a)The total resistance of the rod R = 2.1 * 10^(3)Ω
b) current Density when voltage ΔV is applied between two ends is J(x) = [tex]=\frac{12\sigma_o\Delta V}{L}[/tex]
c) Steady-state electric field is E(x) = [tex]\frac{12\Delta V}{L^3} x^2\hat{i}[/tex]
a) Consider a small slice of the rod of thickness dx situated at a distance x from the center of the rod.
L = length of rod = 2cm, d= diameter = 0.5cm,
Given [tex]\sigma(x)=\sigma_oL^2/x^2[/tex] where σ is the rod's conductivity.
[tex]\sigma_o = 4 * 10^{-2}(\Omega.m)^{-1}[/tex] (given)
The resistance dR of this small section of the rod is
dR=[tex]\frac{\rho_rdx}{A}=\frac{dx}{\sigma_rA} = \frac{4x^{2} dx}{\sigma_o L^2\pi d^2}[/tex]
The total resistance of the rod can be found by the integral of these smalls sections over the whole rod
[tex]R = \int\limits^{L/2}_{-L/2} \, dR = \int\limits^{L/2}_{-L/2} \,\frac{4x^2dx}{\sigma_oL^2\pi d^2}=\frac{4x^3}{3\sigma_oL^2\pi d^2} |_{-L/2}^{L/2} = \frac{L}{3\sigma_o\pi d^2}[/tex]
⇒R = (2*10^(-2)) / (3 * 4 * 10 ^(-2)* π * 0.5 * 10^(-2))
⇒R = 2.1 * 10^(3) Ω
Thus the total resistance of the rod R = 2.1 * 10^(3) Ω
b)The current density when voltage ΔV is applied between two ends is given by
J(x) [tex]=\frac{I}{A}=\frac{4\Delta V}{R\pi d^2} =\frac{12\sigma_o\Delta V}{L}[/tex]
c) the steady-state electric field is
[tex]E(x) = \frac{J(x)}{\sigma} =\frac{12\sigma_o \Delta V / L}{\sigma_o L^2 / x^2} \hat{i} = \frac{12\Delta V}{L^3} x^2\hat{i}[/tex]
The question is incomplete. The full question is probably " A cylindrical glass rod is heated with a torch until it conducts enough current to cause a light bulb to glow. The rod has a length of L=2.0cm, and a diameter of d= 0.5cm, and its ends, plated with the material of infinite conductivity, are connected to the rest of the circuit. When red hot, the rod’s conductivity varies with position x measured from the center of the rod as [tex]\sigma(x)=\sigma_oL^2/x^2[/tex] with [tex]\sigma_o = 4 * 10^{-2}(\Omega.m)^{-1}[/tex] a)What is the resistance of the glass rod? Express your answer both symbolically and as a value in ohms. b)When a voltage ΔV is applied between the two ends, what is the current density J(x)? c)What is the steady-state electric field E(x)? "
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Two ice skaters stand facing each other at rest on a frozen pond. They push off against one another and the 49 kg skater acquires a speed of 2. 10 m/s. If the other skater acquires a speed of 3. 81 m/s, what is her mass in kilograms?
Her mass is approximately equal to 27 kilograms.
How do you prove that?First of all, you need to understand that momentum is a conserved quantity and the solution to this problem involves elastic collision.
Momentum can be defined as p = mv where p is momentum, m is mass, and v is velocity. Just like energy, momentum is a physical quantity that is conserved in an isolated system. Momentum is conserved as a result of Newton's third law, which states that [tex]F_A=-F_B[/tex].
You are given that the ice skaters bounce off each other, meaning the collision is elastic. Remember that in an elastic collision, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ where
m₁ is the mass of the first body, m₂ is the mass of the second body,u₁ is the initial velocity of m₁,u₂ is the initial velocity of m₂,v₁ is the final velocity of m₁, andv₂ is the final velocity of m₂.Suppose that m₁ = 49 kg, m₂ = x, u₁ and u₂ = 0 m/s, v₁ = 2.1 m/s, and v₂ = 3.81 m/s. Then the mass of the other ice skater is as follows:
49 · 0 + x · 0 = 49 · 2.1 + x · 3.81
0 = 102.9 + 3.81x
3.81x + 102.9 = 0
3.81x = -102.9
x ≈ -27
Since a mass value can't be negative, the absolute value of x is 27. Therefore, it's her actual mass in kilograms.
