Let us treat a helicopter rotor blade as a long thin
rod, as shown in Fig. 8–49. (a) If each of the three rotor
helicopter blades is 3.75 m long and has a mass of 135 kg,
calculate the moment of inertia of the three rotor blades
about the axis of rotation. (b) How much torque must the
motor apply to bring the blades from rest up to a speed
of 6.0 rev/s in 8.0 s?
Rotor

Answer:

Option A. 1.1×10¯²⁴ N

Explanation:

The following data were obtained from the question:

Charge 1 (q1) = - 4e

Charge 2 (q2) = + 3e

Distance apart (r) = 0.05 m

Electric field constant (K) = 9×10⁹ N•m²/C²

Electron (e) = 1.6×10¯¹⁹ C.

Electric Force (F) =..?

Next, we shall determine the value of the two charges.

This is illustrated below:

Charge 1 (q1) = - 4e

Charge 1 (- q1) = 4e

Electron (e) = 1.6×10¯¹⁹ C.

Charge 1 (- q1) = 4 × 1.6×10¯¹⁹ C.

Charge 1 (- q1) = 6.4×10¯¹⁹ C.

Charge 2 (q2) = + 3e

Electron (e) = 1.6×10¯¹⁹ C.

Charge 2 (q2) = 3 × 1.6×10¯¹⁹ C.

Charge 2 (q2) = 4.8×10¯¹⁹ C.

Finally, we shall determine the value of the electric force. This can be obtained as shown below:

Charge 1 (- q1) = 6.4×10¯¹⁹ C.

Charge 2 (q2) = 4.8×10¯¹⁹ C.

Electric field constant (K) = 9×10⁹ N•m²/C².

Distance apart (r) = 0.05 m

Electric Force (F) =..?

F = Kq1q2 /r²

F = (9×10⁹× 6.4×10¯¹⁹× 4.8×10¯¹⁹)/(0.05)²

F = 1.1×10¯²⁴ N

Therefore, the electric force between the two point charge is 1.1×10¯²⁴ N

refer to the attachment for the explanation

Answer:

(a) 17.0eV

(b) 10.55W

Explanation:

(a) The amount of work done (W) on an electron by an ideal battery of emf value of V as it moves from the positive to the negative terminal is given by;

W = q x V                 --------(i)

Where;

q = charge on the electron = 1e

From the question;

V = 17.0 V

Substitute the values of q and V into equation (i) as follows;

W = 1e x 17.0

W = 17.0eV

Therefore, the work done in electron volts is 17.0

(b) The power (P) of the battery as some electrons (n) pass through it at time t, is given as;

P = (n q V) / t            --------------(ii)

Where;

n = number of electrons = 3.88 x 10¹⁸

t = 1s

q = 1.6 x 10⁻¹⁹C

V = 17.0V

Substitute these values into equation (ii) as follows;

P = (3.88 x 10¹⁸ x 1.6 x 10⁻¹⁹ x 17.0) / 1

P = 10.55W

Therefore the power of the battery is 10.55W

Answer:

34.34 °C

Explanation:

From the question,

Heat lost by the silver block = heat gained by the iron block.

cm(x-y) = c'm'(y-z)................... Equation 1

Where c = specific heat capacity of the silver block, m = mass of the silver block, c' = specific heat capacity of the iron, m' = mass of the iron. x = initial temperature of the silver block, z = initial temperature of the iron,  y = final temperature of the mixture.

make y the subject of the equation

y = (cmx+c'm'z)/(cm+c'm')............... Equation 2

Given: c = 50 g, c = 0.2350 J/g·°C, x = 100°C, m' = 50 g, c' = 0.4494 J/g.°C, z = 0°C

Substitute these values into equation 2

y = [(50×0.2350×100)+(50×0.4494×0)]/[(50×0.2350)+(50+0.4494)]

y = 1175/(11.75+22.47)

y = 1175/34.22

y = 34.34 °C

Answer:

the mass of one sun

Explanation:

its really heavy

Answer:

0.572

Explanation:

First examine the force of friction at the slipping point where Ff = µsFN = µsmg.

the mass of the car is unknown,

The only force on the car that is not completely in the vertical direction is friction, so let us consider the sums of forces in the tangential and centerward directions.

