The projectile hit the ground 3,992.97 m in front of the release point. The projectile speed when it hits the ground is 438.5 m/s
When an airplane flying horizontally fires a projectile horizontally in its direction of motion it means
v₁ = speed of an airplane = 500 km/hThe projectile moves in horizontally but it has projectile motion that move horizontally and vertically according to the parabolic curve.
In vertical, the projectile moves in a non-uniform motion.
uy = the initial speed in vertically = 0 m/sh = the height = 850 m g = acceleration due to gravity = 9.8 m/s²[tex]h = \frac{1}{2} gt^2[/tex]Horizontal, the projectile moves in uniform motion.
DistanceWhen the projectile almost hits the ground
In verticalFinal speed for the projectile
v² = vx² + vy²
v² = 428.89² + 91.24²
v² = 183,946.63 + 8,324.37
v² = 192,271.004
[tex]v = \sqrt{192,271.004}[/tex]
v = 438.5 m/s
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a cd has a mass of 17 g and a radius of 6.0 cm. when inserted into a player, the cd starts from rest and accelerates to an angular velocity of 21 rad/s in 0.52 s. assuming the cd is a uniform solid disk, determine the net torque acting on it.
The net torque acting on it hen inserted into a player, the cd starts from rest and accelerates to an angular velocity of 21 rad/s in 0.52 s are 2.059[/tex.
The net torque is the force applied that is usually quite different from normal acting force.
Here solid disk =Torque[tex]Iα[/tex]
Mass of 17 g and a radius of 6.0 cmI = [tex]1/2mR^2[/tex]wf= 21 rad/swf = w0 +αtα= wf - w0 / t = wf /wtTorque = [tex](1/2mR^2)( wf/t)[/tex] = 1/2(0.017)(6.0) (21/0.52)Torque = 2.059So the net torque acting on it is [tex]Torque = 2.059[/tex].Read more about mass :
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a circular ring in the xy plane (radius r, centered at the origin) carries a uniform line charge λ. find the first three terms (n
A circular ring in the x y plane (radius r, centered at the origin) carries a uniform line charge λ. find the first three terms (n) is 2π λ ( 1 - (a/2r)² ( 3cos²0 -1).
Calculation:-
The first three of uniform charge carrying loop is.
V (r,theta) = q/r + 1/2r³ ( Q sin²0 cos²0 + q sin²0 sin²0 + Q cos²0)
= q/r - qa²/4r³ (3 cos²0 -1 )
= 2π λ ( 1 - (a/2r)² ( 3cos²0 -1)
A radius is a line section with one endpoint at the middle of the circle and the other endpoint at the circle. Radius = Diameter of a Circle: A line segment passing through the center of a circle, and having its endpoints at the circle, is referred to as the diameter of the circle. Diameter = 2 × radius.
underneath the Uniform rate techniques, we rate depreciation at the constant belongings which can be uniformly productive on a uniform basis every year. for this reason, the quantity of depreciation stays the same each 12 months.
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Imagine a ball that is pushed off a desk completely horizontal and falls 9.47 m down to the floor. If it landed 3.32 m away from the edge of the desk, how fast was it moving in the horizonal direction just before it hit the ground? Round to 1 decimal.
Itis going to the speed of obstinacy.
what is speed?speed is the fastest movement of something.
n the question time of flight of blocked ball time off flight of the ball that is represented by capital D This is the time of flight. It is given time of flight, height of time of flight, and hi of both ball, the same or equal, yet. We need to find out how fast production is. We need to find the projection that is represented by you. It was not possible to be on the time of projectile flight. The value of time of flight is equal to the number of years you have left in your life. We'll get equal to 11.1 until 9.81 upon two and two signed 27.4, because he dies at 27.4. Two is 118.31 little per second. obstinacy is the right answer. I think that is Mhm. Correct answer is obstinacy It is necessary to explain this questio.
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hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. as the truck approaches, you hear a tone of 470 hzhz ; as the truck recedes, you hear a tone of 420 hzhz . How much time will it take for the truck to get from your position to the fire 5.0km away, assuming it maintains a constant speed? Express your answer using two significant figures.
The time taken by the truck to get to the required position 5 km away from the fire is 261.55 s.
