An helicopter lowers a probe into lake Chad which is suspended on a cable. the probe has a mass of 500kg and its average density is 1400kg/m³. what is the tension in the cable?​

Answer:

K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x

Explanation:

To find the variation of kinetic energy, let's use the work energy theorem

            W = ΔK

           ∫ F .dx = K -K₀

If the body starts from rest K₀ = 0

           ∫ F dx cos θ = K

Since the force and displacement are in the same direction, the angle is zero, so the cosine is 1

we substitute  and integrate

          α ∫ x³ dx + β ∫ dx = K

          α x⁴ / 4 + β x / 1 = K

we evaluate from the lower limit F = 0 to the upper limit F

         α (x⁴ / 4 -0) + β (x -0) = K

        K = αX⁴ / 4 + β x

        K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x

in order to finish the calculation we must know the displacement

Answer:

1.1 x 10^10J

Explanation:

∫x2,x1F(x)dx = ∫7.5 x 10^4 m ,0 (αx3+β)dx.

(αx4/4+βx) 7.5 x 10^4 m, 0

((6.1×10−9N/m3)( 7.5×104m)^4)/4 - (4.1×106N)( 7.5×104m) -0)

= 4.825 x 10^10 - 30.75 x 10^10

= 25.925 x 10^10J

= 2.5925 x 10^11J

The kinetic energy KE2 is,

KE2 = KE1 + ∫x2,x1F(x)dx

       = 2.7×1011J - .5925 x 10^11J

        = 0.1065 x 10^11J

        = 1.1 x 10^10J

Answer:

Sports drink will show increase in specific gravity

While

Water will decrease in SG

Explanation:

This is because the relative density of urine will increase because of presence of ions in the sport drink unlike in water that has very little ions

Answer: q = -52.5 μC

Explanation:

The complete question is given thus;

A point charge Q moves on the x-axis in the positive direction with a speed of 280 m/s. A point P is on the y-axis at y=+70mm. The magnetic field produced at the point P, as the charge moves through the origin, is equal to -0.30uTk. What is the charge Q? (uo=4pi x 10^-7 T m/A).

SOLVING:

from the given parameters we can solve this problem.

Given that the

Speed = 280 m/s

y = 70mm

B =  -30 * 10⁻⁶T

Using the equation for magnetic field we have;

Β = μqv*r / 4πr²

making q (charge) the subject of formula we have that;

q  = B * 4 *πr² / μqv*r

substituting the values gives us

q = (-0.3*10⁻⁶Tk * 4π * 0.07²) / (4π*10⁻⁷ * 280 ) = - [14.7 * 10⁻¹⁰k / 2.8 * 10⁻⁵ k ]

q = -52.5 μC

cheers i hope this helped !!!

Answer:

90 m

Explanation:

Given that

Mass of the car, m = 500 kg

Initial speed of the car, u = 0 m/s

Final speed of the car, v = 30 m/s

Time taken to travel, t = 6 s

average speed v = (30 + 0) / 2 = 15

We are going to be using the most very basic equations to solve this.

speed can be defined as the ratio of distance with respect to time.

v = d/t, Where

v = speed.

d = distance travelled and

t = time taken

if we invert this, we can get that

d = v.t

distance is multiplication of speed and time. We will be using the average speed we calculated above, so

Distance travelled in 6 s,

d = 15 * 6

d = 90 m.

therefore, the distance travelled by the car in this 6 s is 90 m

Answer:

The charge that flow through the calculator is 0.384 C

Explanation:

Given;

current drawn by the calculator, I = 0.0008 A

time of current flow, t = 8 min = 8min x 60s = 480 s

The charge that flow through the calculator is given;

q = It

where;

q is the charge that flow through the calculator

I is the current drawn

t is the time

q = 0.0008 x 480

q = 0.384 Coulombs

Therefore, the charge that flow through the calculator is 0.384 C

Answer:

A) E_min = 36.21 × 10^(-20) J

B) 549 nm

Explanation:

A) The formula for energy of a photon is given as;

E = hc / λ

Where;

h is Planck's constant = 6.626 x 10^(-34) J.s

c is the speed of light = 3 × 10^(8) m/s

λ is wavelength

Wavelength is given as; 540 nm = 540 × 10^(-9) m

Thus;

E = (6.626 × 10^(-34) × 3 × 10^(8))/(540 × 10^(-9))

E = 36.81 × 10^(-20) J

We are given kinetic energy as;2.60 x 10^(-20) J

Now formula for E_min is;

E_min = E - K.E

E_min = (36.81 × 10^(-20)) - (2.60 x 10^(-20))

E_min = 36.21 × 10^(-20) J

B) the longest wavelength, in nanometers, that will eject electrons from cesium would have an energy that would be equal to E_min.

