The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
What is Temperature ?Temperature is a unit used to describe hotness or coldness. It can be stated in terms of any number of arbitrary scales and shows the direction in which heat energy will naturally flow, i.e., from a hotter body to a colder body (one at a lower temperature). Temperature does not equal the energy of a thermodynamic system; for instance, an iceberg has a far larger total thermal energy than a match, despite the fact that a match is burning at a much higher temperature.
According to the given information
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
Q/t = K × A ×([tex]T_{1} - T_{j}[/tex] )/L
However you have the Y shape so that half the heat transfer goes into each part of the Y. So you need a factor of 2 when you add in the Y parts.
(Q/t)bottom = 2x(Q/t)top
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
[tex]T_{1} + 2T_{0} = 3T_{j}[/tex]
[tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
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consider a very long rope at rest on a frictionless surface and placed parallel to the -axis. if its left end is quickly shaken up and down once, a perturbation of the shape of a pulse propagates along the rope from the left to the right end. if there is no energy losses, the pulse will propagate along the rope without changing its original shape.
Yes if there is no energy losses, the pulse will propagate along the rope without changing its original shape.
In every rope, the least dense rope has the largest wavelength. Crossing a barrier does not change a wave's frequency. If a wave in a less dense rope is traveling toward a border with a more dense rope, the reflected pulse will become inverted. The pulse will travel the length of the rope without altering its original shape if there are no energy losses.After reflecting off the fixed end, the pulse is inverted. To put it another way, a pulse with an upward displacement will reflect off the end and return with a downward displacement. When the medium's end is fixed, this characteristic of inversion will always be seen. When a wave or pulse moving through one medium encounters the boundary of another, a portion of the incident pulse is reflected off the border and a portion is transmitted over the boundary.
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an earth satellite has its apogee at 2500 km above the surface of earth and perigee at 500 km above the surface of earth. at apogee its speed is 6260 m/s. what is its speed at perigee? earth's radius is 6370 km (see below).
When a satellite revolves around the Earth at a speed of v2=31300 m/s, there is no torque on the Earth.
What does the term "torque" mean?
A torque is an angular force that tends to generate rotation along an axis, which could be a fixed point or the center of mass. Torque can also be conceived of as a spinning object's capacity to overcome turning resistance, such as a gear or a shaft.
In vehicles, what does torque mean?
When used to describe internal combustion engines or electric motors, torque refers to the force acting on the driving shaft. Torque is measured in newton-meters or pounds-feet (lb-ft) (Nm). Engine power is determined by the relationship between torque and engine speed (rpm).
Briefing:
mv1r1=mv2r2
2500*6260=v2*500
v2=31300m/s
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a fellow student makes the following comment during a study session: ""a freely falling object falls a greater distance during each second than the total distance fallen in all the previous seconds."" this statement (a) is always true. (b) is true only for sufficiently short times. (c) is true for sufficiently long times. (d) is never true.
The correct answer is b.
The given statement is true for sufficiently short distances.
At the end of t seconds, the distance travelled by a freely falling object with zero initial velocity is [tex]s=ut+1/2 gt^{2}[/tex]
where s is the displacement, t is the time, u is the initial velocity and g is the acceleration due to gravity.
Here, when the object is under free fall, its initial velocity, [tex]u=0 m/s[/tex]
Gravity continuously accelerates an object (increases its velocity) during free fall until it reaches terminal velocity. In particular, for every second that passes, gravity accelerates a falling object by 9.8 (m/s). (Acceleration is measured in meters per second squared, or m/s2, whereas velocity is measured in m/s.)
It is only sometimes true that an object falling freely needs to travel a greater distance in one second than it did in all the preceding seconds. However, if the object is falling under the influence of gravity for very short distances, the above claim can be approximately true.
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If you measure and calculate the density of a cube by the method of displacement, and then later use that same cube to measure and calculate the density by the method of flotation should you expect to obtain the same density? why or why not?.
