How do you stay hydrated during warm-up and scheduled activity?

Complete question:

if two point charges are separated by 1.5 cm and have charge values of +2.0 and -4.0 μC, respectively, what is the value of the mutual force between them.

Answer:

The mutual force between the two point charges is 319.64 N

Explanation:

Given;

distance between the two point charges, r = 1.5 cm = 1.5 x 10⁻² m

value of the charges, q₁ and q₂ = 2 μC and - μ4 C

Apply Coulomb's law;

[tex]F = \frac{k|q_1||q_2|}{r^2}[/tex]

where;

F is the force of attraction between the two charges

|q₁| and |q₂| are the magnitude of the two charges

r is the distance between the two charges

k is Coulomb's constant = 8.99 x 10⁹ Nm²/C²

[tex]F = \frac{k|q_1||q_2|}{r^2} \\\\F = \frac{8.99*10^9 *4*10^{-6}*2*10^{-6}}{(1.5*10^{-2})^2} \\\\F = 319.64 \ N[/tex]

Therefore, the mutual force between the two point charges is 319.64 N

Answer:

C) 200 m/s

Explanation:

The sound travels a total distance of 360 m in 0.03 minutes.

v = (360 m) / (0.03 min × 60 s/min)

v = 200 m/s

Answer:

The rate at which the magnetic field changes is  [tex]\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s[/tex]

Explanation:

From the question we are told that

   The  electric field strength is [tex]E = 4.0 mV/m = 4.0 *10^{-3} V/m[/tex]

   The  radius of the  circular region where the electric field is induced is

   [tex]d = 1.5 \ m[/tex]

Generally the induced electric field is mathematically represented as

     [tex]E = - \frac{r}{2} * \frac{\Delta B }{\Delta t }[/tex]

The  negative sign show that the induced electric field is acting in opposite direction to the change in magnetic field

Where  [tex]\frac{\Delta B }{\Delta t }[/tex] is the change in magnetic field

So  

       [tex]\frac{\Delta B }{\Delta t } = - \frac{2 * E }{r}[/tex]

substituting values

       [tex]\frac{\Delta B }{\Delta t } = - \frac{2 * 4.0 *10^{-3}}{ 1.5 }[/tex]

       [tex]\frac{\Delta B }{\Delta t } = - 5.33*10^{-3} \ T/ s[/tex]

Answer:

The  percentage of the kinetic energy that is left in the system after collision to that before is 0.174 %

Explanation:

Given;

mass of bullet, m₁ = 4g = 0.004kg

initial velocity of bullet, u₁ = 589 m/s

mass of block of wood, m₂ = 2.3 kg

initial velocity of the block of wood, u₂ = 0

let the final velocity of the system after collision = v

Apply the principle of conservation of linear momentum

m₁u₁ + m₂u₂ = v(m₁+m₂)

0.004(589) + 2.3(0) = v(0.004 + 2.3)

2.356 = 2.304v

v = 2.356 / 2.304

v = 1.0226 m/s

Initial kinetic energy of the system

K.E₁ = ¹/₂m₁u₁² + ¹/₂m₂u₂²

K.E₁ = ¹/₂(0.004)(589)² = 693.842 J

Final kinetic energy of the system

K.E₂ = ¹/₂v²(m₁ + m₂)

K.E₂ = ¹/₂ x 1.0226² x (0.004 + 2.3)

K.E₂ = 1.209 J

The kinetic energy left in the system = final kinetic energy of the system

The percentage of the kinetic energy that is left in the system after collision to that before = (K.E₂ / K.E₁) x 100%

                       = (1.209 / 693.842) x 100%

                        = 0.174 %

Therefore, the  percentage of the kinetic energy that is left in the system after collision to that before is 0.174 %

Answer:

The induced  emf is  [tex]\epsilon =7.68 \ V[/tex]

Explanation:

From the question we are told that

     The number of turns is  [tex]N = 1300 \ turns[/tex]

    The diameter is  [tex]d = 2.2 \ cm = 2.2*10^{-2}[/tex]

     The initial magnetic field is  [tex]B_i = 0.14 \ T[/tex]