Thus,

36.21 × 10^(-20) = (6.626 × 10^(-34) × 3 × 10^(8))/λ

Making λ the subject gives;

λ = (6.626 × 10^(-34) × 3 × 10^(8))/36.21 × 10^(-20) = 549 x 10(-9) = 549 nm

The minimum energy of the electron is [tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

The longest wavelength of the electron is 549 nm.

Given that, in the photoelectric effect, electrons are ejected from a metal surface when light strikes it. A certain minimum energy, Emin, is required to eject an electron. Also given wavelength of the light is 540 nm. The kinetic energy ejected by the electron is 260 x 10-20 J.

When the wavelength is 400 nm, the kinetic energy is 1.54 x 10-19 J.

The energy of the electron can be calculated as,

[tex]E = hc/\lambda[/tex]

Where, [tex]E[/tex] is the energy of the electron, [tex]h=6.626\times10^{(-34)} \;\rm Js[/tex] is plank's constant, [tex]c[/tex] is the speed of light that is [tex]3 \times 10^8 \;\rm m/s[/tex] and [tex]\lambda[/tex] is the wavelength.

So the energy of the electron is,

[tex]E = \dfrac{6.626\times 10^{(-34)} \times 3\times 10^8}{540\times 10^{(-9)}}[/tex]

[tex]E = 3.68 \times 10^{(-19)} \;\rm J[/tex]

The energy of the electron is  [tex]E = 3.68 \times 10^{(-19)} \;\rm J[/tex].

The Emin can be calculated as given below.

[tex]E_{min} = E - KE[/tex]

Where [tex]KE[/tex] is the kinetic energy of the electron that is given as [tex]260 \times 10^{(-20)} \;\rm J.[/tex]

So [tex]E_{min} = 3.68\times 10^{(-19)} - 2.60\times 10^{(-20)}[/tex]

[tex]E_{min} = 36.8\times 10^{(-20)} - 2.60\times 10^{(-20)}[/tex]

[tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

The minimum energy of the electron is [tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

For the longest wavelength, the electron will have its minimum energy that is Emin.

Hence, the longest wavelength can be calculated as given below.

[tex]\lambda = \dfrac {h\times c} {E_{min}}[/tex]

[tex]\lambda=\dfrac{6.626\times 10^{(-34)} \times 3\times 10^8} {34.2 \times 10^{(-20)}}[/tex]

[tex]\lambda = 549 \times 10^{(-9)} \;\rm m\\\lambda = 549 \;\rm nm[/tex]

The longest wavelength of the electron is 549 nm.

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Answer:

 r₁₀ = 52.9 nm

Explanation:

In Bohr's model of the hydrogen atom, the radius of the orbitals can be written as a function of the radius of the first orbit

               rₙ = n² a₀

where ao is 0.0529 nm and is the radius of the ground state of the atom

the radius for the excited state with n = 10

        r₁₀= 10² a₀

        r₁₀ = 100 a₀

        r₁₀ = 52.9 nm

Answer:

0.44c

Explanation:

We know that

Time interval at speed (ts)= time interval at rest(tr) / gamma

where

gamma = √[1-(v/c)²]

ts = tr / gamma

tr/ts = gamma

But

Ss/Sr = gamma

Where

Sr = clock speed at rest, Ss at speed):

So

√[1-(v/c)²] = 2/5

1 - (v/c)² = 4/25

(v/c)²= 5/25

v/c = √5 / 5

v = 0.444c

Answer:

Elementary school teachers.

Explanation:

Elementary school teachers create teaching strategies and introduce a variety of subjects to learners. Teachers at the elementary school develop lesson plans on subjects like social studies, science, mathematics, etc. Elementary school teachers empower and encourage young children to cultivate a passion for learning and education that lasts for life. They are charged for creating a positive learning atmosphere within the classroom for all students.

Answer:

Far point = is the farthest point where you can see the object

near point= is the nearest distance where you can see the object.

Explanation:

The far point of human eye is upto infinity & the near point is 25cm.