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Someone is standing on a trampoline. They have a mass of 65kg and each of their feet a 25cm x 10cm, what is the pressure exerted by both on the trampoline?
The pressure exerted by both on the trampoline is 25,480 N/m².
What is the pressure exerted?The pressure exerted by both on the trampoline is the force per unit area which is calculated as follows;
P = F/A
where;
F is the force applied by their weight A is the area of their feetP is the pressure exertedSubstitute the given parameters and solve for the pressure exerted.
P = (mg)/A
A = 0.25 m x 0.1 m
A = 0.025 m²
P = (65 x 9.8) / (0.025)
P = 25,480 N/m²
Thus, the pressure exerted at any given surface depends on the applied force and the area of the given surface.
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a baseball player exerts a force of 100n on a ball for a distance of 0.5m as he throws it. if the ball has a mass of 0.15kg, what is its velocity as it leaves his hand?
similar to the case in the experiment you use two rubber bands, side to side first, to hold a weight of 3 reference objects. then, as in the experiment, the bands are pulled apart in their free ends until they form an angle of 30 degrees with respect to the horizontal. what are the deformations observed in these bands? ...
Three units deformations observed in these bands.
What forces do a rubber band encounter?Elastic force is the force that permits some materials to regain their former shape after being stretched or crushed. Thus, a stretched rubber band is subject to an elastic force.
The rubber band experiment uses a straightforward rubber band to show entropic force and a refrigeration cycle. The rubber band experiment involves stretching and then releasing a rubber band while measuring its temperature.
Always acting in the opposite direction of motion is friction. This indicates that if friction is there, it cancels out some of the force driving the motion (if the object is being accelerated). This results in a decreased acceleration and a smaller net force.
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a cliff diver steps off a cliff and hits the water 2.2 seconds later. How high was the cliff?
The height of the cliff is 24.2 m.
Let:
'h' be the height of the cliff'u' be the initial velocity of diver; u = 0m/s'+'ve been the annotation for the Downward directiona = 10m/s^2 be the approximation of acceleration due to gravityUsing the Second Equation of Motion:
[tex]h = ut + 1/2 at^{2} \\h = 0 + 1/2 (10)(2.2)^{2} \\h = 0 + 5(2.2)^{2} \\h = 5(4.84)\\h = 24.2m[/tex]
The Second Equation of Motion establishes a relationship between displacement and time. It can be used to calculate the displacement and time, in different conditions.
The cliff was 24.2m high above the water surface, into which the cliff diver dived.
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assume that you weight yourself on a bathroom scale. would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that was accelerating upward?
The springs inside a bathroom scale will be more compressed.
What is acceleration due to gravity?
In physics, gravitational acceleration is the acceleration of an object in free fall in a vacuum (hence no resistance). This is a steady increase in velocity caused solely by the gravitational pull. All objects accelerate at the same speed in a vacuum, regardless of their mass or composition . The measurement and analysis of these velocities is known as gravimetry.
At a fixed point on the surface, the magnitude of the Earth's gravity is the combined effect of gravity and the centrifugal force due to the rotation of the Earth. Free-fall acceleration at various points on the Earth's surface ranges from 9.764 to 9.834 m/s2 (32.03 to 32.26 ft /s2) depending on altitude, latitude and longitude . The old standard is precisely defined as 9.80665 m/s2 (32.1740 ft/s2). Locations that deviate significantly from this value are called gravity anomalies. Other effects such as lift and air resistance are not taken into account.
When the elevator accelerates and shows a higher weight reading. As the lift accelerates and descends, the springs in the bathroom scale are compressed less and the displayed weight value is reduced.
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a 68.1-kg boy is surfing and catches a wave which gives him an initial speed of 1.60 m/s. he then drops through a height of 1.56 m, and ends with a speed of 8.51 m/s. how much nonconservative work (in kj) was done on the boy?
The non-conservative work done on the boy is 1.337 kJ
Given that,
Mass of boy, m = 68.1 kg
Initial speed of boy, u = 1,60 m/s
The boy then drops through a height of 1.56 m
Final speed of boy, v = 8.51 m/s
Now, we have to find the non-conservative work was done on the boy.
