Answer:
The intensity is [tex]I_1 = 263.35 \ W/m^2[/tex]
Explanation:
From the question we are told that
The intensity of the beam is [tex]I = 285\ W/m^2[/tex]
The angle is [tex]\theta = 16^o[/tex]
The intensity of the light that emerges from the polarizer is mathematically represented by Malus' law as
[tex]I_1 = I * cos^2 (\theta )[/tex]
substituting values
[tex]I_1 = 285 * [cos(16)]^2[/tex]
substituting values
[tex]I_1 = 285 * [cos(16)]^2[/tex]
[tex]I_1 = 263.35 \ W/m^2[/tex]
15.Restore the battery setting to 10 V. Now change the number of loops from 4 to 3. Explain what happens to the magnitude and direction of the magnetic field. Now change to 2 loops, then to 1 loop. What do you observe the relationship to be between the magnitude of the magnetic field and the number of loops for the same current
Answer:
we see it is a linear relationship.
Explanation:
The magnetic flux is u solenoid is
B = μ₀ N/L I
where N is the number of loops, L the length and I the current
By applying this expression to our case we have that the current is the same in all cases and we can assume the constant length. Consequently we see that the magnitude of the magnetic field decreases with the number of loops
B = (μ₀ I / L) N
the amount between paracentesis constant, in the case of 4 loop the field is worth
B = cte 4
N B
4 4 cte
3 3 cte
2 2 cte
1 1 cte
as we see it is a linear relationship.
In addition, this effect for such a small number of turns the direction of the field that is parallel to the normal of the lines will oscillate,
In a certain process a gas ends in its original thermodynamic state. Of the following, which is possible as the net result of the process?
A. It is adiabatic and the gas does 50 J of work.
B. The gas does no work but absorbs so J of energy as heat.
C. The gas does no work but rejects 50 J of energy as heat.
D. The gas rejects 50 J of energy as heat and does 501 of work.
E. The gas absorbs 50 of energy as heat and does 50」ot work.
Answer:
E. The gas absorbs 50 of energy as heat and does 50」ot work
Explanation:
This is following the law of thermodynamics that energy is neither created nor destroyed
A major strike-slip earthquake on the San Andreas fault in California will cause a catastrophic tsunami affecting residents of San Francisco.
a) true
b) false
Answer:
a) true
Explanation:
The san andres is a transform fault that forms boundary between the Pacific and the North Atlantic plate and this slip strike is characterized by the latex motion the fault runs in the length of the California state. This plate is widely estimated for the high magnitude of earthquakes and varies from 7.7 to 8.3 magnitude. They are capable of producing a deadly tsunami that can devastate the pacific northwest.A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 Hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.)
Answer:
Change in the frequency (in Hz) = 104.96 Hz
Explanation:
Given:
Speed of sound in air (v) = 343 m/s
Speed of car (v1) 36 m/s
Frequency(f) = 500 Hz
Find:
Change in the frequency (in Hz)
Computation:
Frequency hear by the observer(before)(f1) = [f(v+v1)] / v
Frequency hear by the observer(f1) = [500(343+36)] / 343
Frequency hear by the observer(f1) = 552.48 Hz
Frequency hear by the observer(after)(f2) = [f(v-v1)] / v
Frequency hear by the observer(f2) = [500(343-36)] / 343
Frequency hear by the observer(f2) = 447.52 Hz
Change in the frequency (in Hz) = f1 - f2
Change in the frequency (in Hz) = 552.48 Hz - 447.52 Hz
Change in the frequency (in Hz) = 104.96 Hz
One of your summer lunar space camp activities is to launch a 1090 kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 211 km . What gain Δ???? in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36×1022 kg and 1740 km, respectively.