First the tangential direction

∑Ft =Fft =mat

And then in the centerward direction ∑Fc =Ffc =mac =mv²t/r

Going back to our constant acceleration equations we see that v²t = v²ti +2at∆x = 2at πr/2

So going backwards and plugging in Ffc =m2atπr/ 2r =πmat

Ff = √(F2ft +F2fc)= matp √(1+π²)

µs = Ff /mg = at /g √(1+π²)=

1.70m/s/2 9.80 m/s² x√(1+π²)= 0.572

Answer:

ugmd = 1/2 kx²

d = (1/2 kx²) / (ugm)

= (1/2 * 250 N/m * (0.2 m)²) / (0.23 * 9.81 m/s² * 0.3 kg)

= 7.4 m

ugmd = 1/2 mv²

v = √2ugd

= √(2(0.23)(9.81 m/s²)(7.4 m)

= 5.8 m/s

Explanation:

The box's launch speed is 5.8 m/s.

Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.

Given in question spring with spring constant 210 Nm is compressed by 20 cm and then used to launch a 250 g box across the floor,

ugmd = 1/2 kx²

d = (1/2 kx²) / (ugm)

= (1/2 * 250 N/m * (0.2 m)²) / (0.23 * 9.81 m/s² * 0.3 kg)

= 7.4 m

ugmd = 1/2 mv²

v = √2ugd

= √(2(0.23)(9.81 m/s²)(7.4 m)

= 5.8 m/s

The box's launch speed is 5.8 m/s.

To learn more about energy refer to the link:

brainly.com/question/1932868

 #SPJ5

Answer:

Explanation:

In the decibel scale , intensity of sound changes logarithmically as follows

[tex]10log\frac{I}{I_0} =[/tex] Value in decibel scale , the value of I₀ = 10⁻¹² W /m².

Putting the values

[tex]10log\frac{I}{10^{-12}} = 71[/tex]

[tex]log\frac{I}{10^{-12}} = 7.1[/tex]

[tex]\frac{I}{10^{-12}} = 10^{7.1}[/tex]

[tex]I= 10^{-4.9}[/tex] W/m²

Similarly for 54 dB sound intensity can be given as follows

I = 10⁻¹² x [tex]10^{5.4}[/tex]

[tex]I= 10^{-6.6 }[/tex] W / m²

For intensity of sound the relation is as follows

I = 2π²υ²A²ρc where υ is frequency , A is amplitude , ρ is density of air and c is velocity of sound .

Putting the given values for 71 dB

[tex]I= 10^{-4.9}[/tex]  = 2π² x 504²xA²x 1.21 x  346

A² = 60.03 x 10⁻¹⁶

A = 7.74 x 10⁻⁸ m

For 54 dB sound

[tex]10^{-6.6}[/tex] = 2π² x 504²xA²x 1.21 x  346

A² = 1.1978 x 10⁻¹⁶

A = 1.1 x 10⁻⁸ m

Answer:

The water is at the top because when the water is stored at the top it does not need as much energy to get it to flow because it will be flowing down and be affected by gravity to make the water pressure.

Answer:

The water is at the top because when the water is stored at the top it does not need as much energy to get it to flow because it will be flowing down and be affected by gravity to make the water pressure.

Explanation:

Answer:

Acceleration(a)=21.60 km/h or 21,600 m/s

Explanation:

Since you have the initial velocity(0, because it starts from rest) and the final velocity 72 km/h or 72,000 m/s. so...

[tex]a=\frac{Vf-Vi}{t}\\ a=\frac{72,000 m/s-0}{2s}\\ a=\frac{72,000 m/s}{2s}\\ a=36,000m/s or 36 km/h[/tex]

Answer:

Center of Gravity is the point in a body where the gravitational force may be taken to act.  Center of Buoyancy is the center of gravity for the volume of water which a hull displaces.

