a ball is floating at equilibrium in water, and exactly half of the ball is in the water. oil is slightly less dense than water. if you float the ball at equilibrium in oil,

Answers

Answer 1

If you float the ball at equilibrium in oil, the ball will have more than half of its volume submerged in the oil.

When an object floats, it moves the same volume of fluid as the object itself weighs. The displaced fluid exerts an upward buoyant force on the object, balancing its weight and allowing it to float at equilibrium.

Since oil is less dense than water, it provides less buoyant force per unit volume compared to water. To achieve equilibrium in oil, the ball would need to displace a greater volume of oil to counteract its weight. As a result, more than half of the ball's volume would need to be submerged in the oil for it to float at equilibrium.

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Complete question:

A ball is floating at equilibrium in water, and exactly half of the ball is in the water. oil is slightly less dense than water. if you float the ball at equilibrium in oil, the ball would have ______


Related Questions

Energy is transferred as heat between two objects, one with a temperature of 5C and the other with a temperature of 20C. If two other objects are to have the same amount of energy transferred between them, what might their temperatures be? I need procedure plss asap, thx

Answers

Answer:

lauda and lasan I am fine with me lit Q ans pg-14

how do icebergs form

Answers

Answer:

They break off large ice sheets found at the North and South poles.

Answer:

The answer is D

Explanation:

They break off large ice sheets found at the poles.

Which of the following individuals would be best classified as being in identity diffusion?
A.
Pauline isn’t interested in politics because she’d like to enjoy being a kid longer.
B.
Richard has decided to become a Democrat after much soul searching.
C.
Maria has adopted her parents’ identification as Protestant without considering other options.
D.
Pierce is trying many different identities but hasn’t decided on one yet.

Answers

Answer: C

Explanation: after reading it over and over shes the most reasonable. But I could be wrong so be cautious.

According to the question, Maria would be best classified as being in identity diffusion. So, option (C) is correct answer.

What is identity diffusion?

People who are experiencing identity diffusion haven't chosen an ideological or occupational route for the future and aren't making any effort to do so. Identity diffusion occurs during adolescence, a time when individuals are attempting to define their identities, but it can also last into adulthood.

When a person isn't actively forming an identity or committing to one, identity diffusion happens.Many people go through a phase of identity diffusion in their early years of adolescence or in childhood, which they eventually grow out of. Long-term identity diffusion is yet conceivable.James Marcia created four "identity statuses" in the 1960s, and identity diffusion is one of them. These identity statuses are a continuation of Erik Erikson's research on the formation of teenage identities.

In the question, Maria has adopted her parents’ identification as Protestant without considering other options. She   haven't chosen an ideological or occupational route for the future and aren't making any effort to do so.  So, Maria  would be best classified as being in identity diffusion.

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How would newton law of motion relate to the movement of bumper car how might the ma of the rider and the peed of the car affect thi movement

Answers

According to the Newtons third law of motion, the collision between the bumper car and the rider will affect both of them as both the systems have mass and are moving with certain velocities.

Collision is a case where one moving object or person violently collides with another.

The law of interaction or the Newton's third law of motion, says that if one body exerts a force on a second body, the second body exerts a force equal in magnitude and opposite in direction on the first body.

It's the law of action-reaction, and it helps to explain why you feel a jolt when you collide with another bumper car.

As we know momentum is P = m*v i.e. momentum (P) is directly proportional to the mass and velocity.

Heavier bodies have more mass, therefore have more momentum.

here, the bumper car is the heavy system and hence, it will exerts more impact on the rider.

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which of the following definitions applies to either rotational or linear accelerations?multiple select question.the rate of change of the rotational displacement.the rate of change of the distance traveled.the rate of change of the velocity.the rate of change of the rotational velocity.

Answers

The definitions that apply to either rotational or linear accelerations are:

The rate of change of the velocity.

The rate of change of the rotational velocity.

Accelerations can be either linear or rotational, depending on the type of motion being considered. Linear acceleration describes the change in velocity of an object that is moving in a straight line, while rotational acceleration describes the change in rotational velocity of an object that is spinning around an axi

In both cases, acceleration is defined as the rate of change of velocity. This means that the acceleration of an object can be calculated by determining the change in velocity over a certain time period.

Linear acceleration is often measured in units of meters per second squared (m/s²), while rotational acceleration is typically measured in units of radians per second squared (rad/s²).

Both types of acceleration are important concepts in physics, and are used to describe a wide range of phenomena, from the motion of vehicles and machines to the behavior of celestial bodies in space.

