what is the magnification and the length of an astronomical telescope with
Fo=985mm
Fe=5.0mm
a. -5,197mm
b.-140,985mm
c.-120,197mm
d.-167,990mm
e.-197,990mm

the slope of the spring force v. position plot should be negative. True

The spring force is given by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement or change in position of the spring from its equilibrium position. Mathematically, this can be expressed as F = -kx, where F is the spring force, k is the spring constant, and x is the displacement.

Since the spring force is proportional to the displacement with a negative sign, it means that as the position or displacement increases in one direction, the spring force will be in the opposite direction, resulting in a negative slope on the force versus position plot.

Learn more about Hooke's Law:

https://brainly.com/question/2648431

#SPJ11

The condition that determines whether a block will sink or float is based on the density of the block compared to the density of the fluid it is placed in. The density of an object is determined by its mass per unit volume.

If the density of the block is greater than the density of the fluid, the block will sink. This is because the block is denser than the fluid, and therefore, the buoyant force exerted on the block by the fluid is not enough to overcome the gravitational force acting on the block.

On the other hand, if the density of the block is less than the density of the fluid, the block will float. This is because the block is less dense than the fluid, and the buoyant force exerted on the block is greater than the gravitational force acting on it, allowing it to float on the surface of the fluid.

In summary, whether a block sinks or floats is determined by the relationship between the densities of the block and the fluid it is placed in.

To learn more about density visit: https://brainly.com/question/1354972

#SPJ11

The flux through surface 1 (φ1) is 3200 Newton meters squared per coulomb.

To calculate the flux through surface 1 (φ1) in Newton meters squared per coulomb, we can use the formula:

φ1 = E * A * cos(θ)

where E is the magnitude of the electric field, A is the area of the surface, and θ is the angle between the electric field vector and the normal vector of the surface.

In this case, the magnitude of the electric field is given as 400 N/C. The surface is a rectangle with sides measuring 4.0 m in width and 2.0 m in length.

First, let's calculate the area of the surface:

A = width * length

A = 4.0 m * 2.0 m

A = 8.0 m²

Since the surface is a rectangle, the angle θ between the electric field and the normal vector is 0 degrees (cos(0) = 1).

Now, we can substitute the given values into the flux formula:

φ1 = E * A * cos(θ)

φ1 = 400 N/C * 8.0 m² * cos(0)

φ1 = 3200 N·m²/C

Therefore, the flux through surface 1 (φ1) is 3200 Newton meters squared per coulomb.

The question should be:
what is the flux through surface 1 φ1, in newton meters squared per coulomb? The magnitude of electric field is 400N/C. Where, the surface is a rectangle, and the sides are 4.0 m in width and 2.0 min length.

Learn more about flux at: https://brainly.com/question/10736183

#SPJ11

The charge when you charge a foam block by rubbing with fur or hair is localized in the spots where the foam was rubbed. This is due to the transfer of electrons from one object to another.

When we rub a foam block with fur or hair, the foam gains a negative charge while the fur or hair gains a positive charge. This is due to the transfer of electrons from one object to another. However, the charge is not evenly distributed through the foam block and is localized in the spots where the foam was rubbed. The other part of the foam will remain neutral in charge.

This is because the electrons only transfer in the region where the rubbing occurs. Hence, the charge is concentrated in the rubbed region only.In conclusion, it can be said that when a foam block is charged by rubbing with fur or hair, the charge is not evenly distributed through the block. It is localized in the spots where the foam was rubbed.

To know more about electrons visit:

https://brainly.com/question/12001116

#SPJ11

When air resistance is ignored, only the initial velocity and the angle of projection affect the range and maximum height of the projectile.

The range refers to the horizontal distance covered by the projectile, while the maximum height refers to the highest point reached during its flight.

To understand how the initial velocity and angle of projection influence the projectile's range and maximum height, let's consider a simple example of a projectile being launched at an angle.

1. Initial velocity: The initial velocity of the projectile determines how fast it is launched. A higher initial velocity will result in a greater range and a higher maximum height. This is because a higher velocity allows the projectile to cover more distance horizontally and reach a higher vertical position before gravity brings it back down.

2. Angle of projection: The angle at which the projectile is launched also affects its range and maximum height. The optimal angle for maximum range is 45 degrees, as it allows for an equal distribution of horizontal and vertical displacement. At this angle, the projectile will reach the maximum distance. However, the maximum height will be lower compared to a different angle of projection.

In conclusion, when air resistance is ignored, only the initial velocity and angle of projection affect the range and maximum height of the projectile. By adjusting these factors, we can manipulate the projectile's trajectory and achieve the desired outcomes.