Answer:
ΔP.E = 6.48 x 10⁸ J
Explanation:
First we need to calculate the acceleration due to gravity on the surface of moon:
g = GM/R²
where,
g = acceleration due to gravity on the surface of moon = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
M = Mass of moon = 7.36 x 10²² kg
R = Radius of Moon = 1740 km = 1.74 x 10⁶ m
Therefore,
g = (6.67 x 10⁻¹¹ N.m²/kg²)(7.36 x 10²² kg)/(1.74 x 10⁶ m)²
g = 2.82 m/s²
now the change in gravitational potential energy of rocket is calculated by:
ΔP.E = mgΔh
where,
ΔP.E = Change in Gravitational Potential Energy = ?
m = mass of rocket = 1090 kg
Δh = altitude = 211 km = 2.11 x 10⁵ m
Therefore,
ΔP.E = (1090 kg)(2.82 m/s²)(2.11 x 10⁵ m)
ΔP.E = 6.48 x 10⁸ J
At the B end of the recessed horizontal bar, forces F1 and F2 of magnitudes 3 KN and 2KN respectively are applied and oriented as shown in the figure. Determine the magnitude of the resulting force and its orientation with respect to the horizontal.
Answer:
2.98 kN, 69.1° below the horizontal
Explanation:
Sum of forces in the x direction:
Fₓ = 3 kN cos 30° − 2 kN cos 40°
Fₓ ≈ 1.07 kN
Sum of forces in the y direction:
Fᵧ = -3 kN sin 30° − 2 kN sin 40°
Fᵧ = -2.79 kN
Magnitude of the resultant force is:
F² = Fₓ² + Fᵧ²
F = 2.98 kN
The direction of the resultant force is:
tan θ = Fᵧ / Fₓ
θ = -69.1°
Two long, parallel wires are separated by a distance of 2.60 cm. The force per unit length that each wire exerts on the other is 4.30×10^−5 N/m, and the wires repel each other. The current in one wire is 0.520 A.Required:a. What is the current in the second wire? b. Are the two currents in the same direction or in opposite directions?
Answer:
10.75 A
The current is in opposite direction since it causes a repulsion force between the wires
Explanation:
Force per unit length on the wires = 4.30×10^−5 N/m
distance between wires = 2.6 cm = 0.026 m
current through one wire = 0.52 A
current on the other wire = ?
Recall that the force per unit length of two wires conducting and lying parallel and close to each other is given as
[tex]F/l[/tex] = [tex]\frac{u_{0}I_{1} I_{2} }{2\pi r }[/tex]
where [tex]F/l[/tex] is the force per unit length on the wires
[tex]u_{0}[/tex] = permeability of vacuum = 4π × 10^−7 T-m/A
[tex]I_{1}[/tex] = current on the first wire = 0.520 A
[tex]I_{2}[/tex] = current on the other wire = ?
r = the distance between the two wire = 0.026 m
substituting the value into the equation, we have
4.30×10^−5 = [tex]\frac{4\pi *10^{-7}*0.520*I_{2} }{2\pi *0.026}[/tex] = [tex]\frac{ 2*10^{-7}*0.520*I_{2} }{0.026}[/tex]
4.30×10^−5 = 4 x 10^-6 [tex]I_{2}[/tex]
[tex]I_{2}[/tex] = (4.30×10^-5)/(4 x 10^-6) = 10.75 A
The current is in opposite direction since it causes a repulsion force between the wires.
An electron and a proton both moving at nonrelativistic speeds have the same de Broglie wavelength. Which of the following are also the same for the two particles?
(A) speed
(B) kinetic energy
(C) frequency
(D) momentum
Explanation:
The De-Broglie wavelength is given by :
[tex]\lambda=\dfrac{h}{p}[/tex]
h is Planck's constant
p is momentum
In this case, an electron and a proton both moving at nonrelativistic speeds have the same de Broglie wavelength. Mass of electron and proton is different. It means their velocity and energy are different.
Only momentum is the factor that remains same for both particles i.e. momentum.
7. A sound wave begins traveling through a thin metal rod at one end with a speed that is 15 times the speed of sound in air. If an observer at the other end of the rod hears the sound twice, one from the sound traveling through the rod and one from the sound traveling through the air, with a time delay of 0.12 s, how long is the rod? The speed of sound in air is 343 m/s.
