(d) The drawing shows four different situations in which a light ray is traveling from one medium into another. Without doing any calculations, but taking note of the relative sizes of the angles of incidence and refraction, decide which situation shows a refraction that is physically possible.

Part A: The electric potential V at a point on the disk's axis a distance x from the center of the disk is given by:

V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)

Part B: After calculating for −∂V/∂x we get:

-∂V/∂x = σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)

Part A:

The disc can be split into a number of thin, concentric rings in order to compute the electric potential V at a point on its axis that is located x distance from the disk's centre.

Each ring's potential is determined by:

\(V_{ring}\) = 1/4πε₀ × (\(Q_{ring}\) /  \((x^{2} +R^{2} )^{1/2}\))

where

\(Q_{ring}\) is the charge of the ring and

ε₀ is the permittivity of free space.

Since

the disk has uniform surface charge density σ, the charge on each ring is given by:

\(Q_{ring}\) = σ × 2πr × dr

where

r is the radius of the ring and

dr is its thickness.

By substituting \(Q_{ring}\) into the expression for \(V_{ring}\), we get:

\(V_{ring}\) = 1/4πε₀ × (σ × 2πr × dr / \((x^{2} +R^{2} )^{1/2}\))

By integrating across all the rings, it is possible to get the total potential V at any point along the axis of the disc:

V = ∫V_ring

V = ∫(1/4πε₀ × (σ x 2πr × dr / \((x^{2} +R^{2} )^{1/2}\))

V = σ/2ε₀ × ∫(r / \((x^{2} +R^{2} )^{1/2}\)) dr from 0 to R

By evaluating the integral and simplifying, we get:

V = σ/2ε₀ × [\((R^{2}/(x^{2} +R^{2} )^{1/2})\) - \((0/(x^2+0^2)^{1/2})\)]

V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)

Therefore, the electric potential V at a point on the disk's axis a distance x from the center of the disk is given by:

V = σ/2ε₀ × \((R^{2}/(x^{2} +R^{2} )^{1/2})\)

Part B:

To find the value of −∂V/∂x,

The derivative of the equation for V with regard to x must be taken:

∂V/∂x = -σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)

Hence, the expression for −∂V/∂x is:

-∂V/∂x = σR²x/2ε₀\((x^{2}+R^{2})^{3/2}\)

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From the principle of conservation of linear momentum, the mass of Lee is 50 Kg.

Momentum is the product of mass and velocity. The principle of conservation of linear momentum states that the total momentum before collision is equal to the total momentum after collision.

Let the mass of Lee be m

Hence;

(4.0-kg  × 3.0 m/s) + (m × 3.0 m/s) = (4.0-kg  × 15.5 m/s) + (m × 2.0 m/s)

12 + 3m = 62 + 2m

12 - 62 = 2m - 3m

-50 = -m

m = 50 Kg

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Answer:

1.439 × 10¹¹ m is the answer.

Explanation:

1 light-second = 2.998 × 10⁸m

480 light-seconds = 480 × 2.998 × 10⁸

= 1439.04 × 10⁸

= 1.439 × 10¹¹

∴ 1.439 × 10¹¹ m is the answer.

The distance converted into the meter will be 1.439×10¹¹ m.In one light second, there are 2.998 ×10⁸ m.

Distance is a numerical representation of the distance between two objects or locations.

The distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.

The given data in the problem is;

The  distance between the sun and moon is,d= 480 light second

\(\rm d_m\) is the distance in meter

As we know,

\(\rm 1\ light\ second = 2.998 \times 10^8m \\\\ 480\ light\ seconds = 480 \times 2.998 \times 10^8\ m \\\\ d_m= 1439.04 \times 10^8 \\\\ d_m = 1.439 \times 10^{11}\)

Hence the distance converted into the meter will be 1.439×10¹¹ m.

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Answer:

A black hole is a region of spacetime where gravity is so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole.

An object starting from rest and experiencing constant acceleration travels 2.0 m in the first second. Additional 4.0 m in the next second.

