Water is flowing at a rate of 0.25 m3/s, and it is assumed that head loss in the system is 2V2/2g from the reservoir to the gage, where V is the velocity in the 30 cm pipe. What power must the pump supply

Answer:

0.25 J

Explanation:

Given that

Force on the spring, F = 30 N

Natural length of the spring, l1 = 20 cm = 0.2 m

Final length of the spring, l2 = 35 cm = 0.35 m

Extension of the spring, x = 0.35 - 0.2 = 0.15 m

The other extension is 40 - 35 cm = 5 cm = 0.05 m

Work done = ?

Considering Hooke's Law of Elasticity.

We're told that the spring stretches through 15 cm, and thereafter asked to find the work done in stretching it through 5 cm

The question is solved in the attachment below

Answer:

1.2 s

Explanation:

Given:

v₀ = 8.0 m/s

v = -4.0 m/s

a = -10 m/s²

Find: t

v = at + v₀

(-4.0 m/s) = (-10 m/s²) t + (8.0 m/s)

t = 1.2 s

Answer:

100 on average

Explanation:

The human body is a physical substance from where a human can breathe, drink, eat, walk, etc, and consists of various cells. A human being cannot live with their functions and when functions stop working that means a human being is dead.

Therefore, in the human body, there is also electricity that contains 100 watts on average.

So, According to the given situation, the correct answer is 100 on average.

Answer:

You will have to move 12.2 ft to decrease the initial intensity to 17 mRem/h.

Explanation:

The distance can be calculated using the following equation:

[tex] \frac{I_{1}}{I_{2}} = \frac{D_{2}^{2}}{D_{1}^{2}} [/tex]

Where:

I₁ = 158 mRem/h

I₂ = 17 mRem/h

D₁ = 4 ft.

D₂=?

Hence, the distance D₂ is:

[tex] D_{2} =\sqrt{\frac{I_{1}}{I_{2}}*D_{1}^{2}} = \sqrt{\frac{158 mRem/h}{17 mRem/h}*(4 ft)^{2}} = 12.2 ft [/tex]

Therefore, you will have to move 12.2 ft to decrease the initial intensity to 17 mRem/h.

I hope it helps you!

Answer:

[tex]I = 0.083 kg m^2[/tex]

Explanation:

Mass of the bucket, m = 23 kg

Radius of the pulley, r = 0.050 m

The bucket is released from rest, u = 0 m/s

The time taken to fall, t = 2 s

Speed, v = 8.0 m/s

Moment of Inertia of the pulley, I = ?

Using the equation of motion:

v = u + at

8 = 0 + 2a

a = 8/2

a = 4 m/s²

The relationship between the linear and angular accelerations is given by the equation:

[tex]a = \alpha r[/tex]

Angular acceleration, [tex]\alpha = a/r[/tex]

[tex]\alpha = 4/0.050\\\alpha = 80 rad/s^2[/tex]

Since the bucket is falling, it can be modeled by the equation:

mg - T = ma

T = mg - ma = m(g-a)

T = 23(9.8 - 4)

The tension, T = 133.4 N

The equation for the pulley can be modeled by:

[tex]T* r = I * \alpha\\133.4 * 0.050 = I * 80\\6.67 = 80 I\\I = 6.67/80\\I = 0.083 kg m^2[/tex]

Answer:

Explanation:

ω = angular velocity = 2π n = 2π x 72 / 60

= 7.536 rad /s

mass of head = 90 x .07 = 6.3 kg

moment of inertia of head = 2 /5 m R²

= .4 x 6.3 x .08²

= .016128 kg m²

moment of inertia of trunk + legs

= 1/2 m R²

= .5 x .8 x 90 x .12²

= .5184 kg m²

moment of inertia of arms

= 1/3 m L²

= 1 / 3 x .13 x 90 x .60²

= 1.404 kg m²

Total moment of inertia

I = 1.938 kg m²

kinetic energy = 1/ 2 I ω ²

where I is moment of inertia and ω is angular velocity

= .5 x 1.9338 x  7.536²

=55 J approx .