If you measure and calculate the density of a cube by the method of displacement, and then later use that same cube to measure and calculate the density by the method of flotation you should expect to obtain the same density.
All matter has mass and takes up space. Density , a calculated value, measures the amount of matter in a space. To calculate the density of a material, find the mass and the volume of the object. Calculate the density of the object using the formula density equals mass divided by volume.Once you've measured the mass and volume of an object, finding the density requires putting the measurements into the density formula.To know more about density visit:
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NASA's Skylab, the largest spacecraft ever to fall back to the Earth, reentered the Earth's atmosphere on July 11,1979, and broke into a myriad of pieces. One of the largest fragments was a 1770-kg, lead-lined film vault, which landed with an estimated speed of 120 m/s.If its speed at an altitude of 146 km was 7950 m/s, how much nonconservative work was done on the film vault during reentry?
Applying the Work-Energy Theorem, the Work Done by a Non-Conservative Force is [tex]5.3 *10^{10}[/tex] J
The given Parameters are :
Initial Velocity (u) = 120 m/s
Final Velocity (v) = 7950 m/s
Mass (m) = 1770 kg
Displacement (h) = 146 km = 146000 m
According to the Work-Energy Theorem,
The Work Done is given by the difference between the final and initial Kinetic Energies,
Thus,
Work Done = Final Kinetic Energy - Initial Kinetic Energy
Now, Work done = Work done by gravity + Work Done by Non-Conservative Force
So, Work Done by gravity = mgh = 1770 *10*146000 =2482000000 J
Change in Kinetic Energy = [tex]\frac{1}{2} *m*(v^{2} -u^{2} )[/tex]
Putting the values, we get,
Change in Kinetic Energy = [tex]\frac{1}{2} *1770*(7950^{2} -120^{2} )=55921468500[/tex] J
Now, Work Done by Non Conservative Force = Change in Kinetic Energy-Work Done by gravity = 2482000000 - 55921468500 = 53439468500 = 5.3 * [tex]10^{10}[/tex] J
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microscopes use mirrors to magnify objects. please select the best answer from the choices provided t f
It is erroneous to claim that mirrors are not used by microscopes to magnify objects.
What can you say about a microscope?A microscopy is a tool that may be used to examine tiny things, including cells. By at least one lens, the microscope magnifies the picture of an item. This lens twists light in a way that causes it to look as though an item is larger than the amount is.
What kind of microscope is used most frequently?The microscopy, which is the most popular and the first to be created, employs lenses to diffract visible light that has gone through a thinly sheared material to create a viewable picture.
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an astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness. what period, in hours, did she observe?
The astronomer will take 0.086 hours to observe the radius of the black hole.
What is black hole?
In a black hole, the gravity is so intense that not even light can escape. The radius of black hole depends on the mass of the black hole.
The astronomer has determined a black hole's radius to be 51.0 au by examining its period of brightness variability.
The term "astronomical unit" (abbreviated "au") refers to a unit of length used to calculate the separation between the Earth and the sun.
1 au = 93 million miles.
Additionally, the radius is determined by the brightness variation, which takes the speed of light into account.
Light speed = 3 * [tex]10^8[/tex]m/s.
So,
time = distance / speed time
= 93 * [tex]10^9[/tex] / 3 * [tex]10^8[/tex] time = 310 seconds.
1 second = 0.0002 hours.
310 seconds = 0.086 hours.
The astronomer will take 0.086 hours to observe the radius of the black hole.
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a piece of cork has a mass of 15 g in air and a specific gravity of 0.25. the cork is attached to a lead sinker whose mass is 230 g in air. what will be the apparent mass of the pair when they are both submerged in water?
With a piece of cork connected, which has a mass of 15 g in air and a specific gravity of 0.25, the pair weighs 164.736 grammes when they are both submerged in water.