If an object starts from rest and undergoes constant acceleration, we can use the equation of motion to determine its displacement. The equation is given by:

d = ut + (1/2)at²

Where:

d = displacement

u = initial velocity (which is 0 since the object starts from rest)

t = time

a = acceleration

In the first second (t = 1), the object travels 2.0 m. Plugging in the values into the equation, we have:

2.0 = 0(1) + (1/2)a(1²)

2.0 = (1/2)a

a = 4.0 m/s²

Now, we need to find the distance traveled in the next second (t = 2). Again, using the equation of motion:

d = ut + (1/2)at²

d = 0(2) + (1/2)(4.0)(2²)

d = 0 + 4.0

d = 4.0 m

Therefore, the object travels 4.0 meters in the next second.

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Answer:

Momento = 170.8 Kgm/s

Explanation:

Dados los siguientes datos;

Masa = 3,05 kg

Velocidad = 56 m/s

Para encontrar el impulso;

El momento se puede definir como la multiplicación (producto) de la masa que posee un objeto y su velocidad. El momento se considera una cantidad vectorial porque tiene magnitud y dirección.

Matemáticamente, el momento viene dado por la fórmula;

\( Momento = masa * velocidad \)

Sustituyendo en la fórmula, tenemos;

\( Momento = 3.05 * 56 \)

Momento = 170.8 Kgm/s

Answer:

Explanation:

140m

Explanation:

The velocity must be broken down into x (horizontal) and y (vertical) components. We can use the y component to find how high the object gets. To find vertical velocity, vy, use vy=vosinθ.

vy=(75ms)sin45o=53ms

Next we find how long it takes to reach the top of its trajectory using vf=vo+at.

0ms=53ms+(−10ms2)t

t = 5.3s

Finally, find how high the object goes with d=vot+12at2.

d=(53ms)5.3s+12(−10ms2)(5.3s)2=140m

The motion in which a body has constant horizontal component of velocity

but changing vertical component of velocity is called projectile motion. Every projectile body has PROJECTILE MOTION.

The Vertical Velocity will decrease during upward motion and increase during downward motion, by the factor,

\(V_f = V_iSin(theta) - gt (Upward Motion)\\\\V_f = V_iSin(theta) + gt (Downward Motion)\)

Where,

Vf = final velocity

Vi = initial velocity  

Theta θ is the angle at which projectile is fired

g is acceleration due to gravity

t is time  

B) HORIZONTAL VELOCITY:

HORIZONTAL VELOCITY remains constant. According to Newton's 1st Law object in motion stays in motion until a force acts on it. There are no forces acting on a projectile in the horizontal direction (neglecting air resistance), therefore the velocity is constant.

Angle = θ(theta) = 30

Initial Velocity = \(V_0 = 150 ms^{-1}\)

g = 10 m/s^2

Time taken to reach maximum height = T = ?

The time taken by the projectile to reach the maximum height is given by,

                                      \(T = \frac{V_0Sin(theta)}{g}\\\\T = \frac{150Sin(30)}{10}\\\\T = \frac{150x0.5}{10}\\\\T = \frac{75}{10}\\\\T = 7.5 seconds\)

Billy jumps upward with a velocity of 4.2 m/s off a 6m high diving board.  . Billy will take 0.43 sec  to hit the water

The branch of physics that defines motion with respect to space and time, ignoring the cause of that motion, is known as kinematics.

using equation of kinematics

v = u + g*t

sign convention

positive y direction (upward) = +

negative y direction ( downward )  = -

v = u - g*t

0 = 4.2 - ( 9.8 * t )

t = 4.2 / 9.8

t = 0.43 sec

Billy will take 0.43 sec  to hit the water

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(a) the magnitude of the electric field at the origin is : E = (2kλ)/0= 2kλ

(b)  the direction of the electric field at the origin is in the positive x direction.

(a) The magnitude of the electric field at the origin is 2kλ, where k is the Coulomb constant and λ is the linear charge density. (b) The direction of the electric field at the origin is in the positive x direction.