Learn more about projectile at: https://brainly.com/question/8104921

#SPJ11

The speed of the Earth's rotation affects the length of a day, which in turn influences various aspects of life, including the distribution of sunlight, temperature patterns, and the overall dynamics of ecosystems.

To calculate the speed of the Earth's rotation 155 million years ago, we need to consider the rate at which the Earth's rotation is slowing down. According to the given information, the Earth slows down 1/30000 of a minute every 100 years.

Let's first calculate the change in the Earth's rotation speed over 155 million years:

Change in rotation speed = (1/30000 minute/100 years) * (155 million years)

Now we can calculate the speed of the Earth's rotation at that time:

Current rotation speed - Change in rotation speed

Given that the current rotation speed is 1670 kilometers/hour, we can substitute the values and calculate:

Rotation speed at that time = 1670 km/hour - (Change in rotation speed)

Once we have determined the rotation speed at that time, we can assess its potential impact on the movement of dinosaurs or mankind.

A change in the rotation speed could have implications for the behavior, adaptation, and survival of living organisms, including dinosaurs and early humans.

However, it is important to note that the exact magnitude and direct consequences of changes in rotation speed on specific species and their movements would require a more detailed analysis and consideration of various ecological factors.

To know more about  influences refer here:

https://brainly.com/question/30364017#

#SPJ11

The stator core length: Stator core length (Lc) = Ampere conductors per meter / (π × Ds) Lc = 34000 / (π × 1.7634 m)

Lc ≈ 6101.65 m

To determine the main dimensions for the given alternator, we can use the following steps:

Step 1: Calculate the line current:

Line current (IL) = Apparent power (S) / (√3 × Line voltage)

IL = 3000 kVA / (√3 × 6.6 kV)

IL ≈ 246.36 A

Step 2: Calculate the rotor speed:

Rotor speed (N) = Frequency (f) × 60 / Number of poles

N = 50 Hz × 60 / 2

N = 1500 RPM

Step 3: Calculate the rotor diameter:

Rotor diameter (D) = Peripheral speed (V) / (π × N / 60)

D = 60 m/s / (π × 187.5 / 60)

D ≈ 0.963 m

Step 4: Calculate the rotor circumference:

Rotor circumference (C) = π × D

C ≈ π × 0.963 m

C ≈ 3.028 m

Step 5: Calculate the air gap diameter:

Air gap diameter (Da) = Rotor diameter + (2 × Air gap clearance)

Assuming a typical air gap clearance of 0.2 mm (0.0002 m):

Da = 0.963 m + (2 × 0.0002 m)

Da ≈ 0.9634 m

Step 6: Calculate the stator diameter:

Stator diameter (Ds) = Da + (2 × Average air gap flux density)

Ds = 0.9634 m + (2 × 0.6 Wb/m2)

Ds ≈ 1.7634 m

Step 7: Calculate the stator circumference:

Stator circumference (Cs) = π × Ds

Cs ≈ π × 1.7634 m

Cs ≈ 5.54 m

Step 8: Calculate the stator core length:

Stator core length (Lc) = Ampere conductors per meter / (π × Ds)

Lc = 34000 / (π × 1.7634 m)

Lc ≈ 6101.65 m

The main dimensions for the given alternator are as follows:

Rotor diameter (D): Approximately 0.963 meters

Air gap diameter (Da): Approximately 0.9634 meters

Stator diameter (Ds): Approximately 1.7634 meters

Stator core length (Lc): Approximately 6101.65 meters

Stator circumference (Cs): Approximately 5.54 meters

Note: These calculations are based on the given parameters and assumptions. Actual alternator designs may involve additional considerations and engineering factors.

To know more about Stator refer here:
https://brainly.com/question/32404968#

#SPJ11

The total number of electrons transported from the positive electrode to the negative electrode by the charge escalator is Q/(1.6 x 10^-19 C).

The given equation represents the current supplied by a battery as a function of time. The equation is I(t) = (0.930 A)e^(-t/6hr), where I(t) is the current in amperes at time t in hours.

To find the total number of electrons transported from the positive electrode to the negative electrode, we need to determine the total charge transferred. The charge is given by the equation Q = ∫I(t)dt, where Q is the charge in coulombs and the integral is taken over the time interval from when the battery is first used until it is completely dead.

We can rewrite the equation for current as I(t) = (0.930 A)e^(-t/6hr) as I(t) = 0.930e^(-t/6hr).

Now, we can substitute this equation for current into the charge equation: Q = ∫I(t)dt = ∫(0.930e^(-t/6hr))dt.

Integrating this equation gives us Q = -5.58e^(-t/6hr) + C, where C is the constant of integration.

To find the total charge transferred from the positive electrode to the negative electrode, we need to evaluate the integral from the initial time to the final time. Since the battery is completely dead, the final time is infinity.

