler cannot be definitively stated without more specific information such as the specific enthalpies at key points in the cycle.

(c) Thermal efficiency of the cycle also requires further specific information such as the enthalpy or temperature at key points in the cycle to compute.

Moreover, drawing a T-s (Temperature vs Entropy) diagram with respect to the saturation lines would need a graphical interface, so it's not possible to illustrate it here.

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Answer:

250 kg/m3

Explanation:

The total volume of the raft is length times width times height

V = lwh = 2 * 3 * 0.5 = 3 m cubed

The volume of the raft that is submerged in water is 1/4 of total volume

3 /4 = 0.75 m cubed

Let water density = 1000 kg/m cubed and g = 10 m/s2

The buoyant force is equal to the weight of water displaced by the raft

F = 0.75 * 1000 * 10 = 7500 N

This force is balanced by the raft weight, so the weight of the raft is also 7500N

Mass of raft is 7500 / g = 7500 / 10 = 750 kg

Raft density is mass divided by volume = 750 / 3 = 250 kg/m3

Answer:

a. The spheres will attract each other.

Explanation:

When two conducting spheres are connected by a conducting wire and a negatively charged rod is brought near it then this will induce opposite (positive) charge at the nearest point on the sphere and by the conservation of charges there will also be equal amount of negative charge on the farthest end of this conducting system this is called induced polarization.

Answer:

[tex]d=2.5367\times 10^{-6}\ cm[/tex]

Explanation:

Given:

Now the distance moved by the tectonic plate in the stipulated times:

[tex]d=v.t[/tex]

[tex]d=\frac{1}{365\times 12\times 3600} \times 80[/tex]

[tex]d=2.5367\times 10^{-6}\ cm[/tex]

Tectonic plates are the mass rock from of the earth's uppermost mantle and the crust which show similar behavior of movement with respect to the other such groups of lithosphere.

Answer:

42.9 cm

Explanation:

given,

speed of sound, v = 340 m/s

Frequency of tuning fork, f = 198 Hz

The length of the shortest air column closed at one end.

this is the case of the standing wave.

L = N λ

N = the number of complete sine waves in the standing wave.

The standing wave in the problem is the first harmonic of a pipe open at one end.

N = 1/4

we know,

v = f λ

340 = 198 x λ

λ = 1.717 m

now,

L = N λ

[tex]L = \dfrac{1}{4}\times 1.717[/tex]

[tex]L = 0.429\ m[/tex]

   L = 42.9 cm

minimum length of the required pipe is 42.9 cm.

did you find the answer?

Answer:

The force constant of the spring is 317.8 N/m.

Explanation:

Given that,

Frequency [tex]f=7.0\times10^{13}\ Hz[/tex]

We need to calculate the reduced mass

Using formula of reduced mass

[tex]\mu=\dfrac{m_{H}m_{I}}{m_{H}+m_{I}}[/tex]

Where, [tex]m_{H}[/tex]= atomic mass of H

[tex]m_{I}[/tex]= atomic mass of I

Put the value into the formula

[tex]\mu=\dfrac{1\times126.9}{1+126.9}[/tex]

[tex]\mu=0.99\ u[/tex]

[tex]\mu=0.99\times1.66\times10^{-27}\ Kg[/tex]

[tex]\mu=1.643\times10^{-27}\ kg[/tex]

We need to calculate the force constant of the spring

Using formula of frequency

[tex]f=\dfrac{1}{2\pi}\times\sqrt{\dfrac{k}{\mu}}[/tex]

[tex]k=f^2\times 4\pi^2\times\mu[/tex]

Put the value into the formula

[tex]k=(7.0\times10^{13})^2\times4\pi^2\times1.643\times10^{-27}[/tex]

[tex]k=317.8\ N/m[/tex]

Hence, The force constant of the spring is 317.8 N/m.

Answer:

The force constant of the spring is 317.8 N/m.

Explanation:

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The answer provides the speed of the putty just before striking the ceiling and the time it takes for the putty to reach the ceiling. The speed is found to be 5.79 m/s and the time taken is calculated to be 1.5 seconds.

The speed of the putty just before it strikes the ceiling:

Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement, the speed is found to be 5.79 m/s.

The time it takes for the putty to reach the ceiling:

By using the equation v = u + at, where t is time, a is acceleration, u is initial velocity, and v is final velocity, the time taken is calculated to be 1.5 seconds.

Answer:

D

Explanation:

Ball A is a non positively charged non metal while ball B is metal ball.

Given: The ball B positive charge of small magnitude

To prove: Balls will attract each other

IN this condition because of induction negative charges on the sphere B move to the side closer to sphere A,(induction charging) while the positive charges move to the side further away from sphere A. The polarization of charge on B will cause a greater attractive force than the repulsion of the like charges.

Hence the correct answer will be D .

