What is the separation in meters between two slits for which 594 nm orange light has its first maximum at an angle of 32.8°?

Answer:

s=((vf+vi)/2)t vf is final velocity and vi is initial velocity

The correct answer is D. An average city

Explanation:

A neutron star differs from others due to its massive density, this means a lot of matter is compressed in a small area. Indeed, neutron stars have a mass of around 1.4 to 2.8 times the mass of the sun. But these are considerably small as they only measure around 20 kilometers, which is the size of an average city. Additionally, neutron stars are this dense because they are the result of a regular star exploding, which leads to a super-dense core, or neutron star. In this context, the mass of a neutron star is compressed to the size of an average city.

Answer:

C. mv to the right

Explanation:

momentum of thr particle=m1v1

momentum of the wall=m2v2

m1v1+ m2v2 =m1u1+ m2u2 since the wall doesn't move it's momentum is zero.

m1v1 =m1u1

therefore change in that occurs as result of the collision is C. mv to the right

The total change in momentum of the particle of mass m that collides elastically with a vertical rigid wall perpendicularly from the left with velocity v is 2mv to the left (option B).  

The total change in momentum is given by:

[tex] \Delta p = p_{f} - p_{i} [/tex]  

In the initial state, the particle is moving to the right until it collides with the rigid wall, so:

[tex] p_{i} = mv [/tex]

In the final state, the particle moves backward after the collision with the wall, so:

[tex] p_{f} = -mv [/tex]  

The minus sign is because it is moving in the negative x-direction (to the left)

Hence, the total change in momentum is:

[tex] \Delta p = -mv - mv = -2mv [/tex]

Therefore, the total change in momentum of the particle is 2mv to the left (option B).

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Answer:

a. 7.62cm

b. Real and inverted

c. 2.76 cm

d. 3450

Explanation:

We proceed as follows;

a. the lens equation that relates the object distance to the image distance with the focal length is given as follows;

1/f = 1/p + 1/q

making q the subject of the formula;

q = pf/p-f

From the question;

p = 4.70m

f = 7.5cm = 0.075m

Substituting these, we have ;

q = (4.7)(0.075)/(4.7-0.075) = 0.3525/4.625 = 0.0762 = 7.62 cm

b. The image is real and inverted since the image distance is positive

c. We want to calculate how tall the image is

Mathematically;

h1 = (q/p)h0

h1 = (7.62/4.70)* 1.7

h1 = 2.76 cm

d. We want to calculate the number of pixels that fit into this image

Mathematically:

n = h1/8 micro meter

n = 2.76cm/8 micro meter = 2.76 * 10^-2/8 * 10^-6 = 3450

Answer:

63 cm

Explanation:

Mathematically;

The focal length of a double convex lens is given as;

1/f = (n-1)[1/R1 + 1/R2]

where n is the refractive index of the medium given as 1.52

R1 and R2 represents radius of curvature which are given as 60cm and 72cm respectively.

Plugging these values into the equation, we have:

1/f = (1.52-1)[1/60 + 1/72)

1/f = 0.0158

f = 1/0.0158

f = 63.29cm which is approximately 63cm

Answer:

Explanation:

The moon gets the light from the sun. When the moon lies between the sun and the earth, only the back portion of the moon gets the light from the sun. So the side facing the sun does not get any light and appears to be dark or does not appear at all.

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Answer:

The moon is between the sun, and Earth and reflects light back towards the sun.

Explanation:

A P E X test answer. Just took the test and this is the correct answer.

Answer:

81 N

7.1 m/s²

Explanation:

Draw a free body diagram of the sphere.  There are two forces:

Weight force mg pulling straight down,

and tension force T pulling up along the rope.

Sum of forces in the centripetal direction:

∑F = ma

T − mg sin 45° = m v² / r

T = m (g sin 45° + v² / r)

T = (7 kg) (10 m/s² sin 45° + (3 m/s)² / 2 m)

T = 81 N

Sum of forces in the tangential direction:

mg cos 45° = ma

a = g cos 45°

a = (10 m/s²) cos 45°

a = 7.1 m/s²

Answer:

the final angular velocity of the particle is approximately 38.18  Rad/s

Explanation:

To start with, let's make sure that units of angle measure are the same, converting everything into radians:

[tex]4500^o\, \frac{\pi}{180^o}= 25\,\pi[/tex]

And now we can use the kinematic formulas for rotational motion:

[tex]\theta-\theta_0=\omega_0\,t+\frac{1}{2} \alpha\,t^2[/tex]

Therefore we can find the initial angular velocity [tex]\omega_0[/tex]  of the particle:

[tex]\theta-\theta_0=\omega_0\,t+\frac{1}{2} \alpha\,t^2\\25\,\pi=\omega_0\,(3)+\frac{1}{2} (8)\,(3)^2\\25\,\pi-36=\omega_0\,(3)\\\omega_0=\frac{25\,\pi-36}{3} \\\omega_0\approx 14.18\,\,\,rad/s[/tex]

and now we can estimate the final angular velocity using the kinematic equation for angular velocity;

[tex]\omega=\omega_0\,+\alpha\,t\\\omega=14.18+8\,(3)\\\omega=38.18\,\,\,rad/s[/tex]

Answer:

The charge is  [tex]Q = 2.177 *10^{-9} \ C[/tex]

Explanation:

From the question we are told that

     The electric potential is  [tex]V = 25.0 \ kV = 25.0 *10^{3}\ V[/tex]

     The  mass of the drop is  [tex]m = 0.168 \ m g = 0.168 *10^{-3} \ g = 0.168 *10^{-6}\ kg[/tex]

      The  speed is  [tex]v = 18.8 \ m/s[/tex]

Generally the charge on the paint drop due to the electric potential which will give it the speed stated in the question  is mathematically represented as

       [tex]Q = \frac{m v^2 }{ 2 * V }[/tex]

Substituting values

      [tex]Q = \frac{0.168 *10^{-6} (18)^2 }{ 2 * 25*10^3 }[/tex]

       [tex]Q = 2.177 *10^{-9} \ C[/tex]

Answer:

Explanation:

We shall apply conservation of momentum law in vector form to solve the problem .

Initial momentum = 0

momentum of 12 g piece

= .012 x 37 i since it moves along x axis .

= .444 i

momentum of 22 g

= .022 x 34 j

= .748 j

Let momentum of third piece = p

total momentum

= p + .444 i + .748 j

so

applying conservation law of momentum

p + .444 i + .748 j  = 0

p = - .444 i -  .748 j  

magnitude of p

= √ ( .444² + .748² )

= .87 kg m /s

mass of third piece = 58 - ( 12 + 22 )

= 24 g = .024 kg

if v be its velocity

.024 v = .87

v = 36.25 m / s .

Answer:

chk photo

Explanation:

The values of β for which the system will exhibit oscillatory motion are those greater than 0.

To determine the values of β for which the system will exhibit oscillatory motion, you need to perform a damped oscillation analysis on the system.

The equation of motion for a damped oscillator is given by:

F = ma = -kx - βv

where F is the force, m is the mass, a is the acceleration, k is the spring constant, x is the displacement of the mass from its equilibrium position, β is the damping coefficient, and v is the velocity of the mass.

To determine the values of β for which the system will exhibit oscillatory motion, you need to solve for the roots of the characteristic equation, which is obtained by setting the acceleration (a) equal to zero:

0 = -kx - βv

βv + kx = 0

x(β + k) = 0

The roots of this equation are x = 0 and x = -(β + k). If x = 0 is a root of the characteristic equation, then the system will exhibit steady-state behavior (i.e., the mass will come to rest at its equilibrium position and not oscillate). If x = -(β + k) is a root of the characteristic equation, then the system will exhibit oscillatory behavior (i.e., the mass will oscillate around its equilibrium position).

Therefore, the values of β for which the system will exhibit oscillatory motion are those for which x = -(β + k) is a root of the characteristic equation. This means that β must be such that:

-(β + k) < 0

β > -k

Since k is a positive value (the spring constant is always positive), the inequality simplifies to:

β > 0

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Answer:

28.3°C

Explanation:

Using

T(t) = (T(0) - 20)*(e^(-k*t)) + 20

for some positive number k, and some initial temperature T(0).

Boundary conditions:

T(4) = T(0) - 5 _______ (i)

T(8) = T(0) - 7 _______ (ii)

==> solving for T(0) and k :

(i):

(T(0) - 20)*(e^(-k*4)) + 20 = T(0) - 5 ==>

(T(0) - 20)*(e^(-k*4)) = T(0) - 20 - 5

(T(0) - 20)*(e^(-k*4)) = (T(0) - 20) - 5

5 = (T(0) - 20) - (T(0) - 20)*(e^(-k*4))

5 = (T(0) - 20) * ( 1 - e^(-k*4) )

(ii):

(T(0) - 20)*(e^(-k*8)) + 20 = T(0) - 7

(T(0) - 20)*(e^(-k*8)) = (T(0) - 20) - 7

7 = (T(0) - 20) - (T(0) - 20)*(e^(-k*8))

7 = (T(0) - 20) * (1 - e^(-k*8))