So, Q = lim(t→∞) (-5.58e^(-t/6hr) + C).

As t approaches infinity, e^(-t/6hr) approaches 0, so the first term becomes 0. Therefore, Q = C.

The total number of electrons transported is given by Q divided by the elementary charge, e, which is approximately 1.6 x 10^-19 C.

To learn more about electrons

https://brainly.com/question/12001116

#SPJ11

The largest force P that can be applied to the cord without causing motion is approximately 95.4 N.

To determine the largest force P, we need to consider the forces acting on the system and the conditions for static equilibrium.

The blocks A and B are connected by a cord that passes over pulleys at C and D. The coefficient of static friction between block A and the surface it rests on is μ₁, and the coefficient of static friction between block B and the surface it rests on is μ₂.

For block A to remain in equilibrium, the force applied by the cord (P) must be less than or equal to the maximum static friction force (f₁) between block A and the surface:

P ≤ f₁ = μ₁ * m₁ * g

Similarly, for block B to remain in equilibrium, the force applied by the cord must be less than or equal to the maximum static friction force (f₂) between block B and the surface:

P ≤ f₂ = μ₂ * m₂ * g

where m₁ and m₂ are the masses of blocks A and B, g is the acceleration due to gravity.

Given that the masses of blocks A and B are 8 kg and 12 kg respectively, we need the coefficients of static friction (μ₁ and μ₂) to calculate the maximum force P.

To learn more about static fiction

brainly.com/question/29587655

#SPJ11

The approximate maximum velocity of the car is 7.07 m/s.

To find the approximate maximum velocity of the car, we can use the equation of motion:

v^2 = u^2 + 2as

Where:

v = final velocity

u = initial velocity

a = acceleration

s = displacement

In this case, the car starts with an initial velocity (u) of 10 m/s and comes to a stop with a final velocity (v) of 10 m/s. The displacement (s) is given as 100 m. The acceleration (a) will be the same magnitude for both the acceleration and deceleration phases.

For the acceleration phase, the car starts from rest (u = 0 m/s) and accelerates to the maximum velocity. Let's denote this maximum velocity as vmax.

Using the equation of motion for the acceleration phase:

vmax^2 = 0^2 + 2a(100)

Simplifying the equation:

vmax^2 = 200a

For the deceleration phase, the car goes from the maximum velocity (vmax) to a final velocity of 10 m/s. Again, the displacement is 100 m.

Using the equation of motion for the deceleration phase:

10^2 = vmax^2 + 2a(100)

Simplifying the equation:

100 = vmax^2 + 200a

Now, we have a system of two equations with two variables (vmax and a). By solving these equations simultaneously, we can find the approximate maximum velocity (vmax).

Subtracting the first equation from the second equation:

100 - 200a = 200a

Simplifying the equation:

100 = 400a

Solving for a:

a = 0.25 m/s^2

Substituting the value of a into the first equation:

vmax^2 = 200(0.25)

Simplifying the equation:

vmax^2 = 50

Taking the square root of both sides:

vmax ≈ √50

vmax ≈ 7.07 m/s

Learn more about maximum velocity here :-

https://brainly.com/question/30763982

#SPJ11

The Warren Field calendar is not considered to be the oldest calendar in the world. There are older known calendars, such as the archaeological site of Gobekli Tepe in Turkey, which dates back to around 9600 BCE.

The Warren Field calendar, located in Scotland, consists of 12 pits arranged in a roughly circular pattern. It has been suggested that these pits were used to track the lunar phases and mark the passage of time, making it a lunar calendar. However, there is ongoing debate among archaeologists regarding the purpose and exact age of the Warren Field calendar.

As for the claim that the Warren Field calendar builders developed the world's first star catalog and made significant contributions to the calculations of planetary movements during a golden age of astronomy, there is no historical evidence to support this. The Warren Field calendar consists of 12 pits arranged in a circular pattern, which some researchers believe were used to track lunar phases. However, there is ongoing debate and speculation about the purpose and age of the calendar.

While the Warren Field calendar is an intriguing archaeological site, it is not considered the oldest calendar in the world. There are other ancient calendars, such as those found at Gobekli Tepe, that predate it. Additionally, the claim that the Warren Field calendar builders developed the world's first star catalog and made significant contributions to astronomy during a golden age is not supported by historical evidence.

To know more about calendar, visit;
https://brainly.com/question/29468701
#SPJ11

(1) The smallest distance from the grating where the converging lens can be placed is 0.25 meters. (2) The two first-order beams will appear approximately 4.1 × 10⁻⁴ meters apart on the screen.