Answer:
L = 44,096 m
Explanation:
The speed of the sound wave is constant therefore we can use the relations of uniform kinematics
v = x / t
the speed of the wave in the bar is
v = 15 v or
v = 15 343
v = 5145 m / s
The sound at the bar goes the distance
L = v t
Sound in the air travels the same distance
L = v_air (t + 0.12)
as the two recognize the same dissonance,
v t = v_air (t +0.12)
t (v- v_air) = 0.12 v_air
t = 0.12 v_air / (v -v_air)
l
et's calculate
t = 0.12 343 / (5145 - 343)
t = 8.57 10-3 s
The length of the bar is
L = 5145 8.57 10-3
L = 44,096 m
The temperature of the hot spots caused by the impact of transferred matter onto the surface of a pulsar can be 108 K. What is the peak wavelength in the blackbody spectrum of such a spot, and in what range of the electromagnetic spectrum does it occur
Given that,
Temperature = 10⁸ K
We need to calculate the peak wavelength in the blackbody spectrum
Using formula of peak wavelength
[tex]peak\ wavelength = \dfrac{2.898\times10^{-3}}{T}[/tex]
Where, T= temperature
Put the value into the formula
[tex]peak\ wavelength = \dfrac{2.898\times10^{-3}}{10^{8}}[/tex]
[tex]peak\ wavelength = 2.90\times10^{-11}\ m[/tex]
[tex]peak\ wavelength = 290\ nm[/tex]
This range of wavelength is ultraviolet.
Hence, The peak wavelength in the blackbody spectrum is 290 nm and the range of wavelength is ultraviolet electromagnetic spectrum .
g suppose he used an alpha particle with an energy of 8.3 MeV, what would be the speed of this alpha particle
Answer:
speed of the alpha particle is 2 x 10^7 m/s.
Explanation:
energy of alpha particle = 8.3 Mev
1 Mev = 1.602 x 10^-13 J
8.3 Mev = [tex]x[/tex]
solving, [tex]x[/tex] = 8.3 x 1.602 x 10^-13 = 1.329 x 10^-12 J
mass of a alpha particle = 6.645 x 10^−27 kg
The energy of the alpha particle is the kinetic energy KE of the alpha particle
KE = [tex]\frac{1}{2}mv^{2}[/tex]
where m is the mass of the alpha particle
v is the velocity of the alpha particle
substituting values, we have
1.329 x 10^-12 = [tex]\frac{1}{2}*6.645*10^{-27}*v^{2}[/tex]
[tex]v^{2}[/tex] = 4 x 10^14
[tex]v = \sqrt{4*10^{14} }[/tex] = 2 x 10^7 m/s
Electrons are accelerated through a voltage difference of 270 kV inside a high voltage accelerator tube. What is the final kinetic energy of the electrons?
Each electron winds up with kinetic energy of
(270 keV)
plus
(whatever KE it had when it started accelerating).
The element sodium can emit light at two wavelengths, λ1 = 588.9950 nm and λ2 = 589.5924 nm. Light in sodium is being used in a Michelson interferometer. Through what distance must mirror M 2 be moved if the shift in the fringe pattern for one wavelength is to be 1.00 fringe more than the shift in the fringe pattern for the other wavelength?
Answer:
The distance is [tex]d = 0.00029065 \ m[/tex]
Explanation:
From the question we are told that
The first wavelength is [tex]\lambda _1 = 588.9950 nm = 588.9950 *10^{-9} \ m[/tex]
The second wavelength is [tex]\lambda _2 = 589.5924 nm = 589.5924 *10^{-9} \ m[/tex]
The difference in the fringe pattern is n = 1.0
Generally the equation defining the effect of the movement of the mirror M 2 in a Michelson interferometer is mathematically represented as
[tex]2 * d = [\frac{\lambda _1 * \lambda_2 }{\lambda_2 - \lambda _1 } ] * n[/tex]
Here d is the mirror M 2 must be moved
substituting values
[tex]2 * d = [\frac{(588.9950*10^{-9} ) * (589.5924 *10^{-9}) }{(589.5924 *10^{-9}) - (588.9950*10^{-9} ) } ] * 1.0[/tex]
[tex]d = 0.00029065 \ m[/tex]
In the direction perpendicular to the drift velocity, there is a magnetic force on the electrons that must be cancelled out by an electric force. What is the magnitude of the electric field that produces this force
Answer:
E = VdB
Explanation:
This is because canceling the electric and magnetic force means
q.vd. B= we
E= Vd. B
A plastic balloon that has been rubbed with wool will stick to a wall.
a. Can you conclude that the wall is charged? If not, why not? If so, where does the charge come from?
b. Draw a series of charge diagrams showing how the balloon is held to the wall.
Answer:
Explanation:
When plastic balloon is rubbed with wool , charges are created on both balloon and silk in equal amount . Rubber balloon will acquire negative charge and silk will acquire positive charge .