The definition of kinetic energy and moment of inertia allows finding the result for the kinetic energy of the dancer with arms extended is:

Given parameters

       *    Head 7%

       *    Arms 13%

       *   Trunk and legs 80%

To find.

The kinetic energy is the energy due to the movement, in this case the movement is rotational, therefore the expression is:

             KE = ½ I w²

The angular velocity is related to the frequency.

            w = 2π f

            w = 2π 1.2

            w = 7.540 s

The moment of inertia is a scalar, therefore it is a quantity that can be added, the total moment of inertia of the dancer is the sum of the moments of inertia of each part with respect to the axis of rotation of the person.

          [tex]I_{toal}= I_{head}+ I_{trunk}+I_{arms}[/tex]

The moments of inertia with respect to the centers of mass are tabulated.

Sphere        I = 2/5 mr²

Cylinder      I = ½ m r²

Rod             I = ⅓ m r²

The axis of rotation of the head and the trunk are in the axis of rotation of the person, therefore their moment of inertia is those corresponding to the center of mass.

At the end of the arms it is at a distance of D = [tex]\frac{r_2}{2}[/tex]  from the axis of rotation of the dancer, therefore to find the moment of inertia we must use the theorem of parallel axes, see attached.                  

              [tex]I_{arms} = I_{cm} + M D^2[/tex]

             [tex]I_{arms}[/tex]  = ⅓ m L² + m D²

            [tex]I_{arms} = m_{arms} ( \frac{L^2}{3} + D^2)[/tex]            

The masses of each part of the body are:

            [tex]m_{head}[/tex] = m 0.07

            [tex]m_{trunk}[/tex] = m 0.80  

            [tex]m_{arms}[/tex]  = m 0.13

Let's find the total  moment of inertia.  

            [tex]I_{total} = \frac{2}{5} \ 0.07m \ r_1^2 + 0.13m\ ( \frac{L^2}{3} + D^2) + \frac{1}{2} \ 0.80m \ r_2^2[/tex]  

            [tex]I_{total} = m ( 0.028 \ r_1^2 + 0.13 (\frac{L^2}{3} + D^2) + 0.40 \ r_2^2}[/tex]  

Let's calculate.  

           [tex]I_{total} = 90\ ( 0.028 \ 0.08^2 + 0.13\ ( \frac{0.6^2}{3} + 0.06^2) + 0.40 \ 0.12^2 )[/tex]

           [tex]I_{total}= 90 \ 0.0220 \\ \\I_{total} = 1.9806 \ Kg m^2[/tex]

we substitute in the kinetic energy

           KE = ½ 1.9806  7,540²

           KE = 56.3  J

In conclusion using the definition of kinetic energy and moment of inertia we can find the result for the kinetic energy of the dancer with the extended arms is:

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Answer:

same direction = 80 (n)

opposite direction = 20 (n) going one direction

Explanation:

same direction means they are added to each other

and opposite means acting on eachother

Answer: Use this F=Ma.

Explanation: So your answer will be

F=1 Kg+9.8 ms-2

So the answer will be

F=9.8N

How'd I do this?

I just used Newton's second law of motion.

I'll also put the derivation just in case.

Applied force α (Not its alpha, proportionality symbol) change in momentum

Δp α p final- p initial

Δp α mv-mu (v=final velocity, u=initial velocity and p=v*m)

or then

F α m(v-u)/t

So, as we know v=final velocity & u= initial velocity and v-u/t =a.

So F α ma, we now remove the proportionality symbol so we'll add a proportionality constant to make the RHS & LHS equal.

So, F=kma (where k is the proportionality constant)

k is 1 so you can ignore it.

So, our equation becomes F=ma

Answer:

B. A force that is equal in amount but oppositely directed to the force the lighter child is exerting.

Explanation:

If they are sitting at the same distance away from the pivot yet the seesaw is balanced, the only conclusion is the heavier child is exerting a lower force. This causes the pivot exertion and balances to be equal. The equilibrium of the pivot-seesaw is not affected by the weight because of force exertion.