Answer:

English.

Explanation:

English is undeniably accepted by scientists all over the world as the primary language of science. It is a language spoken all over the world and is also the language of science because it is an official language and can be understood by almost everyone.

Answer:

[tex]\boxed{\mathrm{English}}[/tex]

Explanation:

English is undeniably accepted by scientists all over the world as the primary language of science. The scientific methods and experiments are done by communicating and writing in English. Scientists use English to communicate and share knowledge as English is understood by people from around the world.

Answer:

a)  True    b)  True

Explanation:

a) a capacitor is made up of two flat plates and each one has a charge of the same sign, therefore the statement is true

b) the current is the flow of electrons per unit of time, therefore the charge is not zero, therefore the statement is True

Answer:

g, downward

Explanation:

It is given that, a baseball is thrown straight upward. The force acting on the stone is force of gravity. It is moving under the action of gravity. We know that the force of gravity always acts in a downward direction.

At the highest point, the velocity of the stone will be equal to 0. It will move will constant acceleration equal to g and it always acts in downward direction.

Hence, the correct option is (e) "downward direction".

Answer:

The acceleration of the object is 4 m/s².

Explanation:

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass i.e.

[tex]a=\dfrac{k}{m}[/tex] ...(1)

Let us assume that the question is a certain force acting upon an object with mass 2 kg produces an acceleration of 38 m/s². if the same force acts upon another object whose mass is 19 kg, what would this object's acceleration be

Equation (1) can be written as :

[tex]\dfrac{a_1}{a_2}=\dfrac{m_2}{m_1}[/tex]

Here,

a₁ = 38 m/s², a₂ =?, m₁ = 2 kg, m₂ = 19 kg

So,

[tex]\dfrac{38}{a_2}=\dfrac{19}{2}\\\\a_2=4\ m/s^2[/tex]

So, the acceleration of the object is 4 m/s².

Velocity is the description of an object's motion from one point to another.

It tells the speed with which the trip is completed, and the direction from the start-point to the end-point.  It tells nothing about any twists, turns, loops, bends, or stops along the way.

Answer:

Δt=48 s

Explanation:

v: Barry's speed

v.: speed of the walkway

Δx=30 m

Δt1=30 s ,  Δt2=120 s

|Δx1|=|Δx2|

Δx=v*Δt

=> (v+v.)*30=(v-v.)*120

v=v.*5/3

30=(v+v.)*30

=> 30=(5v./3 +v.)*30

v.=3/8 m/s

v=5v./3 , v.=3/8

=> v=5/8 m/s

Δx=v*Δt

30=5/8 *Δt

Δt=48 s

Answer:

[tex]B=2.025\times 10^{11}\ Pa[/tex]

Explanation:

It is given that,

Speed of P- waves, v = 9 km/s = 9000 m/s

The density of rock is about [tex]2500\ kg/m^3[/tex]

We need to find the average bulk modulus of Earth's crust. Let it is given by B. So,

[tex]v=\sqrt{\dfrac{B}{d}} \\\\B=v^2d\\\\B=(9000)^2\times 2500\\\\B=2.025\times 10^{11}\ Pa[/tex]

So, the bulk modulus of the Earth's crust is [tex]2.025\times 10^{11}\ Pa[/tex].

Answer:

a = 85.9 m / s²

Explanation:

For this exercise we can use Newton's second law in the most compressed part

             F - W = m a

force is the spring elastic force

             F = - k Δx

          k Δx - m g = m a

          a = k/m  Δx - g

         Δx = x₀ -[tex]x_{f}[/tex]

         ΔX = 46 - 5 = 41cm (1m / 100cm) = 0.41  m

let's calculate

          a = 1.4 10⁴/60 0.41 - 9.8

          a = 85.9 m / s²

Answer:

C) Mitochondrial DNA

Explanation:

Mitochondrial DNA can help forensic scientists in recovering the follicular tissue that is attached to the hair, they can find out the specific suspect from that hair.