Now when balloon is brought near a wall , there is induction of charge on the wall due to charge on the balloon . On the near surface of wall positive charge is produced and on the surface deep inside the wall negative charge is produced . The charge deep inside goes inside the earth but the positive charge near the surface of wall can not escape . It remains trapped by negative charge on the balloon .
hence there is mutual attraction between balloon and surface of wall is just like attraction between opposite charges . But once the ballon due to mutual attraction comes in contact with the wall , the charge on balloon and on wall neutralises each other and hence after some time the balloon falls off from the wall on the ground . It does not remain attracted to wall for ever . It happens due to neutralisation of charges on balloon and wall .
Parallel light rays with a wavelength of 563 nm fall on a single slit. On a screen 3.30 m away, the distance between the first dark fringes on either side of the central maximum is 4.70 mm . Part A What is the width of the slit
Answer:
The width of the slit is 0.4 mm (0.00040 m).
Explanation:
From the Young's interference expression, we have;
(λ ÷ d) = (Δy ÷ D)
where λ is the wavelength of the light, D is the distance of the slit to the screen, d is the width of slit and Δy is the fringe separation.
Thus,
d = (Dλ) ÷ Δy
D = 3.30 m, Δy = 4.7 mm (0.0047 m) and λ = 563 nm (563 ×[tex]10^{-9}[/tex] m)
d = (3.30 × 563 ×[tex]10^{-9}[/tex] ) ÷ (0.0047)
= 1.8579 × [tex]10^{-6}[/tex] ÷ 0.0047
= 0.0003951 m
d = 0.00040 m
The width of the slit is 0.4 mm (0.00040 m).
Can a car moving with a negative velocity moves faster than a car moving with a positive velocity? explain.
Answer:
Yes.
Explanation:
This is because "negative velocity" just means it is in the negative in relation to the point of 0. Negative velocity doesn't equal a decrease in velocity. For example lets say you were parked next to a cone (this cone represents zero) if you accelerate forwards then that would be positive acceleration. If you were to accelerate backwards, this would be in the negative direction, aka negative velocity.
SUMMARY:
A negative velocity means that the object which has the negative velocity is moving in the opposite direction of an object moving at a positive velocity. This is a question of frame of reference. The possibility for the velocity is what makes it different to the speed. Speed is only positive.
A 1300-turn coil of wire 2.40 cm in diameter is in a magnetic field that increases from 0 T to 0.120 T in 9.00 ms . The axis of the coil is parallel to the field. What is the emf of the coil?
Answer:
The induced emf in the coil is 7.843 V
Explanation:
Given;
number of turns of the coil, N = 1300 turn
diameter of the coil, d = 2.4 cm = 0.024 m
initial magnetic field, B₁ = 0 T
final magnetic field, B₂ = 0.12 T
change in time, dt = 9.0 ms = 9 x 10⁻³ s
Area of the coil is given by;
A = πr²
radius of the coil, r = 0.024 / 2
radius of the coil, r = 0.012 m
A = π(0.012)²
A = 4.525 x 10⁻⁴ m²
The induced emf in the coil is given by;
E = NA(dB/dt)
E = NA [(B₂ - B₁) /dt]
E = 1300 x 4.525 x 10⁻⁴ (0.12 - 0) / (9 x 10⁻³)
E = 7.843 V
Therefore, the induced emf in the coil is 7.843 V
Reading glasses with a power of 1.50 diopters make reading a book comfortable for you when you wear them 1.8 cmcm from your eye. Part A If you hold the book 28.0 cmcm from your eye, what is your nearpoint distance
Answer:
The near point is [tex]n =44.8 \ cm[/tex]
Explanation:
From the question we are told that
The power is [tex]P = 1.50[/tex]
The distance from the eye is [tex]k = 1.8 \ cm[/tex]
The distance of the book from the eye is [tex]z = -28 \ cm[/tex]
Generally the focal length of the glasses is
[tex]f = \frac{1}{P}[/tex]
=> [tex]f = \frac{1}{1.50 }[/tex]
=> [tex]f = 0.667 \ m[/tex]
=> [tex]f = 66.7 \ cm[/tex]
The object distance is evaluated as
[tex]u = z + k[/tex]
=> [tex]u = -28 + 1.8[/tex]
=> [tex]u = -26.2 \ cm[/tex]
The image distance is evaluated from lens formula as
[tex]\frac{1}{v} = \frac{1}{f} + \frac{1}{u}[/tex]
=> [tex]\frac{1}{v} = \frac{1}{66.7} + \frac{1}{-26.2}[/tex]
=> [tex]v=- \frac{1}{0.0232}[/tex]
=> [tex]v=- 43 \ cm[/tex]
The near point is evaluated as
[tex]n = -v + k[/tex]
=> [tex]n =-(-43) + 1.8[/tex]
=> [tex]n =44.8 \ cm[/tex]
Two separate disks are connected by a belt traveling at 5m/s. Disk 1 has a mass of 10kg and radius of 35cm. Disk 2 has a mass of 3kg and radius of 7cm.
