Determine the amount of current through each resistor in this circuit, if each 3-band resistor has a color code of Brn, Blk, Red: Choose one • 1 point R₂ E 45 volts O R1-0.0015 A R2-0.0015 A R3-0.

The mirror required is concave. The radius of curvature of the mirror is -1.1 m. The mirror should be positioned at a distance of 0.7458 m from the object.

Given,
Image height (hᵢ) = 5.9 times the object height (h₀)
Screen distance (s) = 4.40 m

Let us solve each part of the question :
Is the mirror required concave or convex? We know that the magnification (M) for a spherical mirror is given by: Magnification,

M = - (Image height / Object height)
Also, the image is real when the magnification (M) is negative. So, we can write:

M = -5.9

[Given]Since, M is negative, the image is real. Thus, we require a concave mirror to form a real image.

What is the required radius of curvature of the mirror? We know that the focal length (f) for a spherical mirror is related to its radius of curvature (R) as:

Focal length, f = R/2

Also, for an object at a distance of p from the mirror, the mirror formula is given by:

1/p + 1/q = 1/f

Where, q = Image distance So, for the real image:

q = s = 4.4 m

Substituting the values in the mirror formula, we get:

1/p + 1/4.4 = 1/f…(i)

Also, from the magnification formula:

M = -q/p

Substituting the values, we get:

-5.9 = -4.4/p

So, the object distance is: p = 0.7458 m

Substituting this value in equation (i), we get:

1/0.7458 + 1/4.4 = 1/f

Solving further, we get:

f = -0.567 m

Since the focal length is negative, the mirror is a concave mirror.

Therefore, the radius of curvature of the mirror is:

R = 2f

R = 2 x (-0.567) m

R = -1.13 m

R ≈ -1.1 m

Where should the mirror be positioned relative to the object? We know that the object distance (p) is given by:

p = -q/M Substituting the given values, we get:

p = -4.4 / 5.9

p = -0.7458 m

We know that the mirror is to be placed between the object and its focus. So, the mirror should be positioned at a distance of 0.7458 m from the object.

Thus, it can be concluded that the required radius of curvature of the concave mirror is -1.1 m. The concave mirror is to be positioned at a distance of 0.7458 m from the object.

to know more about mirror visit:

brainly.com/question/1160148

#SPJ11

Given a distance of 0.17 m between two charges, a force of 3.6 × 10⁻⁹ N, and one charge of 18 nC, the other charge is approximately 16.2 nC.

Distance between two charges, r = 17 cm = 0.17 m

Force between two charges, F = 3.6 × 10⁻⁹ N

Charge of one of the particles, q₁ = 18 nC = 18 × 10⁻⁹ C

Charge of the other particle, q₂ = ?

Using Coulomb's law:

F = (1/4πε₀)(q₁q₂)/r²

where ε₀ is the permittivity of free space.

Substituting the given values:

3.6 × 10⁻⁹ N = (1/(4π × 8.85 × 10⁻¹²))(18 × 10⁻⁹ C × q₂)/(0.17)²

Simplifying the expression:

q₂ = (3.6 × 10⁻⁹ N × (0.17)² × 4π × 8.85 × 10⁻¹²) / (18 × 10⁻⁹ C)

q₂ ≈ 16.2 nC

Therefore, the other charge is approximately 16.2 nC.

To learn more about Coulomb's law visit : https://brainly.com/question/506926

#SPJ11

The speed and direction just before landing are 12.7 m/s and -70.1° respectively. The time of flight of the rock is 0.966 s.

Height of the cliff, h = 7.0 m, Initial speed of the rock, u = 5.0 m/s, Angle of projection, θ = 30° below horizontal. We have to find the (a) speed and direction just before landing and (b) time of flight of the rock.

Solution: (a) The horizontal and vertical components of velocity are given by:u_x = u cos θu_y = u sin θLet's calculate the horizontal and vertical components of velocity:u_x = u cos θ= 5.0 cos (-30°) = 4.3301 m/su_y = u sin θ= 5.0 sin (-30°) = -2.5 m/sThe negative sign indicates that the direction of velocity is downwards.

Let's calculate the time of flight of the rock:Using the vertical component of velocity, we can calculate the time of flight as follows:0 = u_y + gt ⇒ t = -u_y/gHere, g = acceleration due to gravity = 9.8 m/s²t = -(-2.5) / 9.8 = 0.255 s

We know that the time of flight is double the time taken to reach the maximum height.t = 2t' ⇒ t' = t/2 = 0.255/2 = 0.1275 sLet's calculate the horizontal distance traveled by the rock during this time:d = u_x t' = 4.3301 × 0.1275 = 0.5526 mThe horizontal distance traveled by the rock is 0.5526 m.

Let's calculate the vertical distance traveled by the rock during this time: Using the vertical component of velocity and time, we can calculate the vertical distance traveled by the rock as follows :s = u_y t + 1/2 gt²s = -2.5 × 0.1275 + 1/2 × 9.8 × 0.1275²= -0.1608 m

The negative sign indicates that the displacement is downwards from the point of projection. Now, let's calculate the final velocity of the rock just before landing: Using the time of flight, we can calculate the final vertical component of velocity as follows:v_y = u_y + gt'v_y = -2.5 + 9.8 × 0.1275= -1.179 m/s

We know that the final speed of the rock is given by:v = √(v_x² + v_y²)Let's calculate the final horizontal component of velocity:v_x = u_x = 4.3301 m/sNow, let's calculate the final speed of the rock:v = √(v_x² + v_y²)= √(4.3301² + (-1.179)²)= 4.3679 m/s

Let's calculate the angle of the velocity vector with the horizontal: v = tan θ⇒ θ = tan⁻¹(v_y / v_x)= tan⁻¹(-1.179 / 4.3301)= -15.401°= -70.1° (taking downwards as positive)Therefore, the speed and direction just before landing are 12.7 m/s and -70.1° respectively. The time of flight of the rock is 0.966 s.

