1. A 0.828-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backwards.
a) Find the momentum of the electron.

b) Find the kinetic energy of the electron.

The Kinetic Energy (KE) is calculated using the formula:

KE = 0.5 m v^2

Where,

m = mass of bare helium nucleus = 6.64 ✕ 10^−27 kg

v = velocity = 0.018 c = 0.018 * 3 ✕ 10^8 m / s^2 = 5.4 ✕ 10^6 m / s^2

Calculating:

KE = 0.5 (6.64 ✕ 10^−27 kg) (5.4 ✕ 10^6 m / s^2)^2

KE = 9.68✕ 10^−14 J

Answer:

The answer is A.

Explanation:

I took the test and got the answer.

The speed of a proton is about 5.0 × 10⁵ m/s

[tex]\texttt{ }[/tex]

Let's recall the Kinetic Energy formula:

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

Ek = kinetic energy ( J )

m = mass of object ( kg )

v = speed of object ( m/s )

[tex]\texttt{ }[/tex]

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

potential difference = ΔV = -1300 V

mass of proton = m = 1.67 × 10⁻²⁷ kilograms

charge of proton = q = 1.60 x 10⁻¹⁹ coulombs

initial speed of proton = v₁ = 0 m/s

Asked:

final speed of proton = v = ?

Solution:

[tex]Ep_1 + Ek_1 = Ep_2 + Ek_2[/tex]

[tex]qV_1 + \frac{1}{2}mv_1^2 = qV_2 + \frac{1}{2}mv_2^2[/tex]

[tex]q(V_1 - V_2 ) = \frac{1}{2}m( v_2^2 - v_1^2 )[/tex]

[tex]q( 0 - V ) = \frac{1}{2}m ( v^2 - 0^2 )[/tex]

[tex]-q \Delta V = \frac{1}{2} m v^2[/tex]

[tex]v^2 = -2mq \Delta V[/tex]

[tex]v = \sqrt { (-2q \Delta V) \div m }[/tex]

[tex]v = \sqrt { -2 \times 1.60 \times 10^{-19} \times (-1300) \div (1.67 \times 10^{-27})}[/tex]

[tex]v \approx 5.0 \times 10^5 \texttt{ m/s}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Energy

The speed of a proton that has been accelerated from rest through a potential difference of - 1300 v  would be 4.99 × 10⁵ meters/ second.

Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge.

As given in the problem we have to find out the speed  of a proton that has been accelerated from rest through a potential difference of -1300 volts,

The speed of the proton can be calculated with the expression given as follows,

1/2 × mass ×velocity ² = electric charge × potential difference  

v² = 2qV /m

v = √(2qV/m)

  = √ ( 2×1.6×10⁻¹⁹ ×1300 / 1.67×10⁻²⁷)

  =4.99 × 10⁵ meters/seconds

Thus, the speed of the proton would be 4.99 × 10 ⁵  meters/seconds.

To learn more about an electric charge from here, refer to the link given below ;

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its 2 meters per sec

Final answer:

To find the horizontal force a 47 kg sprinter must exert on the starting blocks to achieve a given acceleration, Newton's Second Law is used. Assuming the acceleration is 4.20 m/s², the required force is calculated to be approximately 197 N.

Explanation:

To determine how much horizontal force (f) a sprinter must exert on the starting blocks to produce a certain acceleration, we can use Newton's Second Law of Motion, which states that force equals mass times acceleration (F = ma). Since the student asked for the amount of force for a sprinter with a mass of 47 kg but did not provide the acceleration, we'll assume the acceleration is the same as provided in the reference problems: 4.20 m/s² (as from a 63.0-kg sprinter).

Using the formula F = ma:

Force (F) = mass (m) × acceleration (a)

F = 47 kg × 4.20 m/s²

F = 197.4 N

Therefore, the sprinter must exert a force of approximately 197 N on the starting blocks to achieve the given acceleration.

Final answer:

To obtain destructive interference between the two speakers, you need to move to a point where the path length difference is equal to half of the wavelength of the musical note.

Explanation:

Answer:

10.35 m

Explanation:

d1 = 5 m at angle 53 degree

d1 = 5 (Cos 53 i + Sin 53 j) = 3 i + 4 j

d2 = 8 m at an angle 130 degree

d2 = 8 (Cos 130 i + Sin 130 j) = - 5.14 i + 6.13 j

Total displacement = d = (3 - 5.14) i + (4 + 6.13) j = - 2.14 i + 10.13 j

magnitude of displacement = [tex]\sqrt{(-2.14)^{2}+(10.13)^{2}}[/tex] = 10.35 m

Without additional information or context regarding the rate of heat transfer or the properties of the fluid flow over the pipe, the heat transfer coefficient cannot be calculated directly from the information provided. Typically, empirical correlations based on experimental data or known flow conditions would be necessary to estimate this coefficient.

