A current of 4.75 A is going through a 5.5 mH inductor is switched off. It takes 8.47 ms for the current to stop flowing. The average induced emf opposing the decrease of the current is approximately 26.125 volts.
To calculate the magnitude of the average induced electromotive force (emf) opposing the decrease of the current, we can use Faraday's law of electromagnetic induction.
Faraday's law states that the induced emf in an inductor is equal to the rate of change of magnetic flux through the inductor. Mathematically, it can be expressed as:
emf = -L * (di/dt)
Where:
emf is the induced emf (in volts)
L is the inductance of the inductor (in henries)
di/dt is the rate of change of current (in amperes per second)
Given:
Current (I) = 4.75 A
Inductance (L) = 5.5 mH = 5.5 x [tex]10^{-3}[/tex] H
Time (t) = 8.47 ms = 8.47 x [tex]10^{-3}[/tex]) s
To find di/dt, we need to calculate the change in current over time. Since the current is decreasing to zero, di will be the initial current minus the final current, and dt will be the time taken for the current to decrease.
Initial current (Iinitial) = 4.75 A
Final current (Ifinal) = 0 A
di = Iinitial - Ifinal = 4.75 A - 0 A = 4.75 A
dt = 8.47 x [tex]10^{-3}[/tex] s
Now we can calculate the magnitude of the average induced emf:
emf = -L * (di/dt)
= - (5.5 x [tex]10^{-3}[/tex] H) * (4.75 A / 8.47 x [tex]10^{-3}[/tex] s)
Calculating the value:
emf = - (5.5 x [tex]10^{-3}[/tex] H) * (4.75 A / 8.47 x [tex]10^{-3}[/tex] s)
= - (5.5 x [tex]10^{-3}[/tex]) H) * (4.75 A / 8.47 x [tex]10^{-3}[/tex] s)
= - (5.5 x 4.75) V
= - 26.125 V
Taking the magnitude, the average induced emf opposing the decrease of the current is approximately 26.125 volts.
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Please help!
You release a pendulum of mass 1 kg from a height of 0.75 m.
A. If there is no air resistance, how fast is the pendulum going when it reaches the bottom?
B. If the pendulum loses 18% of its initial energy by the time it reaches the bottom, how fast is it going when it reaches the bottom?
C. If the pendulum loses another 7% of its remaining energy by the time it reaches the other side, how high does it go?
D. After a few minutes, the pendulum is no longer swinging at all explain why this happens, in terms of energy.
(A) The speed of the pendulum when it reaches the bottom is 3.83 m/s.
(B) The speed of the pendulum when it reaches the bottom after losing 18% of its energy is 3.47 m/s.
(C) The height reached by the pendulum after losing another 7% of its energy is 0.57 m.
(D) When the pendulum stops swinging, it has used all its energy to overcome frictional force of air.
Speed of the pendulum when it reaches the bottomApply the principle of conservation of energy;
K.E = P.E
¹/₂mv² = mgh
v² = 2gh
v = √2gh
v = √(2 x 9.8 x 0.75)
v = 3.83 m/s
Speed pendulum after losing 18% of the its initial energyK.E = (100 - 18)P.E
¹/₂mv² = 0.82mgh
V = √(0.82 x 2gh)
v = √(0.82 x 2 x 9.8 x 0.75)
v = 3.47 m/s
Height reached when its looses another 7%K.E = 0.5(1)(3.47)² = 6.02 J
When it losses 7% = 6.02 - (0.07 x 6.02) = 5.598 J
Height reached:
mgh = 5.598
h = 5.598/mg
h = 5.598/(1 x 9.8)
h = 0.57 m
Final energy of the pendulumWhen the pendulum stops swinging, it has used all its energy to overcome frictional force of air.
Thus, the speed of the pendulum when it reaches the bottom is 3.83 m/s.
The speed of the pendulum when it reaches the bottom after losing 18% of its energy is 3.47 m/s.
The height reached by the pendulum after losing another 7% of its energy is 0.57 m.
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A vector is 14.4 m long and
points in a 133 degree
direction.
Find the x-component of the
vector.
The x-component of the given vector is determined as 10.53 m.
X component of the vector
The x-component of a vector is defined as the value of the vector or component of the vector in the x direction.