To solve this problem we will apply the concepts related to the Electrostatic Force given by Coulomb's law. This force can be mathematically described as

[tex]F = \frac{kq_1q_2}{d^2}[/tex]

Here

k = Coulomb's Constant

[tex]q_{1,2} =[/tex] Charge of each object

d = Distance

Our values are given as,

[tex]q_1 = 1 \mu C[/tex]

[tex]q_2 = 6 \mu C[/tex]

d = 1 m

[tex]k =  9*10^9 Nm^2/C^2[/tex]

a) The electric force on charge [tex]q_2[/tex] is

[tex]F_{12} = \frac{ (9*10^9 Nm^2/C^2)(1*10^{-6} C)(6*10^{-6} C)}{(1 m)^2}[/tex]

[tex]F_{12} = 54 mN[/tex]

Force is positive i.e. repulsive

b) As the force exerted on [tex]q_2[/tex] will be equal to that act on [tex]q_1[/tex],

[tex]F_{21} = F_{12}[/tex]

[tex]F_{21} = 54 mN[/tex]

Force is positive i.e. repulsive

c) If [tex]q_2 = -6 \mu C[/tex], a negative sign will be introduced into the expression above i.e.

[tex]F_{12} = \frac{(9*10^9 Nm^2/C^2)(1*10^{-6} C)(-6*10^{-6} C)}{(1 m)^{2}}[/tex]

[tex]F_{12} = F_{21} = -54 mN[/tex]

Force is negative i.e. attractive

To solve this problem we will apply the concepts related to the conservation of the Momentum. The initial momentum must be equal to the final momentum. Momentum is described as the product between body mass and its respective velocity. Since there is no movement at the end of the collision, the final momentum will be zero.

Our values are given as

Mass of Cadillac

[tex]m_1 = 1000kg[/tex]

mass of VW

[tex]m_2 = 2000kg[/tex]

Let VW impact with speed v, then for conservation of momentum

[tex]m_1v_1+m_2v_2 = 0 \rightarrow[/tex] the Final speed is zero

Replacing,

[tex]1000kg*5mph+2000kg(-v) = 0[/tex]

[tex]v = \frac{1000kg*5mph}{2000kg}[/tex]

[tex]v = 2.5mph[/tex]

Therefore the speed to bring the cadillac to a halt is 2.5mph

The speed that can impact the Cadillac to bring it to a halt is 2.5 mph.

Velocity of the car can be calculated by the conservation of momentum formula,

[tex]\bold {m_1 v_1 =m_2v_2 = 0}[/tex]    Since the final speed is zero,

where,

[tex]\bold {m_1 - mass\ of\ the\ cadillac = 1000 kg}\\\bold {m_2 - mass\ of\ the\ Volks\ Vagon = 2000 kg}[/tex]

[tex]\bold {v_1}[/tex] - velocity of the Cadillac - 5 mph.

Put the values in the formula

[tex]\bold {1000\ kg \times 5\ mph + 2000 kg (-v) = 0 }\\\\\bold {v = \dfrac {1000\ kg \times 5\ mph}{2000\ kg}}\\\\\bold {v = 2.5\ mph}[/tex]

Therefore, the speed that can impact the Cadillac to bring it to a halt is 2.5 mph.

To know more about Speed,

https://brainly.com/question/23774048

Answer:

Mass of rain collected will be 1875 kg

Explanation:

We have given mass of the train [tex]m_i[/tex] = 7500 kg

Velocity of the car [tex]v_i[/tex] = 25 m/sec

After few minutes velocity of the car = 20 m/sec

From conservation of momentum we know that [tex]m_iv_i=m_fv_f[/tex]

So [tex]7500\times 25=m_f\times 20[/tex]

[tex]m_f=9375kg[/tex]

[tex]m_f[/tex] will be sum of mass of car and mass of rain collected

As mass of car is 7500 kg

So mass of rain collected = 9375 - 7500 = 1875  kg

Answer:

a)[tex]p=1.89x10^{-27}kg.m.s^{-1}[/tex]

b)[tex]v=0.565\frac{m}{s}[/tex]

Explanation:

First, we need to obtain the linear momentum of the photons of wavelength 350nm.

We are going to use the following formula:

[tex]\lambda=\frac{h}{p}\\Where:\\\lambda=wavelength\\h=placnk's\_constant\\p=Linear\_momentum[/tex]

So the linear momentum is given by:

[tex]p=\frac{h}{\lambda}\\\\p=\frac{6.626x10^{-34}J.s}{350x10^{-9}m}\\\\p=1.89x10^{-27}kg.m.s^{-1}[/tex]

Having the linear momentum of the photon, we can calculate the speed of the hydrogen molecule to have the same momentum, we can use the classic formula for that:

[tex]p=m.v[/tex]

[tex]where:\\m=mass\\v=speed\\p=linear\_momentum[/tex]

The mass of the hydrogen molecule is given by:

[tex]m=2*(1.0078x10^{-3}\frac{kg}{mol}})x\frac{1}{6.022x10^{23}mol}[/tex]

[tex]3.35x10^{-27}kg[/tex]

What we've done here is to use the molecular weight of the hydrogen, and covert it kilograms, we had to multiply by two because the hydrogen molecule is found in pairs.

so:

[tex]v=\frac{p}{m}\\\\v=\frac{1.89x10^{-27}kg.m.s^{-1}}{3.35x10^{-27}kg}\\\\v=0.565\frac{m}{s}[/tex]

(a) The linear momentum of the photon is 1.89 x 10⁻²⁷ kgm/s.