To solve these problems, we need to use the formula for the angle of diffraction produced by a diffraction grating:

sin(θ) = m * λ / d

where:

θ is the angle of diffraction,

m is the order of the diffraction (1 for first order, 2 for second order, etc.),

λ is the wavelength of the incident light, and

d is the spacing between the grating lines.

Let's solve the problems step by step:

1. Finding the distance of the converging lens:

We need to find the smallest distance from the grating where a converging lens can be placed to make the diffracted light converge to a point 1.0 meter from the grating.

We can use the lens formula:

1/f = 1/v - 1/u

where:

f is the focal length of the lens,

v is the image distance, and

u is the object distance.

In this case, the image distance (v) is 1.0 meter and we need to find the object distance (u). We can assume that the object distance (u) is the distance from the grating to the lens.

Let's rearrange the lens formula to solve for u:

1/u = 1/v - 1/f

1/u = 1/1.0 - 1/0.20

1/u = 1 - 5

1/u = -4

u = -1/4 = -0.25 meters

Therefore, the smallest distance from the grating where the converging lens can be placed is 0.25 meters.

2. Finding the separation between the first order beams on the screen:

For a diffraction grating, the angular separation between adjacent orders of diffraction can be given by:

Δθ = λ / d

In this case, we are interested in the first order beams, so m = 1.

Let's calculate the angular separation:

Δθ = λ / d

Δθ = 6.56 × 10⁻⁷ / 1.6 × 10⁻³

Δθ ≈ 4.1 × 10⁻⁴ radians

Now, we can calculate the separation between the first order beams on the screen using the small angle approximation:

s = L * Δθ

where:

s is the separation between the beams on the screen, and

L is the distance from the grating to the screen.

Calculating the separation:

s = L * Δθ

s = 1.0 * 4.1 × 10⁻⁴

s ≈ 4.1 × 10⁻⁴ meters

Therefore, the two first-order beams will appear approximately 4.1 × 10⁻⁴ meters apart on the screen.

To know more about the diffraction grating refer here,

https://brainly.com/question/14981496#

#SPJ11

Given information, Mass of train, m = 1.0 × 10^77 kg. Acceleration, a = 1.1 m/s^2. The train applies brakes to slow down. This means that the force acting on the train is opposite to the direction of motion.

Using Newton's second law of motion, we can find out the force required to slow down the train. Force, F = ma Where, m is the mass of the train and a is the acceleration produced by applying the brakes.

Now, putting the values in the above equation we get, F = ma

= 1.0 × 10^77 × 1.1

= 1.1 × 10^77 N.

This means that more than 100 (1.1 × 10^77 is greater than 100) newtons of force are required to slow down the train.

To know more about information visit:

https://brainly.com/question/27798920

#SPJ11

To achieve a current of 1.5mA across the terminals of a resistor connected to a 6V battery, the value of the resistor (R) should be 4,000 ohms.

In order to calculate the value of the resistor (R), we can use Ohm's law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across it divided by its resistance (R). Mathematically, Ohm's law can be expressed as I = V/R.

Given that the desired current (I) is 1.5mA (or 0.0015A) and the voltage (V) across the resistor is 6V, we can rearrange the formula to solve for R. Substituting the values, we have 0.0015A = 6V / R.

To find the value of R, we isolate it by multiplying both sides of the equation by R. This gives us 0.0015A * R = 6V. Next, we divide both sides by 0.0015A to solve for R. This results in R = 6V / 0.0015A.

Performing the calculation, we find that R is equal to 4,000 ohms (or 4 kilohms). Therefore, to achieve a current of 1.5mA across the resistor terminals when connected to a 6V battery, the value of the resistor should be 4,000 ohms.

Learn more about resistance here:

https://brainly.com/question/14547003

#SPJ11

Arthur Holly Compton (1892–1962) was a physicist from the United States. He was a Nobel laureate known for his work on scattering photons in the Compton effect.

Arthur Holly Compton (1892–1962) was a physicist from the United States. He was a Nobel laureate known for his work on scattering photons in the Compton effect. Compton's research dealt with the discovery of new kinds of X-ray scattering that were used to study atomic structures and served as evidence for the photon nature of electromagnetic radiation.

In 1922, Arthur H. Compton carried out an experiment to validate the predictions of the photon model of light scattering by a single electron. The experiment was conducted using an X-ray tube and a suitable crystal to generate and transmit monochromatic X-rays. A block of material containing electrons was placed between the X-ray tube and the crystal. The X-rays were scattered in different directions by the electrons in the block. The scattered X-rays were detected by a Geiger counter at a fixed angle relative to the incident beam.

The incident X-ray energy, the scattered X-ray energy, and the scattering angle were all measured. The intensity of the scattered X-ray radiation was then measured. The degree of Compton scattering was determined by measuring the energy loss of the incident photon, which was shown to be a result of its interaction with the electron beam.The results of the experiment validated the photon model of light scattering by a single electron, indicating that the electron beam acted as a photon.