Tone at which the truck approaches at = 470 hz
Tone at which the truck recedes = 420 hz
Distance = 5.0 Km away
Speed = constant
Speed of sound = v
Speed of air = V
Frequency of sound = f
Frequency when truck approaches = f₁ =
= f₁ = [( V + v) / V ] X f
Frequency when the truck recedes = f₂ =
= f₂ = [( V - v) / V ] X f
Thus, equating both equations =
= f₁ / f₂ = (V + v) / (V - v)
= 470/420 = (340.278 + v) / (340.278 - v )
= [ 470 X 340.278 ] - 470v = [ 420 X 340.278 ] + 420v
= 159930.66 - 470v = 142916.76 + 420v
= 17013.9 = 890v
= v = 19.117 m/s
The time taken = t =
= s = ut + (1/2)at²
= 5 X 10³ = 0 + (19.117 X t)
= t = 261.55 s
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assume that one object collides with a second object that is at rest. in which of the following scenarios would you expect that momentum would not be conserved?
The scenario in which there is not the conservation of momentum is when the objects sticks together. Option C.
What is momentum?We know that momentum is a vector quantity. This implies that momentum would have both magnitude and direction. The fact that momentum has both magnitude and direction implies that we have to consider where the arrow of the velocity direction of the momentum is pointing.
By the law of the conservation of linear momentum, we know that the total momentum of a closed system is a constant. The meaning of this is that the total momentum before collision must be equal to the total momentum after collision.
If the objects do stick together after the collision, there would be a loss of the momentum of the objects thus there is no conservation of momentum in that case.
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at a given instant the current and self-induced emf in an inductor are directed in the same direction. determine the inductance if the induced emf is 17 v and the rate of change of the current is 25 ka/s.
The inductance is 680µH if the induced emf is 17 v and the rate of change of the current is 25 ka/s.
The magnetic field will change as a result of growing current, so the inductor will resist the flow of current through it, resulting in a decrease in current.
e=induced emf=17V
e=Ldi/dt [di/dt=25000a/s]
17=L×25000
17/25000=L
0.00068=L
680×10⁻⁶Henry
=680µH
Inductance=680µH
What is emf?The amount of energy delivered per unit of electric charge by a power source, such as a generator or a battery, is known as electromotive force (abbreviated E or EMF).
Energy is converted from one form to another as the generator or battery operates on the electric charge that is carried inside itself. Positive charge is applied to the device's positive terminal, whereas negative charge is applied to the device's negative terminal. The work done on an electrical charge unit, or the energy acquired per electrical charge unit, is known as the electromotive force. It is also referred to as EMF and is denoted by the international metric system's letter E.
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a plane is sitting on a runway, awaiting takeoff. on an adjacent parallel runway, another plane lands and passes the stationary plane at a speed of 45 m/s. the arriving plane has a length of 36 m. by looking out the window (very narrow), a passenger on the stationary plane can see the moving plane. for how long a time is the moving plane visible?
The moving plane is visible for 0.8 second.
What is speed?Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity. SI unit of speed be meter/second and CGS unit of speed be cm/s.
Given that:
Another plane lands and passes the stationary plane at a speed: v = 45 m/s.
length of the arriving plane be : L = 36 m.
So, Time the moving plane remains visible be: t = L/v = 36/45 s = 0.8 second.
Hence, the moving plane is visible for 0.8 second.
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an undamped 1.21 kg1.21 kg horizontal spring oscillator has a spring constant of 26.1 n/m.26.1 n/m. while oscillating, it is found to have a speed of 2.31 m/s2.31 m/s as it passes through its equilibrium position. what is its amplitude ????a of oscillation?
The kinetic energy in the spring is equal to the mechanical work done by the spring
The kinetic energy in then spring is
E = 1 / 2 kA2
The mechanical work done by the spring is,
E= 1 / 2 mv2
Compare the above two equations to find the amplitude of oscillation:
1 / 1 kA2 = 1 / 2 mv2
A = v√ m/k
(3.58 m/s) √ 1.12 kg / 32.3 N/m
= 0.66m
The mechanical work done by the spring is,
E = 1/2 mv2
= 1 / 2 (1.12 kg) (3.58 m/s)2
= 7.17 J
Work modifications the quantity of mechanical and internal energy possessed by gadgets. Whole work is achieved on a machine or item, energy is introduced to it.
The character of work achieved can be categorised in three classes. they are +ve work, -ve work and zero work. The character of work relies upon on the perspective among pressure and displacement.
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consider the points p(,,) and q(,,). a. find and state your answer in two forms: and aibjck. b. find the magnitude of . c. find two unit vectors parallel to .