a. What is the angular velocity of disk 1?
b. What is the angular velocity of disk 2?
c. What is the moment of inertia for the two disk system?
Explanation:
Given that,
Linear speed of both disks is 5 m/s
Mass of disk 1 is 10 kg
Radius of disk 1 is 35 cm or 0.35 m
Mass of disk 2 is 3 kg
Radius of disk 2 is 7 cm or 0.07 m
(a) The angular velocity of disk 1 is :
[tex]v=r_1\omega_1\\\\\omega_1=\dfrac{v}{r_1}\\\\\omega_1=\dfrac{5}{0.35}\\\\\omega_1=14.28\ rad/s[/tex]
(b) The angular velocity of disk 2 is :
[tex]v=r_2\omega_2\\\\\omega_2=\dfrac{v}{r_2}\\\\\omega_2=\dfrac{5}{0.07}\\\\\omega_2=71.42\ rad/s[/tex]
(c) The moment of inertia for the two disk system is given by :
[tex]I=I_1+I_2\\\\I=\dfrac{1}{2}m_1r_1^2+\dfrac{1}{2}m_2r_2^2\\\\I=\dfrac{1}{2}(m_1r_1^2+m_2r_2^2)\\\\I=\dfrac{1}{2}\times (10\times (0.35)^2+3\times (0.07)^2)\\\\I=0.619\ kg-m^2[/tex]
Hence, this is the required solution.
What physical feature of a wave is related to the depth of the wave base? What is the difference between the wave base and still water level?
Answer:
physical feature of a wave is related to the depth of the wave base is The circular orbital motion
B. The wave base is the depth, and the still water level is the horizontal level
An electron has an initial velocity to the south but is observed to curve upward as the result of a magnetic field. This magnetic field must have a component:___________
a) north
b) upwards
c) downwards
d) east
e) west
Answer:
e) west
Explanation:
According to Lorentz left hand rule, the left hand is used to represent the motion of an electron in a magnetic field. Hold out the left hand with the fingers held out parallel to the palm, and the thumb held at right angle to the other fingers. If the thumb represents the motion of the electron though the field, and the other fingers represent the direction of the field, then the palm will push in the direction of the force on the particle.
In this case, if we point the thumb to the south (towards your body), with the palm facing up, then the fingers will point west.
What happens to the deflection of the galvanometer needle (due to moving the magnet) when you increase the number of loops
Answer:
If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil which will increase total induced electromotive force
Explanation:
galvanometer is an instrument that can detect and measure small current in an electrical circuit.
If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil. If it is move in a way into the coil,the needle deflect in that way and if it move in another way, it will deflect in the other way.
The total induced emf is equal to the emf induced in each loop by the changing magnetic flux, then multiplied by the number of loops and an increase in the number of loops will cause increase in the total induced emf.
21.-Una esquiadora olímpica que baja a 25m/s por una pendiente a 20o encuentra una región de nieve húmeda de coeficiente de fricción μr =0.55. ¿Cuánto desciende antes de detenerse?