In both results, subsitute x = e^(-4k) and C = (T(0) - 20)

(i): 5 = C * (1 - x)

(ii): 7 = C * (1 - x^2) = C * (1-x)*(1+x)

Substitute C*(1-x) from (i) into (ii):

(ii): 7 = 5*(1+x) ==> (1+x) = 7/5 ==> x = 2/5

back into (i):

(i): 5 = C * (1 - 2/5) ==> 5 = C * 3/5 ==> C = 25/3

C = T(0) - 20 ==>

T(0) = C + 20 = 25/3 + 20 = 25/3 + 60/3 = 85/3

= 28.3°C

Answer:

The frequency does not change, but the wavelength does

Explanation:

Here are the options

A. When a light wave travels from a medium with a lower index of refraction to a medium with a higher index of refraction, the frequency changes and the wavelength does not.

B. The frequency does change, but the wavelength remains unchanged.

C. Both the frequency and wavelength change.

D. When a light wave travels from a medium with a lower index of refraction to a medium with a higher index of refraction, neither the wavelength nor the frequency changes.

E. The frequency does not change, but its wavelength does.

When light goes through one medium to the next, the frequency doesn't really change seeing as frequency is dependent on wavelength and light wave velocity. And when the wavelength shifts from one medium to the next.

[tex]n= \frac{C}{V} \ and\ \frac{\lambda_o}{\lambda_m}[/tex]

where [tex]\lambda_o[/tex] indicates wavelength in vacuum

[tex]\lambda_m[/tex] indicates wavelength in medium

n indicates refractive index

v indicates velocity of light wave

c indicates velocity of light

And wavelength is medium-dependent. Frequency Here = v[tex]\lambda[/tex] and shift in wavelength and velocity, not shifts in overall frequency.

Therefore the correct option is E

Answer:

a)   Δt = 24.96 s , b)  τ = 0.078 N m

Explanation:

This is a rotational kinematics exercise

        θ = w₀ t - ½ α t²

Let's reduce the magnitudes the SI system

       θ = 60 rev (2π rad / 1 rev) = 376.99 rad

       w₀ = 7.0 rot / s (2π rad / 1 rpt) = 43.98 rad / s

      α = (w₀ t - θ) 2 / t²

let's calculate the annular acceleration

      α = (43.98 10 - 376.99) 2/10²

      α = 1,258 rad / s²

Let's find the time it takes to reach zero angular velocity (w = 0)

        w = w₀ - alf t

         t = (w₀ - 0) / α

         t = 43.98 / 1.258

         t = 34.96 s

this is the total time, the time remaining is

         Δt = t-10

         Δt = 24.96 s

To find the braking torque, we use Newton's law for angular motion

        τ = I α

the moment of inertia of a circular ring is

       I = M r²

we substitute

         τ = M r² α

we calculate

        τ = 0.625  0.315²  1.258

        τ = 0.078 N m

The total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.

Given data:

The initial angular speed of wheel is, [tex]\omega = 7.0 \;\rm rps[/tex]   (rps means rotation per second).

The time interval is, t' = 10.0 s.

The number of rotations made by wheel is, n = 60.0.

The mass of bike wheel is, m = 0.625 kg.

The radius of wheel is, r = 0.315 m.

The problem is based on rotational kinematics. So, apply the second rotational equation of motion as,

[tex]\theta = \omega t-\dfrac{1}{2} \alpha t'^{2}[/tex]

Here, [tex]\theta[/tex] is the angular displacement, and its value is,

[tex]\theta =2\pi \times 60\\\\\theta = 376.99 \;\rm rad[/tex]

And, angular speed is,

[tex]\omega = 2\pi n\\\omega = 2\pi \times 7\\\omega = 43.98 \;\rm rad/s[/tex]

Solving as,

[tex]376.99 = 43.98 \times 10-\dfrac{1}{2} \alpha \times 10^{2}\\\\\alpha = 1.25 \;\rm rad/s^{2}[/tex]

Apply the first rotational equation of motion to obtain the value of time to reach zero final velocity.

[tex]\omega' = \omega - \alpha t\\\\0 = 43.98 - 1.25 \times t\\\\t = 35.18 \;\rm s[/tex]

Then total time is,

T = t - t'

T = 35.18 - 10

T = 25.18 s

Now, use the standard formula to obtain the value of braking torque as,

[tex]T = m r^{2} \alpha\\\\T = 0.625 \times (0.315)^{2} \times 1.25\\\\T = 0.0775 \;\rm Nm[/tex]

Thus, we can conclude that the total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.

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Answer:

λmax = 372 nm

Explanation:

First we find the energy of photon:

E = hc/λ

where,

E = Energy of Photon = ?