The Work done by the non-conservative forces is equal to the sum of total change in kinetic energy and total change in potential energy.
[tex]W=\frac{1}{2}m (v^{2}-u^{2})+(0-mgh)[/tex]
[tex]W=\frac{1}{2}m (v^{2}-u^{2})-mgh[/tex]
[tex]W=\frac{1}{2}(68.1) ((8.51)^{2}-(1.60)^{2})-68.1*9.8*1.56[/tex]
W = 1337.62 Joules
or
W = 1.337 kJ
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What is the main reason sea level is rising?
A: Ice Melting
B: Thermal Expansion
The main reason for the sea level rise is the melting of the ice, as the icebergs are melting due to the increase in the average temperature of the earth, therefore the correct answer is option A.
What is thermal energy?It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.
Thermal expansion is unrelated to the sea level rising.
Since icebergs are melting due to an increase in the earth's average temperature, melting ice is the primary cause of sea level rise, therefore the correct answer is option A.
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points :)
don't mind this just getting to 20 words :)
Answer:
20 20 20 20 25 points 20 20 20 25 points
Explanation:
What is the magnitude of the force that must be applied for the system below to be balanced?
Answer:
20 N
Explanation:
logically it'd be 20 N due to the fact that it's a rectangular shape. You pretty much look at the counterpart and copy and paste it to the other side.
If Earth's circumference at the
equator is 40,070 km, what is the
speed of the stationary satellite
GOES above the equator in km/
hour? (Use the formula: Speed =
Distance/Time)
The stationary satellite crosses the equator at a speed of 1180 kilometres per hour.
How does speed at the equator get calculated?At the equator, where the Earth's circumference is 40,070 kilometres and the day lasts for 24 hours, the speed is 1670 kilometres per hour (1037 miles per hour). This slows down by the latitude's cosine, so at a latitude of 45 degrees, cos(45) =. 707, and the speed is. 707 x 1670 = 1180 kilometres per hour.
How fast would a student travelling at the equator while seated on Earth's surface?
The daily motion felt on our earth is brought on by this spinning. You would move at almost 1,000 miles per hour (1,600 km/hr) if you were standing on the equator of the Earth, but your pace would slow down if you started moving in the direction of the North or South Poles.
A latitude of 45 degrees, cos(45) =. 707, and the speed is. 707 x 1670 = 1180 kilometres per hour.
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a zoologist standing on a cliff aims a tranquilizer gun at a monkey hanging from a distant tree branch. th ebarrel fo the gun is horizontla. just as the zoologigtist pulls the trigger, the monkey lets go and begins to fall. will the dark hit the monkey? neglect air resistance
The Monkey captured Bryce's spirit inside a circle of salt inside a McDonald's bathroom stall and left after escaping from Lady Bullseye. After several weeks, he finally came back and set him free.
When injected, tranquilizer-filled darts fired by tranquilizer guns temporarily sedate a person or an animal so that they can be handled (or captured) safely. The tranquilizer may be a paralytic, sedative, or anesthetic. There is a long history of using tranquilizer weapons to capture wildlife without harm. The most frequent sensations are relaxation and sleepiness. Negative feelings, stress, or anxiety might also gradually fade away once the sedative starts to work. Your entire body could experience tingling, especially in your arms, legs, hands, and feet.
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Both speed and velocity measure how fast something is moving. However, since speed is not a _________ it does not require a(n) ___________ .
Responses
A scalar, directionscalar, direction
B quantity, unitquantity, unit
C magnitude, unitmagnitude, unit
D vector, direction
A bird flies at 10m * s ^ - 1 for 3s, 15m * s ^ - 1 for 3s, and 20m * s ^ - 1 for 4 Calculate the birds's average speed. A 4.5m * s ^ - 1 B 15m * s ^ - 1 C 15.5m * s ^ - 1 D 51.7m * s ^ - 1
The bird's average speed when he flies 10 m/s for 3 s, 15 m/s for 3s and 20 m/s for 4 s is 15.5 m/s. The right option is C 15.5 m/s
What is average speed?Average speed can be defined as the ratio of the total distance to the total time traveled by an object.