The magnitude is 10.2. The two unit vectors parallel to PQ are (6i+2j+8k)/10.2 and -(6i + 2j+ 8k)/10.2.
What is vector?
A quantity with magnitude and direction, typically represented by a directed line segment whose length indicates the magnitude and whose orientation in space represents the direction.
What is unit vector?
These unit vectors are frequently used to denote direction, with the magnitude being provided via a scalar coefficient. The sum of unit vectors and scalar coefficients can then be used to represent a vector decomposition.
P = (11,4,9)
Q = (5,2,1)
So,
PQ = (11,4,9) - (5,2,1) = (6, 2, 8)
PQ= 6i + 2j+ 8k
PQ mag = 10.2
unit vector = non zero vector / magnitude of vector
1st unit vector = (6i + 2j+ 8k)/10.2
2nd unit vector = -(6i + 2j+ 8k)/10.2
The magnitude is 10.2. The two unit vectors parallel to PQ are (6i+2j+8k)/10.2 and -(6i + 2j+ 8k)/10.2.
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a generator supplies 80 v to a transformer's primary coil, which has 59 turns. if the secondary coil has 530 turns, what is the secondary voltage?
The primary coil of a transformer, which has 59 turns, receives 80 v from a generator. The secondary voltage will be 530 if the secondary coil has 530 turns IS 718.644 V
For an ideal transformer
Vs/Vp=Ns/Np
Given that primary voltage V =80 V
Number of turns in primary N = 59 turns
Number of turns in srcondary Ng = 530 turns
Therefore
Vs/80=530/59
Hence voltage across secondary V = 8.98*80 V
=718.644 V.
Voltage is the quantity of potential charge that exists between two points on a circuit. One idea is charge more strongly than another. Voltage refers to the difference in charge between the two points. Volt, denoted by the symbol "V," is the accepted unit of measurement for the voltage expression.
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a solid disk with a mass of 2.00 kg and a radius of 3.00 m is spinning with an angular velocity of 4.00 rad/s. what is the angular momentum of the disk?
Angle of the disk's momentum. 0881 kg*m^2/s.
Given:- mass is 2.00 kg, radius is 3.00 m, velocity of 4.00 rad/s.
How would you define velocity in plain English?The most important metric for determining an object's position and rate of movement is its velocity. The distance that an object travels in a certain amount of time might be used to define it. The object's movement in a unit of time is referred to as velocity.
What are velocity and speed?In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity.
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a beam of light is incident from air on the surface of a liquid. if the angle of incidence is 30.0° and the angle of refraction is 22.0°, find the critical angle for the liquid when surrounded by air.
The critical angle for the liquid when surrounded by air is 48.75°.
What is critical angle?The critical angle is the maximum angle at which a light beam traversing a transparent media can collide with the surface of a second medium having a lower refractive index without being completely reflected within the first medium.
Given that:
Angle of incident: i = 30.0°.
Angle of refraction, r = 22.0°.
Hence, refractive index of the medium: n = sini/sinr
= sin 30.0°/sin22.0°
= 1.34.
Hence, the critical angle for the liquid when surrounded by air:
= sin⁻¹(1/n)
= sin⁻¹(1/1.33)
= 48.75°.
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a 12kg lantern is suspended frm the ceiling by two vertical wires. what is the tension in each wire?
Two vertical wires are used to hoist a 12 kilogram lantern from the ceiling; as a result, each wire is under 58.8 N of tension.
Why is it known as "wires"?The phrase "wire transfer" dates back to a time when banks used telegraph wires to transmit this type of financial transfer. A bank wire stored procedures on who should receive the funds, along with the user's bank account information and the amount they should receive.
Briefing:Well, we know from Newton that, if m is the mass of the lantern,
Fnet = ma
Additionally, it is clear that the two forces pulling on the candle are now the strain on the two wires and the gravitational force. Since the candle isn't moving, its speed is 0, which means that the final quantity of forces acting on it must likewise be zero.
The positive y-axis should point up, and also the negative y-axis should point below. Listing the forces reveals that
-mg + T1 + T2 = 0
The two wires' tensions are also equal because they are both straight and orbital angular momentum, or T1 = T2 = T. The preceding equation can be revised to say
-mg + 2T = 0, or
2T = mg.
Thus,
T = mg/2 = (12kg*9.8m/s2) / 2 = 58.8N
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In comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?.