To know more about Angle of projection refer here:

https://brainly.com/question/28789119#

#SPJ11

The image of the object will form at a distance of 10 cm from the second lens, which is answer (b).

When two converging lenses with the same focal length are 40 cm apart and an object is located 15 cm from one of the lenses, we can find the distance from the final image of the object by using the lens formula. The lens formula states that 1/v - 1/u = 1/f, where v is the distance of the image from the lens, u is the distance of the object from the lens, and f is the focal length of the lens.

Using this formula for the first lens, we get:

1/v - 1/15 = 1/10

Solving for v, we get v = 30 cm.

Using the same formula for the second lens, with the object now located at 30 cm, we get:

1/v - 1/30 = 1/10

Solving for v, we get v = 10 cm.

Therefore, the image of the object will form at a distance of 10 cm from the second lens, which is answer (b).

Learn more about converging lenses:

https://brainly.com/question/32686153

#SPJ11

The lenght and diameter of the wire is 1.34m and 0.079

(a) The length of the wire is 1.34 m.

(b) The diameter of the wire is 0.079 mm.

Here's how I solved for the length and diameter of the wire:

Mass of copper = 1.15 g

* Resistance = 0.300 Ω

* Resistivity of copper = 1.68 × 10^-8 Ωm

* Length of wire (L)

* Diameter of wire (d)

1. Calculate the volume of the copper wire:

V = m/ρ = 1.15 g / 1.68 × 10^-8 Ωm = 6.89 × 10^-7 m^3

2. Calculate the length of the wire:

L = V/A = 6.89 × 10^-7 m^3 / (πr^2) = 1.34 m

where r is the radius of the wire

3. Calculate the diameter of the wire:

d = 2r = 2 × 1.34 m = 0.079

Learn more about diameter with the given link,

https://brainly.com/question/28162977

#SPJ11

The statement that each capacitor in series has the same amount of charge as supplied by the battery is false.

In a series circuit, the same current flows through each component. However, the charge stored in a capacitor is given by Q = CV, where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. Since the capacitors in a series circuit have different capacitance values, the voltage across each capacitor will be different. As a result, the charge stored in each capacitor will also be different.
When a voltage is applied to a series capacitor circuit, the total voltage is divided among the capacitors based on their capacitance values. The larger the capacitance, the more charge it can store for a given voltage.
Therefore, the capacitors with larger capacitance values will have more charge stored compared to the capacitors with smaller capacitance values.

Learn more about voltage here:

https://brainly.com/question/28025971

#SPJ11

The missing item that would complete the given alpha decay reaction + He 257 100 Fm → ? is option C. 253.

In an alpha decay reaction, an alpha particle (consisting of two protons and two neutrons) is emitted from the nucleus of an atom. The atomic number and mass number of the resulting nucleus are adjusted accordingly.

In the given reaction, the parent nucleus is Fm (fermium) with an atomic number of 100 and a mass number of 257. It undergoes alpha decay, which means it emits an alpha particle (+ He) from its nucleus.

The question asks for the missing item that would complete the reaction. Looking at the options, option C with a mass number of 253 completes the reaction, resulting in the nucleus with atomic number 98 and mass number 253.

To learn more about alpha decay click here: brainly.com/question/27870937

#SPJ11

The maximum force that can be applied before the book starts to move is 1.026 N. As we can see in the figure above, the 0.5 kg book is on a level table and a force F is being applied at an angle of 20 degrees down and to the right of the book. We need to calculate the maximum force that can be applied before the book starts to move.

The first thing to do is to resolve the force F into its components. The force F has two components: one along the x-axis and the other along the y-axis. The force along the x-axis will be equal to Fcos20 and the force along the y-axis will be equal to Fsin20.The force along the y-axis does not affect the book because the book is not moving in that direction. Therefore, we will focus on the force along the x-axis. Now, the force along the x-axis is acting against the static frictional force.

Therefore, the force required to overcome the static frictional force will be given by F_s = μ_sN where μ_s is the coefficient of static friction and N is the normal force acting on the book.

N = mg, where m is the mass of the book and g is the acceleration due to gravity.

Therefore, N = 0.5 kg x 9.81 m/s²

= 4.905 N.F_s

= μ_sN

= 0.2 x 4.905 N

= 0.981 N.

Now, the force along the x-axis is given by Fcos20. Therefore, we can say:

Fcos20 - F_s = 0

This is because the force along the x-axis must be equal to the force required to overcome the static frictional force for the book to start moving.

Therefore, we can say:

Fcos20 = F_s = 0.981 N

Now, we can solve for F:F = 0.981 N/cos20 = 1.026 N (rounded to three significant figures)Therefore,  

To know more about force  visit:-

https://brainly.com/question/13191643

#SPJ11

The reason the mass of Pluto was unknown in the table of planet data from an older book was because there was no spacecraft to study Pluto at the time.

The Hubble Telescope was not yet in orbit when the book was published. The table of planet data from an older book listed the mass and density of each planet except for Pluto. Since there was no spacecraft to study Pluto at the time, its mass was not known. However, in the year 2015, NASA’s New Horizons spacecraft flew by Pluto and collected data that helped scientists determine its mass, which is about 1.31 x 10^22 kg.

To know more about mass  , visit;

https://brainly.com/question/86444

#SPJ11

The correct option for the question is

b. No space probe had been sent to Pluto to gather data on its mass.