      The final magnetic field is  [tex]B_f = 0 \ T[/tex]

      The  time taken is  [tex]dt = 9.0ms = 9.0*10^{-3} \ s[/tex]

The radius is mathematically evaluated as

      [tex]r = \frac{d}{2 }[/tex]

substituting values

     [tex]r = \frac{2.2 *10^{-2}}{2 }[/tex]

     [tex]r = 1.1*10^{-2} \ m[/tex]

The induced emf is mathematically represented as

    [tex]\epsilon =- N * \frac{d\phi }{dt }[/tex]

Where  [tex]d\phi[/tex] is the change in magnetic field which is mathematically represented as

        [tex]d\phi = dB * A * cos\theta[/tex]

=>   [tex]d\phi = [B_f - B_i ] * A * cos\theta[/tex]

Here  [tex]\theta = 0[/tex] given that the axis of the coil is parallel to the field

Also A is the cross-sectional area which is mathematically represented as

       [tex]A = \pi r^2[/tex]

substituting values

      [tex]A = 3.142 * [1.1*10^{-2}]^2[/tex]

       [tex]A = 3.8 *10^{-4] \ m^2[/tex]

So

    [tex]d\phi = [0 - 0.14 ] * 3.8*10^{-4}[/tex]

    [tex]d\phi = -5.32*10^{-5} \ weber[/tex]

So  

     [tex]\epsilon =- 1300 * \frac{-5.32*10^{-5} }{ 9.0*10^{-3} }[/tex]

    [tex]\epsilon =7.68 \ V[/tex]

Answer:

Maximum acceleration is 800m/s^2

Explanation:

See attached file

Answer:

Explanation:

Given the formula for calculating the depth in metres expressed as

depth in meters = ½ (1500 m/sec × Echo travel time in seconds)

Given depth of the challenger = 10, 994 meters, we will substitute this given value into the formula given to calculate the time take for the echo to travel.

10, 994 = depth in meters = ½ * 1500 m/sec × Echo travel time in seconds

10,994 = 750 * Echo travel time in seconds

Dividing both sides by 750;

Echo travel time in seconds = 10,994 /750

Echo travel time in seconds ≈ 14.66secs (to two decimal places)

Therefore, it would take an echo sounder’s ping 14.66secs to make the trip from a ship to the Challenger Deep and back

Answer:

Body inertia I = 4.5 kg/m^2

Explanation:

Here, we want to calculate the body inertia when the arms are stretched outwards.

We know from the question that angular momentum is conserved

Thus;

I * 3 = 4.5 * 3

I = 4.5 kg/m^2

Answer:

a) using

R=V/I =117/12.3

R=9.5 ohms

b)

E=V-I*R =117-3.38*9.5

E=84.8Volts

c)

at (1/3)rd of normal speed ,back emf is (1/3) of its maximum

value

E=(1/3)*84.8=28.3Volts

Current drawn

I=V-Eback/R =117-28.3/9.5

I=9.33A

Explanation:

The resistance is = 9.5 ohms

The back emf developed at normal speed is = 84.90 volts

The current drawn at one-third normal speed =9.33 A.

To calculate the resistance of the armature coil this formula is used;

V = IR

make R the subject of formula,

R = V/I

where R = resistance

V = voltage

I = Current

R = 117/12.3

R = 9.5 ohms

To calculate the back emf developed at normal speed, this formula is used;

E = V + Ir ( for normal emf)

But for back emf which is the difference between the supplied voltage and the loss from the current through the resistance, this formula is used;

E = V - Ir

where V = 117v

I = 3.38

r = 9.5

E = 117 - ( 3.38 × 9.5)

= 117 - 32.11

= 84.90 volts

To calculate the current drawn at one-third normal speed;

1/3 of Emf = 1/3 × 84.90

= 28.3volts

Therefore current (I) = V - E/ R

= 117- 28.3/9.5

= 88.7/9.5

= 9.33 A

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Answer:

Plss see attached file

Explanation:

Answer:

Explanation:

[tex]mass = 2.5kg\\height = 4.0\\Acceleration \: due \:to\:gravity = 10m/s^2\\\\P.E = mgh\\P.E = 2.5kg\times10\times4\\\\Potential \: Energy = 100 joules[/tex]

The potential energy if g = 10m/s² is 98 J

Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

Formula for potential energy :

P.E. = mgh

Given :

The book is held from the ground of a distance  = 4.0 m,

so

h = 4.0 m

we know that the book weighs,

2.5 kg

so

m = 2.5 kg.