The answer is:

The formula  to calculate average velocity is a) V (average ) = x(f) - x(i) /t(f) - t(i)

Average velocity is a vector quantity . It is defied as the change in displacement  over a time interval .

Average velocity can be calculated as

Average velocity  = change in displacement / change in time travel

correct answer is a) V (average ) = x(f) - x(i) /t(f) - t(i)

where

x(f) = final position

x(i) = initial position

t(f) = final time

t(i) = initial time

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Answer:

The energy value is expected to rise steadily until it is equal to a value that depends on the temperature T of the environment.

Explanation:

If a system is immersed into an environment with a constant high temperature, the temperature of the system will also rise until it comes to equilibrium with the temperature of the environment. When this happens, the energy expectation value of the system will now be dependent on the temperature of the environment. This means that the energy of the system will be a function of the temperature of the environment.

This means that

E = f(T)

where E is the energy value of the system

T is the temperature of the environment.

Answer:

Option B - The fringe spacing will increase

Explanation:

We are given;

Wavelength; λ = 532nm

slit separation; d = 20um

For double-slit experiment, the fringe width is given by the expression;

β = λD/d

Where;

β is the fringe width

λ is the wavelength

D is the distance between the screen and the slit

d is the slit separation

Now, when immersed in water, the slit separation distance will decrease.

Now, from the fringe width equation, when "d" decreases, it means that we will have a bigger value of fringe width.

Thus, as slit separation decreases, the fringe width increases.

Answer:

The acceleration of the proton is 1.403 x 10⁹ m/s²

Explanation:

Given;

speed of proton, v = 7.7 m/s

magnitude of magnetic field, B = 1.9 T

Magnetic force of moving proton is given by;

F = qvBsinθ

Centripetal force on the moving proton is given by;

[tex]F = m(\frac{v^2}{r})\\\\F = m(a_c) \\\\a_c \ is \ the \ centripetal \ acceleration[/tex]

[tex]qvBsin\theta = ma_c\\\\ac = \frac{qvBsin(90)}{m}[/tex]

where;

q is charge of the proton = 1.602 x 10⁻¹⁹ C

m is mass of proton = 1.67 x 10⁻²⁷ kg

[tex]ac = \frac{(1.602*10^{-19})(7.7)(1.9)sin(90)}{1.67*10^{-27}}\\\\a_c = 1.403*10^{9} \ m/s^2[/tex]

Therefore, the acceleration of the proton is 1.403 x 10⁹ m/s²

Answer:

0.96 g/mL

Explanation:

The volume of 800 g of water is:

(800 g) / (1 g/mL) = 800 mL

The volume of 160 g of alcohol is:

(160 g) / (0.8 g/mL) = 200 mL

Density = mass / volume

ρ = (800 g + 160 g) / (800 mL + 200 mL)

ρ = 0.96 g/mL

Answer:

4.5 meters is your Answer goood luck please give 5 star

Explanation:

Answer:

Explanation:

The change in the trucks kinetic energy is same as the net work done by the truck in covering the said distance

Given data

mass of truck m= 1890 kg

initial velocity of truck u1= 34 km/h

final velocity v1= 62 km/h

applying the kinetic energy formula we have

[tex]K.E= \frac{1}{2}mv^2[/tex]

K.E(initial)

[tex]K.E(initial)= \frac{1}{2}*1890*34^2\\\\ K.E(initial)= \frac{1}{2}*1890*1156\\\\ K.E(initial)= \frac{1}{2}*2184840\\\\ K.E(initial)= 1092420J\\\\\ K.E(initial)= 1092.4kJ[/tex]

K.E(final)

[tex]K.E(initial)= \frac{1}{2}*1890*62^2\\\\ K.E(initial)= \frac{1}{2}*1890*3844\\\\ K.E(initial)= \frac{1}{2}*7265160\\\\ K.E(initial)= 3632580J\\\\\ K.E(initial)= 3632.58kJ[/tex]

The change in K.E= K.E(final)- K.E(initial) = 3632.58-1092.4= 2540.18 kJ

the change in the truck's K.E is 2540.18 kJ

Answer:

Explanation:

Knowledge of vectors is important because many quantities used in physics are vectors. If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect.

Some of the key vector quantities in physics: force, displacement, velocity, and acceleration.

An example of the importance of vector addition could be the following:

Two cars are involved in a collision. At the time of the collision car A was travelling at 40 mph, car B was travelling at 60 mph. Until I tell you in which directions the cars were travelling you don't know how serious the collision was.