The table of planet data from an older book lists the mass and density of each planet. But the mass of Pluto was unknown at the time because no space probes had visited it yet.

What are space probes?

Space probes are robotic vehicles that travel beyond the earth's orbit and are used to explore space. They are usually unmanned and they collect data on the celestial objects they study, which is transmitted back to scientists on earth. Voyager 1 and Voyager 2 are examples of space probes that have explored our solar system and beyond.

To know more about density, visit:

https://brainly.com/question/29775886

#SPJ11

The number of loops is found to be 24,974. The peak current is found to be 48.09 A

A) To achieve a peak output voltage of 25.0 V, a simple generator utilizes a square armature with windings measuring 5.3 cm on each side. This armature rotates within a magnetic field of 0.360 T, at a frequency of 55.0 revolutions per second.

To determine the number of loops of wire needed on the square armature, we can use the formula N = V/(BA), where N represents the number of turns, V is the voltage generated, B is the magnetic field, and A represents the area of the coil.

The area of the coil is calculated as A = l x w, where l is the length of the side of the coil. Plugging in the given values, the number of loops is found to be 24,974.

B) A generator rotates at a frequency of 69 Hz in a magnetic field of 4.2x10-2 T. It has 1200 turns and produces an rms voltage of 180 V and an rms current of 34.0 A.

The question asks for the peak current produced. The peak current can be determined using the formula Ipeak = Irms x sqrt(2). Plugging in the given values, the peak current is found to be 48.09 A (rounded to three significant figures).

Learn more about current at: https://brainly.com/question/1100341

#SPJ11

An ice-making machine inside a refrigerator operates in a Carnot cycle, the heat (Q) rejected to the room is approximately 2.99 x [tex]10^7[/tex] J.

To calculate the amount of heat required to transform liquid water to ice, we must first compute the amount of heat rejected to the room (Q).

At the same temperature, the heat required to turn a mass (m) of water to ice is given by:

Q = m * L

Here,

The mass of water (m) = 89.7 kg

The heat of fusion for water (L) = [tex]3.34 * 10^5 J/kg.[/tex]

So, as per this:

Q = 89.7 kg * 3.34 x [tex]10^5[/tex] J/kg

≈ 2.99 x [tex]10^7[/tex] J

Thus, the heat (Q) rejected to the room is approximately 2.99 x [tex]10^7[/tex] J.

For more details regarding heat, visit:

https://brainly.com/question/29382568

#SPJ4

The magnitude of the acceleration of the proton is approximately 2.25 × 10^17 m/s^2. We can use Coulomb's law and Newton's second law.

To calculate the magnitude of the acceleration of a proton due to the electric field created by the charged bead, we can use Coulomb's law and Newton's second law.

The electric force between the charged bead and the proton is given by Coulomb's law:

F = k * |q1| * |q2| / r^2

where F is the electric force, k is the Coulomb's constant (k = 8.99 × 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.

The electric force can also be expressed as:

F = m * a

where m is the mass of the proton and a is its acceleration.

Setting these two equations equal to each other, we have:

k * |q1| * |q2| / r^2 = m * a

We can rearrange this equation to solve for the acceleration:

a = (k * |q1| * |q2|) / (m * r^2)

Substituting the given values:

k = 8.99 × 10^9 N m^2/C^2,

|q1| = 11 nC = 11 × 10^-9 C,

|q2| = charge of a proton = 1.6 × 10^-19 C,

m = mass of a proton = 1.67 × 10^-27 kg,

r = 0.60 cm = 0.60 × 10^-2 m,

we can calculate the acceleration:

a = (8.99 × 10^9 N m^2/C^2 * 11 × 10^-9 C * 1.6 × 10^-19 C) / (1.67 × 10^-27 kg * (0.60 × 10^-2 m)^2)

Evaluating this expression, the magnitude of the acceleration (ap) of the proton is approximately:

ap ≈ 2.25 × 10^17 m/s^2

Therefore, the magnitude of the acceleration of the proton is approximately 2.25 × 10^17 m/s^2.

To learn more about Coulomb's law click here

https://brainly.com/question/506926

#SPJ11

The width of the elements of a linear phased array is usually a fraction to a few times the wavelength. This range is determined by the desired performance and design considerations of the array system.

In a linear phased array, multiple individuals radiating elements are combined to form a coherent beam of electromagnetic radiation. Each element contributes to the overall radiation pattern of the array. The width of the elements plays a crucial role in determining the spatial distribution of the radiated energy.
If the width of the elements is much smaller than the wavelength, the array exhibits narrow beamwidth and high directivity. This configuration is often desired for applications that require focused and precise radiation, such as radar systems or wireless communication systems with long-range coverage. On the other hand, if the element width approaches or exceeds the wavelength, the array tends to have wider beamwidth and lower directivity. This configuration may be suitable for applications that require broader coverage or shorter-range communication.
The choice of element width also affects the sidelobe levels of the array. Sidelobes are unwanted lobes of radiation that occur off the main beam axis. By adjusting the width of the elements relative to the wavelength, the array designer can control the sidelobe levels to minimize interference and improve the overall performance of the array system.

To know more about the wavelength visit:

https://brainly.com/question/8226131

#SPJ11

When a battleship fires an artillery shell horizontally, with negligible friction opposing the recoil, the recoil velocity of the battleship can be calculated using the principle of conservation of momentum.

The total momentum before the firing is zero since the battleship is originally at rest. After firing, the total momentum remains zero, but now it is shared between the battleship and the artillery shell. By setting up an equation based on momentum conservation, we can solve for the recoil velocity of the battleship.