To calculate the average speed of the bird, we use the formula below.
Formula:
S = Total distance/total timeS = s₁t₁+s₂t₂+s₃t₃/(t₁+t₂+t₃)............. Equation 1From the question,
Givne:
s₁ = 10 m/st₁ = 3 ss₂ = 15 m/st₂ = 3 ss₃ = 20 m/st₃ = 4 s
Substitute these values into equation 1
S = [(10×3)+(15×3)+(20×4)]/(3+3+4)S = (30+45+80)/10S = 155/10S = 15.5 m/sHence, the average velocity of the bird is 15.5 m/s.
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This equation shows how the number of biscuits Olivia can bake is related to the amount of flour she has.
c = 15f
The variable f represents the number of scoops of flour Olivia has, and the variable c represents the number of biscuits she can bake. With 1 scoop of flour, how many biscuits can Olivia bake?
With 1 scoop of flour, Olivia can bake 15 biscuits if the the equation that shows the relation between number of biscuits and amount of flour is c = 15f.
c = 15 f
c = Number of biscuits
f = Number of scoops of flour
f = 1
c = 15 * 1
c = 15
This equation shows that number of biscuits that can be made is 15 times the number of scoops of flour. So if the number of scoops of flour is 1, the number of biscuits that can be made is 15.
Therefore, with 1 scoop of flour, Olivia can bake 15 biscuits
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a box of books with mass 40 kg rests on the level floor of the campus bookstore. the floor is freshly waxed and has negligible friction. a bookstore worker applies a constant horizontal force with magnitude 25 n to the box. what is the magnitude of the acceleration of the box?
The magnitude of the acceleration of the box is = 0.625 m/s²
Friction is the pressure resisting the relative movement of strong surfaces, fluid layers, and material elements sliding in opposition to each other. There are numerous kinds of friction: Dry friction is a pressure that opposes the relative lateral motion of strong surfaces in touch.
Pressure is a power that could exchange the movement of an object. A pressure can reason an item with mass to alternate its speed, i.e., to boost up. pressure also can be defined intuitively as a push or a pull. A force has each magnitude and course, making it a vector amount.
Acceleration is the price of trade of the rate of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by way of the orientation of the net force performing on that object.
Force = mass × acceleration
acceleration = force / mass
= 25 / 40
= 0.625 m/s²
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Ida Haitarun is captain of the Varsity cross country team. During the after-school practice on Tuesday, he led the team on the following run from school to a nearby park. From the road, he ran at a 20 degree angle North of East for 8 miles. Determine how far east and how far north they are from where they started.
The displacement of the team is 2.74 miles due east and 7.52 miles due north from where they started.
What is the eastward displacement of the team?
The eastward displacement of Ida Haitarun and his team during the cross country race is calculated by forming a right triangle from the displacement of the team.
The angle of inclination of the displacement is calculated as follows;
θ = 90⁰ - 20⁰ = 70⁰ (above the horizontal)
The eastward displacement is the base of the triangle and it is calculated as follows;
cos θ = base / hypotenuse side
cos 70 = base / 8 miles
base = (8 miles) x (cos 70)
base = 2.74 miles
The northward displacement is calculated as follows;
sin θ = height / hypotenuse side
sin 70 = height / 8 miles
height = (8 miles) x (sin 70)
height = 7.52 miles
Thus, the team is 2.74 miles due east and 7.52 miles due north from where they started.
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a powerful motorcycle can produce an acceleration of while traveling at 90.0 km/h. at that speed, the forces resisting motion, including friction and air resistance, total 400.0 n. (air resistance is analogous to air friction. it always opposes the motion of an object.) what is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg? 34. a car with a mass o
1257.5 N is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration.
What is a magnitude in physics?The definition of magnitude is simply "distance or quantity." It displays an object's size, direction, or speed, whether relative or absolute. It's used to indicate that something has a certain size or scope.
Briefing:A = 3.50 m/s² is the motorcycle's acceleration.
f = 400.0 N, the force of resistance to motion
M = 245 kg for the motorcycle's mass
F is the amount of force a motorcycle exerts when moving rearward.