λ = Wavelength of Light = 233 nm = 2.33 x 10⁻⁷ m

c = speed of light = 3 x 10⁸ m/s

h = Planks Constant = 6.626 x 10⁻³⁴ J.s

Therefore,

E = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(2.33 x 10⁻⁷ m)

E = 8.5 x 10⁻¹⁹ J

Now, from Einstein's Photoelectric Equation:

E = Work Function + Kinetic Energy

8.5 x 10⁻¹⁹ J = Work Function + (1.98 eV)(1.6 x 10⁻¹⁹ J/1 eV)

Work Function = 8.5 x 10⁻¹⁹ J - 3.168 x 10⁻¹⁹ J

Work Function = 5.332 x 10⁻¹⁹ J

Since, work function is the minimum amount of energy required to emit electron. Therefore:

Work Function = hc/λmax

λmax = hc/Work Function

where,

λmax = maximum wavelength of light that will produce photoelectrons = ?

Therefore,

λmax = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(5.332 x 10⁻¹⁹ J)

λmax = 3.72 x 10⁻⁷ m

λmax = 372 nm

Answer:

Objects that are closer together have a stronger force of gravity between them.

Explanation:

For example, the moon is closer to Earth than it is to the more massive sun, so the force of gravity is greater between the moon and Earth than between the moon and the sun.

Answer:

The velocity is  [tex]v_h = 19.2 \ m/s[/tex]

Explanation:

From the question we are told that

   The speed of the roller coaster at ground level  is [tex]v = 26 \ m/s[/tex]

Generally we can define the roller coaster speed at ground level using the an equation of motion as

     [tex]v^2 = u^2 + 2 g s[/tex]

 u is  zero given that the roller coaster started from rest

      So

            [tex]26^2 = 0 + 2 * g * s[/tex]

So  

           [tex]s = \frac{26^2}{ 2 * g }[/tex]

=>       [tex]s = 37.6 \ m[/tex]

Now the displacement half way is mathematically represented as

    [tex]s_{h} = \frac{37.6}{2}[/tex]

     [tex]s_{h} = 18.8 \ m[/tex]

So

      [tex]v_h ^2 = u^2 + 2 * g * s_h[/tex]

Where  [tex]v_h[/tex] is the velocity at the half way point

=>  [tex]v_h = \sqrt{ 0 + 2 * 9.8 * 18.8 }[/tex]

=>   [tex]v_h = 19.2 \ m/s[/tex]

Answer:

1.The temperature of each sample will increase by the same amount

Explanation:

This is because, since their specific heat capacities are the same and we have the same mass of each substance, and the same amount of energy due to heat flow is supplied to both the glass and brick at room temperature, their temperatures would thereby increase by the same amount.

This is shown by the calculation below

Q = mcΔT

ΔT = Q/mc where ΔT = temperature change, Q = amount of heat, m = mass of substance and c = specific heat capacity of substance.

Since Q, m and c are the same for both substances, thus ΔT will be the same.

So, the temperature of each sample will increase by the same amount

Polarized sunglasses creates filter of vertical openings for light. The light rays will reach the eyes of human vertically only.

The sun rays will not reach human eye directly which will create a shield for sun light burden on human eye.

Polarized sunglasses are best used for blocking and eliminating certain wavelengths of light.

Therefore the correct answer is option C. Polarizes Sunglasses are polarized and it filter out certain wavelengths of light.

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Answer:

it is either constant or zero

Explanation:

Answer:

65.3

Explanation:

1 foot = 12 inches

Sammy is 5 feet tall.

5 feet = ? inches

Multiply the feet value by 12 to find in inches.

5 × 12

= 60

Add 5.3 inches to 60 inches.

60 + 5.3

= 65.3

Answer:

It will be 》》》》1.664716m

Answer:

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.

Explanation:

The decay of radioisotopes are represented by the following ordinary differential equation:

[tex]\frac{dm}{dt} = -\frac{t}{\tau}[/tex]

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]\tau[/tex] - Time constant, measured in seconds.

[tex]m[/tex] - Mass of the radioisotope, measured in grams.

The solution of this expression is:

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]

Where [tex]m_{o}[/tex] is the initial mass of the radioisotope, measured in kilograms.

The ratio of current mass to initial mass is:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

The time constant is now calculated in terms of half-life:

[tex]\tau = \frac{t_{1/2}}{\ln2}[/tex]

Where [tex]t_{1/2}[/tex] is the half-life of the radioisotope, measured in seconds.