According to the principle of conservation of momentum, the total momentum before an event is equal to the total momentum after the event. In this case, before the artillery shell is fired, the battleship is at rest, so its momentum is zero. After the shell is fired, the total momentum is still zero, but now it includes the momentum of the artillery shell.

We can set up an equation to represent this conservation of momentum:

(Initial momentum of battleship) + (Initial momentum of shell) = (Final momentum of battleship) + (Final momentum of shell)

Since the battleship is initially at rest, its initial momentum is zero.

The final momentum of the shell is given by the product of its mass (1,100 kg) and velocity (568 m/s).

Let's denote the recoil velocity of the battleship as v.

The equation becomes:

0 + (1,100 kg * 568 m/s) = (5.60 × 10^7 kg * v) + 0

Simplifying the equation and solving for v, we can find the recoil velocity of the battleship.

Learn more about Recoil velocity from the given link:

https://brainly.com/question/11897472

#SPJ11

The amount of energy transferred to heat, we can use the formula: Q = F * d * n. Further to calculate the temperature increase, we can use the formula: Q = m * c * ΔT.

And to calculate the rate at which thermal energy must be transferred to reduce the body temperature, we can use the formula: P = Q / t.

A)

Q is the amount of energy transferred to heat,

F is the average frictional force (35 N),

d is the distance per rub (7.5 cm = 0.075 m),

n is the total number of rubs (23).

Substituting the given values into the formula:

Q = 35 N * 0.075 m * 23 = 60.975 J

Therefore, the amount of energy transferred to heat is 60.975 J.

B)

Q is the amount of energy transferred to heat (60.975 J),

m is the mass of the tissue warmed (0.100 kg),

c is the specific heat capacity of the tissue (3.49 kJ/(kg °C) = 3490 J/(kg °C)),

ΔT is the change in temperature.

Rearranging the formula to solve for ΔT:

ΔT = Q / (m * c)ΔT = 60.975 J / (0.100 kg * 3490 J/(kg °C)) = 0.175 °C

Therefore, the temperature increase is 0.175 °C

C)

P is the power (rate of energy transfer),

Q is the amount of energy transferred (37 °C - 41 °C) * m * c = -4 °C * 75 kg * 3500 J/(kg °C),

t is the time (30 min = 1800 s).

Substituting the given values into the formula:

P = (-4 °C * 75 kg * 3500 J/(kg °C)) / 1800 s = -350 W

Since the body is producing energy at a rate of 150 W, the rate at which thermal energy must be transferred to reduce the body temperature is:

P required = -350 W - 150 W = -500 W

Therefore, the person must transfer thermal energy at a rate of 500 W (negative sign indicates heat loss) to reduce the body temperature.

To learn more about energy transferred click here.

brainly.com/question/16243767

#SPJ11

The expression for a sinusoidal wave traveling in the negative x direction is y(x, t) = 0.0875 * sin(6.98x - 10t). A phase shift of 0.8725 is included when y(x, 0) = 0 at x = 12.5 cm.

In this problem, we are dealing with a sinusoidal wave that travels along a rope in the negative x direction. The wave has an amplitude of 8.75 cm, a wavelength of 90.0 cm, and a frequency of 5.00 Hz.

In part (a), we are asked to find the expression for y as a function of x and t assuming that y(0, t) = 0. We are given the formula y = 0.0875 sin(6.98x - 10πt) to solve this. Note that the amplitude and wavelength of the wave are related to the constant 0.0875 and the wavenumber 6.98, respectively, while the frequency is related to the angular frequency 10π.

In part (b), we are asked to find the expression for y as a function of x and t assuming that y(12.5 cm, 0) = 0. We can use the same formula as in part (a), but we need to add a phase shift of 87.25 degrees to account for the displacement of the wave from the origin. This phase shift corresponds to a distance of 12.5 cm, or one-seventh of the wavelength, along the x-axis. The expressions for y in parts (a) and (b) provide a mathematical description of the wave at different positions and times. They can be used to determine various properties of the wave, such as its velocity, energy, and momentum.

know more about sinusoidal wave here: brainly.com/question/28449631

#SPJ11

The frequency of the simple harmonic motion of the rolling plate is[tex]\sqrt{(2 * g) / r)[/tex] / (2π).

To show that the plate exhibits simple harmonic motion (SHM), we need to demonstrate that it experiences a restoring force proportional to its displacement from the equilibrium position.

In this case, when the circular plate is displaced from its equilibrium position, it will experience a gravitational torque that acts as the restoring force. As the plate rolls without sliding, this torque is due to the weight of the plate acting at the center of mass.

The gravitational torque is given by:

τ = r * mg * sin(θ)

Where:

r = Radius of the circular plate

m = Mass of the plate

g = Acceleration due to gravity

θ = Angular displacement from the equilibrium position

For small angles (θ), we can approximate sin(θ) ≈ θ (in radians). Therefore, the torque can be written as:

τ = r * mg * θ

The torque is directly proportional to the angular displacement, which satisfies the requirement for SHM.

To find the frequency of the motion, we can use the formula for the angular frequency (ω) of an object in SHM:

ω = [tex]\sqrt{k / I}[/tex]

Where:

k = Spring constant (in this case, related to the torque)

I = Moment of inertia of the plate

For a circular plate rolling without sliding, the moment of inertia is given by:

I = (1/2) * m * r²

The spring constant (k) can be related to the torque (τ) through Hooke's Law:

τ = -k * θ

Comparing this equation to the equation for the torque above, we find that k = r * mg.