Now we just put it in the formula  ;

PE = (2.5kg) × (9.8 m/s²) × ( 4.0 m)

P E = 98 J

Therefore, The potential energy if g = 10m/s² is 98 J

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Answer:

Explanation:

The greatest speed is attained at middle point or equilibrium point or where displacement from equilibrium point is zero .

When the object remains at one of the extreme point it experiences greatest acceleration but at that point velocity is zero . Due to acceleration , its velocity goes on increasing till it come to equilibrium point . At this point acceleration becomes zero . After that its velocity starts decreasing because of negative acceleration . Hence at middle point velocity is maximum .

The greatest acceleration is attained at maximum displacement or at one of the two extreme end .

Greatest restoring force too will be at position where acceleration is maximum because acceleration is produced by restoring force .

Restoring force is proportional to displacement or extension against restoring force . So it will be maximum when displacement is maximum .

Zero restoring force exists at equilibrium position or middle point or at point where displacement is zero . It is so because acceleration at that point is zero .

Answer:

6.8%

Explanation:

According to Stefan-Boltzmann law, radiation is directly proportional with temperature raised to the fourth power:

P ∝ T⁴

Writing a proportion:

P₁ / P₂ = T₁⁴ / T₂⁴

1.3P / P = (T₁ / T₂)⁴

T₁ / T₂ = ∜1.3

T₁ = 1.068 T₂

The temperature increased by 6.8%.

Answer:

  R = v √(2h / g)

Explanation:

This exercise can be solved using the concepts of science, projectile launching

let's calculate the time it takes to get to the water

           y = y₀ +[tex]v_{oy}[/tex] t - ½ g t²

as the stone is skipped the vertical speed is zero

           y = y₀ - ½ g t²

for y=0

           t = √ (2y₀ / g)

the horizontal distance it covers in this time is

           R = v₀ₓ t

            R = v₀ₓ √(2 y₀ / g)

let's call the horizontal velocity as v and the height is h

            R = v √(2h / g)

Answer:

D. Metallic atoms have valence shells that are mostly empty, which

means these atoms are more likely to give up electrons and allow

them to move freely.

Explanation:

Metals usually contain very few electrons in their valence shells hence they easily give up these few valence electrons to yield metal cations.

In the metallic bond, metal cations are held together by electrostatic attraction between the metal ions and a sea of mobile electrons.

Since metals give up their electrons easily, it is very easy for them to participate in metallic bonding. They give up their electrons easily because their valence shells are mostly empty, metal valence shells usually contain only a few electrons.

Answer:

A) geometric optics, B) geometric optics , c) geometric optics ,

e) geometric optics, f)  geometric optics

Explanation:

For this exercise we must use the condition for interference and diffraction so that these phenomena are relevant the wavelength must be comparable to the gap spacing

                λ> = a

Lam when the spacing is much greater than the wavelength, the description of geometric optics is more and more exact

let's analyze each situation

a) let's find the wavelength

                v = λ f

                λ= v / f

                λ= 343/1000

                λ = 0.343 m

                 0.343 << 1m

therefore the description of the geometric optics of

b) red light passes through the pupil of the eye

red light has a wavelength of 700 num or more, the lojo pupil has a maximum of 8 me

         λ = 700 10⁻⁹ m = 7 10⁻⁷ m

         a = 8 mm 10⁻³

longitudinal is much less therefore the geometric optics is correct

c) luz azul lam = 450 nm = 450 10⁻⁹ m = 4.5 10⁻⁷ m

again the wavelength is much less than the diameter of the pupil, for which the description with the optics is generally sufficient

d) a radio A transmits up to a maximum of f = 1400 Khz = 1,400 10⁶ Hz

let's find the wavelength

          c = λf

          λ = c / f

           λ= 3 108 / 1,400 106

          λ= 2.14 102 m

in this case the wavelength is greater than the width of the gate, so the description of diffraction should be used to explain the phenomenon

e) X-rays have wavelength lam = 10-10 m

the separation of the elbow bones is of the order of a few millimeters, for local the wavelength is much less than the separation, therefore with the relations of geometric optics it is sufficient

Answer:

absorbent    p = S / c

reflective         p = 2S/c

Explanation:

The moment of radiation on a surface is

          p = U / c

where U is the energy and c is the speed of light.