Answer:

Explanation:

a )

for convex mirror, focal length

f = + 20 / 2 = 10 cm

object distance u = 12 cm ( negative )

Using mirror formula

[tex]\frac{1}{v} + \frac{1}{u} = \frac{1}{f}[/tex]

Putting the values

[tex]\frac{1}{v} - \frac{1}{12} = \frac{1}{10}[/tex]

[tex]\frac{1}{v} =\frac{1}{10} + \frac{1}{12}[/tex]

[tex]v=\frac{12\times 10}{12+10}[/tex]

v = 5.45 cm

Size of image

=[tex]\frac{v}{u} \times size of object[/tex]

[tex]=\frac{5.45}{12} \times 9[/tex]

= 4.08 mm .

It will be erect because only erect image is formed in convex mirror .

It will be virtual .

b )

Draw ray from tip of object parallel to principal axis and after reflection appears to be coming from  focus . Second ray falls on the pole and reflects back making equal angle with principal axis . Draw the reflected ray backwards to cut the other ray . They cut each other where image is formed .

Answer:

1/4 of its original value

Explanation:

Newton's law of universal gravitation states that when two bodies of masses M₁ and M₂ interact, the force of attraction (F) between these bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between these bodies. i.e

F ∝ [tex]\frac{M_1 M_2}{r^2}[/tex]       ------------(i)

From the equation above, it can be deduced that;

F ∝ [tex]\frac{1}{r^2}[/tex]

=> F = G [tex]\frac{1}{r^2}[/tex]       -----------(ii)

Where;

G = constant of proportionality called the gravitational constant

Equation (ii) can be re-written as

Fr² =  G

=> F₁r₁² = F₂r₂²              -----------(iii)

Where;

F₁ and r₁ are the initial values of the force and distance respectively

F₂ and r₂ are the final values of the force and distance respectively

From the question, if the distance doubles i.e;

r₂ = 2r₁,

Then the final value of the gravitational force F₂ is calculated as follows;

Substitute the value of r₂ = 2r₁ into equation (iii) as follows;

F₁r₁² = F₂(2r₁)²

F₁r₁² = 4F₂r₁²          [Divide through by r₁²]

F₁ = 4F₂                 [Make F₂ subject of the formula]

F₂ = F₁ / 4              [Re-write this]

F₂ = [tex]\frac{1}{4} F_1[/tex]

Therefore the gravitational force will be 1/4 of its original value when the distance between the bodies doubles.

Answer:

12.5 rad/s²

Explanation:

Angular Acceleration: This can be defined as the ratio of linear acceleration and radius. The S.I unit is rad/s²

From the question,

a = αr................... Equation 1

Where a = linear acceleration, α = angular acceleration, r = radius.

But,

a = (v-u)/t.............. Equation 2

Where v = final velocity, u = initial velocity, t = time.

Substitute equation 2 into equation 1

(v-u)/t = αr

make α the subject of the equation

α = (v-u)/tr................. Equation 3

Given: v = 30 m/s, u = 0 m/s, t = 6 s, r = 0.4 m

Substitute into equation 3

α = (30-0)/(0.4×6)

α = 30/2.4

α = 12.5 rad/s²

Answer:

The pressure produced on the air in the pump is 37.209 pounds per square inch.

Explanation:

By definition, the pressure is the force exerted on the piston divided by its area. Given that, force is distributed uniformly on the piston area, the formula to determine the pressure is:

[tex]p = \frac{F}{A}[/tex]

Where:

[tex]p[/tex] - Pressure, measured in pounds per square inch.

[tex]F[/tex] - Force exerted on the piston, measured in pounds.

[tex]A[/tex] - Piston area, measured in square inches.

If [tex]F = 16\,lb[/tex] and [tex]A = 0.43\,in^{2}[/tex], the pressure produced on the air in the pump is:

[tex]p = \frac{16\,lb}{0.43\,in^{2}}[/tex]

[tex]p = 37.209\,psi[/tex]

The pressure produced on the air in the pump is 37.209 pounds per square inch.

Answer:

(a) max. height = 3.641 m

(b) flight time = 1.723 s

(c) horizontal range = 31.235 m

(d) impact velocity = 20 m/s

Above values have been given to third decimal.  Adjust significant figures to suit accuracy required.