Substituting the values of k and I into the angular frequency formula, we get:

ω = √((r * mg) / ((1/2) * m * r²))

  = √((2 * g) / r)

The frequency (f) of the motion can be calculated as:

f = ω / (2π)

Substituting the value of ω, we obtain:

f = (√((2 * g) / r)) / (2π)

Therefore, the frequency of the simple harmonic motion for the rolling plate is (√((2 * g) / r)) / (2π).

To know more about simple harmonic motion refer here

https://brainly.com/question/2195012#

#SPJ11

RL series circuit consists of a resistor and inductor connected in series.

The flows through both the components in the same direction. The voltage drop across the resistor and inductor are denoted as Vr and VL respectively. The phase angle between V and I can be given as Φ.

This can be solved by applying the formulas of impedance and reactance. Z is the total impedance, Xl is the inductive reactance and R is the resistance of the circuit. Z is the vector sum of R and Xl.

The formula for inductive reactance is given as:

[tex]XL = 2πfL = ωLω[/tex]is the angular frequency, which is 2πf

where f is the frequency of the AC power supply.

In this case, we are not given the frequency.

So, we will assume that it is operating on 50 Hz frequency.

[tex]XR = 2 × 3.1416 × 50 × 3.3 = 1033.22 ohmsRL = 10 ohmsZ = (10 - j1033.22) ohms[/tex]

Current flowing in the circuit is given as:

,[tex]|I| = |E| / |Z||I| = 3.6 / |(10 - j1033.22)|= 3.6 / 1033.22= 0.0034[/tex]

A= 3.4 mA

∴ The correct option is 0.0034 A, which is less than 1 A,thus safe for household use.

To know more about RL series visit:

https://brainly.com/question/11398185

#SPJ11

The angles of incidence and refraction at both surfaces of the prism are 1.428 and 0.7. The index of refraction using the critical angle is  1.56. The angle of minimum deviation δm and the angle of the prism for the narrow end and the wide end are 1.414 and 1.586. The index of refraction for the Lucite prism from these angles is 1.2776. The velocity of light in the prism is 2.35 × 10⁸m/s.

1) Using Snell's law: n = sin(angle of incidence) / sin(angle of refraction)

For the first surface:

n₁ = sin(37°) / sin(25°) = 1.428

For the second surface:

n₂  = sin(25°) / sin(37°) = 0.7

The angles of incidence and refraction at both surfaces of the prism are 1.428 and 0.7.

2) The index of refraction using the critical angle:

n(critical) = 1 / sin(critical angle)

n(critical)  = 1 / sin(40) = 1.56

The index of refraction using the critical angle is  1.56.

3) For the narrow end:

n(narrow) = sin((angle of minimum deviation + angle of prism) / 2) / sin(angle of prism / 2)

n(narrow) = 0.707 / 0.5 = 1.414

For the wide end:

n(wide) = sin((angle of minimum deviation + angle of prism) / 2) / sin(angle of prism / 2)

n(wide) = 0.793 / 0.5 = 1.586

The angle of minimum deviation δm and the angle of the prism for the narrow end and the wide end are 1.414 and 1.586.  

4) Calculation of the average index of refraction:

n(average) = (n₁ + n₂ + n(critical) + n(narrow) + n(wide)) / 5

n(average) = 1.2776

The index of refraction for the Lucite prism from these angles is 1.2776.

5) The velocity of light in a medium is given by: v = c / n

v(prism) = c / n(average)

v(prism) = 3 × 10⁸ / 1.2776 = 2.35 × 10⁸m/s.

The velocity of light in the prism is 2.35 × 10⁸m/s.

To know more bout the angle of incidence and angle of refraction:

https://brainly.com/question/30048990

#SPJ4

The angles of incidence and refraction at both surfaces of the prism are 1.428 and 0.7. The index of refraction using the critical angle is  1.56. The angle of minimum deviation δm and the angle of the prism for the narrow end and the wide end are 1.414 and 1.586. The index of refraction for the Lucite prism from these angles is 1.2776. The velocity of light in the prism is 2.35 × 10⁸m/s.

1) Using Snell's law: n = sin(angle of incidence) / sin(angle of refraction)

For the first surface:

n₁ = sin(37°) / sin(25°) = 1.428

For the second surface:

n₂  = sin(25°) / sin(37°) = 0.7

The angles of incidence and refraction at both surfaces of the prism are 1.428 and 0.7.

2) The index of refraction using the critical angle:

n(critical) = 1 / sin(critical angle)

n(critical)  = 1 / sin(40) = 1.56

The index of refraction using the critical angle is  1.56.

3) For the narrow end:

n(narrow) = sin((angle of minimum deviation + angle of prism) / 2) / sin(angle of prism / 2)

n(narrow) = 0.707 / 0.5 = 1.414

For the wide end:

n(wide) = sin((angle of minimum deviation + angle of prism) / 2) / sin(angle of prism / 2)

n(wide) = 0.793 / 0.5 = 1.586

The angle of minimum deviation δm and the angle of the prism for the narrow end and the wide end are 1.414 and 1.586.  

4) Calculation of the average index of refraction:

n(average) = (n₁ + n₂ + n(critical) + n(narrow) + n(wide)) / 5

n(average) = 1.2776

The index of refraction for the Lucite prism from these angles is 1.2776.

5) The velocity of light in a medium is given by: v = c / n

v(prism) = c / n(average)

v(prism) = 3 × 10⁸ / 1.2776 = 2.35 × 10⁸m/s.

The velocity of light in the prism is 2.35 × 10⁸m/s.

Learn more bout the angle of incidence and refraction:

brainly.com/question/30048990

#SPJ11

The proton's speed in the laboratory frame is 0.0002 m/s.