To calculate the heat transfer coefficient as a result of convection between the outer pipe surface and the surrounding air, we'd typically use the convection heat transfer equation:

Q = hAΔT

Where Q is the heat transfer rate, h is the heat transfer coefficient, A is the area of the pipe exposed to convection, and ΔT is the temperature difference between the surface and the air. However, additional information is needed to proceed with the calculation, such as the heat transfer rate from the pipe to the air or the convective heat transfer properties of the fluid surrounding the pipe.

In the case provided, without further context or information regarding the rate of heat transfer or properties of the flow over the pipe, the heat transfer coefficient (h) cannot be calculated directly. Usually, in such scenarios, experimental data or empirical correlations are used to estimate the heat transfer coefficient based on the flow conditions (e.g., Reynolds number, Prandtl number).

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707 N

185×0.39×9.8

I just did it and found the answer

Answer:

In the field of radioactivity, the half-life is usually defined as the time required by an unstable radioactive isotope to disintegrate half of its initial composition. For different radioactive isotope elements, this value of half-life is different.

For example, the half-life of uranium-238 is approximately 4.5 billion years and the half-life of Carbon-14 is nearly 5700 years.

During the time of one half-life of a radioactive isotope, half of the parent atoms are disintegrated and forms a comparatively stable daughter isotope. This means that half of the initial concentration of the unstable isotope is reduced.

To solve this problem, let us recall that the formula for gases assuming ideal behaviour is given as:

rms = sqrt (3 R T / M)

where

R = gas constant = 8.314 Pa m^3 / mol K

T = temperature

M = molar mass

Now we get the ratios of rms of Argon (1) to hydrogen (2):

rms1 / rms2 = sqrt (3 R T1 / M1) / sqrt (3 R T2 / M2)

or

rms1 / rms2 = sqrt ((T1 / M1) / (T2 / M2))

rms1 / rms2 = sqrt (T1 M2 / T2 M1)

Since T1 = 4 T2

rms1 / rms2 = sqrt (4 T2 M2 / T2 M1)

rms1 / rms2 = sqrt (4 M2 / M1)

and M2 = 2 while M1 = 40

rms1 / rms2 = sqrt (4 * 2 / 40)

rms1 / rms2 = 0.447

Therefore the ratio of rms is:

rms_Argon / rms_Hydrogen = 0.45

Answer:

I would like to add to the above answer that .447 is equal to [tex]\frac{1}{\sqrt{5} }[/tex].

Explanation:

To solve this problem, let us consider that the Earth is the origin, the initial reference point. Therefore the speed of rocket plus the missile would be 0.8 C

Now after the rocket had moved away from Earth, it fired a missile at a speed of 0.7 C. Now the reference made to this is relative to the rocket. We have established that our initial reference point is the Earth, therefore the real speed of the missile with reference to Earth is:

Speed of missile relative to Earth = 0.8 C + 0.7 C

Speed of missile relative to Earth = 1.5 C

Answer is:

A

(a) It will strike the ground in 7.14 seconds

(b) The tourist at the bottom must get out in 6.10 seconds

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem !

Given:

h = 250 m

Unknown:

t₁ = ?

t₂ = ?

Solution:

We can use the following formula to calculate time taken for the rock to reach the ground,

[tex]h = v ~ t + \frac{1}{2} ~ g ~ t^2[/tex]

[tex]250 = 0 \times t + \frac{1}{2} \times 9.8 ~ t^2[/tex]

[tex]250 = \frac{1}{2} \times 9.8 ~ t^2[/tex]

[tex]250 = 4.9 ~ t^2[/tex]

[tex]t^2 = 250 \div 4.9[/tex]

[tex]t = \sqrt{250 \div 4.9}[/tex]

[tex]t = \frac{50}{7} ~ seconds[/tex]

[tex]\large {\boxed {t \approx 7.14 ~ seconds} }[/tex]

Firstly, we will find the time taken by sound to reach the tourist.

[tex]t_{sound} = \frac{250 ~ m}{335 ~ m/s}[/tex]

[tex]\boxed{ t_{sound} = \frac{50}{67} ~ s }[/tex]

Next, we will find how long will a tourist have to get out of the way.

[tex]t_2 = t_1 - ( t_{sound} + t_{reaction})[/tex]

[tex]t_2 = \frac{50}{7} - ( \frac{50}{67} + 0.300})[/tex]

[tex]\large {\boxed {t_2 \approx 6.10 ~ seconds} }[/tex]

The tourist only has about 6 seconds before getting hit by the stone.

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

The boulder will be going approximately 70.0 m/s when it strikes the ground, and a tourist will have approximately 1.046 seconds to react and move out of the way after hearing the sound of the rock breaking loose.