In the case of a fully absorbent object, the energy is completely absorbed. The energy carried by the light is given by the Poynting vector.

           p = S / c

in the case of a completely reflective surface the energy must be absorbed and remitted, therefore there is a 2-fold change in the process

           p = 2S/c

Answer:

Explanation:

Carton cycle consists of four thermodynamic processes . The first is isothermal expansion at higher temperature , then adiabatic expansion which lowers the temperature of gas . The third process is isothermal compression at lower temperature and the last process is adiabatic compression which increases the temperature of the gas to its original temperature .

So the given process of isothermal compression must have been done at the temperature of 300K  , keeping the temperature constant .

Work done on gas at isothermal compression is equal to heat transfer .

work done on gas = 80 x 10³ J

work done on gas = n RT ln v₁ / v₂

n is number of moles v₁ and v₂ are initial and final volume

molecular weight of gas = 28.97 g

1.5 kg = 1500 / 28.97 moles

= 51.77 moles

work done on gas = n RT ln v₁ / v₂

Putting the values in the equation above

80 x 10³ = 51.78 x 8.31 x 300 x ln v₁ / .2

ln v₁ / .2 = .62

v₁ / .2 = 1.8589

v₁ = 0.37 m³

Answer:

c. 66 V

Explanation:

p =IV

I =P/V

P1/V1=P2/V2

60/110=36/V2

0.55 = 36/V2

V2 =36/0.55 = 65.5V

V2 = 66V

Answer:

The wave will be travelling in the y-axis

Explanation:

An e-m wave has a spatially varying electric field that is always associated with a magnetic field that changes over time and vice versa. The electric field and the magnetic field oscillates perpendicularly to each other, and together form a wave that travels in a perpendicular direction to the magnetic and the electric field in space. The movement of the e-m wave through space is usually away from the source where it is generated. So, if the electric field travels in the z-axis, and the magnetic field travels through along the x-axis, then the e-m wave generated will travel in the y-axis direction.

Answer:

The value of the inductance is 0.955 mH

Explanation:

Given;

frequency of the oscillator, f = 18 kHz = 18,000 Hz

the peak current, I₀ = 70 mA = 0.07 A

the root mean square voltage, [tex]V_{rms}[/tex] = 5.4 V

The root mean square current is given as;

[tex]I_{rms}= \frac{I_o}{\sqrt{2} }[/tex]

[tex]I_{rms} = \frac{0.07}{\sqrt{2} } \\\\I_{rms} = 0.05 \ A[/tex]

Inductive reactance is given by;

[tex]X_L =\frac{V_{rms}}{I_{rms}} \\\\X_L = \frac{5.4}{0.05} \\\\X_L = 108 \ ohms[/tex]

Inductance is given by;

[tex]L = \frac{X_L}{2\pi f} \\\\L = \frac{108}{2\pi *18,000} \\\\L = 9.55 *10^{-4} \ H[/tex]

L = 0.955 mH

Therefore, the value of the inductance is 0.955 mH

The value of the inductance (L) for this oscillating circuit is equal to [tex]9.55 \times 10^{-4}[/tex] Henry.

