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zmey [24]
3 years ago
7

Normalize the equations

Physics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

Solution is in explanation

Explanation:

part a)

For normalization we have

\int_{0}^{\infty }f(x)dx=1\\\\\therefore \int_{0}^{\infty }ae^{-kx}dx=1\\\\\Rightarrow a\int_{0}^{\infty }e^{-kx}dx=1\\\\\frac{a}{-k}[\frac{1}{e^{kx}}]_{0}^{\infty }=1\\\\\frac{a}{-k}[0-1]=1\\\\\therefore a=k

Part b)

\int_{0}^{L }f(x)dx=1\\\\\therefore Re(\int_{0}^{L }ae^{-ikx}dx)=1\\\\\Rightarrow Re(a\int_{0}^{L }e^{-ikx}dx)=1\\\\\therefore Re(\frac{a}{-ik}[\frac{1}{e^{ikx}}]_{0}^{L})=1\\\\\Rightarrow Re(\frac{a}{-ik}(e^{-ikL}-1))=1\\\\\frac{a}{k}Re(\frac{1}{-i}(cos(-kL)+isin(-kL)-1))=1

\frac{a}{k}Re(\frac{1}{-i}(cos(-kL)+isin(-kL)-1))=1\\\\\frac{a}{k}Re(icos(-kL)+sin(kL)+\frac{1}{i})=1\\\\\frac{a}{k}sin(kL)=1\\\\a=\frac{k}{sin(kL)}

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Explicar los avances que dieron los estudioas de robert hooke y antonie van leeuwnhook
Dafna11 [192]

Answer:

El microscopio y el descubrimiento de microorganismos. Antonie van Leeuwenhoek (1632-1723) fue una de las primeras personas en observar microorganismos, utilizando un microscopio de su propio diseño, e hizo una de las contribuciones más importantes a la biología. Robert Hooke fue el primero en usar un microscopio para observar seres vivos.

5 0
2 years ago
A 1500 kg elevator, suspended by a single cable with tension 16.0 kN, is measured to be moving upward at 1.2 m/s. Air resistance
kirill115 [55]

Tension in the Cable is 0.87 m/s6^2, Elevator's speed after it has moved 10m is 1.6*10^5 N, Work done by gravity is  1.47 * 10^3 N, Elevator Kinetic Energy is 13897.5J and Elevator Speed after rising to 10m is 4.312 m/s.

Tension is a pulling force that operates in one dimension along the cables' axes in the opposite direction from the direction of the applied force. The combined weight of the elevator box and the passenger riding inside it, in the case of an elevator, provides the pulling force in the cables is called Tension.

A moving object or particle's kinetic energy, which depends on both mass and speed, is one of its characteristics. The type of motion can be vibration, translation, rotation around an axis, or any combination of these. Kinetic energy is a type of energy that an item or particle possesses as a result of motion.

We know that,

Tension in the Cable

T = m(g+a)  = g+a = T/m = 16 * 103 / 1500 = 10.67 m/s2

a = 10.67 - 9.8 = 0.87 m/s6^2

Elevator's speed after it has moved 10m.

U^2 = u^2 +2as

= 1.22 +2*0.87*10

=1.6*10^5 N

Work done by gravity  = mg * 10 = 14700 * 10 = 1.47 * 10^3 N

Elevator Kinetic Energy = 1/2 mv^2 = 1/2*1500*18.53 = 13897.5J

Elevator Speed after rising to 10m ,

U^2 = u^2 +2as =  1.2 +2*0.87*10 = 18.6

U =(18.6)^1/2=4.312 m/s

Learn more about Kinetic Energy here

brainly.com/question/26472013

#SPJ4

6 0
1 year ago
If the average time it takes for the cart from point 1 to point 2 is 0.2 s, calculate the angle θ from the horizontal of the tra
inn [45]

Answer:

hehe

Explanation:

I dont know because I am a noob ant study

5 0
2 years ago
What is the resistance of a light bulb if a potential difference of 120 V will produce a current of 0.5 A in the bulb?
Yakvenalex [24]

Explanation:

Ohm's law:

V = IR

120 V = (0.5 A) R

R = 240 Ω

6 0
3 years ago
Read 2 more answers
How much power does it take to lift a 30.0 n box 10.0 m high in 5.00 s, if you must apply a 62n force to lift the box?
Illusion [34]
Power is defined as the rate at which the body is doing work:
P=\frac{W}{t}
Work is defined as displacement done by the force times that displacement:
W=F\cdot h
We know that we need 62N to move the box, so when we apply this force along the path of 10m we have done:
W=62N\cdot10m=620J
of work.
Now we just divide that by 5s to get how much power is required:
P=\frac{620J}{5s}=124W
5 0
3 years ago
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