For a vector of 14.4 m long and pointing in a 133 degree direction.
The x-component of the vector is calculated as follows;
Vx = V cosθ
where;
θ is the angle of inclination measured from positive x axisθ = 133⁰ - 90⁰ = 43⁰
Vx = 14.4 x cos(43)
Vx = 10.53 m
Thus, the x-component of the given vector is determined as 10.53 m.
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(a) A certain parallel-plate capacitor has plates of area 4.00m2 , separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage
The applied voltage is 1.41* 10⁴ kV.
Calculation of applied voltage-
The capacitance of parallel plates in the absence of a dielectric is:
C = ∈₀A/d
where, "d" = the spacing between the plates = 0.01 * 10⁻³ m
"A" = the area of the plates = 4 m²
"∈₀" = the constant = 8.85419*10⁻¹² C²/Nm²
So, C₀ = [tex]\frac{8.85419*10^{-12}*4 }{0.0100*10^{-3} }[/tex]
= 3541.67 *10⁻⁹ F
The dielectric constant, κ= 3.4, is defined as:
κ = C/C₀
The effective capacitance (with the dielectric) is denoted by "C", whereas the original capacitance is denoted by "C₀". (without the dielectric).
As a result, the new capacitance is:
C = κC₀
However, capacitance is connected to a voltage by:
C = Q/V
utilizing the increased capacitance and accounting for "V":
κC₀ = Q/V
V = Q/κC₀ = [tex]\frac{0.170}{3.4 * 3541.67 *10^{-9} }[/tex] = 1.41* 10⁴ kV
Therefore the applied voltage is 1.41* 10⁴ kV.
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On what does the magnitude of an applied torque depend?
Answer:
See below
Explanation:
The force applied and the length of the arm
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
What is torque?
The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is a torque.
Torque is defined as Γ=r×F=rFsin(θ). In other words, torque is the cross product of the force vector, where 'θ' is the angle between r and F, and the distance vector (the distance between the pivot point and the place where force is applied).
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
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If a car increases its velocity from zero to 60 km/h in 10 seconds, its acceleration is______.
Answer:
1.66m/s
Explanation:
here
initial velocity(u): 0m/s
final velocity (v):60km= 60×1000/60×60
:16.6m/s
time taken(t): 10s
now
acceleration:v-u/t
or a: 16.6-0/10
:16.6/10
acceleration: 1.66 m/s
In physics, acceleration is the rate at which the velocity of an object changes in relation to time. The sum of all forces exerted on an object results in its acceleration. The acceleration is 1.66 m/s².
The rate at which velocity, either in terms of speed or direction or both, varies over time is known as acceleration. A circle's motion accelerates despite its constant speed because its direction is continually shifting.
Here
initial velocity(u) = 0m/s
final velocity (v) = 60km
v = 60 × 1000 / 60 × 60
v = 16.6 m/s
Time taken(t) = 10s
Now.
acceleration = v-u / t
a = 16.6-0/10
a = 16.6/10
a = 1.66 m/s²
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2) Which pattern of organization did Alicia choose for her speech outline?
The pattern of organization Alicia chose for her speech outline is referred to as topical.
What is Topical pattern of organization?
This type of organization involves the arrangement of subtopics within a large or broad topic.
Alicia talked about speech pathology and the different subtopics include challenges, therapy etc which depicts topical pattern.
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When a 3.0 N weight is attached to a vertical coil spring, it stretches 5.0 cm. What weight would be required to stretch the spring 12.5 cm?
Group of answer choices
a. 7.5 N
b. 15 N
c. 4.5 N
d. 1.2 N
The weight required to stretch the spring 12.5 cm is 7.5 N (Option A)
Data obtained from the questionInitial weight (W₁) = 3 N Initial Length (L₁) = 5 cmNew length (L₂) = 12.5 cmNew Weight (W₂) =? How to determine the new weightThe new weight required to stretch the spring can be obtained as follow:
W₁ / L₁ = W₂ / L₂
3 / 5 = W₂ / 12.5
Cross multiply
W₂ × 5 = 3 × 12.5
Divide both sides by 5
W₂ = (3 × 12.5) / 5
W₂ = 7.5 N
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Complete the following nuclear reaction:
Answer choice
a) γ
b) α
c) β–
d) p
The particle that was given off in the reaction beta rays is β–. Option C
What is a nuclear reaction?A nuclear reaction will involve the change in the nucleus of an atom. It often leads to the production of new nucleus. As we can see the equation, there was a transformation from nitrogen nucleus to oxygen atom.
