An oscillating particle has the equation x = 10cos(8πt +π ) (x in cm, t in s). The number of times the object passes through the equilibrium position in one second is

Answer:

The power of the eye is 51.64 diopters

Explanation:

The power of the eye is given by;

[tex]P = \frac{1}{f} = \frac{1}{d_o} +\frac{1}{d_i}[/tex]

where;

P is the power of the eye in diopter

f is the focal length of the eye

[tex]d_o[/tex] is the distance between the eye and the object

[tex]d_i[/tex] is the distance between the eye and the image

Given;

[tex]d_o[/tex] = 61.0 cm = 0.61 m

[tex]d_i[/tex] = 2.0 cm = 0.02 m

[tex]P = \frac{1}{d_o} +\frac{1}{d_i} \\\\P = \frac{1}{0.61} + \frac{1}{0.02} \\\\P = 51.64 \ D[/tex]

Therefore, the power of the eye is 51.64 diopters.

The power P of the eye when viewing an object 61.0 cm away is 51.639D

The power of a lens is a reciprocal of its focal length and it is expressed as:

[tex]P=\frac{1}{f}[/tex]

According to the mirror formula

[tex]\frac{1}{f} =\frac{1}{d_i} +\frac{1}{d_0}[/tex]

where

[tex]d_i[/tex] is the distance from the lens to the image = 61.0cm = 0.61m

[tex]d_0[/tex] is the distance from the lens to the object = 2.00cm = 0.02m

[tex]P=\frac{1}{f} =\frac{1}{0.02} +\frac{1}{0.61}\\P=50+1.639\\P=51.639D[/tex]

Hence the power P of the eye when viewing an object 61.0 cm away is 51.639D

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Answer:

speed of the alpha particle is 2 x 10^7 m/s.

Explanation:

energy of alpha particle = 8.3 Mev

1 Mev = 1.602 x 10^-13 J

8.3 Mev = [tex]x[/tex]

solving, [tex]x[/tex] = 8.3 x 1.602 x 10^-13 = 1.329 x 10^-12 J

mass of a alpha particle = 6.645 x 10^−27 kg

The energy of the alpha particle is the kinetic energy KE of the alpha particle

KE = [tex]\frac{1}{2}mv^{2}[/tex]

where m is the mass of the alpha particle

v is  the velocity of the alpha particle

substituting values, we have

1.329 x 10^-12 = [tex]\frac{1}{2}*6.645*10^{-27}*v^{2}[/tex]

[tex]v^{2}[/tex] = 4 x 10^14

[tex]v = \sqrt{4*10^{14} }[/tex] = 2 x 10^7 m/s

Answer;

26.45cm

See attached file for explanation

Answer:

amplification

Explanation:

reflection can happen

some amount of lighr get absorbed

something gets refracted

but amplification cant

Answer:

21.55 m

Explanation:

Answer:

Static friction is greater than kinetic friction, but they both act opposite the applied force.

Explanation:

Newton's 3rd law states that every action has and equal but opposite reaction.

If an object has static friction, that means it stays in one spot, and it takes a great amount of force to get it moving.

Once the object is moving it has kinetic friction, but it's easier to keep it moving unless you are trying to stop it.

The equal but opposite reaction to something moving it is stopping it, and the equal but opposite reaction to stopping something is moving it.

The same amount of force used to move/stop something is used to stop/move it.

Static friction is greater than kinetic friction, but they both act opposite the applied force.

Friction is the force that opposes motion. Frictional force always acts in opposition to the direction of motion.

There are two kinds of friction;

Since more forces tend to act on a body at rest and prevent it from getting into motion than the forces that tend to stop an already moving body, it follows that static friction is greater than kinetic friction. Both act in opposite direction to the applied force.

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Answer:

C

Explanation:

intensity = Power delivered by the sound (Watt)/ Surounding Area (m²)

I = P/A

A = πr²

r = is the distance between you and the cricket.

so in other form we can get

I = P/πr²

let take I(1) as first intensitilynyou heard and I(2) as the increased intensity.

I(1) / I(2) = r(2)² / r(1)²

1/4 = r(2)²/r(1)²

1/2 = r(2) / r(1)

r(2) = ½ r(1)

or r(2) is decreaases by a factor of 2.

Answer:

Stay the same

Explanation:

Since, friction is negligible:

Initial Momentum = Final Momentum

Initial KE = Final KE

m1 * v1 = m2 * v2

When m increases v decreases.