(a) To find the magnitude of the electric field at the origin, we can use the formula for the electric field due to a line of charge :E = (2kλ)/r where E is the electric field, k is the Coulomb constant, λ is the linear charge density, and r is the distance from the line of charge.

Since the line of charge extends from x = 0 to positive infinity, the distance from the origin to the line of charge is r = 0. Therefore, the magnitude of the electric field at the origin is: E = (2kλ)/0= 2kλ

(b) The direction of the electric field is always directed away from a positive charge and towards a negative charge. Since the line of charge is positive, the electric field at the origin will be directed away from the line of charge, which is in the positive x direction.

Therefore, the direction of the electric field at the origin is in the positive x direction.

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As the air cools, it becomes denser and sinks below warmer air (option b). Cooling causes a decrease in air molecules' kinetic energy, reducing their speed and increasing their proximity to each other.

This increased density leads to higher air pressure. According to the ideal gas law, decreasing temperature decreases the air pressure.

This denser, cooler air displaces the warmer, less dense air, causing it to rise. This process is known as convection.

It creates vertical air movements, with cooler air sinking and warmer air rising.

The resulting circulation patterns play a crucial role in weather and climate systems, influencing wind patterns, cloud formation, and precipitation. Thus, the correct option is b.

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Answer:

f = 0.365 Hz

Explanation:

The angular velocity of a simple pendulum is

           w = \(\sqrt{g/L}\)

angular velocity and frequency are related

           w = 2π f

we substitute

           2π f = \(\sqrt{g/L}\)

Let's find the initial length of the pendulum

            L = \(\frac{g}{4\pi^2 } \ f_o\)

            L₀ = \(\frac{9.8}{4 \pi ^2} \ 0.4\)

            L₀ = 0.6206 m

Indicates that the length of the chord triples

             L = 3 L₀

             L = 3 0.6206

             L = 1.8618 m

let's find the frequency

             f = \(\frac{1}{2\pi } \ \sqrt{\frac{9.8}{1.8618} }\)

             f = 0.365 Hz

The graphs of velocity vs time and acceleration versus time depict the motion of a falling object in a straight line.

The position-time graph depicts how the moving object's position has changed over time.

With regard to the displacement-time graph of the velocity-time graph and the acceleration-time graph i.e.  Only the velocity and acceleration of the falling object are depicted in these three graphs as straight lines.

Therefore, the graphs of velocity versus time and acceleration versus time represent the motion of a falling object on a straight line.

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Step 2: Draw a diameter of the circle, labeling its endpoints A and C, option B.

Step 3: Draw intersecting arcs, using the compass set to a width larger than the radius of the circle, centered at A and C, on each side of the diameter, option C.

Step 4: Draw a line through the intersecting arcs and the center of the circle. Label the points of intersection with the circle as B and D, option A.

A polygon is a 2-dimensional geometric shape that is defined as a closed figure formed by straight lines or segments. It can have three or more sides and angles, and the sides do not intersect or overlap.

Examples of polygon shapes include triangles, squares, rectangles, pentagons, hexagons, and so on. The type of polygon is determined by the number of sides it has, with triangular polygon having three sides, square polygons having four sides, and so on.

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The correct option is A, accelerate the rotation of the moon across the sun.

The Sun is a star that is at the center of the solar system. It is classified as a G-type main-sequence star, which means that it is a relatively average star in terms of size, temperature, and luminosity. The Sun is about 4.6 billion years old and is expected to remain stable for another 5 billion years or so before it begins to run out of fuel and eventually dies.

The Sun is a massive object, with a diameter of about 1.39 million kilometers, which is about 109 times the size of Earth. It is made up mostly of hydrogen and helium, which undergo nuclear fusion in its core, producing enormous amounts of energy that radiate out into space as light and heat. This energy drives the weather and climate on Earth, and also powers all life on our planet.