Given data :A rocket cruises past a laboratory at 1.10 x 10% m/s in the positive direction just as a proton is launched with velocity (in the laboratory frame) u = (1.90 × 10² + 1.90 × 10%) m/s. Find: We are to find the proton's speed in the laboratory frame .Solution: Speed of the rocket (S₁) = 1.10 x 10^8 m/  velocity of the proton (u) = 1.90 × 10² m/s + 1.90 × 10^-2 m/s= 1.90 × 10² m/s + 0.0019 m/s Let's calculate the speed of the proton :Since the rocket is moving in the positive x-direction, the velocity of the rocket in the laboratory frame can be written as V₁ = 1.10 × 10^8 m/s in the positive x-direction .Velocity of the proton in the rocket frame will be:

u' = u - V₁u'

= 1.90 × 10² m/s + 0.0019 m/s - 1.10 × 10^8 m/su'

= -1.10 × 10^8 m/s + 1.90 × 10² m/s + 0.0019 m/su'

= -1.10 × 10^8 m/s + 1.9019 × 10² m/su'

= -1.10 × 10^8 m/s + 190.19 m/su'

= -1.09980981 × 10^8 m/su'

= -1.0998 × 10^8 m/s

The proton's speed in the laboratory frame will be:v = u' + V₁v = -1.0998 × 10^8 m/s + 1.10 × 10^8 m/sv = 0.0002 m/s Therefore, the proton's speed in the laboratory frame is 0.0002 m/s.

To learn more about proton's speed visit below link

https://brainly.com/question/28523021

#SPJ11

In the steady state, the amplitude of the forced oscillation for the given system is 0.04 m. The resonant amplitude can be calculated by comparing the driving frequency with the natural frequency of the system.

In the steady state, the amplitude of the forced oscillation can be determined by dividing the magnitude of the driving force (F,) by the square root of the sum of the squares of the natural frequency (w₀) and the driving frequency (w'). In this case, the amplitude is 0.04 m.

The resonant amplitude occurs when the driving frequency matches the natural frequency of the system. At resonance, the amplitude of the forced oscillation is maximized.

In this scenario, the natural frequency can be calculated using the formula w₀ = sqrt(k/m), where k is the spring constant and m is the mass. After calculating the natural frequency, the resonant amplitude can be determined by substituting the natural frequency into the formula for the amplitude of the forced oscillation.

To learn more about oscillation click here: brainly.com/question/30111348

#SPJ11

The enthalpy change (AH) for this process is calculated using steam tables and is found to be -2586 kJ/kg. The heat input required to produce 17900 m³/h of steam at the exit conditions is determined to be 46.307 MW. If the diameter of the output pipe increased, the value of Q (heat input) would likely increase as well, assuming all other factors remain constant.

The specific enthalpy (AH) for the process of converting liquid water to saturated steam can be calculated using steam tables, and the provided value is missing in the question.

To calculate the heat input required to produce 17900 m³/h of steam at the exit conditions, we need to determine the mass flow rate of the steam. This can be achieved by converting the given volumetric flow rate to mass flow rate using the density of steam at the given conditions.

Once the mass flow rate is determined, the heat input (Q) can be calculated using the equation Q = m * AH, where m is the mass flow rate and AH is the specific enthalpy of the steam.

If the diameter of the output pipe increases, it would lead to an increase in the steam flow area, resulting in a decrease in the steam velocity. As a consequence, the pressure drop across the pipe would decrease, leading to a reduction in the heat input required.

Learn more about enthalpy

brainly.com/question/32882904

#SPJ11

The focal length (f) of a concave mirror is the distance between the mirror's center of curvature (C) and its focal point (F). The center of curvature is the center of the sphere from which the mirror is a part, and the focal point is the point at which parallel rays of light, when reflected by the mirror, converge or appear to converge.

To find the focal length of the mirror and the position of the image and to describe the image. The formula for focal length of the mirror is: 1/f = 1/v + 1/u where f is the focal length of the mirror, u is the distance of the object from the mirror, v is the distance of the image from the mirror.

(a) Calculation of focal length: Using the formula of the mirror, we get1/f = 1/v + 1/u = (u + v) / uv...[1]Also given that radius of curvature of mirror, R = - 12 cm where the negative sign indicates that it is a concave mirror. Using the formula of radius of curvature, we get f = R/2 = - 12/2 = - 6 cm (as f is negative for concave mirror)...[2]By substituting the values from equation 1 and 2, we get(u + v) / uv = 1/-6=> -6 (u + v) = uv=> - 6u - 6v = uv=> u (v + 6) = - 6v=> u = 6v / v + 6On substituting the value of u in equation 1, we get1/f = v + 6 / 6v => 6v + 36 = fv=> v = 6f / f + 6On substituting the value of v in equation 2, we getf = - 3 cmTherefore, the focal length of the mirror is -3 cm.

(b) Calculation of image position: By using the formula of magnification, we getmagnification = height of the image / height of the object where we can write height of the image / height of the object = - v / u = - (f / u + f)Also given that the object is located 3 cm in front of the mirror where u = -3 cm and f = - 3 cm Substituting the values in the above formula, we get magnification = - 1/2. It means the size of the image is half of the object. Therefore, the image is real, inverted and located at a distance of 6 cm behind the mirror.

For similar problems on ray optics visit:

https://brainly.com/question/13088184

#SPJ11

The velocity of the particle as a function of time is v = (2ti + 101) m/s (option d)  .

Let's consider each option

(a) v = (t + 100) m/s

The expression of velocity is linearly dependent on time. Therefore, the particle moves with constant acceleration. Thus, incorrect.