A physical body's mass is its total amount of matter. Inertia, or the body's resistance to acceleration (change of velocity) when a net force is applied, is also measured by this property. The gravitational pull an object has on other bodies is also influenced by its mass. A substance will float on water if its specific gravity is less than 1. sp gr, or specific gravity, is a common abbreviation. The following formula represents specific gravity, which is also known as relative density: Substance formula: substance / reference The purpose of comparing densities
60 grammes of water are equal to 15 grammes of cork when divided by 15.25. Lead's specific gravity is 11.35; its mass is (230+15)-(60+20.264); and its mass is 245 - (80.264) grammes.
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after stealing your sister's easy-bake oven (which uses a 100 watt light bulb to cook cupcakes and stuff), you place a glass of water inside. ignoring the glass (and assuming all of the light is used to heat the water), how long would it take to raise the temperature of 0.6 kg of water by 60 k? express your answer in minutes.
Answer: To raise the temperature of 0.6 kg of water by 60k 4200jkg-¹c-¹
Reason:
Using the formula Pt = (4.2 × L × T ) ÷ 3600 you can calculate the time it takes to heat a specific quantity of water from one temperature to another temperature.
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orange light with wavelength 600nm in vacuum is incident on a material with index of refraction 50. calculate the velocity and frequency of the light in the material.
The speed of light in vacuum is(3*10^8 m/s).
What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or even the size of the change in that object's position per unit of time, making it a scalar quantity. The initial speed is the upper limit of a average speed as that of the duration of a time interval gets closer to zero. The average speed of the object in a period of time is indeed the distance travelled by object divided by duration of the interval. Velocity and speed are not the same thing. The dimensions of speed are time divided by distance.
The velocity of the light in the material is 0.2c, where c is the speed of light in vacuum (3*10^8 m/s).
The frequency of the light in the material is equal to the frequency of the light in vacuum divided by the index of refraction, which is equal to (3*10^8 m/s) / 50 = 6*10^6 m/s.
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you are helping a friend study the eight planets in order from the sun outward. they also need to know if they are terrestrial or jovian. how can you help them memorize these specifics?
The Jovian planets lack solid surfaces, in contrast to the terrestrial planets Mercury, Venus, Earth, and Mars that make up our inner solar system.
How are the eight planets positioned in relation to one another and the Sun?Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune are listed in order of their angular separation from the sun. Previously thought to be the furthest planet, Pluto is now categorized as a dwarf planet.
What traits distinguish Jovian planets?The Jovian planets lack solid surfaces, in contrast to the terrestrial planets Mercury, Venus, Earth, and Mars that make up our inner solar system. As opposed to that, their atmospheres contain minute amounts of methane, ammonia, water, and other gases, and they are largely made of hydrogen and helium.
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a total lunar eclipse is visible: group of answer choices only within a narrow path on earth only during new moon phase visible to observers on a whole hemisphere of earth an opportunity to observe the solar corona
The correct answer is only within a narrow path on earth. This is because the shadow of the earth during a total lunar eclipse is only large enough to cover a small area on the earth's surface.
Lunar eclipse:A total lunar eclipse is visible only within a narrow path on earth, where the moon passes directly through the center of the Earth's shadow. This path, which is typically around 160 to 270 kilometers (100 to 170 miles) wide, moves eastward as the Moon orbits Earth.
During a total lunar eclipse, the moon is fully engulfed in Earth's shadow, making it visible to observers on a whole hemisphere of earth. However, an opportunity to observe the solar corona is not visible during a total lunar eclipse. The solar corona can only be seen during a total solar eclipse.
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A simple pendulum is known to have a period of oscillation, t = 1. 55 s. Student a uses a digital stopwatch to measure the total time for 5 oscillations and calculates an average period t = 1. 25 s. Student b uses an analog wristwatch and the same procedure to calculate an average period for the 5 oscillations and finds t = 1. 6 s. Which period is more accurate, and why?.
The period measured by student b using analog wristwatch is more accurate because of less percentage of error.
What is accuracy in measurement?Accuracy is the capacity of an instrument to measure the precise value. In other words, it refers to how closely the measured value resembles a reference or genuine value. Small readings can be taken to increase accuracy. The calculation's error is decreased by the little reading.