Calculating the Speed of a Falling Boulder and Reaction Time for Safety

For part (a) of the question, we want to calculate how fast a boulder will be going when it strikes the ground after falling from a height of 250 meters. We can use the equation of motion under the influence of gravity, which is v = sqrt(2gh), where g is the acceleration due to gravity (9.81 m/s²) and h is the height (250 m). Plugging in these values, we get the final velocity v as the square root of (2 * 9.81 m/s² * 250 m), which is approximately 70.0 m/s.

For part (b), we need to determine how long a tourist has to react and move out of the way after hearing the sound of the rock breaking loose. The sound travels at 335 m/s, so it will take the sound approximately 250 m / 335 m/s to reach the tourist, which is roughly 0.746 s. We must also add the tourist's reaction time of 0.300 s to this. Therefore, the total time the tourist has to react is the sum, which would be approximately 0.746 s + 0.300 s = 1.046 s.

During a lunar eclipse, the half of the planet that is in night mode can see it, because during that type of an eclipse, the earth gets in between the sun and the moon and the reason the moon turns red is because earth's atmosphere bends some light and that light hits the moon.

To add, the lunar eclipse is an astronomical phenomenon and happens about two times per year, and a large portion of the Earth can see this type of eclipse, compared to solar eclipses.

Around 75% of the Earth can see a lunar eclipse at any given time due to the duration of the event and the rotation of the Earth.

Roughly 75% of the Earth can see a lunar eclipse at one time. During a lunar eclipse, Earth's shadow covers the entire Moon, and because the event lasts several hours, more people can observe the eclipse as the Earth rotates. In comparison to a solar eclipse, which is visible in a very narrow path on Earth, a lunar eclipse is observable from anywhere on the night side of the Earth. Since the eclipse takes about 5-6 hours from start to finish, different regions come into view of the eclipse over time, allowing for broad visibility.

A push or a pull is called a 'force' in physics. This force can make an object change its velocity, such as starting to move, stopping, or changing its direction.

In the field of physics, a push or a pull is referred to as a force. Option C is the correct answer to your question. Forces cause an object to change its velocity, meaning it can start moving, stop moving, or change its direction based on this influence. For example, if you push a stationary bike, it starts to move - that's an illustration of a force at work. Even gravity is a type of force that pulls objects towards the Earth's surface.

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An electron moves in an electric field towards regions of lower potential due to the decrease in its electric potential energy.

An electron moves in an electric field towards regions of lower potential. This is because the electron will move in the direction that tends to decrease its electric potential energy.

An electron moves toward lower electrical potential in an electric field, and will exhibit motion based on the Lorentz force when in a magnetic field. If both electric and magnetic fields are present, perpendicular velocity filtering can occur.

When an electron with initial velocity is introduced into a region where an electric field is present, it will be accelerated by the electric field. An electron moves toward regions of lower potential because it has a negative charge and is repelled by areas of higher negative potential and attracted to areas of higher positive potential. For example, if the electric field is uniform and points in the direction opposite to the electron's initial velocity, the electron will decelerate until it comes to rest, then accelerate in the direction of the field.

In a uniform magnetic field, the electron will start to move in a circular path due to the magnetic force acting perpendicular to its velocity. The radius of this path and the direction of the magnetic force can be determined using the Lorentz force law. If there is both an electric field and a magnetic field present, perpendicular to each other and the velocity of the charged particle, there exists a particular velocity at which the particle will experience no net force, leading to the concept of a velocity filter.

Assuming that all energy of the small ball is transferred to the bigger ball upon impact, then we can say that:

Potential Energy of the small ball = Kinetic Energy of the bigger ball

Potential Energy = mass * gravity * height

Since the small ball start at 45 cm, then the height covered during the swinging movement is only:

height = 50 cm – 45 cm = 5 cm = 0.05 m

Calculating for Potential Energy, PE:

PE = 2 kg * 9.8 m / s^2 * 0.05 m = 0.98 J

Therefore, maximum kinetic energy of the bigger ball is:

Max KE = PE = 0.98 J

A point charge with a charge q1 = + 2.90 uC is held stationary at the origin hence coordinates are (0, 0).

A second point charge with a charge q2= - 5.40 uC moves from the point x = 0.110 m, y = 0 to the point x = 0.280 m, y = 0.280 m  [(0.110, 0) to (0.28, 0.28)]

The initial distance between the two charges is:

Initial distance = r1 = 0.110 m

The final distance between the two charges is calculated using hypotenuse formula:

Final distance = r2 = sqrt [0.28^2 + 0.28^2]

r2 = sqrt [2 * 0.0784]

r2 = sqrt [0.1568]

r2 = 0.396 m

Δr = r1 - r2 = 0.110 - 0.396 = - 0.286 m

r1r2 = 0.04356 m^2

Work is done by the electric force on q2= W. The formula to use with change in location is:

W =k q1 q2 [1/r2 - 1/r1]

W = 9*10^9 * 2.9*10^-6 * -5.3*10^-6 [(1/0.396) – (1/0.110)]

W = 0.908 J = 9.08*10^-1 J            (ANSWER)