To know more about Compton effect visit:

https://brainly.com/question/30683759

#SPJ11

The question asks to calculate the energy per nucleon released in the nuclear reaction Li + 2H → 2He and compare it with the energy per nucleon released in the fission of a 235U nucleus.

In the given nuclear reaction, lithium (Li) combines with two hydrogen (H) nuclei to form two helium (He) nuclei. To calculate the energy per nucleon liberated in this reaction, we need to determine the initial and final masses and use Einstein's famous equation, E = mc², to calculate the energy difference. By subtracting the initial mass from the final mass and dividing it by the total number of nucleons, we can obtain the energy per nucleon.

Now, comparing this energy per nucleon with the energy per nucleon liberated in the fission of a 235U nucleus, we consider the process of nuclear fission where a heavy nucleus (in this case, 235U) splits into two or more lighter nuclei. Fission is accompanied by the release of a significant amount of energy. The energy per nucleon liberated in nuclear fission is usually higher than that in fusion reactions, like the one involving lithium and hydrogen. The fission of a 235U nucleus typically releases more energy per nucleon due to the large energy released during the splitting of a heavy nucleus into lighter fragments.

Learn more about Nuclear Reactor:

https://brainly.com/question/9566647

#SPJ11

The given circuit is a voltage doubler circuit which is used to double the input voltage. The circuit is connected by using C1 capacitor only and the resistor R1. The measured value of the C1 capacitor is 0.14 F and the value of the resistor R1 is 1.0 kΩ.

In the given problem, the value of the capacitor C1 and the resistor R1 are given. Using the given components, the voltage doubler circuit is connected. The voltage doubler circuit doubles the input voltage. During the charging of the capacitor C1, the diode D1 is forward biased and it conducts. After the charging of capacitor C1, the voltage across the capacitor C1 is equal to the input voltage. During the discharge of capacitor C1, the diode D2 is forward biased and it conducts.

When the diode D2 conducts, the voltage across the capacitor C2 is equal to the voltage across the capacitor C1 and the input voltage. Hence, the voltage across the capacitor C2 is equal to two times the input voltage.Thus, we have obtained the measured values of the components used in the voltage doubler circuit and connected the circuit by using the given components. We have also analyzed the working of the voltage doubler circuit and understood that it doubles the input voltage.

Therefore, the given problem is solved and the measured values of the components used in the voltage doubler circuit are obtained. The voltage doubler circuit is connected by using the given components and its working is analyzed.

To know more about circuit visit:

brainly.com/question/29245200

#SPJ11

The wagon still accelerates despite exerting an equal force on the horse because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

Newton's third law of motion states that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. In this scenario, the horse exerts a force of 500 N on the wagon, and as a reaction, the wagon pulls back on the horse with an equal force of 500 N.

Despite the equal and opposite forces, the wagon still accelerates. This is because the forces act on different objects. The 500 N force exerted by the horse on the wagon causes the wagon to accelerate forward.

At the same time, the 500 N force exerted by the wagon on the horse does not affect the horse's motion significantly, as the horse is generally much larger and more massive than the wagon.

As a result, the net force acting on the wagon is not zero, leading to its acceleration. The wagon experiences a forward force from the horse and a negligible backward force from the wagon itself, allowing it to accelerate in the direction of the applied force.

Learn more about third law here:

https://brainly.com/question/29768600

#SPJ11

The numbers at a, b, f and g have two significant figures while the numbers at c, d and h have three significant figures. the number at e has four significant figures.

Here are the number of significant figures in each of the given numbers:

(a) 60 - The number 60 has two significant figures

(b) 5.6 x 10^4 - This number has two significant figures

(c) 5.60 x 10^4 - It has three significant figures

(d) 6.05 x 10^4 - It has three significant figures

(e) 6.050 x 10^4 - It has four significant figures

(f) 0.0056 - It has two significant figures

(g) 0.065 - It has two significant figures

(h) 0.0506 - It has three significant figures.

Learn more about significant figures at https://brainly.com/question/29153641

#SPJ11

The unknown elements in the parallel circuit are a resistor with a value of approximately 16.65 Ω and an inductor with a reactance of approximately 6.13 Ω. The equivalent resistance is approximately 14 Ω, and the equivalent reactance is approximately 34.02 Ω.

The unknown elements in the given parallel circuit are the resistance (R) and the inductive reactance (XL). Their values are found by equating the voltage and current phasors and solve for R and XL separately.

From the given voltage and current:

E = 250∠60° V

i = 12∠25° A

By equating the magnitudes:

250 = 12 × √2 × cos(60° - 25°)

Solving this equation gives us R = 16.65 Ω.