Given the following data:

To determine the value of the inductance (L):

First of all, we would find the root mean square (rms) current by using the formula:

[tex]I_{rms} = \frac{I_o}{\sqrt{2} }\\\\I_{rms} = \frac{70 \times 10^{-3}}{1.4142} \\\\I_{rms} = 0.050 \;A[/tex]

Next, we would calculate the inductive reactance of the oscillator by using the formula:

[tex]X_L = \frac{V_{rms}}{I_{rms}} \\\\X_L = \frac{5.4}{0.050} \\\\X_L = 108 \; Ohms[/tex]

Now, we can solve for the value of the inductance (L):

[tex]L = \frac{X_L}{2\pi f}[/tex]

Where:

Substituting the parameters into the formula, we have;

[tex]L = \frac{108}{2 \times 3.142 \times 18 \times 10^3} \\\\L = \frac{108}{113112}[/tex]

L = [tex]9.55 \times 10^{-4}[/tex] Henry.

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Answer:

Explanation:

correct options

a ) Their electrical potential energy keeps decreasing

Actually as they move apart , their electrical potential energy decreases due to increase of distance between them and kinetic energy increases

so a ) option is correct

b ) Their acceleration keeps decreasing

As they move apart , their mutual force of repulsion decreases due to increase of distance between them so the acceleration decreases .

c ) c. Their kinetic energy keeps increasing

Their kinetic energy increases because their electrical potential energy decreases . Conservation of energy law will apply .

The moving apart should be true statements:

a. The electrical potential energy should be reduced.

b. The acceleration should be reduced.

c. The kinetic energy should be increased.

At the time when the moving part, there is the reduction of the electric potential energy because there is a rise in the distance due to which the increment of the kinetic energy.  The reduction of the mutual force of repulsion because of increment in the distance due to this the acceleration should be reduced. There is the increase in the kinetic energy due to the reduction of the electrical potential energy. here the law of conversation of energy should be applied.

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Answer:

100 degrees Celsius

Explanation:

Water starts to boil at 100 degrees celcius or 212 degrees fahrenheit.

At 100 degrees Celsius water begin to boil and turns to steam.

The melting point for water is 0 degrees C (32 degrees F). The boiling point of water varies with atmospheric pressure. At lower pressure or higher altitudes, the boiling point is lower. At sea level, pure water boils at 212 °F (100°C).

If the temperature is much above 212°F, the water will boil. That means that it won't just evaporate from the surface but will form vapor bubbles, which then grow, inside the liquid itself. If the water has very few dust flecks etc.

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Answer:

Explanation:

Work required = q x V

where q is charge on electron and V is potential difference

= 1.6 x 10⁻¹⁹  x 12

= 19.2 x 10⁻¹⁹ J

Answer:

The positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.

Explanation:

Given;

distance between the conducting planes, d = 80 cm

frequency of the electromagnetic wave, f = 750 MHz

speed of light, c = 3 x 10⁸ m/s²

Determine the wavelength

λ = C/f

where;

λ is the wavelength

C is the speed of light

f is the frequency

λ = C/f

λ = (3 x 10⁸) / (750 x 10⁶)

λ = 0.4 m = 40 cm

One complete cycle = one wavelength = 40 cm

half of the wavelength ( λ / 2) = 20 cm

one wavelength + half wavelength (3λ / 2) = 60 cm

The positions of the wave at zero amplitude (between 0 and 80 cm) = 20 cm, 40 cm, 60 cm

Thus, the positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.

Answer:

Power=50.17dioptre

Power=50.17D

Explanation:

P=1/f = 1/d₀ + 1/d₁

Where d₀ = the eye's lens and the object distance= 5.70m=

d₁= the eye's lens and the image distance= 0.02m

f= focal length of the lense of the eye

We know that the object can be viewed clearly by the person ,then image and lens of the eye's distance needs to be equal with the retinal and the eye lens distance and this distance is given as 0.02m

Therefore, we can calculate the power using above formula

P= 1/5.70 + 1/0.02

Power=50.17dioptre

Therefore, the power the eye's is using to see the object from distance is 5.70D

Answer:

Using ohms law

The current is found from Ohm's Law.

I = V /R = E /R = Bxy /Rt.

Answer:

Convection and Radiation mechanisms carry most of the heat

Explanation:

This is because Convection proceeds strongy as heated air rises from the hot element while Radiation is also strong, although the material of the cooking pots will how effective it is.

Answer:

B=uonI/2

Explanation:

See attached file