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3 years ago

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How many diffraction maxima are contained in a region of the Fraunhofer single-slit pattern, subtending an angle of 2.12°, for a

slit width of 0.110 mm, using light of wavelength 582 nm?

1 answer:

Luba_88 [7]3 years ago

5 0

Answer:

6

Explanation:

We are given that

$\theta=2.12^{\circ}$

Slid width,a=0.110 mm= $0.11\times 10^{-3} m$

$1mm=10^{-3} m$

Wavelength, $\lambda=582 nm=582\times 10^{-9}$ m

$1nm=10^{-9} m$

We have to find the number of diffraction maxima are contained in a region of the Fraunhofer single-slit pattern.

$asin\theta=\frac{2N+1}{2}\lambda$

Using the formula

$0.11\times 10^{-3}sin(2.12)=\frac{2N+1}{2}(582\times 10^{-9})$

$2N+1=\frac{0.11\times 10^{-3}sin(2.12)\times 2}{582\times 10^{-9}}$

$2N+1=13.98$

$2N=13.98-1=12.98$

$N=\frac{12.98}{2}\approx 6$

Hence, 6 diffraction maxima are contained in a region of the Fraunhofer single-slit pattern

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A pendulum of length L=36.1 cm and mass m=168 g is released from rest when the cord makes an angle of 65.4 degrees with the vert

pychu [463]

(a) -0.211 m

At the beginning the mass is displaced such that the length of the pendulum is L = 36.1 cm and the angle with the vertical is

$\theta=65.4^{\circ}$

The projection of the length of the pendulum along the vertical direction is

$L_y = L cos \theta = (36.1 cm)(cos 65.4^{\circ})=15.0 cm$

the full length of the pendulum when the mass is at the lowest position is

L = 36.1 cm

So the y-displacement of the mass is

$\Delta y = 15.0 cm - 36.1 cm = -21.1 cm = -0.211 m$

(b) 0.347 J

The work done by gravity is equal to the decrease in gravitational potential energy of the mass, which is equal to

$\Delta U = mg \Delta y$

where we have

m = 168 g = 0.168 kg is the mass of the pendulum

g = 9.8 m/s^2 is the acceleration due to gravity

$\Delta y = 0.211 m$ is the vertical displacement of the pendulum

So, the work done by gravity is

$W=(0.168 kg)(9.8 m/s^2)(0.211 m)=0.347 J$

And the sign is positive, since the force of gravity (downward) is in the same direction as the vertical displacement of the mass.

(c) Zero

The work done by a force is:

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement

$\theta$ is the angle between the direction of the force and the displacement

In this situation, the tension in the string always points in a radial direction (towards the pivot of the pendulum), while the displacement of the mass is tangential (it follows a circular trajectory): this means that the tension and the displacement are always perpendicular to each other, so in the formula

$\theta=90^{\circ}, cos \theta = 0$

and so the work done is zero.

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2 years ago

A body is dropped from the roof of a 20 m high building by how much:

USPshnik [31]

Answer:

t = 2.01 s

Vf = 19.7 m/s

Explanation:

It's know through the International System that the earth's gravity is 9.8 m/s², then we have;

Data:

Height (h) = 20 m
Gravity (g) = 9.8 m/s²
Time (t) = ?
Final Velocity (Vf) = ?

==================================================================

Time

Use formula:

$\boxed{t=\sqrt{\frac{2*h}{g}}}$

Replace:

$\boxed{t=\sqrt{\frac{2*20m}{9.8\frac{m}{s^{2}}}}}$

Everything inside the root is solved first. So, we solve the multiplication of the numerator:

$\boxed{t=\sqrt{\frac{40m}{9.8\frac{m}{s^{2}}}}}$

It divides:

$\boxed{t=\sqrt{4.08s}}$

The square root is performed:

$\boxed{t=2.01s}$

==================================================================

Final Velocity

use formula:

Vf = g * t

Replace:

Vf = 9.8 m/s² * 2.01 s

Multiply:

Vf = 19.7 m/s

==================================================================

How long does it take to reach the ground?

Takes time to reach the ground in <u>2.01 seconds.</u>

How fast does it hit the ground?

Hits the ground with a speed of <u>19.7 meters per seconds.</u>

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3 years ago

You are wearing earbuds or headphones to listen to your music but your family members can hear it as well. They tell you that it

allsm [11]

If it’s loud enough for your family to hear it, it’s best you turn it down. It could cause permanent damage to your ear drums if it’s loud enough and you could start to lose your hearing. So if your family were to tell you to turn it down, you should probably just turn it down!

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3 years ago

A 300-kg piano being held by a crane is accidentally dropped from a height of 15 meters. a. What is the speed of the piano just

FinnZ [79.3K]

Answer:

a) 17.16m/s

b) 44,145J

c) Sound the piano makes when hitting the ground, vibration of the ground, heat.

d) i) It's smaller due to the energy dissipated by the friction between air and the parachute.

ii) It stays the same, the only difference is that the dissipated energy is distributed between air resistance and the kinetic energy dissipated by the ground whent he piano hits it.

Explanation:

a)

In order to solve this problem we must start by doing a drawing of the situation, which will help us visualize the problem better. (See attached picture).

So, in this problem we can ignore air resistance so we can say that the energy is conserved, this is the total initial energy is the same as the total final energy, so we get that:

$U_{0}+K_{0}=U_{f}+K_{f}$

When the piano is released it has an initial speed of zero, so the initial kinetic energy is zero. When the piano hits the ground it will have a height of 0m, so the final potential energy is zero as well. This will simplify our equation:

$U_{0}=K_{f}$

We know that potential energy is given by the formula:

U=mgh

and kinetic energy is given by the formula:

$K=\frac{1}{2}mv^{2}$

which can be substituted in our equation:

$mgh=\frac{1}{2}mv^{2}$

we can divide both sides of the equation into the mass of the piano, so we get:

$gh=\frac{1}{2}v^{2}$

which can be solved for the final velocity which yields:

$v=\sqrt{2gh}$

we can now substitute the data provided by the problem so we get:

$v=\sqrt{2(9.81m/s^{2})(15m)}$

which yields:

v=17.16m/s

b)

Since energy is conserved, this means that the total dissipated energy will be the same as the potential energy, so we get that:

E=mgh

so

$E=(300kg)(9.81m/s^{2})(15m)$

which yields:

E=44,145J

c)

When the piano hits the ground, the kinetic energy it had will be transformed to other types of energy, mostly vibration and heat. The vibration will turn to sound due to the movement of air created by the piano itself and the ground. And heat is created by the friction between the molecules created by the vibrations and the collition itself. So some of the indicators of this release of energy could be:

-Sound

-Vibration

-Heat.

d)

i) The amount of inetic energy dissipated would decrease due to the friction between air and the parachute. Since air is resisting the movement of the piano, this will translate into a loss of energy, if we did an energy balance we would get that:

$U_{0}=K_{f}+E_{p}$

The total amount of energy is conserved but it will be distributed between the energy lost due to air resistance and the kinetic energy the piano has at the time it hits the ground.

ii) So the total amount of energy dissipated remains the same, the only difference is that it will be distributed between air resistance and the kinetic energy of the piano.

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3 years ago

A force of 100 newtons is used to move an object a distance of 15 meters with a power of 25 watts. Find the

valentina_108 [34]

work is distance * force so 15*100=1500

and to find time you know power = diastance * force / time

so 25=15*100/t

25=1500/t

25/1500=t

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3 years ago