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Complete Question:

you are a superman (or superwomen). With what terrific-human feat may want to you growth the length of a tidal day?

a. accelerate the rotation of the moon across the sun

b. increase the mass of the moon

c. speed up the rotation of the earth around its axis

d. slow the rotation of the moon across the earth

e. decrease the mass of the earth

The primary difference between speed and velocity is that speed is a scalar quantity that describes how fast an object is moving, while velocity is a vector quantity that describes how fast an object is moving in a particular direction

Speed and velocity are two critical concepts in physics. They are used to describe the motion of an object. While both describe how fast an object is moving, there are some fundamental differences between the two. Let's explore these differences.

What is speed?

Speed is a scalar quantity that describes how quickly an object moves. It is measured in meters per second (m/s) or kilometers per hour (km/h).

Speed can be calculated using the following formula:

speed = distance ÷ time

For example,

if an object covers a distance of 150 meters in 10 seconds, its speed can be calculated as follows:

Speed = distance ÷ time= 150 meters ÷ 10 seconds= 15 meters per second (m/s)

What is velocity?

Velocity, on the other hand, is a vector quantity that describes how fast an object is moving in a particular direction. It is measured in meters per second (m/s) or kilometers per hour (km/h).

Velocity can be calculated using the following formula:

velocity = displacement ÷ time

For example, if an object travels a displacement of 150 meters in 10 seconds in a specific direction, its velocity can be calculated as follows:

Velocity = displacement ÷ time= 150 meters ÷ 10 seconds= 15 meters per second (m/s) in a specific direction.

In conclusion, the primary difference between speed and velocity is that speed is a scalar quantity that describes how fast an object is moving, while velocity is a vector quantity that describes how fast an object is moving in a particular direction.

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Answer:

Explanation:

The answer to your question would be number 2 amplitude and frequency are the same so the higher the frequency the higher the amplitude. As you can see in the picture wave E has the  highest frequency. which means since A has the lowest  frequency and E has the highest frequency answer 2 would be correct the amplitude increases from A to E.

Amplitude of a wave is the strength of the wave. It is measured from the central line of the wave to the top of the crest or bottom of the trough. Thus, higher amplitude waves will gives sharp crests and troughs. Here amplitude is increasing from A to E.

Amplitude is a parameter measuring the strength of a wave. It is the maximum displacement moved by the wave from its equilibrium position. The vibrational path will be twice that of the amplitude of the wave.

As the amplitude of the wave increases its intensity increases. Both are in direct proportion with the frequency and energy of a wave. For instance the amplification of sound waves increases the intensity of waves that we hear.

The distance between two consecutive crests or troughs is the wavelength of the wave not amplitude. Amplitude is measured from the axis line to the top of the crest thus, from exact middle of the wave crest to the top or to the bottom of trough.

Thus, higher amplitude waves will gives sharp crests and troughs. Here amplitude is increasing from A to E

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A rigid insulated rod, with two unequal charges attached to its ends, is placed in a uniform electric field E. The rod experiences a net force to the left and a counterclockwise rotation. The correct option is B.

The unequal charges attached to the ends of the rod experience a force due to the uniform electric field. The upper charge experiences a force to the left, while the bottom charge experiences a force to the right.

According to Coulomb's Law, the magnitude of the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Since the upper charge is twice the magnitude of the bottom charge, the force on the upper charge will be twice as strong.

Therefore, the net force on the rod will be to the left, since the force on the upper charge to the left is greater than the force on the bottom charge to the right. Additionally, the torque on the rod will be counterclockwise since the forces are acting in opposite directions and creating a rotational force.

Thus, the correct option is (B) net force to the left and a counterclockwise rotation.

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K12 is a term that refers to the education system that covers primary and secondary education, typically from kindergarten through 12th grade. A K12 test would, therefore, be an assessment or examination that is designed for students within this educational framework.

Question 1:

DNA (deoxyribonucleic acid) is a molecule that carries the genetic instructions for the development, functioning, and reproduction of all living organisms. It consists of two strands twisted into a double helix structure and is composed of nucleotides containing a sugar-phosphate backbone and nitrogenous bases (adenine, thymine, cytosine, and guanine).

Question 2:

The cell needs to make copies of DNA before dividing to ensure that each daughter cell receives a complete set of genetic information. During cell division, the DNA is replicated through a process called DNA replication, where each strand of the double helix is used as a template to create two identical DNA molecules. This ensures genetic continuity and the transmission of genetic information to offspring cells.