The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of 100 mph!

Vector is defined as a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another

Vector is defined as a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another

Knowledge of vectors is important because many quantities used in physics are vectors. If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect.

Some of the key vector quantities in physics: force, displacement, velocity, and acceleration.

An example of the importance of vector addition could be the following:

Two cars are involved in a collision. At the time of the collision car A was travelling at 40 mph, car B was travelling at 60 mph. Until I tell you in which directions the cars were travelling you don't know how serious the collision was.

The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of 100 mph!

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Answer:

1.260

Explanation:

103.5 has 4 significant figures.

102.24 has 5 significant figures.

We will need to round the answer to the least number of significant figures available (in this case, 4).

103.5 − 102.24 = 1.26 = 1.260

The difference between 103.5 and 102.24 is equal to 1.3 in the correct number of significant figures.

Significant figures can be utilized to produce numbers that can be written in the form of figures. We can determine the number of significant figures by simply counting the values starting from the first non-zero digit placed on the left.

We can calculate the number of significant digits by counting from the first non-zero figure placed on the left. The significant digits of a given number are those significant digits, which convey the meaning with respect to its accuracy.

In the case of division or multiplication or subtraction and addition, the number of significant figures must be the same as the value with the fewest significant figures.

We have to find the difference between 103.5 and 102.24:

103.5 - 102.24 = 1.26 = 1.3

The number 103.5 has one significant figure after the decimal. Therefore, the answer will be equal to 1.3.

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Answer:

4f   E₄ = 0.85 eV,    L₄ = 4.22 10⁻³⁴ ,  

5d          E₅ = 0.544 eV ,    L5 = 5.28 10⁻³⁴

Explanation:

Let's use the Bohr model, stable the energy of the hydrogen atom

              E = -13.606 / n2

where Eo = 13.606 eV is the energy of the ground states.

a) the energy of each atom

level 4f

In this nomenclature enumeration is the number n

               E = -13606 / 42

               E₄ = 0.85 eV

level 5d

                E₅ = -13.606 / 5 2

                E₅ = 0.544 eV

b) The angular momentum is given in Boh's model

                     L = n h / 2pi

let's calculate

level 4f             L₄ = 4 6.63 10⁻³⁴-34 / 2 pi

                        L₄ = 4.22 10⁻³⁴

level 4d

                       L5 = 5 6.63 10-⁻³⁴ / 2pi

                       L5 = 5.28 10⁻³⁴

c) The hydrogen atom in state n = 5 has lower energy than the other state

d) Atom 1 has less angular momentum than atom 2

Given that,

Wavelength of the human light is 560 nm

To find,

The temperature of a black body that would radiates most intensely at this wavelength.

Solution,

The relation between temperature and the wavelength is given by :

[tex]\lambda=\dfrac{c}{T}[/tex]

T is temperature

c is [tex]2.898\times 10^{-3}\ m-K[/tex]

So,

[tex]T=\dfrac{c}{\lambda}\\\\T=\dfrac{2.898\times 10^{-3}}{560\times 10^{-9}}\\\\T=5175\ K[/tex]

So, the temperature of a black body that would radiates most intensely at this wavelength is 5175 K.

Answer:

a) 0 metres

b) From time 0 s to 10 s , the car was accelerated. Its velocity accelerated from 0m/s to 20 m/s

c) 20 m/s

Explanation:

a) Formula of displacement= velocity x time

time=40 s

velocity =0 m/s

∴ displacement= 0 x 40 = 0 m

Magnitude of displacement is 0 m

b) The increase in velocity shows that there has been acceleration.

c) The average velocity of the car is =[tex]\frac{0+40}{2\\}[/tex]   {initial velocity + final velocity}

                                                            =[tex]\frac{40}{2}[/tex]

                                                             =20

Therefore, the magnitude of the average velocity  of the car is 20 m/s

Answer:

Explanation:

Given data

power P= 2 kW

time t= 15 min to hours = 15/60= 1/4 h

cost of power consumption per kWh= 10 cent = $0.1

We are expected to compute the cost of operating the heater for 30 days

but let us computer the energy consumption for one day

Energy of heater  for one day= 2* 1/4 = 0.5 kWh

the cost of operating the heater for 30 days= 0.5*0.1*30= $1.50

Hence it will cost  $1.50 for 30 days operation

Given that,

Diameter of the loop, d = 19.5 cm

Magnetic field, B = 1.8 T

The loop is rotated so that its plane is parallel to the field direction in 0.22 s. We need to find the average induced emf in the loop.