Thus, the particle that was given off in the reaction beta rays is β–. The fact that the mass number remained the same but the atomic number increased by one unit from left to right implies that a beta decay has occurred.
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Two objects X and Y move directly towards each other. The objects have the same mass.
Object X has a velocity of 5.0 m/s to the right. Object Y has a velocity of 3.0 m/s to the left.
Object X and object Y collide and stick together.
What is their velocity after colliding?
X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.
Their velocity after colliding is 1.0 m / s to the right.
What is the velocity during the collision?
In a collision, the velocity change is always computed by subtracting the initial value from the final value. If an object is moving in one direction before a collision and rebounds or somehow changes direction, then its velocity after the collision has the opposite direction as before.Inelastic collisions occur when only the momentum is conserved but not the system's kinetic energy. Perfectly inelastic collisions happen when objects stick together and have a common velocity after collision. To solve for the final velocity in perfectly inelastic collisions, use v' = (m1v1 + m2v2)/m1 + m2.The magnitude of the relative velocity is the same before and after the collision.To learn more about velocity, refer to:
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If a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver __________________.
If a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake or he is not conscious of his driving
What is traffic light?Traffic light can simply be defined as a set of automatically operated coloured lights such as red, amber, and green, for controlling traffic at road junctions, pedestrian crossings and roundabouts.
Below are the meaning of some traffic light colours:
Red means stop or dangerGreen means go. I.e it is safe to proceedYellow means move with caution or get ready to stopSo therefore, if a truck in front of your car begins to turn left, but its right turn signals are flashing, it is most likely that the truck driver is making a mistake
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The amount of excess load that can be imposed on the wing of an airplane depends upon the:.
The amount of excess load that can be imposed on the wing of an airplane depends upon the speed of the airplane.
What is meant by wing loading?
Wing loading in aerodynamics is the ratio of the loaded weight of the aircraft and the area of each wing. It is given as:
W_L = W (weight of the aircraft) / S (gross wing area of the airplane)
The more speed an aircraft gains, the more lift is produced by each unit of wing area.
Thus, with a high value of wing loading the aircraft lands and takes-off at higher speeds with low maneuvering control. Generally, Airliners have high wing loading while smaller airplanes have lower wing loading.
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Two men standing on the same side of wall and at the same distance from It, such that they are 4oom apart when one fires a gun the other hears the first report in 1.2s and the second in 0.5s after the first. calculate 1) Velocity of sound in air . 2)the perpendicular distance of the men from the wall.
Answer:
1. 571.43m/s
2. 142.9m and 342.9m
Explanation:
1.Take the difference in time.
1.2-0.7=0.7 seconds
Take the distance between them and divide with differnce in time.
400÷0.7=571.43 seconds.
2.Take the time of the two men and divide by two.
0.5÷2= 0.25 secs
1.2÷2= 0.6 secs
multiply each with the velocity.
0.25×571.43=142.9m
0.6×571.43=342.9m
Two large parallel conducting plates are 9.0 cm apart and carry equal but opposite charges on their facing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 3.7 nC/m 2. Determine the magnitude of the electric potential difference between the plates.
The magnitude of the electric potential difference between the plates is 37.63 V.
Given:
Distance between the plates, d = 9 cm
Surface charge density, ρ = 3.7 nC/m² = 3.7 × 10⁻⁹ C/m²
Calculation:
For two parallel plate conductors, the electric field is given as:
E = ρ/ε₀
where ρ is the charge density
ε₀ is the permeability of free space
Applying values in the above equation we get:
E = ( 3.7 × 10⁻⁹ C/m²)/(8.85 × 10⁻¹² C²/m)
= 418.08 V/m
Now, the potential difference between the plates separated by a distance 'd' is given as:
ΔV = Ed
where E is the electric field
d is the distance of separation between the plates
Applying values in the above equation we get:
ΔV = (418.08 V/m) × (0.09 m)
= 37.63 V
Therefore, the magnitude of the electric potential difference between the plates is 37.63 V.