Question 3:

Mutations in DNA can be caused by errors that occur during DNA replication, where mistakes or changes in the nucleotide sequence may occur. Additionally, mutations can be caused by external factors known as mutagens, such as radiation, certain chemicals, or environmental factors, which can damage or alter the DNA sequence.

Question 4:

When we say that DNA strands are complementary, it means that the nucleotide bases on one strand pair specifically with their complementary bases on the opposite strand through hydrogen bonding. Adenine (A) always pairs with thymine (T), and cytosine (C) always pairs with guanine (G). This complementary base pairing ensures the accurate replication and transcription of DNA.

Question 5:

During DNA replication, the new DNA strand formed is complementary to the original template strand. This means that the sequence of nucleotides in the new strand is precisely complementary to the sequence in the original strand. However, it is important to note that both strands of the double helix are used as templates during replication, resulting in two new DNA molecules, each with one original strand and one newly synthesized complementary strand. Therefore, each new DNA molecule consists of one original strand and one newly synthesized strand, making them identical to each other and slightly different from the original DNA molecule.

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The complete question is:

Question 1: What is DNA?

Question 2: Why must the cell make copies of DNA before it can divide?

Question 3: What causes mutations in DNA?

Question 4: What does it mean for DNA strands to be complementary?

Question 5: How is the new DNA strand formed during replication different from the original strand?

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The speed of the plane relative to the ground is approximately 63.25 mi/hr, the position vector is v_g = (-42)i + (-42)j + (-21)k.

To find the position vector representing the velocity of the plane relative to the ground, we need to consider the vectors representing the velocity of the plane relative to the air (v_a), the velocity of the horizontal crosswind (v_w), and the velocity of the vertical downdraft (v_d).

Given:

Velocity of the plane relative to the air: v_a = 42 mi/hr south

Velocity of the horizontal crosswind: v_w = 42 mi/hr west

Velocity of the vertical downdraft: v_d = 21 mi/hr downward

The position vector representing the velocity of the plane relative to the ground is obtained by adding these vectors together:

v_ground = v_a + v_w + v_d.
v_g = (0 - 42 + 0)i + (-42 + 0 + 0)j + (0 + 0 - 21)k
v_g = (-42)i + (-42)j + (-21)k
b. To find the speed of the plane relative to the ground, we compute the magnitude of the vector v_g:
|v_g| = √((-42)^2 + (-42)^2 + (-21)^2)
|v_g| ≈ 63.25 mi/hr
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Answer:

low melting point

Ionic compounds have high melting and boiling points. This is because a considerable amount of energy is required to break the strong inter-ionic attraction

Explanation:

Answer:

Neodymium (Nd)

Explanation:

An element is made up of atom, which contains three subatomic particles namely; proton, electron, and neutron. In a neutral atom, the number of protons determines the atomic number of that element and the atomic number of an element is the identity of that element in the periodic table.

Hence, a change in the proton number of an element means a change in the atomic number and ultimately a change of that element. In this question, Europium (Eu) element with atomic number, 63, loses three protons. This means that that atom now has 60 protons, which denotes the atomic number of another element called Neodymium (Nd).

Therefore, Europium (Eu) element has become Neodymium (Nd) due to loss of protons.

The scientist responsible for the modern periodic table that we study today is Dmitri Mendeleev. Mendeleev was a Russian chemist who lived in the 19th century. He is often credited as the creator of the periodic table because of his significant contributions to its development.

In the mid-1860s, Mendeleev was working on organizing the known elements based on their chemical properties. He noticed that there was a recurring pattern in the properties of the elements when they were arranged in order of increasing atomic mass. Mendeleev proposed that these elements could be arranged in a table format, where elements with similar properties would fall into the same groups or columns.

Mendeleev's breakthrough came when he realized that there were some gaps or missing elements in his proposed table. Instead of discarding these gaps, he made a bold move and predicted the existence and properties of the yet-to-be-discovered elements. He left spaces for these elements, specifying their properties based on the patterns he observed.