The momentum and kinetic energy remain the same if you drop paper clips into an open cart rolling along a straight horizontal track with negligible friction.

Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Friction always moves an object in a direction that is counter to the direction that it is traveling or attempting to move.

Given:

The paperclips into an open cart rolling along a straight horizontal track with negligible friction,

Calculate the momentum, Since friction is negligible,

Initial Momentum = Final Momentum

Initial Kinetic Energy = Final Kinetic Energy

m₁ × v₁ = m₁  × v₂

When m increases, v decreases,

Thus, momentum will remain the same.

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#SPJ5

Answer:

cross-sectional

Explanation:

The full definition of this is ''a research design in which several different age-groups of participants are studied at one particular point in time.''

Answer:

It tell you that the velocity is constant, what means that there's no acceleration

Answer:

Water.

Explanation:

To know which of the substance that will absorbed the greatest amount of thermal energy, we'll simply determine the amount of energy absorbed by each substance.

This is illustrated below:

For Air:

Mass (M) = 1 kg

Change in temperature (ΔT) = 15 °C

Specific heat capacity (C) = 1.01 KJ/Kg°C

Heat Absorbed (Q) =..?

Q = MCΔT

Q = 1 x 1.01 x 15

Q = 15.15 KJ

Therefore, the heat absorbed by air is 15.15 KJ.

For Plastic:

Mass (M) = 1 kg

Change in temperature (ΔT) = 15 °C

Specific heat capacity (C) = 2.60 KJ/Kg°C

Heat Absorbed (Q) =..?

Q = MCΔT

Q = 1 x 2.60 x 15

Q = 39 KJ

Therefore, the heat absorbed by plastic is 39 KJ.

For Water:

Mass (M) = 1 kg

Change in temperature (ΔT) = 15 °C

Specific heat capacity (C) = 4.18 KJ/Kg°C

Heat Absorbed (Q) =..?

Q = MCΔT

Q = 1 x 4.18 x 15

Q = 62.7 KJ

Therefore, the heat absorbed by water is 62.7 KJ.

For Wood:

Mass (M) = 1 kg

Change in temperature (ΔT) = 15 °C

Specific heat capacity (C) = 1.68 KJ/Kg°C

Heat Absorbed (Q) =..?

Q = MCΔT

Q = 1 x 1.68 x 15

Q = 25.2 KJ

Therefore, the heat absorbed by Wood is 25.2 KJ.

Summary:

Substance >>>>> Heat Absorbed

Air >>>>>>>>>>>> 15.15 KJ.

Plastic >>>>>>>>> 39 KJ

Water >>>>>>>>>> 62.7 KJ

Wood >>>>>>>>>> 25.2 KJ.

From the above calculations, we can see that water will absorb the greatest amount of thermal energy.

The substance that will have the smallest change in temperature is water because it has the highest specific heat capacity.

The specific heat capacity of each substance can be used to determine the substance with the smallest change in temperature.

Q = mcΔθ

where;

Δθ = Q/mc

Δθ = (250)/(1.01)

Δθ = 247.5 ⁰C

Δθ = (250)/(2.6)

Δθ = 96.15 ⁰C

Δθ = (250)/(4.18)

Δθ = 59.81 ⁰C

Δθ = (250)/(1.68)

Δθ = 148.81 ⁰C

Thus, the substance that will have the smallest change in temperature is water because it has the highest specific heat capacity.

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Answer:

SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit system.

Answer:

R = 36.885 km

Explanation:

In order to distinguish the two planes we must use the Rayleigh criterion that establishes two distinguishable objects if in their diffraction the central maximum of one coincides with the first minimum of the other

The diffraction equation for slits is

            a sin θ = m λ

the first minimum occurs for m = 1

             sin θ = λ a

as the diffraction experiments the angles are very small, we approximate

             sin θ = θ

             θ = λ / a

This expression is for a slit, in the case of circular objects, when solving the system in polar coordinates, a numerical constant appears, leaving the expression of the form

            θ = 1.22 λ / a

In this problem they give us the frequency, let's find the wavelength with the relation

           c = λ f

           λ = c / f

           θ = 1.22 c/ f a

since they ask us for the distance between the planes, we can use the definition of radians

          θ = s / R

if we assume that the distance is large, we can approximate the arc to the horizontal distance

          s = x

we substitute

             x / R = 1.22 c / fa

             R = x f a / 1.22c

Let's reduce the magnitudes to the SI system

            f = 9000 MHz = 9 109 Hz

            a = 15 m

           x = 100 m

let's calculate

            R = 100 10⁹ 15 / (1.22 3 108)

            R = 3.6885 10⁴ m

let's reduce to km

            R = 3.6885 10¹ km

            R = 36.885 km

Answer:

Explanation:

       Kirchhoff's Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.