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Consider the function e(h) = ε h h 2 6 m where m is a bound for the third derivative of a function. Show that e(h) has a minimum at p3 3ε/m
Since , e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum of function.
In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex
e(h) = ∈ /h +( [tex]h^{2}[/tex]/6) M
e'(h) = - ∈ /[tex]h^{2}[/tex] + (2h/6) M
putting , e'(h) = 0
- ∈ /[tex]h^{2}[/tex] + (2h/6) M = 0
h = [tex](3 /M)^{1/3}[/tex] * (∈^(1/3))
e"(h) = 2∈ / [tex]h^{3}[/tex] + (2M)/6 equation 1
substituting value of h in equation 1, we get
e"(h) = 2∈M / 3∈ + M/3
e"(h) = M >0
hence , At p3 3ε/M function e(h) has a minimum
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An electric heater,rated 15 volts 40 watts fitted into a metal block supplies heat to the block of mass 1.5kg and specific heat capacity of 460. calculate the temperature rise of in the block if the current flows for 10 minutes
The temperature rises of in the block if the current flows for 10 minutes is, 34.78K.
To find the answer, we need to know about the power of the electric heater.
How to find the temperature rise of in the block if the current flows for 10 minutes?We have given with the variables,[tex]P=40 W\\m=1.5kg\\S=460\\t=10minutes=10*60s=600s[/tex]
We have an expression the heat given to the system as,[tex]P*t= mS[/tex]ΔT
We have to find the temperature rise ΔT,ΔT [tex]=\frac{P*t}{mS} =\frac{40*600}{1.5*460} =34.78K[/tex]
Thus, we can conclude that, the temperature rises in the block if the current flows for 10 minute is 34.78K.
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If the current flows for 10 minutes, the temperature in the block rises by 34.78 K.
We must understand the electric heater's power in order to determine the solution.
How can you determine the block's temperature increase if the current flows for ten minutes?With the variables that we have provided,[tex]P=40Watts\\m=1.5kg\\s=460\\t=10 min=600s[/tex]
The heat supplied to the system is referred to as,[tex]Pt=ms[/tex]ΔT
We must determine the increase in temperature, T.
ΔT[tex]=\frac{Pt}{ms} =34.78 K[/tex]
Thus, we can infer that if the current flows for 10 minutes at 34.78K, the temperature in the block will increase.
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Normal human body temperature is 98.6°F. What is this temperature expressed in Celsius (°C) and in Kelvin (K)?
Answer: 37 Celsius and 310.15 K
Explanation:
C/5 = (F-32)/9 = (98.6-32)/9 = 66.6/9 = 7.4
C = 7.4 * 5 = 37 so the temperature is 37 Celsius
K = C + 273.15 = 37 + 273.15 = 310.15 K
Color is a result of the absorption and reflection of light. A shirt appears a color because it reflects that color of light. A shirt appears black when it absorbs all wavelengths of light. Why does a shirt appear white outside on a sunny day
The clothing seems white because the entire light is reflected.
what is absorption and reflection?Absorption:
This occurs when light is transformed into another type of energy. This happens when light vanishes while travelling through another medium.
reflection:
It is referred to as light reflection when a light ray hits a polished, smooth surface and bounces back. The incident light rays hit the surface and are reflected off of it. The beam that returns is referred to as the reflected ray.
according to the question we know that a shirt appears a color because it reflects that color of light. A shirt appears black when it absorbs all wavelengths of light. In case of white shirt no wavelength is absorbed by the shirt due to which the shirt appears white and in simple words the entire light is reflected back.
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In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of .........rpm for shifting is recommended for gas engines.
In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of 2,500 rpm for shifting is recommended for gas engines.
The maximum thermal efficiency of modern gasoline engines is over 50%, but legal cars on the road are only about 20% to 35% when used to power cars.
Unfortunately, even with regular car maintenance such as tuning and oil changes, the efficiency of today's gasoline engines is about 30-35%. In other words, about 65 cents per dollar spent on gasoline is wasted.
EPA's 2020 Automotive Trend Report preliminary data shows that the average fuel economy of 2020 model light trucks has increased to 25.7 miles per gallon (MPG). If this preliminary data holds, it will mark the highest average fuel economy ever for a new light commercial vehicle.