Explanation:

This problem requires the use of kinematics equations

v1^2-v0^2=2aS .............(1)

v1.t + at^2/2 = S ............(2)

where

v0=initial velocity

v1=final velocity

a=acceleration

S=distance travelled

SI units and degrees will be used throughout

Let

theta = angle of elevation = 25 degrees above horizontal

v=initial velocity at 25 degrees elevation in m/s

a = g = -9.81 = acceleration due to gravity (downwards)

(a) Maximum height

Consider vertical direction,

v0 = v sin(theta) = 8.452 m/s

To find maximum height, we find the distance travelled when vertical velocity = 0, i.e. v1=0,

solve for S in equation (1)

v1^2 - v0^2 = 2aS

S = (v1^2-v0^2)/2g = (0-8.452^2)/(2*(-9.81)) = 3.641 m/s

(b) total flight time

We solve for the time t when the vertical height of the object is AGAIN = 0.

Using equation (2) for vertical direction,

v0*t + at^2/2 = S    substitute values

8.452*t + (-9.81)t^2 = 3.641

Solve for t in the above quadratic equation to get t=0, or t=1.723 s.

So time for the flight = 1.723 s

(c) Horiontal range

We know the horizontal velocity is constant (neglect air resistance) at

vh = v*cos(theta) = 25*cos(25) = 18.126 m/s

Time of flight = 1.723 s

Horizontal range = 18.126 m/s * 1.723 s = 31.235 m

(d) Magnitude of object on hitting ground, Vfinal

By symmetry of the trajectory, Vfinal = v = 20, or

Vfinal = sqrt(v0^2+vh^2) = sqrt(8.452^2+18.126^2) = 20 m/s

Answer:

because gravitational potential enegry is directly proportional to the height so more the height more the gravitational potential enegry. therefore gravitational potential enegry is greatest at high point than lower points.

Answer:

Q = 23.49 C

Explanation:

We have,

Electric current drawn by the air conditioner is 16.2 A

Time, t = 1.45 s

It is required to find the electric charge passes through the circuit during this period. We know that electric current is defined as the electric charge flowing per unit time. So,

[tex]I=\dfrac{q}{t}\\\\q=It\\\\q=16.2\times 1.45\\\\q=23.49\ C[/tex]

So, the charge of 23.49 C is passing through the circuit during this period.

Answer:

Explanation:

given:

radius (r) = 1.88 km

velocity (v) = 136.3 km/hr

required:

banking angle ∡ ?

first:

convert 1.88 km to m = 1.88km * 1000m / 1km

r = 1880 m

convert velocity v = 136.3 km/hr to m/s = 136.3 km/hr * (1000 m/ 3600s)

v = 37.86 m/s

now.. calculate the angle

Ф = inv tan (v² / r * g)            we know that gravity = 9.8 m/s²

Ф = inv tan (37.86² / (1880 * 9.8))

Ф = 4.4°

Answer:

7.2 N

Explanation:

length of wire L  = 240 m

current I = 500 A

field strength B = 3 x 10^-5 T

magnetic force on a current carrying conductor F is given as

F = BILsin∅

The wires are perpendicular with field therefore sin∅ = sin 90° = 1

therefore,

F = BIL = 3 x 10^-5 X 500 X 240 = 3.6 N

If the wire exists between this two transmission lines, then total magnetic force on the wire = 2 x 3.6 = 7.2 N

Answer:

-   maximum displacement = 3.00nm

-   λ = 1.79m

-  f = 286.47 s^-1

Explanation:

You have the following equation for a sound wave:

[tex]s(x,t)=3.00nm\ cos(3.50m^{-1}x- 1,800s^{-1} t)[/tex]              (1)

The general form of the equation of a sound wave can be expressed as the following formula:

[tex]s(x,t)=Acos(kx-\omega t)[/tex]            (2)

A: amplitude of the wave = 3.00nm

k: wave number = 3.50m^-1

w: angular frequency = 1,800s^-1

- The maximum displacement of the wave is given by the amplitude of the wave, then you have:

maximum displacement = A = 3.00nm

- The wavelength is given by :

[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{3.50m^{-1}}=1.79m[/tex]

The values for the wavelength is 1.79m

- The frequency is:

[tex]f=\frac{\omega}{2\pi}=\frac{1,800s^{-1}}{2\pi}=286.47s^{-1}[/tex]

The frequency is 286.47s-1

Answer:

5

Explanation:

Answer:

Explanation:

In a conductor, electric current can flow freely, in an insulator it cannot.