The amount of force a motorcycle exerts when moving rearward is described as
F = f + ma
Inserting the values
F = 400.0 + (245) (3.50)
F = 1257.5 N
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The complete question is -
A powerful motorcycle can produce an acceleration of 3.50 m/s² while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, total 400.0 N. (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg?
the barrel of a shotgun: group of answer choices is generally shorter than that of a rifle. is wider at the end to concentrate shot. is smooth without the grooves and lands found in rifles. is indistinguishable from that of a rifle.
Measures the diameter of a shotgun's barrel in terms of the quantity of lead balls needed to make the bore weigh one pound (12 gauge is the diameter of a lead ball weighing one-twelfth of a pound).
What differentiates a shotgun from a rifle?A shotgun has many projectile properties while a rifle only comes with one. Shotguns are helpful at close ranges when rifles are useful at a distance. Shotguns only have a front sight, whereas rifles have both front and rear sights.
Rifles are typically a little noisier than shotguns. Analyzing test results reveals that shotguns and rifles have decibel levels that are comparable. The typical decibel range
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suppose we want to place a weather satellite into a circular orbit 300 kmkm above the earth's surface. what speed, period, and radial acceleration must it have? the earth's radius is 6380km
a. The speed of the satellite is 244 m/s
b. The period of the satellite is 1.72 × 10⁷ s
c. The radial acceleration of the satellite is 8913 rad/s
What is the speed of the satellite?The speed of the satellite is given by v = √(GM/R) where
G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.972 × 10²⁴ kg and R = radius of orbit = r + r' where r = radius of earth = 6380 km and r' = radius of orbit = 300 kmSo, substituting the values of the variables into the equation, we have that
v = √(GM/R)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6380 km + 300 km)
v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg /6680 km)
v = √(39.83324 × 10¹³ Nm²/kg ÷ 6.680 × 10⁶ m)
v = √(5.963 × 10⁻³ × 10⁷ Nm²/kg)
v = √(5.963 × 10⁴ Nm/kg)
v = 2.44 × 10² m/s
V = 244 m/s
So, the speed of the satellite is 244 m/s
b. What is the period of the orbit?The period of the orbit is given by T = 2πR/v where
R = radius of orbit = 6680 km and v = speed of orbit = 244 m/sSo, substituting the values of the variables into the equation, we have
T = 2πR/v
T = 2π × 6680 km/244 m/s
T = 2π × 6680 × 10³ m/244 × 10⁵ m/s
T = 13660π × 10³ m/244 × 10⁵ m/s
T = 41971.68 × 10³ m/244 × 10⁵ m/s
T = 17201.5 × 10³ s
T = 1.72015 × 10⁷ s
T ≅ 1.72 × 10⁷ s
So, the period of the satellite is 1.72 × 10⁷ s
What is the radial acceleration of the satellite?The radial acceleration of the satellite is given by a = v²/R where
v = speed of satellite = 244 m/s and R = radius of orbit = 6680 kmSubstituting the values of the variables into the equation, we have
a = v²/R
a = (244 m/s)²/6680 km
a = 59536 m²/s²/6680 × 10³ m
a = 8.913 × 10³ rad/s
a = 8913 rad/s
So, the radial acceleration of the satellite is 8913 rad/s
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10 N of force is applied to a spring and its length increases by 4 cm. If the spring is obeying Hooke's law, what will its extension be if 30 N of force is applied?
I think Twelve is the answer
an apple drops from a tree and hits the ground in 1.4 s how far does it fall?
It falls 9.8m far for the apple to drop from tree in 1.4sec.
Apple fall time t = 1.4 s
The free fall distance in time t is given by
d = 1/2at²
where a = g = 10 m/s² = free fall acceleration
calculation:
Using the above formula and the values given, the distance the apple will fall free in 1.4 seconds is
d = 1/2(10)(1.4)²
= 9.8 m
Therefore the distance um the apple will fall is 9.8 m.
Isaac Newton formulated gravitational theory in 1665 or 1666 after watching an apple fall. An apple falling from a tree is an example of Straight-line motion because gravity causes it to fall vertically in a straight line.
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a site was measured to have an average wind velocity of 5.2 m/s at 13m above ground. if the surface roughness exponent is assumed to be 0.23, what will the predicted wind velocity be at 32m above ground?