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Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph?
Increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.
What is work?Work is a measure of energy expended in moving an object. It is calculated by multiplying the force by the distance.
According to this question, work is required to move a car from one position to another.
The distance moved from 0 - 30mph is more than that moved from 50 - 60mph, therefore, increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.
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useful and inconvenience of frictional force of a soccor player running with soccer boots
They are useful in providing larger frictional force.
The force produced by two surfaces coming into contact and sliding against one another is referred to as frictional force.
The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest impact on these forces.
Football shoes have spikes or studs because they offer more frictional force when running on grass than regular shoes do.
The studs make it easier for players to move faster and change directions rapidly without slipping while also preventing them from slipping on the grass.
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A car approaches a stationary police car at 36 m/s. The frequency of the siren (as heard in the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car
The frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
Frequency hear by the observerThe frequency heard by the observer is calculated by applying the principle of Doppler effect.
f₀ = f'[(v/v - vs)]
where;
f₀ is the observed frequencyv is speed of sound = 343 m/svs is the speed of the sourcef₀ = 500[(343 / 343 - 36)]
f₀ = 500(343/307)
f₀ = 558.6 Hz
Thus, the frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.
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A proton exits the cyclotron 1. 0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1. 0 ms ?.
(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.
(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.
What is kinetic energy?
The kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Formula of KE:
K.E = 1/2mv²
mv² = 2 K.E
v = sqrt( 2*KE / M)
Here,
(a)
The KE of the medical isotopes = 6.5 MeV
substituting the values,
v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )
v = 3.53 × 10⁷ m/s
Now the centripetal force:
mv² / R = qvB
r = q*v / mv²
r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )
r = 0.19415 m
diameter d = 2r,
d= 2(0.19415 m)
d= 0.39 m ≅ 39 cm
(b)
The time period to complete a revolution around the spiral trajectory is:
T = 2πr / v
T = 2*3.14* 0.1941 / 3.53*10^7
T = 0.7 × 10⁻⁷ s
Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:
n = t / T
n = 10^-3 / (0.7*10^-7)
n = 14285.71 ≅ 14000 revolutions
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Your question is incomplete, but most probably full question was:
A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.
(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous
(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?
What is the acceleration of a 2-kg mass if a 100-N force acts on it?
SOLUTION:
Acceleration = Force/mass
= 100N / 2 kgs
= 50 m/s
.
.
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In the pinball game, momentum is transferred from the plunger to the ___
In the pinball game, momentum is transferred from the plunger to the ball.
What is momentum?
Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity.
The formula of the momentum is: p = m*v
Here a pinball game machine is given.
We know that,
A plunger in a pinball is a spring loaded rod used to shoot the ball out into the playing field.When the plunger tugged all the way back and released, the plunger will send the ball flying around the playfield. so here elastic potential energy is converted to kinetic energy.That is how the momentum is transferred to the pinball from the plunger.Hence,
In the pinball game, momentum is transferred from the plunger to the ball.
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The innermost satellite of jupiter orbits the planet with a radius of 422 × 103 km and a period of 1.77 days. what is the mass of jupiter? (g = 6.67 × 10-11 n ∙ m2/kg2)?
The mass of Jupitar is obtained from the calculations as 5.8 * 10^-14 Kg.
What is the mass of Jupitar?There are nine planets in the solar system and the sun lies at the enter of our solar system. This is the heliocentric model of the solar system.
Given that;
T^2 = GMr^3/4π
T = period
G = gravitational constant
r = radius
M = mass of Jupitar
Now;
1 day = 86400 seconds
1.77 days = 1.77 days * 86400 seconds/1 day
= 152928 seconds
Making M the subject of the formula;
M =4πT^2/Gr^3
M = 4 * 3.142 * (152928)^2/6.67 × 10^-11 * (422 × 10^9)^3
M = 2.9 * 10^11/5.0 * 10^24
M = 5.8 * 10^-14 Kg
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Question :
Which of the following has more inertia(mass)
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupees coin and a one-rupee coin?
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Please let ZzTheAmrcnNgtMareZz answer
A rubber ball and a stone of the same size are examples which will have more inertia and is therefore denoted as option A.