           #I AM ILLITERATE

Answer:

The values is  [tex]m_{max} = 8001 \ bright \ spots[/tex]

Explanation:

From the question we are told that

    The slit distance is  [tex]d = 2 \ mm = 2*10^{-3} \ m[/tex]

    The  wavelength is  [tex]\lambda = 500 \ nm = 500 *10^{-9} \ m[/tex]

At the first half of the screen from the central maxima

   The number of bright spot according to the condition for constructive interference is  

          [tex]n = \frac{d * sin (\theta )}{\lambda}[/tex]

For maximum number of spot [tex]\theta = 90^o[/tex]

So  

       [tex]n = \frac{2*10^{-3} * sin (90 )}{500 *10^{-9}}[/tex]

        [tex]n =4000[/tex]

Now for the both sides plus the central maxima  we have

      [tex]m_{max} = 2 * n + 1[/tex]

substituting values

       [tex]m_{max} = 2 * 4000 + 1[/tex]

       [tex]m_{max} = 8001 \ bright \ spots[/tex]

Answer:

The complete question is

NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low-mass sail and the energy and momentum of sunlight for propulsion. (a) Should the sail be absorbing or reflective? Why? (b) The total power output of the sun is 3.9 x 10^26  W. How large a sail is necessary to propel a 10,000-kg spacecraft against the gravitational force of the sun? Express your result in square kilometers. (c) Explain why your answer to part (b) is independent of the distance from the sun.

a) The sail should be reflective because, an incident electromagnetic wave, in this case, light wave, impacts twice the energy density on a reflective sail, and hence twice the force on a totally reflective sail as would be impacted on a sail that is totally absorbing.

For totally reflective, F = (2I/c)A    ....1

for totally reflective, F = (I/c)A       ....2

where I is the intensity of the light

c is the speed of light = 3 x 10^8 m/s

A is the area the sail

b) The intensity of the light from the sun = power/area

==> I = [tex]\frac{3.9*10^{26}}{4\pi r^{2} }[/tex]

where r is the distance from the sun and the sail

The Force from the sail from equation 1  is therefore

[tex]F[/tex] = [tex]\frac{2*3.9*10^{26}*A}{4\pi r^{2} *3*10^{8}}[/tex] = [tex]2.069*10^{17}\frac{A}{r^{2}}[/tex]

gravitational force between the sail and the sun [tex]F_{g}[/tex] = [tex]\frac{GMm}{r^{2}}[/tex]

where

G is the gravitational constant = 6.67 x 10^−11 m^3⋅s−2⋅kg−1.

m is the mass of the sail = 10000 kg

M is the mass of the sun = 1.99 x 10^30 kg.

==> [tex]F_{g}[/tex] = [tex]\frac{6.67*10^{-11}*1.99*10^{30}*10000}{r^{2}}[/tex] = [tex]\frac{1.33*10^{24}}{r^{2}}[/tex]

Equating the forces, we have

[tex]2.069*10^{17}\frac{A}{r^{2}}[/tex]  =  [tex]\frac{1.33*10^{24}}{r^{2}}[/tex]

the distance cancels out

A = (1.33 x 10^24)/(2.069 x 10^17) = 6428226.196 m^2

==> 6428.2 km^2

c) The force of the solar radiation is proportional to the intensity of the sun from the light, and the intensity is inversely proportional to the square of the distance from the source. Also, the force of gravitation  is inversely proportional to the square of the distance, so they both cancel out.

Answer:

20.96 m/s^2 (or 21)

Explanation:

Using the formula (final velocity - initial velocity)/time = acceleration, we can plug in values and manipulate the problem to give us the answer.

At first, we know a car is going 8 m/s, that is its initial velocity.

Then, we know the acceleration, which is 1.8 m/s/s

We also know the time, 7.2 second.

Plugging all of these values in shows us that we need to solve for final velocity. We can do so by manipulating the formula.

(final velocity - initial velocity) = time * acceleration

final velocity = time*acceleration + initial velocity

After plugging the found values in, we get 20.96 m/s/s, or 21 m/s

Answer:

» The image is laterally inverted.

» The image is upright.

» The image geometry is same as object geometry.

» Image distance is same as object distance.

» Image is not real, it's virtual ( not formed on screen ).