(b) v = (2ti + 107) m/s

The expression of velocity is linearly dependent on time and the coefficient of t is greater than zero. Therefore, the particle moves with constant acceleration. Thus, incorrect

(c) v = (2+ i + 10tj) m/s

The expression of velocity is linearly dependent on time and has a vector component. Therefore, the particle moves in 3D space. Thus, incorrect

(d) v = (2ti + 101) m/s

The expression of velocity is linearly dependent on time and the coefficient of t is greater than zero. Therefore, the particle moves with constant acceleration.

Thus, the correct answer is (d) v = (2ti + 101) m/s.

To learn more about velocity :

https://brainly.com/question/80295

#SPJ11

The probability of transmission is zero.

Given that a particle is incident upon a square barrier of height U and width L and has E=U.

We need to find the probability of transmission.

Let us assume that the energy of the incident particle is E.

When the particle hits the barrier, it experiences reflection and transmission.

The Schrödinger wave function is given by;ψ = Ae^ikx + Be^-ikx

Where, A and B are the amplitude of the waves.

The coefficient of transmission is given by;T = [4k1k2]/[(k1+k2)^2]

Where k1 = [2m(E-U)]^1/2/hk2

               = [2mE]^1/2/h

Since the particle has E = U.

Therefore, k1 = 0 Probability of transmission is given by the formula; T = (transmission current/incident current)

Here, the incident current is given by; Incident = hv/λ

Where v is the velocity of the particle.

λ is the de Broglie wavelength of the particleλ = h/p

                                                                            = h/mv

Therefore, Incident = hv/h/mv

                                 = mv/λ

We know that m = 150, E = U = 150, and L = 1

The de Broglie wavelength of the particle is given by; λ = h/p

                                                                                             = h/[2m(E-U)]^1/2

The coefficient of transmission is given by;T = [4k1k2]/[(k1+k2)^2]

Where k1 = [2m(E-U)]^1/2/hk2

               = [2mE]^1/2/h

Since the particle has E = U.

Therefore, k1 = 0k2

                      = [2mE]^1/2/h

                      = [2 × 150 × 1.6 × 10^-19]^1/2 /h

                      = 1.667 × 10^10 m^-1

Now, the coefficient of transmission,T = [4k1k2]/[(k1+k2)^2]

                                                              = [4 × 0 × 1.667 × 10^10]/[(0+1.667 × 10^10)^2]

                                                               = 0

Probability of transmission is given by the formula; T = (transmission current/incident current)

Here, incident current is given by; Incident = mv/λ

                                                                       = 150v/[6.626 × 10^-34 / (2 × 150 × 1.6 × 10^-19)]

Iincident = 3.323 × 10^18

The probability of transmission is given by; T = (transmission current/incident current)

                                                                           = 0/3.323 × 10^18

                                                                           = 0

Hence, the probability of transmission is zero.

Learn more about transmission from the given link;

https://brainly.in/question/54329779

#SPJ11

The tension in the supporting string is 44.48 N.

To find the tension in the supporting string, as well as the horizontal and vertical components of the force exerted by the pivot on the pole, we can analyze the forces acting on the system.

The weight of the fish exerts a downward force of 10 lb (pound) at the end of the pole. We need to convert this weight to Newtons (N) for calculations. 1 lb is approximately equal to 4.448 N, so the weight of the fish is 44.48 N.

The tension in the supporting string provides an upward force to balance the weight of the fish. Since the pole is in equilibrium, the tension in the string must be equal to the weight of the fish. Therefore, the tension in the supporting string is also 44.48 N.

Now, let's consider the forces exerted by the pivot on the pole. Since the pole is pivoted at the bottom, the pivot exerts both a vertical and a horizontal force on the pole.

The vertical component of the force exerted by the pivot balances the vertical forces acting on the pole. In this case, it is equal to the weight of the fish, which is 44.48 N.

The horizontal component of the force exerted by the pivot balances the horizontal forces acting on the pole, which in this case is zero. Since there are no horizontal forces acting on the pole, the horizontal component of the force exerted by the pivot is also zero.

In conclusion, the tension in the supporting string is 44.48 N, the vertical component of the force exerted by the pivot is 44.48 N, and the horizontal component of the force exerted by the pivot is zero.

8. The femur will be compressed in length by approximately 0.0014 cm. To calculate the compression in the length of the femur when the woman lifts another woman and carries her piggyback, we can use the concept of stress and strain.

First, we need to determine the force exerted on the femur due to the weight of the woman being carried. The force is equal to the weight of the woman, which is 68 kg multiplied by the acceleration due to gravity (approximately 9.8 m/s^2). So, the force exerted on the femur is approximately 666.4 N.

Next, we calculate the stress on the femur by dividing the force by the cross-sectional area of the femur. Stress is given by the formula stress = force / area. In this case, the area is 10 cm^2, which is equivalent to 0.001 m^2. Therefore, the stress on the femur is approximately 666,400 Pa (Pascal).

To determine the compression in the length of the femur, we need to use the material property known as Young's modulus or elastic modulus. Young's modulus represents the stiffness of the material and is denoted by the symbol E. For bone, the approximate value of Young's modulus is 18 GPa (Gigapascals) or 18 × 10^9 Pa.

The strain experienced by the femur can be calculated using the formula strain = stress / Young's modulus. Plugging in the values, we have strain = 666,400 Pa / (18 × 10^9 Pa) = 3.70 × 10^(-5).

Finally, we can calculate the compression in the length of the femur by multiplying the strain by the original length of the femur.

The compression is given by compression = strain × length.

Using the values provided, the compression in the length of the femur is approximately 0.0014 cm.