When it is placed perpendicular to the magnetic field, angle between Area vector and Magnetic Field will be 0. Flus is BA.

When it is rotated so that its plane is parallel to the field direction, angle between Area vector and Magnetic Field will be 90. Flus is 0.

The induced emf is given by :

[tex]\epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=\dfrac{BA}{t}\\\\\epsilon=\dfrac{1.8\times \pi \times (19.5/2)^2}{0.22}\\\\\epsilon=2443.48\ V[/tex]

So, the average induced emf in the loop is 2443.48 volts.

Answer:

A)  K = ½ U / r , B)     T² = (4π² / G M) r³

Explanation:

A) It asks us for the kinetic energy of the satellite and they give us the relation of the potential synergy

         U = - G M m / r

the force can be found from this expression

          F = - dU / dr

          F = - G M m / r²

The kinetic energy is given by the formula

          K = ½ m v²

let's use Newton's second law

        F = m a

        G M m / r² = m a

where the acceleration is centripetal

        a = v² / r

         G M r² = v² / r

         v² = G M r³

we substitute the expression for the kinetic energy

         K = ½ m v²

         K = ½ m G M r³

in terms of potential energy is

         K = ½ (G M m r²) 1 / r

         K = ½ U / r

B) The period of the orbit

We write Newton's second law

            G M m / r² = m a

            a = v² / r

in a circular orbit the speed of the velocity is constant

            v = d / t

the longitude of the orbit is

             d = 2π r

            v = 2π r / T

we substitute

            G Mm / r² = m (2πr / T)² / r

            G M / r³ = 4π² / T²

            T² = (4π² / G M) r³

(A) The kinetic energy of satellite in terms of potential energy is,

       K =  1/2 U / R.

(B)  The expression for the square of the orbital period is,

         T² = (4π² / G M) R³

Given data:

The potential energy of object is, U.

The mass of object is, m.

The distance from the other object of mass M is, R.

A.

The kinetic energy of the satellite and they give us the relation of the potential synergy,

U = - G M m / R

And the force can be found from this expression

F = - dU / dR

F = - G M m / R²

The kinetic energy is given by the formula

K = 1/2 m v²

Now use Newton's second law

F = m a

G M m / R² = m a

where the acceleration is centripetal

a = v² / R

G M R² = v² / R

v² = G M R³

we substitute the expression for the kinetic energy

K = 1/2 m v²

K = 1/2 m G M R³

in terms of potential energy is

K = 1/2 (G M m R²) 1 / R

 K =  1/2 U / R

Thus, we can conclude that the kinetic energy of satellite in terms of potential energy is K =  1/2 U / R.

(B)

Now we need to obtain the period of the orbit of satellite. For that we   write Newton's second law as

G M m / r² = m a

Since,

a = v² / r

In a circular orbit the speed is constant,

v = d / t

For the longitude of the orbit is

d = 2π R

v = 2π R / T

here,

T is the orbital period of satellite.

Substituting the values as,

G Mm / R² = m (2πR / T)² / R

G M / R³ = 4π² / T²

T² = (4π² / G M) R³

Thus, we can conclude that the expression for the square of the orbital period is T² = (4π² / G M) R³.

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Answer:

hey!

Your answer will be EXACTLY 113.97899 Pounds

Explanation:

BUT IF YOU ROUND THIS UP TO THE WHOLE NUMBER etc IT WILL BECOME 114 POUNDS!

Hope This Helped!

itsMATT04

Answer:

b. Projectiles A & B have the same likelihood of breaking the glass since they have the same initial momentum

.

c. Projectile A has the greater likelihood of breaking the glass since its momentum change is larger.

Explanation:

for option b, the two projectiles have the same initial mass and velocity, hence they posses the same amount of momentum that if sufficient enough could break the glass.

for option c, projectile A changes direction, maintaining the same speed v. Its momentum changes from from mv to -mv, since its speed changed direction.

the difference in momentum becomes

Δp = -mv - mv = -2mv

this is twice the initial momentum.

projectile B changes momentum from mv to 0

Δp = 0 - mv = -mv.

this is half of the final momentum of projectile A.

Also we know that force is proportional to to the rate of change of momentum, which is greater in projectile A, therefore projectile A impacts more force on the glass. Projectile A therefore has the greater likelihood of breaking the glass since its momentum change is larger.