Two forces produce the same torque but this will not ensure that they have the same magnitude of torque because torque is the product of force times distance.
Explain about Torque?Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics, torque is what causes an object to acquire angular acceleration. Torque is a vector quantity.The physical quantities for which both magnitude and direction are defined distinctly are known as vector quantities. For example, a boy is riding a bike with a velocity of 30 km/hr in a north-east direction.The quantity torque (or moment of force) may be thought of as the cross product of force and distance and the SI unit for torque is Newton metre, N m (m2 kg s-2).We need to complete the description of the problem, searching in internet we have:"Sometimes, even with a wrench, one cannot loosen a nut that is frozen tightly to a bolt. It is often possible to loosen the nut by slipping one end of a long pipe over the wrench handle and pushing at the other end of the pipe.No, Because torque is the product of force times distance, two different forces that act at different distances could still give the same torque.
T = F * d
where:
T = torque [N*m]
F = force [N]
d = distance [m]
We can see in the above equation, that increasing the distance increases torque proportionally.
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an object starts from rest and falls freely for 40 meters near the surface of planet p if the time of fall is 4 seconds what is the magnitue of the acceleration due to gravioty on planet p
The magnitude of the acceleration due to gravity on planet p is 5 meters per seconds squared.
What is the magnitude of the acceleration due to gravity on planet p?From the Second Equation of Motion;
s = ut + (1/2)gt²
Where v is final velocity, u is initial velocity, g is acceleration due to gravity and t is time elapsed.
Given the data in the question;
Initial velocity u = 0m/sHeight s = 40mElapsed time t = 4 sAcceleration due to gravity g = ?Plug the given data in the above formula and solve for g.
s = ut + (1/2)gt²
40m = (0 × 4s) + ( (1/2) × g × (4s)²
40m = (1/2) × g × 16s²
Multiply both sides by 2
2 × 40m = 2 × (1/2) × g × 16s²
80m = g × 16s²
g × 16s² = 80m
g = 80m / 16s²
g = 5m/s²
Therefore, the acceleration due to gravity is 5m/s².
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an object of mass m rests on a frictionless surface and is attached to a horizontal ideal spring with spring constant k . the system oscillates with amplitude a . the oscillation frequency of this system can be increased by
By decreasing M. Because its acceleration is in the same direction as its velocity, it accelerates as it moves closer to the equilibrium position.
The item moves at its fastest speed when it is in the equilibrium position, where there is no acceleration. Due to the acceleration now being in the opposite direction from the direction of its velocity, it overshoots the equilibrium position and begins to slow down. When the spring is squeezed by a distance A, it accelerates back towards the equilibrium position before coming to a stop, disregarding friction. When the spring is stretched by a distance A, it overshoots once more before stopping at the starting position. The movement continues. The thing swings back and forth.
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the two ropes seen in (figure 1) are used to lower a 255 kg piano 6.10 m from a second-story window to the ground.
The work done have been calculated as : Wgravity = 15,250 joules, W rope1 = - 9667.158 joules and W rope2 = - 5584.94 joules
Given ; Force of gravity on piano = 2500 N
r = distance of the ground = 6.10 m
As the angles are mentioned in the diagram, thus we can write
Work done can be calculated by ;
Wgravity = 2500 N . 6.10m . cos 0 = 15,250 joules
W rope1 = 1830 N . 6.10 m . cos 150 = - 9667.158 joules
W rope2 = 1295 N . 6.10 m . cos 135 = - 5584.94 joules
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Answer:
W = 12500 J
T1 = -7920 J
T2 = - 4580 J
Explanation:
The angle between the force w and the displacement is 0 degrees, therefore:
[tex]W_{w} = wdcos(0) = (2500)(5)(1) =[/tex] 12500 J
The angle between the force T1 and the displacement is 90 + 60 = 150 degrees, therefore:
[tex]T_{1}= T_{1} dcos (150) = (1830)(5)(cos(150)) =[/tex] - 7920 J
The angle between the force T2 and the displacement is 90 + 45 = 135 degrees, therefore:
[tex]T_{2} = T_{2} dcos(135) = (1295)(5)(cos (135)) =[/tex] - 4580 J
Nuclear decay occurs according to first-order kinetics. Argon-37 decays with a rate constant of 0. 0198 days–1. After 98. 3 days, a sample has a mass of 2. 14 g. What was the original mass of the sample?.