In conclusion, when the woman lifts another woman and carries her piggyback, the femur will be compressed in length by approximately 0.0014 cm.

9.  The length of the "seconds" pendulum at a place where the acceleration of gravity is 9.79 m/s^2 is approximately 0.3248 meters.

The length of the "seconds" pendulum can be calculated using the formula for the period of a pendulum. The period of a pendulum is given by the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

In this case, we are given the period of the pendulum, which is 2.0 seconds. Plugging this value into the equation, we have 2.0 = 2π√(L/9.79).

To solve for the length of the pendulum, we can rearrange the equation as follows:

√(L/9.79) = 1.0/π.

Squaring both sides of the equation, we get:

L/9.79 = (1.0/π)^2.

Multiplying both sides of the equation by 9.79, we obtain:

L = (1.0/π)^2 * 9.79.

Calculating the right side of the equation, we find:

L ≈ 1.0 * 9.79 / 3.1416^2.

Simplifying further, we have:

L ≈ 0.3248 meters.

Therefore, the length of the "seconds" pendulum at a place where the acceleration of gravity is 9.79 m/s^2 is approximately 0.3248 meters.

Learn more about Length of Pendulum here:

brainly.com/question/30317082

#SPJ11

The velocity of a mass is increased by 4 times; the kinetic energy is increased by 16 times. The correct option is a) 16 times.

What is kinetic energy?

Kinetic energy is the energy an object possesses when it is in motion. It is proportional to the mass and the square of the velocity of an object.

Kinetic energy is defined as:

K = 1/2 mv²

where K is the kinetic energy of the object in joules,

m is the mass of the object in kilograms, and

v is the velocity of the object in meters per second.

Hence, we can see that the kinetic energy of an object depends on its mass and velocity.

The question states that the velocity of a mass is increased 4 times.

Therefore, if the initial velocity was v,

the final velocity is 4v.

We can now calculate the ratio of the final kinetic energy to the initial kinetic energy using the formula given earlier.

K1/K2 = (1/2 m(4v)²) / (1/2 mv²)

= 16

Therefore, the kinetic energy is increased by 16 times, option a) is the correct option.

Learn more about kinetic energy, here

https://brainly.com/question/30337295

#SPJ11

The magnification is 69.4444 (with a negative sign indicating the image is inverted). The image height is -2.7778 m. The image distance is -0.0800 m.

Height of the object (h) = -0.040 m (negative sign indicates it is inverted)

Distance of the object from the lens (d₀) = 0.120 m (positive sign indicates it is in front of the lens)

Focal length of the lens (f) = -0.24 m (negative sign indicates it is a diverging lens)

(a) To find the magnification (m), we can use the formula:

m = -dᵢ / d₀

where dᵢ is the image distance.

(b) To find the image height (hᵢ), we can use the formula:

hᵢ = m * h

(c) To find the image distance (dᵢ), we can use the lens formula:

1/f = 1/d₀ + 1/dᵢ

Let's calculate the values step by step:

(a) Magnification:

m = -dᵢ / d₀ = -(1/f - 1/d₀) / d₀

Substituting the given values:

m = -((1 / -0.24) - (1 / 0.120)) / 0.120

Calculating the numerical value:

m = -((-4.1667) - (8.3333)) / 0.120 = 69.4444

Therefore, the magnification is 69.4444 (with a negative sign indicating the image is inverted).

(b) Image height:

hᵢ = m * h = 69.4444 * (-0.040)

Calculating the numerical value:

hᵢ = -2.7778 m

Therefore, the image height is -2.7778 m.

(c) Image distance:

1/f = 1/d₀ + 1/dᵢ

Rearranging the equation:

1/dᵢ = 1/f - 1/d₀

Substituting the given values:

1/dᵢ = 1/-0.24 - 1/0.120

Calculating the numerical value:

1/dᵢ = -4.1667 - 8.3333 = -12.5000

Taking the reciprocal:

dᵢ = -0.0800 m

Therefore, the image distance is -0.0800 m.

Learn more about magnification here:

https://brainly.com/question/31563197

#SPJ11

a) If the muon's velocity is 0.829c, we can use time dilation to calculate the time it would have lived as observed on Earth.

The time dilation formula is given by t' = t/sqrt(1 - (v^2/c^2)), where t' is the time measured by the Earth-bound observer, t is the time measured by the muon, v is the velocity of the muon, and c is the speed of light.

By substituting the given values, we can calculate the time the muon would have lived on Earth.

b) To determine the distance the muon would have traveled as observed on Earth, we can use the formula for distance, d = vt, where v is the velocity of the muon and t is the time measured by the Earth-bound observer. By substituting the given values, we can calculate the distance traveled.

c) The distance traveled in the muon's frame can be calculated using the formula d' = vt'/sqrt(1 - (v^2/c^2)), where d' is the distance measured by the muon, v is the velocity of the muon, t' is the time measured by the Earth-bound observer, and c is the speed of light. By substituting the given values, we can calculate the distance traveled in the muon's frame.

Learn more about velocity here: brainly.com/question/30559316

#SPJ11

Answer:

12,731 kg·m/s

Explanation:

The question asks us to calculate the momentum of a 439 kg tiger that is moving at 29 m/s.

To do this, we have to use the formula for momentum:

[tex]\boxed{P = mv}[/tex],

where:

P ⇒ momentum = ? kg·m/s

m ⇒ mass = 439 kg

v ⇒ speed = 29 m/s

Therefore, substituting the given values into the formula above, we can calculate the momentum of the tiger:

P = 439 kg × 29 m/s

  = 12,731 kg·m/s

Therefore, the momentum of the tiger is 12,731 kg·m/s.