What is Inertia?This is referred to as the property exhibited by a body in which it has the tendency to remain at rest or in uniform motion.This property is dependent on the mass of the substance as we can deduce that the greater the mass, the greater the inertia and vice versa.
The size of a rubber ball and stone will have different masses in which that of the stone will be greater. This is as a result of the difference in the nature of the substances which are used to make both items mentioned above.
This is therefore the reason why a rubber ball and a stone of the same size as having more inertia(mass) where chosen as the most appropriate choice in this scenario.
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An 80. 0 kg person will need to climb a 30. 0 m stairway how many times to ""work off"" each excess cal (kcal) consumed?
The answer is 5.618928 kcal
The work done going up the stairway is the amount of gravitational potential energy that you gain.
GPE = m * g * h
= 80 * 9.8 * 30
=23,520J
converting to kcal
= 23520 * (0.2389 cal / 1J) * (1kcal / 1000cal)
= 5.618928 kcal
A calorie is a unit of energy. In nutrition, calories refer to the energy people get from the foods and drinks they eat, and the energy they use in physical activity. calories are indexed in the dietary records on all food packaging. Many weight loss programs center round reducing the consumption of calories.
There are many factors that go into determining your calorie needs. Your age, weight, height, and activity level all play a role. according to nutritional guidelines in the united states, adults 21 years old and older must consume anywhere between 1,600 and 3,000 calories per day.
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After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cmcm. She finds that the pendulum makes 110 complete swings in a time of 145 ss.
Hi there!
First, let's find the period of the pendulum. This can be found by solving for the amount of time it takes for the pendulum to make ONE complete swing.
[tex]T = \frac{\text{Total time}}{\text{Number of complete swings} }\\\\T = \frac{145}{110} = 1.318 s[/tex]
Now, let's use the equation for the period of a simple pendulum:
[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]
T = Period (1.318 s)
L = length of string (0.55 m)
g = acceleration due to gravity on planet (? m/s²)
Let's solve for 'g' doing some quick rearranging of the equation:
[tex]T^2 = 4 \pi^2 (\frac{L}{g})\\\\g = \frac{4\pi^2 L}{T^2}\\\\[/tex]
Solving for 'g' by plugging in values:
[tex]g = \frac{4\pi^2 (0.55)}{(1.318)^2}\\ \\= \boxed{12.496 \frac{m}{s^2}}[/tex]
an ambulance with a siren emitting a whine at 1600Hz overtakes and passes a cyclist pedaling a bike at 2.44 m/s. After being passed the cyclist hears a frequency of 1590 Hz. How fast was ambulance moving
The speed of the ambulance is 4.61 m/s.
Calculation:Doppler's effect formula is used, which is
[tex]f' = f (\frac{v + vo}{v + vs})[/tex]
Where,
f' = observer frequency of sound
f = actual frequency of sound waves
v = speed of sound waves
vo = velocity of observer
vs = velocity of source
Here, observer is the cyclist and source is the ambulance.
Given,
f' = 1590 Hz
f = 1600 Hz
v = 343 m/s
vo = 2.44 m/s
Now put the given values in the above formula,
[tex]f' = f (\frac{v + vo}{v + vs})[/tex]
[tex]1590 = 1600 (\frac{343 + 2.44}{343 + vs})[/tex]
[tex]1590 = 1600( \frac{345.44}{343 + vs})[/tex]
[tex]1590 = \frac{552,704}{343+vs}[/tex]
[tex]343+vs = \frac{552,704}{1590\\}[/tex]
[tex]343 + vs = 347.61\\[/tex]
[tex]vs = 347.61 - 343[/tex]
[tex]vs = 4.61 m/s[/tex]
Hence, the speed of the ambulance is 4.61 m/s.
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What would be the wavelength of the 21-cm-line if it was coming from a distance of 8,000,000,000 (8*10^9) light-years
21 cm is the wavelength of the 21-cm-line if it was coming from a distance of 8,000,000,000 (8*10^9) light-years
Only when relative velocity changes do wavelength alter. Thus, the wavelength will not change. A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in consecutive cycles.
This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm). The relationship between frequency and wavelength is inversely proportional. The wavelength of the wave with the highest frequency is the shortest. Half the wavelength corresponds to twice the frequency. The wavelength in the red spectrum is the longest.
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