The original mass of the Argon-37 sample (N₀) was 14.98651g or approximately 15g. We Use the equation for first-order kinetics for determining the original mass of the given Argon-37 sample.
What is first order rate equation?If the rate of radioactive decay is first order, we can write r = k[N]1, where N is the quantity of radioisotope present at the time the rate is recorded, k is the isotope's first order rate constant, and r is the rate of decay as observed.
According to First-Order Rate Equation,
[tex]ln(\frac{N}{N_{0} } )=-kt[/tex]
Here,
N = The amount of radioisotope left after "t" time.
N₀= The initial amount of radioisotope,
k = Rate constant of the radioisotope.
t = Time
Given,
N = 2. 14 g.
N₀ = ?
k = 0. 0198
t = 98. 3 days
Now, substituting these values in the first order rate equation we get,
[tex]ln(\frac{N}{N_{0} } )=-kt\\ln(\frac{2.14}{N_{0} } )=-0.0198*98.3\\ln(\frac{2,14}{N_{0} } )=-1.94634\\\frac{2.14}{N_{0} } =e^{-1.94634} \\\frac{2.14}{N_{0} }=0.142795\\N_{0} = 14.98651g[/tex]
Hence, the original mass of the sample (N₀) was 14.98651 g or approximately 15 g.
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If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever? Why?
If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever Since little is currently known about the source of the dark energy which is causing the present accelerated expansion of the Universe, it cannot be concluded that it will continue unchanged in the future? Thus, the Universe might, or might not expand forever.
According to the relativistic perspective, although the space around the Earth is contracting, its atoms are resisting this compression. This implies that the Earth's surface is moving higher at a constant rate. On Earth, falling would be the only option to avoid accelerating up. When you are at rest, you fall.
A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.
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a cylinder is filled with of gas and a piston is put into it. the initial pressure of the gas is measured to be . the piston is now pushed down, compressing the gas, until the gas has a final volume of . calculate the final pressure of the gas. be sure your answer has the correct number of significant digits.
The final pressure of the gas will be 26.8 kPa when has a final volume of 78.0L.
Boyle's law, also known as the Boyle-Mariotte law, is an experimental gas law that explains the connection between a confined gas's pressure and volume. The pressure of a gas is inversely related to its volume at constant temperature, as well as its number of moles, according to Boyle's law.
P ∝ 1/V
[tex]PV=k[/tex] or [tex]P_{1} V_{1} =P_{2} V_{2}[/tex]
[tex]P_{1}[/tex]= initial gas pressure is 209 kPa
[tex]P_{2}[/tex]= final pressure which is unknown.
[tex]V_{1[/tex]= 10.0 L, which is the gas's initial volume.
[tex]V_{2}[/tex]= 78.0 L, which is the gas's final volume.
We can now use this formula to obtain the final gas pressure by entering all the specified variables.
[tex](209kPa)(10.0L)=P_{2}(78.0L)\\P_{2}=26.8kPa[/tex]
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when a rigid object rotates about a fixed axis, what is true about all the points in the object? (there could be more than one correct choice.)
When a rigid object rotates about a fixed axis, it is true about all the points in the object.
The idea of a body that does not deform or alter shape is a hard body. It is described as a collection of particles having the property that the distance between them stays constant throughout the body's motions.
The rotation of a rigid body, or an item that does not deform when it moves around a fixed axis is referred to as fixed axis rotation. We'll demonstrate how to apply the theories we've discovered so far regarding translational motion to a rotating object around a fixed axis.
Every body experiences the same angular acceleration.
Therefore, when a rigid object rotates around a fixed axis, it is true about all the points in the object.
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An object has 23 Kg*m/s of momentum and a mass of 3 Kg. What is the objects velocity
Answer:
23 m/s
Explanation:
A 600 kg mass person wishes to push a 100-kg mass box across a level floor. the coefficient of static friction between the persons shoes and the floor is 0.700. what is the maximum coefficient of static friction between the box and the floor such that the person can push horizontally on the box and cause it to start moving
The maximum coefficient of static friction between box and floor such that the person can push horizontally on the box and cause it to start moving is; μ₂ = 4.2
What is static friction?A force that keeps an object at rest is called static friction. It is the friction experienced when we try to move a stationary object on a surface without actually triggering any relative motion between the body and surface.
To move the box, force exerted by the person on the box must equal the force exerted by the box
F₁= F₂
m₁*g*μ₁ = m₂*g*μ₂
Given; m₁ = 600kg ; m₂= 100kg; μ₁= 0.7
600 * 0.7 = 100 * μ₂
μ₂ = 4.2
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Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain _____ lenses.