Given that:
period of oscillation, t = 1. 55 s.
an average period for the 5 oscillations obtained by student a: t = 1. 25 s.
average period for the 5 oscillations obtained by student b: t = 1. 6 s
Hence, error percentage of student a = (1.55-1.25)/1.55 × 100% = 19.35%
error percentage of student b = (1.60-1.55)/1.60 × 100% = 3.22%
Hence, period measured by student b is more accurate because of less percentage of error.
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a solenoid of length 1.50 cm and radius 0.650 cm has 49 turns. if the wire of the solenoid has 1.45 amps of current, what is the magnitude of the magnetic field inside the solenoid?
The magnetic field of the solenoid will be 30.79 T.
Magnetic field strength is a quantitative measure of the strength or weakness of a magnetic field.
It is also the force experienced by a north pole unit of one weber force at a certain point in the magnetic field. SI unit for the magnetic field is Tesla (T).Magnetic field is denoted by B and has the formula as B = μ₀I/2πrAlso it has an another formula as B = (N*r*I) /LLength of solenoid, L = 1.5 cm = 0.015 m
Radius of solenoid, r = 0.65 cm = 0.0065 m
Number of turns, N = 49 turns
Current, I = 1.45 A
Magnetic field, B, can be calculated as B = (N*r*I) /L
B = (49 * 0.0065 * 1.45)/0.015
B = 30.79 T
The magnitude of the magnetic field inside the solenoid is 30.79 T.
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a 1.5 kg 1.5 kg ball rotates on the end of a 3 m 3 m string in a vertical circle with a speed of 7 m/s 7 m/s. what force does the ball exert on the rope at the top of the vertical circle?
Force exerted by the ball on the rope is 24.5 N.
Force is an external influence that can change the velocity or motion of an object.
It can also be defined as the product of mass and acceleration.Mathematically, force F = m*amass of the ball = 1.5 kg
Radius of the circle = 3 m
Speed at which the ball is rotating = 7 m/s
Since the ball is rotating in a vertical circle, centripetal force acts on it.
Centripetal force is the force exerted on a rotating object and the gravitational force in a vertical circle is zero.
Mathematically centripetal force is Fc = mv²/r
Fc = 1.5 * (7)²/ (3)
Fc = 24.5 N
Force exerted by the ball on the rope at the top of the vertical circle is 24.5 N.
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which type of which type of orbit is shown in the picture below?
I don't see a picture attached to your question. Without one, I don't think I will be able to determine what type of orbit is displayed.
if they broadcast 4.0 cm microwaves, what minimum receiving dish diameter is needed to resolve (by rayleigh's criterion) the two transmissions?
Diameter will be 1.8914m
What is rayleigh's criterion equation ?The Rayleigh criteria, which is given by the equation θ = 1.22 λ/D, yields the best resolution or shortest angle between point sources. Once this angle has been determined, it is possible to determine the distance between stars since we already know how far away they are.
In our case,
λ = 4.0 cm.
sin(θ) ≈ tan(θ) ≈ θ = y/D = 31/1200 ≈ 0.0258
According to Rayleigh's criterion,
R = 1.22 λ/D = 1.22 * 4.0 * 10-2 / D = 0.0258
∴ D = 1.22 * 4.0* 10-2 / 0.0258 m ≈ 1.8914m.
D = 1.8914m
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speedboat a negotiates a curve whose radius is 120 m. speedboat b negotiates a curve whose radius is 240 m. each boat experiences the same centripetal acceleration. what is the ratio of the speeds of the boats
Ratio of the speeds of the boats with equal centripetal acceleration is 0.7.