Mitochondrial DNA is maternally inherited and enables forensic scientists to trace maternal lineage.

Answer:

Mitochondrial DNA

Explanation:

Mitochondrial DNA should be used to prove that the hair in the victim's fist belonged to a specific suspect. Mitochondrial DNA enables scientists to trace maternal lineage from which it can be known that who is the suspect.

Answer:

Option D. 4.4 m/s²

Explanation:

The following data were obtained from the question:

Velocity (v) = 21 m/s

Radius (r) = 100 m

Centripetal acceleration (a) =.?

The centripetal acceleration of the car can be obtained as follow:

Centripetal acceleration (a) = Velocity square (v²) / radius (r)

a = v²/r

a = 21²/100

a = 441/100

a = 4.41 ≈ 4.4 m/s²

Therefore, the centripetal acceleration of the car is 4.4 m/s².

Answer:

17 m/s west

Explanation:

Runner 1 has velocity = 10 m/s west

runner 2 has velocity = 7 m/s east

From the frame of reference of runner 2, we can imagine runner 2 as standing still, and runner 1 moving away from him, towards the west with their combined velocity of

velocity = 10 m/s + 7 m/s = 17 m/s west

Answer:

17 m/s west

Explanation:

Hope this helps!

Answer:

Because ocean tides are the effect of ocean water responding to a gravitational gradient, the moon plays a larger role in creating tides than does the sun. But the sun's gravitational gradient across the earth is significant and it does contribute to tides as well.

i hope this help i

i try to explain and like i sayed i hope this help u.

Answer:

the moon

Explanation:

ive passed the grade you learned this in

Answer:

1.92 x 10⁻¹²J

Explanation:

The magnetic force from the magnetic field gives the circulating protons gives the particle the necessary centripetal acceleration to keep it orbiting round the circular path. And from Newton's second law of motion, the force(F) is equal to the product of the mass(m) of the proton and the centripetal acceleration(a). i.e

F = ma

Where;

a = [tex]\frac{v^2}{r}[/tex]             [v = linear velocity, r = radius of circular path]

=> F = m[tex]\frac{v^2}{r}[/tex]           ------------(i)

We also know that the magnitude of this magnetic force experienced by the moving charge (proton) in a magnetic field is given by;

F = q v B sin θ       ----------(ii)

Where;

q = charge of the particle

v = velocity of the particle

B = magnetic field

θ = the angle between the velocity and the magnetic field.

Combining equations (i) and (ii) gives

m[tex]\frac{v^2}{r}[/tex] = q v B sin θ           [θ = 90° since the proton is orbiting at the maximum orbital radius]

=> m[tex]\frac{v^2}{r}[/tex] = q v B sin 90°

=> m[tex]\frac{v^2}{r}[/tex] = q v B

Divide both side by v;

=> m[tex]\frac{v}{r}[/tex] = qB

Make v subject of the formula

v = [tex]\frac{qBr}{m}[/tex]

From the question;

B = 1.25T

m = mass of proton = 1.67 x 10⁻²⁷kg

r = 0.40m

q = charge of a proton = 1.6 x 10⁻¹⁹C

Substitute these values into equation(iii) as follows;

v = [tex]\frac{(1.6*10^{-19})(1.25)(0.4)}{(1.67*10^{-27})}[/tex]

v = 4.79 x 10⁷m/s

Now, the kinetic energy, K, is given by;

K = [tex]\frac{1}{2}[/tex]mv²

m = mass of proton

v = velocity of the proton as calculated above

K = [tex]\frac{1}{2}(1.67*10^{-27} * (4.79 * 10^7)^2 )[/tex]

K = 1.92 x 10⁻¹²J

The kinetic energy is 1.92 x 10⁻¹²J

Explanation:

Given that,

Force, [tex]F=2i+3j-5k[/tex]

The particle displaces from (1,2,-3) m to (2,5,-1) m.

We need to find the work done by the force. Work done by the force is given by :

W = Fd

It is equal to the dot product of force and displacement.