Mountain --- Tree --- Squirrel --- Joe
converging
diverging
Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain less than lenses.
What is Lenses?
Lenses are essentially curved-sided magnifying glasses. A lens is a transparent piece of glass that, when light rays travel through it through refraction, either focuses or disperses them. Lenses are employed in telescopes and other magnifying equipment because of their enlarging capabilities. For the purpose of collecting light, they are used in cameras.
For the purpose of collecting light, cameras utilise a number of lenses rather than just one. The relationship between the size of the image generated by a lens and the size of the object is known as magnification. In order to prevent blurriness or distortion in the picture the lens creates, lenses can also be utilized in groups.
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When the height of the cylinder increased from 100 m to 1000 m, what happened to the amount of heat generated in the system? it decreased by a factor of 10. it decreased by a factor of 5. it increased by a factor of 5. it increased by a factor of 10.
When the height of the cylinder increased from 100 m to 1000 m, the heat generated is 10 times.
The energy of possessed by the body by virtue its position is called potential energy. This energy is converted in the form of heat.
The formula of potential energy is given by
P.E. = mgh
where, m is the mass of body, h be the height of body and g be the acceleration due to gravity.
The potential energy of the body when it is at a height of 100 m is
P = m x g x 100 = 100 mg
The potential energy of the body when it is at a height of 1000 m is
P' = m x g x 1000 = 1000 mg
The ratio of P' and P is 10.
So, the heat generated is 10 times.
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Answer:
D. It increased by a factor of 10.
Explanation:
a weather emergency siren is mounted on a tower, 105 m above the ground. on one hand, it would be a good idea to make the siren very loud so that it will warn as many people as possible. on the other hand, safety regulations prohibit the siren from exceeding an intensity level of 116 db for workers standing on the ground directly below the siren. assuming that the sound is uniformly emitted, what is the maximum power that the siren can put out? maximium power output: 4387.95 tools x10y w how far away from the base of the tower can a person be and still be able to hear the siren? neglect any absorption of sound energy by the air; although, in reality, such absorption would be significant at long distances. maximum audible distance:
The maximum power that the siren can put out is of 4.74 dB.
Given that,
The height of the tower above the ground is, h = 105 m
Sound intensity from the siren is, I = 116 dB
We know that, the maximum intensity of sound allowed is 11.6 B.
Then the intensity of sound in terms of W/m² can be found as follows,
log(I / I₀) = 11.6
I / I₀ = 10¹¹°⁶
I = 10¹¹°⁶ * I₀
⇒ 10¹¹°⁶ * 10⁻¹²
⇒ 10⁻⁰°⁴
At 105 m above the ground the intensity will be 105² times.
Then the intensity at source point = 10⁻⁰°⁴ * 105²
⇒ 0.398 * 105² = 4387.95 W/m²
The energy of sound from the source is given as,
4π* intensity= 4* 3.14* 4387.95 = 55112.65 W/m²
To convert into decibels:
log(55112.65/ 10⁻¹²) = log(55112.65+12) = 4.74 dB
Thus, we can conclude that the maximum power that the siren can put out is of 4.74 dB.
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a stereo speaker is placed between two observers who are 33 m apart, along the line connecting them. if one observer records an intensity level of 62 db, and the other records an intensity level of 79 db, how far is the speaker from each observer?
Ra = 32.1 m far is the speaker from each observe .
What does "intensity" in science mean?In physics, the power supplied per unit area is known as the intensities or flux of cosmic rays, where the area is expressed on a plane plane perpendicular of the energy's propagation.
Briefing :
Let's solve this problem in parts, let's start by finding the intensity of the sound in each observer
observer A β = 64 db
β = 10 log Iₐ / I₀
where I₀ = 1 10⁻¹² W / m²
Iₐ = I₀ 10 (β/ 10)
let's calculate
Iₐ = 1 10⁻¹² (64/10)
Iₐ = 2.51 10⁻⁶ W / m²
Observer B β = 85 db
I_b = 1 10-12 10 (85/10)
I_b = 3.16 10⁻⁴ W / m²
now we use that the emitted power that is constant is the intensity over the area of the sphere where the sound is distributed
P = I A
therefore for the two observers
P = Ia Aa = Ib Ab
the area of a sphere is
A = 4π R²
we substitute
Ia 4pi Ra2 = Ib 4pi Rb2
Ia Ra2 = Ib Rb2
Let us call the distance from the observer be to the haughty R = ax, so the distance from the observer A to the haughty is R = 35 ax; we substitute
Ia (35 -x) 2 = Ib x2
we develop and solve
35-x = Ra (Ib / Ia) x
35 = [Ra (Ib / Ia) +1] x
x (11.22 +1) = 35
x = 35 / 12.22
x = 2,864 m
This is the distance of observer B
The distance from observer A
Ra = 35 - x
Ra = 35 - 2,864
Ra = 32.1 m
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is it possible for a heat engine to operate without rejecting any waste heat to a low-temperature reservoir? explain.