Centripetal acceleration is defined as the change in tangential velocity and is experienced during uniform circular motion. It has a magnitude equal to the square of the body's speed v along the curve divided by the radius r (or distance) from the centre of the circle to the moving body. The centripetal acceleration ac is given by:
ac = v^2/ r
For the boat A:
ac = va^2/ 120
For the boat B:
ac = vb^2/ 240
As provided, the centripetal acceleration is equal for both boats, hence
va^2/ 120 = vb^2/ 240
va^2/vb^2 = 120/240
va^2/vb^2 = 0.5
va/vb = √0.5 = 0.7
Hence, the ratio of the speeds of the boats is 0.7
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A 30-cm-diameter, 1.4 kg solid turntable rotates on a 1.4-cm-diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 12 seconds. Part A How much friction force does the brake pad apply to the shaft?
The friction force the brake pad applies to the shaft f = 0.34 N.
Solution:
∝ = Rf sin∅
(-3.05 x 10⁻³) = (9 x 10⁻³) f sin(-90°)
f = 0.34N
As the two surfaces slide over each other small ridges are pressed against each other. Friction creates a force on a surface that opposes its motion. Friction can be reduced by applying lubricant. Friction is a type of contact force. It exists between tangent faces.
Friction is the force the resistance to movement when one object rubs against another. Friction occurs when two objects rub against each other. Friction works against the motion and works in the opposite direction. The amount of friction depends on the materials that make up the two surfaces.
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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?
The angular momentum of the disk: 0881 kg*m^2/s.
In Newtonian mechanics, momentum is the made of the mass and velocity of an item. it's far a vector quantity, owning a value and a route. If m is an item's mass and v is its speed, then the object's momentum p is mathbf{p} = m mathbf{v}.
-A truck complete of goods has a huge mass and so it has to gradually down earlier than a prevent light as it has a massive momentum with the same speed and so it's far very difficult to forestall. -A shifting bullet has a large momentum since it has an extremely big pace although it consists of a very small mass.
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How much force would be required to make a mass of 8kg accelerate at
8m/s^2?
64 N force would be required to make a mass of 8 kg accelerate at
8m/s².
What is force?The term "force" is defined precisely in science. It is acceptable to refer to a force of this level as a push or a pull. An item does not "have in it" or "contain" a force. Another item applies force to another. The concept of a force does not apply only to living or non-living entities.
The newton (sign N) is the SI unit of force.
The fundamental formula for force is F = ma, where F represents force, m represents mass in kilograms, and a represents acceleration in m×s⁻². It is the second law of motion established by Newton.
Given that,
Acceleration (a) = 8m/s²
Mass (m) = 8 kg
Force (F) = ?
As we know,
Force= mass × acceleration
F = 8 kg × 8 m/sec²
F = 64 N
Therefore, force of 64 N is required to accelerate the body.
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A glider on an air track is connected by springs to either end of the track. Both springs have the same spring constant, k, and the glider has mass Ma) Determine the frequency of the oscillation, assuming no damping, if k = 125 N/m and M = 210 g .b) It is observed that after 55 oscillations, the amplitude of the oscillation has dropped to one-half of its initial value. Estimate the value of γγ, using x(t)=A* e^γt * cosω′tc) How long does it take the amplitude to decrease to one-quarter of its initial value?
The amplitude drops to one-quarter of the initial value after 102.7 oscillations.
λ=1/51⋅0.20slog(1/2)=−0.68s^-1
Using the previous result we can evaluate the amplitude as a function of time to obtain the elapsed time until the amplitude drops to one-quarter of its initial value,
1/4=Aeλt.
Solving for the time,
t=1/λlog(1/4)=20.4s
Comparing this result with the period,
t=102.7T.
The maximum displacement or distance made by a point on a vibrating body or wave relative to its equilibrium location is known as the amplitude in physics. It is equivalent to the length of the vibration path divided in half. Amplitude is the separation between the wave's resting position and its highest displacement. Frequency is the number of waves that cross a particular place in a second. Period—the length of time needed for a wave cycle to complete
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how much larger is the skater's moment of inertia with their arms extended as opposed to their arms at their side? express your answer as a ratio
The ratio of the skater's moment of inertia when they have their arms extended to when their arms are not is r²/(r+r₁)².
The moment of inertia of any particular object can be defined as the opposition displayed by the object in question whenever its speed of rotation is changed when any external(turning) force is applied.