By equating the angles:

tan(XL/R) = tan(60° - 25°)

Solving this equation gives us XL = 6.13 Ω.

Therefore, the unknown element in parallel is a resistor with a value of approximately 16.65 Ω and an inductor with a reactance of approximately 6.13 Ω.

The current (I = 10 A), voltage (V = 140 V), and power (P = 450 W) of a coil connected to a 50 Hz source. We find the equivalent resistance (R) and reactance (X) when the coil is joined in parallel.

Using the power formula for AC circuits:

P = VI cos(θ)

450 = 140 × 10 × cos(θ)

Solving for the power factor angle (θ), we find:

cos(θ) = 450 / (140 × 10) = 0.3214

θ ≈ arccos(0.3214) ≈ 71.41°

The power factor angle (θ) represents the phase difference between the voltage and current. Since they are joined in parallel, the voltage and current in the coil are in phase (θ = 0°). Thus, the power factor angle should ideally be 0° for a purely resistive component.

Calculating the equivalent resistance:

R = V / I = 140 V / 10 A = 14 Ω

Calculating the equivalent reactance:

tan(θ) = X / R

tan(71.41°) = X / 14 Ω

Solving for X, we find:

X ≈ 34.02 Ω

Therefore, the equivalent values for resistance and reactance in the parallel circuit are approximately R = 14 Ω and X = 34.02 Ω.

To know more about parallel circuits, refer to the link:

https://brainly.com/question/4069479#

#SPJ11

When you run and jump onto a stationary skateboard to ride forward, you receive an impulse from the skateboard in the forward direction. The statement "For an isolated system, the magnitude of the total momentum can change" is false because total momentum of an isolated system remains constant.

This is because the impulse is the change in momentum of an object, and momentum is a vector quantity. When you land on the skateboard, it applies a force on you in the forward direction over a short period of time, which causes a change in your momentum. As a result, you gain forward momentum, allowing you to move forward on the skateboard.

For the second question, in an isolated system, the magnitude of the total momentum remains constant. This statement is false. According to the law of conservation of momentum, the total momentum of an isolated system remains constant if there are no external forces acting on the system.

However, this does not mean that the magnitude of the total momentum cannot change. The direction and distribution of momentum within the system can change, but the total momentum remains constant. In other words, the vector sum of all momenta within the system is conserved, but the individual magnitudes of those momenta can change.

Learn more about isolated system here: https://brainly.com/question/13176875

#SPJ11

The time taken by the rod to turn through a right angle after an impulse is applied to the end B is 2ti ml.

When an impulse is applied to the end B of the uniform rod AB, it imparts an angular momentum to the rod. The angular momentum of the rod is given by the product of the moment of inertia and the angular velocity. Initially, the rod is at rest, so its angular momentum is zero. As the impulse is applied, the angular momentum of the rod increases. In order to turn through a right angle, the rod needs to acquire an angular momentum equal to its moment of inertia multiplied by the angular velocity required for a right angle turn. The time taken for the rod to turn through a right angle can be calculated using the equation of angular momentum. Since the impulse is applied at the end B, the moment of inertia of the rod about B is ml^2/3. The angular velocity required for a right angle turn is π/2 radians. Therefore, the angular momentum required for the rod to turn through a right angle is (ml^2/3) * (π/2). Using the equation of angular momentum, we can equate the initial angular momentum (zero) to the final angular momentum and solve for time. The final angular momentum is (ml^2/3) * (π/2). By substituting the values and solving the equation, we find that the time taken by the rod to turn through a right angle is 2ti ml.

Learn more about impulse;

https://brainly.com/question/16980676

#SPJ11

The charge on each electrode right after the battery is disconnected can be determined using the formula for the capacitance of a parallel-plate capacitor and the voltage of the battery.

The capacitance of a parallel-plate capacitor is given by the formula C = ε₀A/d, where C is the capacitance, ε₀ is the permittivity of free space, A is the area of one electrode, and d is the separation between the electrodes.

In this case, the electrodes have a diameter of 11 cm, which means each electrode has a radius of 5.5 cm. Using the formula for the area of a circle, we can calculate the area of each electrode. The separation between the electrodes is given as 0.60 cm.

Next, we need to consider the voltage of the battery, which is 11 V. When the battery is connected to the capacitor, it charges the capacitor and establishes a potential difference across the electrodes. This potential difference is equal to the voltage of the battery.

After a long time, when the capacitor is disconnected from the battery, it retains the charge on its plates. The charge on each electrode can be calculated by multiplying the capacitance by the voltage.