The wind velocity at 32 m above the ground is 6.39m/s when the roughness exponent of the surface is 0.23
Given in the problem is
Wind velocity at 13m above the ground v1 =5.2 m/s
Height initially h1 = 13m
height at which wind velocity is to be predicted h2= 32m
surface roughness exponent α = 0.23
Let velocity to be predicted be v2
We know that from the formula
v2= v1*(h2/h1)^α
⇒v2= 5.2 * (32/13)^ 0.23 = 6.39 m/s
Thus the wind velocity at 32m above the ground is 6.39m/s
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a car is traveling at 100 mph down the highway. at some time the driver sees an obstruction in the road and slams on the brakes skidding to a halt reducing its kinetic energy to zero. what happened to the kinetic energy of the car?
The kinetic energy is changed to thermal energy by brake friction and turns to zero.
We need to know about kinetic energy to solve this problem. Kinetic energy is the energy from a moving object. It can be determined as
KE = 1/2 . m . v²
where KE is kinetic energy, m is mass and v is speed.
From the question above, we know that
v1 = 100 mph
KE2 = 0 joule
When the car moves at 100 mph, the car has kinetic energy. But on the way when the driver brakes the car, the kinetic energy is changed to thermal energy by brake friction. Hence, the kinetic energy is reduced every time and finally turns to zero.
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In 1993 itleana salvador at italy walked 30 km under 12 min suppose that during 115m at her walk she steadly increased her speed from 42m/s to 5m/s how long does it increase took
When acceleration is constant, we may connect displacement to time and velocity, two of the other three parameters that describe motion, using the following three equations: d = ( 1 2 ) ( 1 2 ) (v f + v I (t) (Equation 1) D = v I t + a t + 1 2 (Equation 2) V I 2 + 2 a d = v f 2 (Equation 3).
Defining displacement If acceleration is constant, then?Displacement is directly proportional to the square of the length of the linear motion when acceleration is constant and beginning velocity is zero.
Solution:-
vi =+245km/h
aavg = -3.0m/s2
vf =vi -(0.200)vi
vi =(245km/h)(1h/3600s)(103m/1km)= +68.1m/s
vf =(1.000-0.200)vi =(0.800)(68.1m/s)=+54.5m/s
Δt=vf -vi /aavg
= 54.5m/s - 68.1m/s / -3.0m/s2
=-13.6m/s /-3.0 m/s2
= 4.5s
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If you wanted to visit a area with very little wind whear might you go
Answer:Ohio
Explanation:
Hello! I am currently trying to answer this question. Could you provide the steps to help me solve it?
Given:
The length of the pipe is L.
The third harmonic has teh wavelength,
[tex]\frac{2L}{3}[/tex]To find:
The type of the pipe
Explanation:
The wavelength of the harmonics for a pipe closed at one end is,
[tex]\lambda=\frac{4L}{2n-1}[/tex]The wavelength of the harmonics for a pipe open at both the ends is,
[tex]\lambda=\frac{2L}{n}[/tex]Here,
[tex]n=1,\text{ 2, ......}[/tex]The given wavelength is,
[tex]\frac{2L}{3}[/tex]which resembles the form,
[tex]\frac{2L}{n}[/tex]Hence, the pipe is open at the other end.
scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as , where is in nm. if a 295-nm-thick coating is placed on glass for what visible wavelengths will the reflected light have maximum constructive interference?
The wavelength of the reflected light will have a range from 360 nanometers to 700 nanometers.
Constructive Interference may be defined as the process which occurs when the maxima of any two waves add up and the amplitude of the resulting wave will be equal to the sum of the two individual waves. According to the question thickness of coating, d = 295 nm and wavelength varies as n = [(30nm) ^1/2]/λ^1/2.
Also, the wavelength will be expressed as
λ = 2nd/M where M = 1,2,3......
λ = 2d[(30nm)^1/2]/Mλ^1/2
λ^3/2 = (d60nm^1/2)/M
λ = ∛d² 3600 nm/M
Now, if M = 1 then,
λ = ∛295² 3600nm/1 = 679.18 nm
Now, if M = 2 then,
λ = ∛295² 3600nm/2 = 679.18 nm
Now, if M = 3 then,
λ = ∛295² 3600nm/3 = 326.51 nm
So, the range is approximately 360 nm to 700 nm.