Let us assume that the moment of inertia of the skater when they don't extend their arms be = mr² (i)
Here, r is the radius of their body with their arms squeezed in.
The moment of inertia when the skater will extend their arms outwards is going to be = m(r+r₁)² (ii)
Here, r₁ is the radius of the hands when they are extended.
Comparing and equating (i) and (ii), we get -
Ratio = r²/(r+r₁)² (m is common for both so it gets canceled)
Henceforth, here is the ratio for when the skater has their arms extended to when their arms are not.
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what is the total electric potential energy utotutotu tot of this system of charges? express your answer in terms of qqq , ddd , and appropriate constants.
Electrostatic potential energy overall The unit of this charge system is -6.71kq2/d.
Who was the first to define energy?
The term "energy" was originally used in the field of science by Thomas Younger in 1800, but it did not catch on. Young later used interfered experiments to prove that light is a wave.
Briefing-
The expression for the electric potential energy is,
U= k*q1q2/d
The electric potential energy due to charges +2q and +5q is,
U25=k*(10q2)/d
The electric potential energy due to charges +2q and +q is,
U21=k*(2q2)/d
From the above figure, the distance between charges +2q and -3q is
√d² +√ d² = √2d²
= √2d
The electric potential energy due to charges +2q and -3q is,
U23=-k(6q2)/√2d
Thus, the total electric potential energy of the system is,
Utot=U25 +U21+U23 +Us1+U53 +U31
=k*(10q²)/d+k*(2q²)/d-k*(6q2)+k* (5q2)/√2d + k (10g2)/√2d
-k. (15q2)/d-k(3q2)/d
= [10+2-6/√2 + 5/√2 -15-3]kq2/d
=-6.707 kq2/d
=-6.71kq2/d
Utot=-6.71kq2/d =(approximately)
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The complete question is-
Four point charges form a square with sides of length dd, as shown in the figure. In the questions that follow, use the constant k in place of 1/4πϵ0.
Part A: What is the electric potential Vtot at the center of the square? Make the usual assumption that the potential tends to zero far away from a charge. Express your answer in terms of q, d, and appropriate constants.
Part B: What is the contribution U2q to the electric potential energy of the system, due to interactions involving the charge 2q? Express your answer in terms of q, d, and appropriate constants.
Part C: What is the total electric potential energy Utot of this system of charges? Express your answer in terms of q, d, and appropriate constants.
how much work does a supermarket checkout attendant do on a can of soup he pushes 0.450 m horizontally with a force of 5.10 n? express your answer in joules and kilocalories.
The work done in by the attendant on a can of soup is 2.3 J.
What is Work in physics?
Work in physics is defined as the dot product of force and the displacement produced by it.
Given is an attendant who pushed 0.450 m horizontally with a force of 5.10 N.
From the definition of work done, we can write -
W = F.d
W = Fd cosФ
Then angle between force and displacement is 0°. Therefore, cosФ is equal to 1.
Work = Fd
Work = 5.10 x 0.450
Work = 2.295 joules = 2.3 J
Therefore, the work done in by the attendant on a can of soup is 2.3 joules.
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disregarding air resistance, what is the speed of a ball dropped from 12 feet just before it hits the ground? (use 1 ft
Answer: Since the ball is free-falling, you use this equation:
v^2 = 2gh
where v is the velocity
g is the acceleration due to gravity
h is the height at which the object is dropped from
Plugging in the values and converting ft to m,
v^2 = 2 (9.8) (12) (0.3)
v = 8.4 m/s
A vertical wire carries a current straight down. To the east of this wire, the magnetic field points.
A current flows down a vertical wire in a straight line. Using right hand thumb rule,the magnetic field is directed southward to the east of this wire.
Define right hand thumb rule ?
The relationship between the movements of the magnetic field surrounding a specific conductor and its current direction can be found in a straightforward manner. This method would be known as the right-hand thumb rule. According to the right-hand rule, the magnetic field lines produced by a wire carrying current may be oriented in a manner similar to that of a person's right hand's folded fingertips, with the thumb pointing in the direction of the current flow.