Metals such as copper typify conductors, while most non-metallic solids are said to be good insulators, having extremely high resistance to the flow of charge through them.

Most atoms hold on to their electrons tightly and are insulators.

Explanation:

dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total mass–energy density or about 2.241×10⁻²⁷ kg/m³. Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts think that dark matter is abundant in the universe and that it has had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with the electromagnetic field, which means it doesn't absorb, reflect or emit electromagnetic radiation, and is therefore difficult to detect.

Answer:

V = 3.6 volts

Explanation:

From Ohm's Law, we know that:

V = IR

but,

R = ρL/A

Therefore,

V = IρL/A

where,

V = Potential Difference = ?

I = Current = 4 A

ρ = resistivity of copper = 1.68 x 10⁻⁸ Ω.m

L = Length = 70 m

A = Cross-sectional Area = πd²/4 = π(1.29 x 10⁻³ m)²/4     [16 gauge wire has a diameter of 1.29 mm]

A = 1.31 x 10⁻⁶ m²

V = (4 A)(1.68 x 10⁻⁸ Ω.m)(70 m)/(1.31 x 10⁻⁶ m²)

V = 3.6 volts

The potential difference across the given length of copper wire is obtained to be 3.6 V.

The resistance of the wire depends on the length, area of cross-section of the wire and resistivity of the material.

Given the length of the wire, [tex]L = 70\,m[/tex].

The diameter of a 16 gauge copper wire is given by, [tex]d = 1.29\times 10^{-3}\,m[/tex].

Therefore, the radius of the cross-section is;

[tex]r=\frac{d}{2} = \frac{1.29\times 10^{-3}\,m}{2} =6.45\times 10^{-4}\,m[/tex]

So, the resistance of the given length of wire can be written as,

[tex]R= \rho\, \frac{L}{A} =(1.68 \times 10^{-8} \, \Omega .m)\times \frac{70\,m}{\pi \times (6.45\times 10^{-4}m)^2} = 0.9\, \Omega[/tex]

According to Ohm's Law, we can write;

[tex]V=IR[/tex]

Substituting the known values, we get the voltage drop is;

[tex]V = 4A \times 0.9\Omega = 3.6\,V[/tex]

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Answer:

It is calculated as Force × perpendicular distance.

Explanation:

Torque is a rotational force and twisting force that can cause an object to rotate in it's axis. This cause angular rotation.

The torque due to gravity on a body about its centre of mass is zero because the centre of mass is the that point of the body at which the force acts by the gravity that is mg.

But if the pivot point of a balance is not at the centre of mass of the balance, it will be FORCE × PERPENDICULAR DISTANCE because at that point, there is no centre in which the force act on a body by gravity. The distance and force will be use to calculate.

Answer:

Explanation:

v= u + at

v is final velocity , u is initial velocity . a is acceleration and t is time

Initial velocity u = 0 . Putting the given values in the equation

v = 0 + g sin 18 x 3.5

= 10.6 m /s

For a skateboarder who starts from the rest, the speed when he reaches the bottom of the ramp will be 10.6 m/s.

The term "velocity" refers to a vector measurement of the rate and direction of motion. Velocity is the rate of movement in a single direction, to put it simply. Velocity can be used to determine how fast a rocket is heading into space and how fast a car is moving north on a congested motorway.

There are several types of velocity :

The pace at which a person's velocity changes is known as acceleration. This implies that an object is accelerating if its velocity is rising or falling. An object that is accelerating won't have a steady change in location every second like an item moving at a constant speed does.