[tex].[/tex]

Answer:

335206922km

Explanation:

Pls see attached file

Answer:

6ms^-1

Explanation:

Given that the frequency difference is

( 563- 544) = 19

So alsoThe wavelength of each wave is = v/f = 344 /544

and there are 19 of this waves

So it is assumed that each motorcycle has moved 0.5 of this distance

in one second thus the speed of the motorcycles will be

=> 19/2 x 344/544 = 6.0 m/s

Answer:

42000N

Explanation:

First you calculate how much it would contract, and secondly you then calculate the force to stretch it by that amount.

1) linear thermal expansion coef brass 19e-6 /K

∆L = αL∆T = (19e-6)(1.85)(110) = 0.00387 meter or 3.87 mm

Second part involves linear elasticity.

for brass, young's modulus is 15e6 psi or 100 GPa

cross-sectional area of rod is π(0.008)² = 0.0002 m²

F = EA∆L/L

F = (100e9)(0.0002)(0.00387) / (1.85)

F = 42000 or 42 kN

Answer:

C

They allow light to pass only if their directions of polarizations are exactly 90° apart.

Answer:

B 5s

Explanation:

Because of the Displacement in the nth second of the free fall is 

Snth=21g(t12−t22)

Given that (tn−tn−1)=1

Displacement in 3 seconds of the free fall 

S=21gt2

S=21×10×32

S=45m

Given that: Snth=45

On solving that we get:

t1=5sec

Answer:

Here, m=9×10

−31

kg,

q=1.6×10

−19

C,v=3×10

7

ms

−1

,

b=6×10

−4

T

r=

qB

mv

=

(1.6×10

−19

)(6×10

−4

)

(9×10

−31

)×(3×10

7

)

=0.28m

v=

2πr

v

=

2πm

Bq

=

2×(22/7)×9×10

−31

(6×10

−4

)×(1.6×10

−19

)

=1.7×10

7

Hz

Ek=

2

1

mv

2

=

2

1

×(9×10

−31

)×(3×10

7

)

2

J

=40.5×10

−17

J=

1.6×10

−16

40.5×10

−17

keV

=2.53keV

Answer:

2,66

Explanation:

The refractive index= real depth/ apparent depth

real depth = refractive index * apparent depth

Let's assume index for water is 1.33

real depth = 2*1,33 = 2,66

Answer:

Apparent depth (Da) = 60.15 cm (Approx)

Explanation:

Given:

Distance from fish (D) = 80 cm

Find:

Apparent depth (Da)

Computation:

We know that,

Refractive index of water (n2) = 1.33

So,

Apparent depth (Da) = D(n1/n2)

Apparent depth (Da) = 80 (1/1.33)

Apparent depth (Da) = 60.15 cm (Approx)

The apparent depth of the fish is 60 cm.

To calculate the apparent depth of the fish, we use the formula below.

Formula:

Where:

Make D' The subject of the equation.

From the question,

Given:

Substitute these values into equation 2

Hence, the apparent depth of the fish is 60 cm

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Answer:

At the end of the handle farthest from the head of the hammer.

Explanation:

The force of the hammer is greatest the longer the radius is on a which would be the length of the handle. Simple mechanical advantage.

Answer:

Answer A : Fusion followed by beta decay (electron emission)

Explanation:

Notice that you want the Atomic number to increase, that is the number of protons in a nucleus. So if all four cases given experience the same fusion of nuclei, the only one that net increases the number of protons in the last stage, is the reaction that undergoes a beta decay (with emission of an electron) thus leaving a positive imbalance of positive charge (proton generated in the beta decay of a neutron).

Therefore, answer A is the correct one.

Answer:

A : Fusion followed by beta decay (electron emission)

Explanation:

Ap3x

Answer:

16 times.

Explanation:

The rate of the radiation dose is , R = 200 ×10^{-3} rad/hr

Time consumed, t = 40 hr

The magnitude of Q.F for the neutrons, Q.F = 2

Thus the effective radiation dose is:

[tex]R_{Eff} = Rt(Q.F) \\= 200 \times 10^{-3} \frac{rad}{hr} (40hr)(2) \\= 16 \ rad[/tex]

Thus, the effective dose allowable yearly = 16 times

Explanation:

F = ma

[tex]a = \frac{f}{m} [/tex]

[tex]a = \frac{1500}{500} = 3[/tex]

[tex]a = \frac{v2 - v1}{t} [/tex]

[tex]3 = \frac{v2 - 10}{10} [/tex]

v2 (final) = 40 m/s to the right direction