Answer:
y = 12.82 m
Explanation:
We can solve this exercise using the energy work theorem
W = ΔEm
friction force work is
W = fr . s = fr s cos θ
the friction force opposes the movement, therefore the angle is 180º
W = - fr s
we write Newton's second law, where we use a reference frame with one axis parallel to the plane and the other perpendicular
N -Wy = 0
N = mg cos θ
the friction force remains
fr = μ N
fr = μ mg cos θ
work gives
W = - μ mg s cos θ
initial energy
Em₀ = ½ m v²
the final energy is zero, because it stops
we substitute
- μ m g s cos θ = 0 - ½ m v²
s = ½ v² / (μ g cos θ)
let's calculate
s = ½ 20² / (0.55 9.8 cos 20)
s = 39.49 m
this is the distance it travels along the plane, to find the vertical distance let's use trigonometry
sin 20 = y / s
y = s sin 20
y = 37.49 sin 20
y = 12.82 m
A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 9.6 V/m and points eastward. What are the magnitude (in T) and direction of the magnetic field at this instant?
Answer:
The values is [tex]B = 3.2 *10^{-8} \ T[/tex]
The direction is out of the plane
Explanation:
From the question we are told that
The magnitude of the electric field is [tex]E = 9.6 \ V/m[/tex]
The magnitude of the magnetic field is mathematically represented as
[tex]B = \frac{E}{c}[/tex]
where c is the speed of light with value
[tex]B = \frac{ 9.6}{3.0 *10^{8}}[/tex]
[tex]B = 3.2 *10^{-8} \ T[/tex]
Given that the direction off the electromagnetic wave( c ) is northward(y-plane ) and the electric field(E) is eastward(x-plane ) then the magnetic field will be acting in the out of the page (z-plane )
In which example is kinetic friction most involved? a sled stuck on a snowy hill a bottle of water wedged in a vending machine an explorer unsuccessfully pushing on a massive stone that is blocking the entrance to a cave a volleyball player sliding across the court while diving for the ball
Answer:
I believe the answer is A volleyball player sliding across the court while diving for the ball.
Explanation:
Kinetic friction is a body moving on the surface experiences a force in the opposite direction of its movement.
Hope this helps! （づ￣3￣）づ╭❤～
A nozzle with a radius of 0.22 cm is attached to a garden hose with a radius of 0.89 cm that is pointed straight up. The flow rate through hose and nozzle is 0.55 L/s.
Randomized Variables
rn = 0.22 cm
rh = 0.94 cm
Q = 0.55
1. Calculate the maximum height to which water could be squirted with the hose if it emerges from the nozzle in m.
2. Calculate the maximum height (in cm) to which water could be squirted with the hose if it emerges with the nozzle removed assuming the same flow rate.
Answer:
1. 0.2m
1. 66m
Explanation:
See attached file
The expressions of fluid mechanics allows to find the result for the maximum height that the water leaves through the two points are;
1) The maximum height when the water leaves the hose is: Δy = 0.20 m
2) The maximum height of the water leaves the nozzle is: Δy = 68.6m
Given parameters
The flow rate Q = 0.55 L/s = 0.55 10⁻³ m³ / s Nozzle radius r₁ = 0.22 cm = 0.22 10⁻² m Hose radius r₂ = 0.94 cm = 0.94 10⁻² mTo find
1. Maximum height of water in hose
2. Maximum height of water at the nozzle
Fluid mechanics studies the movement of fluids, liquids and gases in different systems, for this it uses two expressions:
The continuity equation. It is an expression of the conservation of mass in fluids.
A₁v₁ = A₂.v₂
Bernoulli's equation. Establishes the relationship between work and the energy conservation in fluids.P₁ + ½ ρ g v₁² + ρ g y₁ = P₂ + ½ ρ g v₂² + ρ g y₂
Where the subscripts 1 and 2 represent two points of interest, P is the pressure, ρ the density, v the velocity, g the acceleration of gravity and y the height.
1, Let's find the exit velocity of the water in the hose.
Let's use subscript 1 for the nozzle and subscript 2 for the hose.
The continuity equation of the flow value that must be constant throughout the system.
Q = A₁ v₁
v₁ = [tex]\frac{Q}{A_1 }[/tex]
The area of a circle is:
A = π r²
Let's calculate the velocity in the hose.
A₁ = π (0.94 10⁻²) ²
A₁ = 2.78 10⁻⁴ m²
v₁ = [tex]\frac{0.55 \ 10^{-3}}{2.78 \ 10^{-4}}[/tex]
v₁ = 1.98 m / s
Let's use Bernoulli's equation.