According to the question, the given values are :

Time, t = 3.50 sec

Initial Velocity, u = 0 m/s

Use equation of motion :

v = u+at

v = 0+ g sin 18 × 3.5

v = 10.6 m/s.

So, the final velocity will be 10.6 m/s.

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Answer:

a) 0.0036 J & 0.0135 J

b) 0.0099 J

Explanation:

Given that

Capacitance of a capacitor, C(i) = 12.5*10^-6 F

Potential difference across the capacitor, V = 24 V

Dielectric constant, k = 3.75

Energy in a capacitor is given by the formula

U = ½ CV²

Now, applying this to our solution, we have.

a, the energy stored before the dielectric was inserted is 0.0036. After inserting the dielectric, we then take cognizance into it, essentially multiplying by the constant of the dielectric, we got 0.0135 J

b) Now, Change in energy is gotten by subtracting the two energies, and we have

ΔU = U - U(1)

ΔU = 0.0036 - 0.0135

ΔU = 00099 J

See attachment for calculation

Answer:

Pls see attached file

Explanation:

Answer:

The corresponding dimensions will be "x = 300 & y = 60".

Explanation:

Available fencing = 600 ft

Fencing,

⇒  [tex]5y+x=600[/tex]

⇒  [tex]x=600-5y[/tex]

As we know,

⇒  [tex]Area =xy[/tex]

On substituting the given values, we get

             [tex]=(600-5y)y[/tex]

             [tex]=600y-5y^2[/tex] ...(equation 1)

On differentiating with respect to y, we get

⇒  [tex]\frac{dA}{dy} =600-10y[/tex]

       [tex]0 = 600-10y[/tex]

    [tex]600=10y[/tex]

       [tex]y=\frac{600}{10}[/tex]

       [tex]y=60[/tex]

On putting the values of y in equation 1, we get

⇒  [tex]600(60)-5(60)^2[/tex]

⇒  [tex]600(60)-5(3600)[/tex]

⇒  [tex]36000 - 18000[/tex]

⇒  [tex]18000[/tex]

Dimensions of the rectangular area:

x = 300

y = 60

Answer: The magnetic field points to the west.

Explanation:

If we take the plane as:

North = positive y-axis

East = positive x-axis.

We have that the electron is moving south, so the velocity of the electron can be written in vector form as:

V = (0, -v, 0)

Now, when the electron interacts with the magnetic field, the electron moves upwards.

We know that the interaction between an electron and a magnetic field is:

F = q*VxB

So we have that this force acts on the z-direction.

Now, to solve this we can use the righ hand rule.

First, we point wit our hand to the direction of the velocity (negative y-axis) now, we want that our thumb points up (the direction of the force) so the side where our palm faces is the direction of the field B.

But, remember that an electron has a negative charge, so the actual equation is:

F = -q*VxB

So the magnetic field actually points in the opposite direction of our palm, to the west.

Now, we can also solve it mathematically as:

F = (0, 0, f) = -q*(0, -v,0)x(a, b, c)

where B = (a, b, c) is the vector of the magnetic field.

     (0, 0, f) = -q*(-v*b -0, -0 + 0, 0 -(- a*v)) = -q*(-v*b, 0, a*v)

then we have that b must be equal to zero, and that:

f = -q*a*v

and f is positive, then we have:

a = -(f/q*v)

then the vector of the magnetic field is:

B = (-(f/q*v), 0, 0)

so it points in the negative x-axis, that is the West, as we found earlier.

Answer:

The remaining percentage of drug concentration is about 88.7% 2 years after manufacture.

Explanation:

Recall the formula for the decay of a substance at an initial [tex]N_0[/tex] concentration at manufacture:

[tex]N(t)=N_0\,e^{-k\,\,t}[/tex]

where k is the decay rate (in our case 0.06/year), and t is the elapsed time in years. Therefore, after 2 years since manufacture we have:

[tex]N=N_0\,e^{-0.06\,\,(2)}\\N=N_0\,e^{-0.12}\\N/N_0=e^{-0.12}\\N/N_0=0.8869[/tex]

This in percent form is 88.7 %. That is, the remaining percentage of drug concentration is about 88.7% 2 years after manufacture.