Displacement from (1,2,-3) m to (2,5,-1) m is (2-1, 5-2, -1-(-3)) or (1, 3, 2) m

Work done,

[tex]W=F{\cdot} d\\\\W=(2i+3j-5k){\cdot} (i+3j+2k)[/tex]

We know that, i.i=j.j=k.k=1

So,

[tex]W=1\ J[/tex]

So, the work done by the force is 1 J.

Answer:

Time seem to flow only in one direction because if it started to go in backward direction that would break the second law of thermodynamics. We do not find time to be moving in any direction because time is not an object that can move nor is it a force that can move any object.

Answer:

average speed =  66.67  km/h

Explanation:

In order to find the average speed of the train, you need to calculate the total distance traveled, divided by the time it took to cover that distance. So for the total distance:

Distance= 120 km + 180 km = 300 km

For the total time we need to add three different quantities, two of which we need to derived based on the information provided:

time for first part of the trip:

[tex]time_1=\frac{D_1}{v_1} =\frac{120}{60} \,h= 2\,h[/tex]

for the time of the stop:

[tex]time_2=0.5\,\,h[/tex]

for the last part of the trip:

[tex]time_3=\frac{180}{90} \,h= 2 \,\,h[/tex]

Which gives a total of 4.5 hours

Then, the average speed is:   300/4.5   km/h = 66.67  km/h

Answer:

20 m

Explanation:

Given in the y direction:

Δy = 10 m

v₀ = 25 m/s sin 37° = 15.0 m/s

a = -10 m/s²

Find: t

Δy = v₀ t + ½ at²

10 m = (15.0 m/s) t + ½ (-10 m/s²) t²

10 = 15t − 5t²

2 = 3t − t²

t² − 3t + 2 = 0

(t − 1) (t − 2) = 0

t = 1 or 2

Since the projectile reaches Q before it reaches the peak, we want the lesser time, so t = 1.

Given in the x direction:

v₀ = 25 m/s cos 37° = 20.0 m/s

a = 0 m/s²

t = 1 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (20.0 m/s) (1 s) + ½ (0 m/s²) (1 s)²

Δx = 20 m

Answer:

1. Concave mirror.

2. 4.17 m or 417 cm.

Explanation:

The following data were obtained from the question:

Object distance (u) = 5 m

Magnification (M) = 5

Focal length (f) =..?

1. Identification of the mirror.

To determine whether or not the mirror is concave or convex, we must first of all calculate the image distance.

This can be obtained as follow:

Object distance (u) = 5 m

Magnification (M) = 5

Image distance (v) =.?

Magnification (M) = image distance (v) /object distance (u).

M = v/u

5 = v/5

Cross multiply

v = 5 x 5

v = 25 m

Since the image distance obtained is positive, the mirror is said to be a concave mirror.

2. Determination of the focal length of the mirro.

This can be obtained as follow:

Object distance (u) = 5 m

Image distance (v) = 25 m

Focal length (f) =...?

1/f = 1/v + 1/u

1/f = 1/25 + 1/5

1/f = 0.04 + 0.2

1/f = 0.24

Cross multiply

f x 0.24 = 1

Divide both side by 0.24

f = 1/0.24

f = 4.17 m

Converting the focal length of cm, we have:

1 m = 100 cm

Therefore, 4.17 m = 4.17 x 100 = 417 cm

Therefore, the focal length of the mirror is 4.17 or 417 cm.

Answer:

The gap between the plates will be 1.2 x 10^-15 m

No, this is not practically achievable.

Explanation:

Capacitance = 1.0 F

area of plate = 1.4 cm^2 = 1.4/10000 m^2 =  m^2

distance = ?

We use the equation

[tex]C[/tex] =  [tex]\frac{A}{d}[/tex]*ε

C is the capacitance

where A is the area

d is the distance of separation of plates

ε is the permeability of free space = 8.854×10^-12 F⋅m−1

substituting values, we have

1 = [tex]\frac{0.00014}{d}[/tex]* 8.854×10^-12

distance between plates = 1.2 x 10^-15 m

This is not practically achievable in real life