When the water leaves the hose the pressure is atmospheric and when it reaches the highest point it has not changed P1 = P2
½ ρ v₁² + ρ g y₁ = ½ ρ v₂² + ρ g v₂
y₂-y₁ = ½ [tex]\frac{v_i^2 - v_2^2}{g}[/tex]
At the highest point of the trajectory the velocity must be zero.
y₂- y₁ = [tex]\frac{v_1^2}{2g}[/tex]
Let's calculate
y₂-y₁ = [tex]\frac{1.98^2}{2 \ 9.8}[/tex]
Δy = 0.2 m
2. Let's find the exit velocity of the water at the nozzle
A₁ = π r²
A₁ = π (0.22 10⁻²) ²
A₁ = 0.152 10⁻⁴ m / s
With the continuity and flow equation.
Q = A v
v₁ = [tex]\frac{Q}{A}[/tex]
v₁ = [tex]\frac{0.55 \ 10{-3} }{0.152 \ 10^{-4} }[/tex]
v₁ = 36.67 m / s
Using Bernoulli's equation, where the speed of the water at the highest point is zero.
y₂- y₁ = [tex]\frac{v^1^2}{g}[/tex]
Let's calculate.
Δy = [tex]\frac{36.67^2 }{2 \ 9.8 }[/tex]
Δy = 68.6m
In conclusion using the expressions of fluid mechanics we can find the results the maximum height that the water leaves through the two cases are:
1) The maximum height when the water leaves the hose is:
Δy = 0.20 m
2) The maximum height of the water when it leaves the nozzle is:
Δy = 68.6 m
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A mechanic wants to unscrew some bolts. She has two wrenches available: one is 35 cm long, and one is 50 cm long. Which wrench makes her job easier and why?
Answer:
50 cm long
When 35cm long wrench is compared to 50cm long wrench, we find that the 50cm long wrench produces more turning effect of force because it has longer distance between fulcrum and line of action of force. At conclusion, the more the turning effect of force the more it is easy to unscrew bolts.
QUESTION 27
The titanium shell of an SR-71 airplane would expand when flying at a speed exceeding 3 times the speed of sound. If the skin of the
plane is 400 degrees C and the linear coefficient of expansion for titanium is 5x10-6/C when flying at 3 times the speed of sound, how
much would a 10-meter long (originally at oC) portion of the airplane expand? Write your final answer in centimeters and show all of your
work.
Answer:
2 cm.
Explanation:
Data obtained from the question include the following:
Original Length (L₁ ) = 10 m
Initial temperature (T₁) = 0°C
Final temperature (T₂) = 400°C
Linear expansivity (α) = 5×10¯⁶ /°C
Increase in length (ΔL) =..?
Next, we shall determine the temperature rise (ΔT).
This can be obtained as follow:
Initial temperature (T₁) = 0°C
Final temperature (T₂) = 400°C
Temperature rise (ΔT) =..?
Temperature rise (ΔT) = T₂ – T₁
Temperature rise (ΔT) = 400 – 0
Temperature rise (ΔT) = 400°C
Thus, we can obtain the increase in length of the airplane by using the following formula as illustrated below:
Linear expansivity (α) = increase in length (ΔL) /Original Length (L₁ ) × Temperature rise (ΔT)
α = ΔL/(L₁ × ΔT)
Original Length (L₁ ) = 10 m
Linear expansivity (α) = 5×10¯⁶ /°C
Temperature rise (ΔT) = 400°C
Increase in length (ΔL) =..?
α = ΔL/(L₁ × ΔT)
5×10¯⁶ = ΔL/(10 × 400)
5×10¯⁶ = ΔL/4000
Cross multiply
ΔL = 5×10¯⁶ × 4000
ΔL = 0.02 m
Converting 0.02 m to cm, we have:
1 m = 100 cm
Therefore, 0.02 m = 0.02 × 100 = 2 cm.
Therefore, the length of the plane will increase by 2 cm.
ametal of mass 0.6kg is heated by an electric heater connected to 15v batter when the ammeter reading is 3A its tempeeature rises feom 20c to 85c in 10 minutes calculate the s.h.c of metal cylinder
Answer:
692 J/kg/°C
Explanation:
Electric energy added = amount of heat
Power × time = mass × SHC × increase in temperature
Pt = mCΔT
(15 V × 3 A) (10 min × 60 s/min) = (0.6 kg) C (85°C − 20°C)
C = 692 J/kg/°C