Such an electric current always produces a magnetic field that is perpendicular to the passage of the current. A magnetic field surrounds a wire whenever a current flows through it. A magnetic field is represented by it, and the magnetic field is shown by arrows on lines in the field.The arrows on the lines show the direction of the field lines, which are represented by the circles. Like with electric field lines, the more lines there are in an area, the stronger the magnetic field.Use the right-hand rule where necessary. lowering our thumb Our fingers reach southward whenever we fix our gaze on the eastern edge of the wire. Field lines are oriented according to the right-hand thumb rule.To learn more about magnetic field click here:
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at rest, a car's horn sounds the note a (440 hz). the horn is sounded while the car is moving down the street. a bicyclist moving in the same direction with one-fifth the car's speed hears a frequency of 422 hz. (a) is the cyclist ahead of or behind the car?
The cyclist is behind the car. The conclusion is from the analysis using the Doppler's effect equation.
What is the Doppler's effect?The Doppler's effect is a phenomenon when the source of a wave and an observer move relative to each other, the frequency heard is not the same with the actual frequency.
The equation of the Doppler's effect is
f₀ = [(v ± v₀)/(v ± vs)] × fs
Where
f₀ = observer frequency of soundv = speed of sound waves (340 m/s)v₀ = observer velocityvs = source velocityfs = actual frequency of sound wavesNote:
v₀ (+) if the observer moves closer to the sound source.vs (+) if the sound source moves away from the observer.We have an actual frequency of 440 Hz from a car's horn. The frequency heard by an observer, i.e. a cyclist, is 422 Hz. The speed of the cyclist is 1/5 the car's speed in the same direction. Determine if the cyclist is ahead of or behind the car!
To answer the question, we should know how the car and the cyclist move relative to each other.
Let's say:
5a = the car's speed (vs)a = the cyclist speed (v₀)Use the equation of the Doppler's effect!
f₀ = [(v ± v₀)/(v ± vs)] × fs
422 = [(v ± a)/(v ± 5a)] × fs
422/440 = (v ± a)/(v ± 5a)
We get:
(v ± a) < (v ± 5a)
In the same direction, one should move closer and another should move away. The arithmetic operation of v₀ and vs would be the same.
If they are positive → (v + a) < (v + 5a)If they are negative → (v - a) > (v - 5a)The equation would be
422/440 = (v + a)/(v + 5a)
The car is moving away from the cyclist and the cyclist is moving closer to the car. Look at the illustration in the attachment!
Hence, the cyclist hearing the frequency of 422 Hz from car's horn is behind the car.
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What is the horizontal distance of the center of gravity of the person-ladder system from the point where the ladder touches the ground?.
A projectile's range is the horizontal distance it has traveled.
x = V * t x = V * t can be used to calculate horizontal distance.The formula y = - g * t2 / 2 describes vertical distance from the ground, where g is the acceleration of gravity and h is an elevation.
What does horizontal distance look like?An illustration of a horizontal distance is the space between a building and the observer, while an illustration of a vertical distance is the height of the building.
Are horizontal range and distance equivalent?The range is the horizontal distance from the launch position to the landing place.An angled-launch projectile's range is influenced by its launch speed and angle .
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(a) does your bathroom mirror show you older or younger than your actual age? (b) compute an orderof-magnitude estimate for the age difference, based on data you specify.
Answer:
a) Bathroom mirror shows the person younger than the actual age.
b) I stand about 47 m from my bathroom mirror
Reason:
a) Light takes a finite time to travel from the object to the mirror and then to the eye. Thus the speed of light in air is approximately equal to 3×108m/s 3 × 10 8 m/s. So the light takes approximately 7 nanoseconds to reflect off the mirror and return to our eyes.
b) This means that the reflection we see in the mirror has an age difference on the order of 10−9 seconds younger than ourselves.
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