Learn more about parallel-plate capacitor

#SPJ11.

brainly.com/question/33224145

The coupling torque per motor required to accelerate the train at 1 kmph/s on an up gradient with G 10 is approximately you will arrive the train at 1 kmph/s on an up gradient with G 10.

To calculate the coupling torque per motor required for acceleration, we need to consider several factors and perform a series of calculations. Here are the steps:

1. Determine the total weight of the train:

  Total weight = Weight of locomotive + Weight of train = 80 tonnes + 400 tonnes = 480 tonnes

2. Calculate the total force required to accelerate the train:

  Acceleration force = Mass of train * Acceleration

  Convert 1 kmph/s to m/s²: 1 kmph/s = (1 * 1000) / (60 * 60) m/s² = 0.278 m/s²

  Acceleration force = 480 tonnes * 0.278 m/s²

3. Calculate the gradient force:

  Gradient force = Total weight * Gradient

  Since G = 10, the gradient force = 480 tonnes * 10

4. Calculate the total resistance force:

  Resistance force = Train resistance * Total weight

5. Calculate the total force required from the motors:

  Total force required = Acceleration force + Gradient force + Resistance force

6. Determine the force required per motor:

  Force per motor = Total force required / Number of motors (4 in this case)

7. Calculate the torque required per motor:

  Torque per motor = Force per motor * Radius of armature core

8. Adjust the torque per motor for the reduction gear:

  Torque per motor = Torque per motor / Gear reduction ratio

  Gear reduction ratio = 1 / (1 - Gear reduction ratio)

  Given gear reduction ratio (a) = 0.3

  Gear reduction ratio = 1 / (1 - 0.3)

9. Adjust the torque per motor for transmission efficiency:

  Torque per motor = Torque per motor / Transmission efficiency

  Transmission efficiency = 95%

After performing these calculations, you will arrive at the value for the coupling torque per motor required to accelerate the train at 1 kmph/s on an up gradient with G 10.

To know more about motor click here:

https://brainly.com/question/12989675

#SPJ11

The following statement is not true about friction option d) Friction always helps motion.

Friction is a force that opposes the relative motion between two surfaces in contact. Friction tends to stop a moving object, and it tends to stop a stationary object from moving. Friction acts in the direction opposite to the direction of motion.

Kinetic and static friction are the two most common types of friction. While kinetic friction is between two moving objects, static friction is between two stationary objects.The formula for kinetic friction is given by:f = µ * Nwhere, µ is the coefficient of friction, and N is the normal force acting on the object.

The formula for static friction is given by:f < µ * Nwhere, f is the frictional force, µ is the coefficient of friction, and N is the normal force. Since friction opposes motion, it cannot always help in motion, which is why the statement "Friction always helps motion" is not correct.The correct answer is option d) .

Know more about  Friction    here:

https://brainly.com/question/24338873

#SPJ8

The photon energy in eV of the electromagnetic radiation at maximum intensity emitted by the Earth is approximately 1.23 eV, and this energy corresponds to a wavelength of approximately 1.006 × 10^-5 meters.

To calculate the photon energy using Wien's displacement law, we need to know the temperature at which the radiation is emitted. The maximum intensity is associated with the peak wavelength of the blackbody radiation spectrum. Wien's displacement law states that the peak wavelength (λ_max) of the blackbody radiation spectrum is inversely proportional to the temperature (T): λ_max = b / T where b is Wien's displacement constant, approximately equal to 2.898 × 10^-3 m·K. To convert the wavelength to energy, we can use the relationship between energy (E) and wavelength (λ) given by the equation: E = h * c / λ where h is the Planck's constant (approximately 6.626 × 10^-34 J·s) and c is the speed of light (approximately 3.00 × 10^8 m/s). Let's assume the temperature of the Earth is T = 288 K (average temperature). We can now calculate the photon energy and corresponding wavelength: λ_max = (2.898 × 10^-3 m·K) / 288 K ≈ 1.006 × 10^-5 m E = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (1.006 × 10^-5 m) ≈ 1.98 × 10^-19 J To convert the energy to electron volts (eV), we can use the conversion factor 1 eV = 1.602 × 10^-19 J: E_eV = (1.98 × 10^-19 J) / (1.602 × 10^-19 J/eV) ≈ 1.23 eV Therefore, the photon energy in eV of the electromagnetic radiation at maximum intensity emitted by the Earth is approximately 1.23 eV, and this energy corresponds to a wavelength of approximately 1.006 × 10^-5 meters.

To learn more about electromagnetic, https://brainly.com/question/31038220

#SPJ11

Hooke's Law is a principle in physics that describes the relationship between the force applied to a spring and the resulting deformation or displacement of the spring. According to Hooke's Law, the force applied to a spring is directly proportional to the amount it is stretched or compressed.