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Complete Question:
Scientists are testing a transparent material whose index of refraction for visible light varies with wavelength as n = 30.0 nm1/2 /l1/2, where l is in nm. If a 295-nm-thick coating is placed on glass 1n = 1.502 for what visible wavelengths will the reflected light have maximum constructive interference?
a 5.25-g bullet is fired into a 360-g block of wood suspended as a ballistic pendulum. the combined mass swings up to a height of 8.75 cm. what was the magnitude of the momentum of the combined mass immediately after the collision?
magnitude of the momentum of the combined mass immediately after the collision p = 0. 478 (kg. m/sec)
Mass of bullet : m = 5. 25 (g) = 0. 00525 (kg)
Mass of block : M = 360 (g) = 0. 360 (kg)
Height : h = 8. 75 (m) = 0. 0875 (m)
Here we need to find the momentum :
Now,
As we know that,
The conservation of energy :
Now,
Kinetic energy = Potential energy
= 1/2( m + M)v² = (m+M)gh (m,M is mass of bullet and block)
Now,
v = [tex]\sqrt{2gh}[/tex]
Now,
Momentum can be defined as :
Here,
p = (m+ M) [tex]\sqrt{2gh}[/tex]. . . eqn 1
Putting the values in eqn 1 :
We get,
p = 0.478 (kg. m/sec)
Hence, the momentum : p = 0. 478 (kg. m/sec)
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In a resonance a turning fork of frequency 330hz produced the first loud sound when water level in a pipe was 17.8cm from the open-end ant the second at 57.3cm. calculate the wavelength of the sound, speed of sound in air, water level of the next resonant length ?
The wavelength, the speed of sound and the water level of the next resonant length (the fifth harmonics) are as follows;
The calculated wavelength of the sound from the tuning fork is 0.79 metersThe speed of the sound is 260.7 m/sThe water level of the fifth harmonics is 96.8 cmWhat is an harmonics of a sound wave?An harmonics are waves with a frequency that is an integer multiple of the fundamental frequency.
The given frequency of the sound wave, f = 330 hz
The first water level that gives the first loud sound, l₁ = 17.8 cm
The water level from the open end at the second loud sound, l₂ = 57.3 cm
First part;
The first harmonics that gives the fundamental frequency for the pipe is expressed as follows;
[tex]\dfrac{\lambda}{4} = l_1+e[/tex]
Where;
e = The distance to the antinode of the wave above the top of the pipe
The third harmonics is given by the formula
[tex]\dfrac{3\cdot \lambda}{4} = l_2+e[/tex]
[tex]\dfrac{3\cdot \lambda}{4}- \dfrac{\lambda}{4} = \dfrac{\lambda}{2} = (l_2+e) - (l_1+e) = l_2 - l_1[/tex]
[tex]\dfrac{\lambda}{2} = l_2 - l_1[/tex]
λ = 2 × (l₂ - l₁)
λ = 2 × (57.3 - 17.8) = 79
The wavelength of the wave, λ = 79 centimeters = 0.79 meters
Second part;
Speed of sound, v = f × λ
Therefore; v = 330 Hz × 0.79 m = 260.7 m/s
The speed of sound in air, v = 260.7 m/sThird part;
[tex]\dfrac{\lambda}{4} = l_1+e[/tex]
[tex]\dfrac{3\cdot \lambda}{4} = l_2+e[/tex]
Which gives; 3·(l₁ + e) = l₂ + e
3·l₁ + 3·e = l₂ + e
3·e - e = l₂ - 3·l₁
2·e = l₂ - 3·l₁
Therefore, 2·e = 57.3 - 3 × 17.8 = 2.9
e = 3.9 ÷ 2 = 1.95The water level for the next resonant length, which is the fifth harmonics, is given by the formula;
[tex]\dfrac{5\cdot \lambda}{4} = l_3+e[/tex]
Which gives;
[tex]l_3 = \dfrac{5\cdot \lambda}{4} - e[/tex]
Therefore;
[tex]l_3 = \dfrac{5\times 79 }{4} - 1.95 = 96.8[/tex]
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