What made Mendeleev's periodic table significant was that it not only organized the elements based on their atomic masses but also successfully predicted the properties of the missing elements. Over time, his predictions were proven correct when the missing elements were discovered and found to match Mendeleev's descriptions.

Mendeleev's periodic table formed the foundation for the modern periodic table that we use today. Although there have been some modifications and improvements to the table since Mendeleev's time, his work laid the groundwork for understanding the periodicity and organizing the elements based on their properties. His contributions to the field of chemistry and the development of the periodic table have had a lasting impact on our understanding of the elements and their relationships.

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Threshold 1 and Threshold 2 Accelerated Remitters will receive a PD7A-AR CRA Statement of Account. Option B is correct.

The CRA Statement of Account that would be received by Threshold 1 and 2 accelerated remitters is PD7A-AR.

CRA Statement of Account. The CRA statement of account is a statement of your account with the Canada Revenue Agency (CRA) which shows the balance owed or the credit available to you. CRA account statements can be used to check your account balance, view transactions, and payments made towards your balance.

In conclusion, Threshold 1 and 2 accelerated remitters receive a PD7A-AR CRA Statement of Account.

Therefore, Option B is correct.

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Space telescopes must be placed in orbit around earth in order to observe short-wavelength radiation.

A telescope is an optical instrument that uses lenses, curved mirrors, or a combination of both to watch distant objects.

When atoms in a gas reach this temperature, they travel so quickly that when they collide, they release X-ray photons with wavelengths smaller than 10 nanometers.

Because the Earth's atmosphere prevents all X-rays from space, these wavelengths must be seen using space telescopes.

To study short-wavelength radiation, space telescopes must be put in orbit around the Earth.

Hence, space telescope is the correct answer.

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Work done = 3 J, stretch distance = 15 cm = 0.15 m The work done in stretching a spring is stored as the potential energy of the spring. The potential energy of the spring is given by the formula PE = ½ kx²Where k is the spring constant and x is.

the stretch distance of the spring .At natural length, the spring has no potential energy because it is not stretched. Therefore, the stretch distance of the spring, x = 0.15 m. Then, 3 J = ½ k(0.15)² ⇒ 3 J = 0.01125 k ⇒ k = 3/0.01125 = 266.67 N/m Hence, the force that holds the spring stretched at the same distance (15 cm) is given by;F = kx = 266.67 N/m × 0.15 m = 40 N. that the force that holds the spring stretched at the same distance (15 cm) is 40 N.T given above. We are given the work done (W) as 3 Joules and stretch distance (x) as 15 cm.

The work done (W) in stretching a spring is stored as potential energy (PE). The potential energy of the spring is given by the formula PE = 1/2 kx²Where k is the spring constant and x is the stretch distance of the spring. At the natural length, the spring has no potential energy because it is not stretched. Therefore, the stretch distance of the spring, x = 0.15 m.Then,3 Joules = 1/2 * k * 0.15²3 = 0.01125 k266.67 N/m = k,  as k = 3/0.01125 = 266.67 N/m Hence, the force that holds the spring stretched at the same distance (15 cm) is given by F = kx = 266.67 N/m × 0.15 m = 40 N.

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A spring-loaded ballistic cart is in contact with a second cart. The velocity of the other cart is 0.25 m/s.

When there is no external force acting on the system, the initial momentum is equal to the final momentum.

Momentum is equal to the product of mass and its velocity.

According to the conservation of linear momentum,

m₁v₁ +m₂v₂ = m₁u₁ +m₂u₂

u and v represents the initial and final velocity. 1 and 2 represents the first and second cart.

Given is m₁ = 0.5 kg, m₂ =0.8kg, u₁ =u₂ =0 m/s and v₁ = 0.4 m/s.

Substituting the values in the conservation of momentum equation, we get the velocity of second cart is

0.5 x 0.4 + 0.8 x v₂ = 0.5 x 0 + 0.8 x 0

v₂ = +0.25 m/s (in the direction of first cart)

Thus,  the velocity of the other cart is 0.25 m/s.

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