In the given problem, a force of 7 pounds is applied to a spring, compressing it by a total of 5 inches. We can use Hooke's Law to determine the variable force exerted by the spring.

Hooke's Law is mathematically expressed as:

F = k * x

Where:

F is the force applied to the spring,

k is the spring constant (a measure of the stiffness of the spring),

x is the displacement or deformation of the spring.

To find the spring constant (k), we can rearrange the equation as:

k = F / x

Given that the force (F) is 7 pounds and the displacement (x) is 5 inches, we can calculate the spring constant:

k = 7 pounds / 5 inches

Once we have the spring constant, we can use it to determine the variable force exerted by the spring for a different displacement. In this case, we want to know the force exerted when the spring is compressed by 8 inches.

F = k * x

Using the spring constant we calculated earlier, and the new displacement of 8 inches:

F = (7 pounds / 5 inches) * 8 inches

F = 56 pounds/inch

So, the variable force exerted by the spring when it is compressed by 8 inches is 56 pounds/inch.

To calculate the work done in compressing the spring by 8 inches, we can use the formula for work:

Work = Force * Distance

In this case, the force is 56 pounds/inch (as we calculated above), and the distance is 8 inches:

Work = 56 pounds/inch * 8 inches

Work = 448 pounds

Therefore, the work done in compressing the spring by 8 inches is 448 pounds.

To know more about Hooke's Law visit:

https://brainly.com/question/30379950

#SPJ11

Dielectrophoresis is a physical phenomenon that occurs when the particles suspended in a medium experience a non-uniform electric field. Dielectrophoresis (DEP) is a phenomenon in which particles suspended in a medium migrate towards regions of higher or lower electric field strength depending on their polarizability.

The following are some of the correct descriptions of dielectrophoresis: Dielectrophoresis (DEP) is a physical phenomenon that occurs when particles suspended in a medium experience a non-uniform electric field. DEP does not require the particles to be charged. The particle size is relevant when determining the strength of the force. The force direction and magnitude can change as a function of frequency. Applications of DEP include cell sorting, enrichment, and separation. Thus, the correct options are A, B, C and D.

to know more about Dielectrophoresis here:

brainly.com/question/33449749

#SPJ11

The governing equation for the car's motion, considering the applied force u(t), the fractional force opposing motion, and the wind force supporting motion, is given by:

[tex]m(d^2x/dt^2) + 5(dx/dt) + 2x(0) = u(t)[/tex]

where m represents the mass of the car and x(0) is the initial displacement.

The equation describes the dynamics of the car's motion, taking into account the applied force u(t), which is a function of time. The term [tex]m(d^2x/dt^2)[/tex] represents the inertia of the car, where m is the mass and [tex](d^2x/dt^2)[/tex] is the acceleration.

The second term, 5(dx/dt), represents the fractional force opposing the motion, which is proportional to the velocity (dx/dt) with a constant of 5. This term accounts for any resistive forces acting against the car's movement.

On the other hand, the wind force is modeled by the term 2x(0), which is proportional to the initial displacement x(0) of the car. This term represents a supporting force that aids the car's motion.

By including both the opposing and supporting forces, the equation captures the complex interplay between different forces acting on the car.

To obtain the transfer function, we apply the Laplace transform to the governing equation. This transforms the differential equation into an algebraic equation in the s-domain, where s is the complex variable.

The resulting transfer function provides a mathematical representation of the system's input-output relationship, which can be used for analysis and control purposes.

Learn more about motion

brainly.com/question/12640444

#SPJ11

The amount of matter, in kilograms, that must be converted to energy to yield 1.0 gigajoule is 1.11 x 10⁻⁴ kg.

To determine the amount of matter, in kilograms, that must be converted to energy to yield 1.0 gigajoule, we can make use of the famous equation by Einstein, E=mc²,

where E represents energy, m represents mass and c represents the speed of light which is approximately 299,792,458 meters per second.

To calculate the amount of matter that needs to be converted to energy, we need to rearrange the formula to make m the subject:

m = E / c²

where E = 1.0 gigajoule

= 1.0 x 10⁹ Jc

= 299,792,458 m/s

Putting these values into the formula, we have:

m = 1.0 x 10⁹ J / (299,792,458 m/s)²

= 1.0 x 10⁹ J / 8.987551787 × 10¹⁶ m²/s²

= 1.112 x 10⁻⁷ kg

Since the answer is in kilograms, we can express it in scientific notation as 1.112 x 10⁻⁴ kg, or rounded off to three significant figures as 1.11 x 10⁻⁴ kg. Therefore, the amount of matter, in kilograms, that must be converted to energy to yield 1.0 gigajoule is 1.11 x 10⁻⁴ kg.

To know more about kilograms visit;

brainly.com/question/29761698

#SPJ11