(b) The speed of hydrogen atom with same momentum is 2,079.35 m/s.

The linear momentum of the photon is calculated as follows;

P = h/λ

P = (6.63 x 10⁻³⁴) / (350 x 10⁻⁹)

P = 1.89 x 10⁻²⁷ kgm/s

p = mv

v = p/m

v = (1.89 x 10⁻²⁷ ) / (9.11 x 10⁻³¹)

v = 2,079.35 m/s

Thus, the speed of hydrogen atom with same momentum is 2,079.35 m/s.

Learn more about linear momentum here: https://brainly.com/question/7538238

The correct answer here is Option A, always equal to a right angle.

Keep in mind that the phase difference that exists between the electric field and the magnetic wave is 90 °, this means that the changing electric field and the electromagnetic wave are always perpendicular and will be forming a right angle.

Answer:

(a) the net charge inside the closed surface.

Explanation:

In Gauss' Law, Qencl refers to the net charge inside the Gaussian surface. This surface is usually taken as a symmetric geometric surface, but this is merely for simplicity. Gauss' Law holds for any closed surface. Inside this surface there can be insulators as well as conductors. Regardless of the geometry or the materials inside, Qencl refers to the net charge inside the closed surface. The charge outside the surface is irrelevant for Gauss' Law, therefore all the charge in the physical system is not included in Gauss' Law.

Answer:

The charged balloon’s mass will be almost equal to the original mass

Explanation:

When an electrically neutral balloon is rubbed on cloth, it losses some electron and becomes positively charged.

The balloon becomes positively charged by the removal of electrons (electrons from the cloth repels electron in the balloon).

The mass of positively charged balloon, will be equal to the original mass minus the mass of electrons removed.

Since Electrons have negligible mass, the removal of electrons from the neutral balloon will have little effect on the original mass of the balloon.

Therefore, the charged balloon’s mass will be almost equal to the original mass

Answer:

final velocity of the objects will be 3 m/sec

Explanation:

We have given there are two identical objects of mass 2 kg

So [tex]m_1=m_2=2kg[/tex]

Initial velocity of object A [tex]v_1=12m/sec[/tex]

Initial velocity of object B [tex]v_2=-6m/sec[/tex]

According to conservation of momentum

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

[tex]2\times 12+2\times -6=(2+2)v[/tex]

[tex]4v=24-12[/tex]

[tex]4v=12[/tex]

v = 3 m/sec

So final velocity of the objects will be 3 m/sec

To find the final velocity of mass B after a collision, you can use the principle of conservation of momentum. The formula for conservation of momentum is (mass of A * initial velocity of A) + (mass of B * initial velocity of B) = (mass of A * final velocity of A) + (mass of B * final velocity of B). By substituting the given values and solving for the final velocity of mass B, we can determine its value.

To find the final velocity of mass B after the collision, we can use the principle of conservation of momentum. Since the collision is elastic, the total momentum before the collision is equal to the total momentum after the collision.

Mass A has an initial velocity of 5.0 m/s in the +x-direction and after the collision, moves with a velocity of 3.0 m/s in the -x-direction. Mass B has an initial velocity of 3.0 m/s in the -x-direction.

Let's assume the final velocity of mass B is vB. Using the principle of conservation of momentum, we can set up the equation:

Initial momentum = Final momentum

(mass of A * initial velocity of A) + (mass of B * initial velocity of B) = (mass of A * final velocity of A) + (mass of B * final velocity of B)

Substituting the given values:

(5.0 kg * 5.0 m/s) + (5.0 kg * 3.0 m/s) = (5.0 kg * 3.0 m/s) + (mass of B * vB)

Simplifying the equation:

25.0 m/s + 15.0 m/s = 15.0 m/s + (mass of B * vB)

40.0 m/s = 15.0 m/s + (mass of B * vB)

Subtracting 15.0 m/s from both sides:

25.0 m/s = (mass of B * vB)

Dividing both sides by the mass of B:

vB = 25.0 m/s / mass of B

Therefore, the final velocity of mass B after the collision is 25.0 m/s divided by the mass of B.

Explanation:

We know that electron always tends to travel in the direction opposite the direction of electric field ( force in directed opposite to the field on electron).

So, since the field points vertically upward , it force the electron move downward. So, the electron will be accelerated in downward in the right direction.