It is difficult for just any device that runs on a cycle to accept heat from a given fluid and create a net quantity of work, according to the Kelvin-Planck formulation of the second law.
There are how many laws in thermodynamics?A first rule, a second law, as well as the third law are the three fundamental laws that thermodynamics has traditionally acknowledged. They are each simply referred to by an ordinal designation.
What is the thermodynamics equation?the equations of thermodynamics. Hrxn is equal to H1, H2, H3, and H4. With a value of 1.38 10 23 J/K, k is indeed the Boltzmann constant, that is the same as the general gas steady, R, divided with Avogadro's quantity, NA. The figure you get in a thermodynamic table is called S°, or standard absolute entropy.
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It is difficult for just any device that runs on a cycle to accept heat from a given fluid and create a net quantity of work, according to the Kelvin-Planck formulation of the second law.
There are how many laws in thermodynamics?A first rule, a second law, as well as the third law are the three fundamental laws that thermodynamics has traditionally acknowledged. They are each simply referred to by an ordinal designation.
What is the thermodynamics equation?the equations of thermodynamics. Hrxn is equal to H1, H2, H3, and H4. With a value of 1.38 10 23 J/K, k is indeed the Boltzmann constant, that is the same as the general gas steady, R, divided with Avogadro's quantity, NA. The figure you get in a thermodynamic table is called S°, or standard absolute entropy.
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The internal energy within a system associated with the motion of particles and that can be added to a substance is called.
Internal energy associated with systems and particles is thermal energy.
What is Internal energy?
A thermodynamic system's internal energy is the entire amount of energy it contains. The energy required to construct or prepare the system in its current internal condition comprises both internal kinetic energy and potential energy contributions.
The internal energy has been described as the energy that has been assessed by the molecules and bonds at the STP. Thermal energy has been the energy of particular molecules and the system comprising all the molecules have the summation of the thermal energy.
Thus, internal energy associated with systems and particles is thermal energy.
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A 80 g , 35-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 11 g ball of clay traveling horizontally at 2.3 m/s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
The maximum angle due to angular momentum measured from vertical, does the rod (with the attached ball of clay) rotate is 57°.
Given that,
Mass of the rod, [tex]\small M= 80\;g=0.08\; kg[/tex]
Mass of the clay ball, [tex]\small m=11\;g=0.011\;g[/tex]
Length of the rod, \small[tex]L=35\;cm=0.35\;m[/tex]
Initial speed of the ball, [tex]\small v_{i}=2.3\;m/s[/tex]
From law of conservation of angular momentum, Total initial angular momentum of the system = total final angular momentum of the system[tex]\small mv_{i}\frac{L}{2}=\frac{1}{2}(I_{rod}+I_{ball})\omega_{f}\small mv_{i}L=(I_{rod}+I_{ball})\frac{V_{f}}{(L/2)}[/tex].
[tex]\small mv_{i}L=\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\frac{V_{f}}{(L/2)}[/tex]
Now, From law of conservation of energy, Initial rotational kinetic energy = final potential energy:
[tex]\small \frac{1}{2}(I_{rod}+I_{ball})\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]
[tex]\small \frac{1}{2}\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]
[tex]\small \left (\frac{1}{12}M+m\left (\frac{1}{2} \right )^{2} \right )\left (\frac{V_{f}}{(1/2)} \right )^{2}=mLg(1-\cos\theta)[/tex]
[tex]\small \therefore \theta=\cos^{-1}\left (0.5496 \right )\small \boldsymbol{\therefore \theta=56.66^{o}}[/tex]
ROUNDING TO 2 SIGNIFICANT FIGURES
[tex]\small \boldsymbol{\therefore \theta=57^{o}}[/tex]
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