Given that [tex]t_{1/2} = 88\,s[/tex], the time constant of the radioisotope is:

[tex]\tau = \frac{88\,s}{\ln 2}[/tex]

[tex]\tau \approx 126.957\,s[/tex]

Now, if [tex]\frac{m(t)}{m_{o}(t)} = \frac{1}{16}[/tex] and [tex]\tau \approx 126.957\,s[/tex], the time is:

[tex]t = -\tau \cdot \ln\frac{m(t)}{m_{o}}[/tex]

[tex]t = -(126.957\,s)\cdot \ln \frac{1}{16}[/tex]

[tex]t \approx 352\,s[/tex]

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.

Answer:

1.8/0.61 =2.95 ft

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Answer:

2.2 ft

Explanation:

0.65 lb / 1 ft = 1.4 lb / x

x ≈ 2.2 ft

Answer:

IMA is always larger than the AMA

Explanation:

IMA is Ideal Mechanical Advantage and it equals the length of effort that is divided by the length of resistance which is given by the formula

IMA= Fr/Fe

Where Fr is the resistance force

Fe is the effort force.

IM= de/dr

Where de is the distance of the applied effort  

dr is the distance traveled by the load.

In any real machine, the effort is needed to overcome friction and because of this, the ideal mechanical advantage(IMA) is always larger than the actual mechanical advantage (AMA)

Answer:

The amplitude of the oscillating electric field is 1316.96 N/C

Explanation:

Given;

frequency of the wave, f = 2.4 Hz

intensity of the wave, I = 2300 W/m²

Amplitude of oscillating magnetic field is given by;

[tex]B_o = \sqrt{\frac{2\mu_o I}{c} }[/tex]

where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

I is intensity of wave

c is speed of light = 3 x 10⁸ m/s

[tex]B_o = \sqrt{\frac{2*4\pi *10^{-7}*2300}{3*10^8} } \\\\B_o = 4.3899 *10^{-6} \ T[/tex]

The amplitude of the oscillating electric field is given by;

E₀ = cB₀

E₀ = 3 x 10⁸ x 4.3899 x 10⁻⁶

E₀ = 1316.96 N/C

Therefore, the amplitude of the oscillating electric field is 1316.96 N/C

Answer:

sinco

Explanation:

Answer:

259 Hz or 269 Hz

Explanation:

Beat: This is the phenomenon obtained when two notes of nearly equal frequency are sounded together. The S.I unit of beat is Hertz (Hz).

From the question,

Beat = f₂-f₁................ Equation 1

Note: The frequency of the other instrument is either f₁ or f₂.

If the unknown instrument's frequency is f₁,

Then,

f₁ = f₂-beat............ equation 2

Given: f₂ = 264 Hz, Beat = 5 Hz

Substitute into equation 2

f₁ = 264-5

f₁ = 259 Hz.

But if the unknown frequency is f₂,

Then,

f₂ = f₁+Beat................. Equation 3

f₂ = 264+5

f₂ = 269 Hz.

Hence the beat could be 259 Hz or 269 Hz

Answer:

a) 360.7 J/s

b) 16.23 °C

c) 34.48 g

Explanation:

The mass of the person = 80 kg

The person is a perfect emitter, ε = 1

surface area of the person = 2.5 m^2

a) If he emits radiation at 37 °C, [tex]T_{out}[/tex] = 37 + 273 = 310 K

and receives radiation at 13 °C, [tex]T_{in}[/tex] = 13 + 273 = 286 K

Rate of energy loss E = Aεσ([tex]T^{4} _{out}[/tex] - [tex]T^{4} _{in}[/tex] )

where σ = 5.67 x 10^-8 J/(s m^2 K^4)

substituting values, we have

E = 2.5 x 1 x 5.67 x 10^-8 x ([tex]310^{4}[/tex] - [tex]286^{4}[/tex]) = 360.7 J/s

b) If they have specific heat about equal to that of water = 1 Cal/kg-°C

but 1 Cal = 1 kcal = 10^3 cal

specific heat of person is therefore = 10^3 cal/kg-°C

heat loss = 360.7 J/s = 360.7 x 3600 = 1298520 J/hr

heat lost in 1 hour = 1 x 1298520 = 1298520 J

This heat lost = mcΔT

where ΔT is the temperature fall

m is the mass

c is the specific heat equivalent to that of water

the specific heat is then = 10^3 cal/kg-°C

equating, we have

1298520 = 80 x 10^3 x ΔT

1298520 = 80000ΔT

ΔT = 1298520/80000 = 16.23 °C

c) 1298520 J = 1298520/4184 = 310.35 Cal

density of fat = 9 Cal/g

gram of fat = 310.35/9 = 34.48 g