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On a 100km track , a train travels the first 30km with a speed of 30km/h . How fast the train travel the next 70 km if the average speed for the entire journey is 40km/h?

Answers

Answer:

v = 46.67 km/h

Explanation:

We will use the following formula throughout this numerical:

s = vt

where,

s = distance covered

v = speed

t =  time taken

FOR FIRST 30 km:

s = 30 km

v = 30 km/h

t = t₃₀ = ?

Therefore,

30 km = (30 km/h)(t₃₀)

t₃₀ = (30 km)/(30 km/h)

t₃₀ = 1 h

FOR TOTAL 100 km:

s = 100 km

v = 40 km/h (Average Speed)

t = total time = ?

Therefore,

100 km = (40 km/h)(t)

t = (100 km)/(40 km/h)

t = 2.5 h

FOR LAST 70 km:

s = 70 km

t₇₀ = t - t₃₀ = 2.5 h - 1 h = 1.5 h

v = v₇₀ = ?

Therefore,

70 km = v(1.5 h)

v = 70 km/1.5 h

v = 46.67 km/h

A car is traveling at a speed of 54 km/h. Breaks are applied so as to produce a uniform acceleration of -0.5 m/s2. Find how far the car will go before it is brought to rest

Answers

Explanation:

u=54 km/h

54*5/18=15 m/s

v=0m/s

t=?

acceleration=-0.5m/s^2

we know that a=v-u/t

so,

t=v-u/a

t=15-0/0.5

=15/0.5

=30

therefore, the time is 30 second

Hope this answer helps you..

A hydraulic lift is used to raise an automobile of mass 1520 kg. The radius of the shaft of the lift is 8.00 cm and that of the piston is 1.00 cm. How much force must be applied to the piston to raise the automobile?

Answers

To raise the automobile with a hydraulic lift, a force of approximately 19,000 N must be applied to the piston.

In a hydraulic lift, the principle of Pascal's law is applied, which states that pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container. By utilizing this principle, a smaller force applied to a smaller piston can generate a larger force on a larger piston.

In this scenario, the force needed to lift the automobile can be calculated using the formula:

\(\frac{F_{1}}{A_{1}} =\frac{F_{2}}{A_{2}}\)

where \(F_{1}\) is the force applied to the piston, \(A_{1}\) is the area of the piston, \(F_{2}\) is the force generated on the larger piston (required to lift the automobile), and \(A_{2}\) is the area of the larger piston.

Given the radius of the shaft (small piston) as 0.08 m and the radius of the piston as 0.01 m, we can calculate the forces applied and generated as follows:

\(A_{1} = \pi (0.08)^2\\A_{2}= \pi (0.01)^2\)

\(\frac{F_{1}}{A_{1}} =\frac{F_{2}}{A_{2}}\)

Simplifying the equation and substituting the values, we can solve for \(F_{2}\):

\(F_{2}=\frac{F_{1}A_{2}}{A_{1}}\)

Plugging in the values, we find:

\(F_{2}=\frac{F_{1} \pi (0.01)^2 }{ \pi (0.08)^2} \\F_{2}= \frac{F_{1}\times 0.0001}{0.0064} \\F_{2}= 0.015625 \times F_{1}\)

Given that the mass of the automobile is 1520 kg and the acceleration due to gravity is \(9.8 \hspace m/s^{2}\), we can equate \(F_{2}\) to the weight of the automobile:

\(F_{2}= mg\\0.015625\times F_{1}= 1520\times 9.8\)

Solving for \(F_{1}\), we find:

\(F_{1}\approx \frac{1520\times 9.8}{0.015624} \\F_{1} \approx 19072 \hspace N\)

Therefore, a force of approximately 19,000 N must be applied to the piston in order to raise the automobile using the hydraulic lift.

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Analyze the image. What's the difference between a car traveling at a constant speed and a car traveling at a constant velocity?

Analyze the image. What's the difference between a car traveling at a constant speed and a car traveling

Answers

Speed has only magnitude but velocity has both magnitude and direction.

What is the difference between speed and velocity?

The main difference between a car traveling at a constant speed and a car traveling at a constant velocity is that the constant speed represents only the magnitude but the constant velocity shows the magnitude as well as direction of the vehicle.

So we can conclude that speed has only magnitude but velocity has both magnitude and direction.

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The twisting joint (type T) of an industrial robot has a range of 322° rotation. In order to study the mechanical errors in the joint and the input/output links, a statistical experiment was conducted by taking 10 samples, each one as follows: the joint was commanded to turn and stop at a certain addressable angle and the deviation (in degrees) from that specific angle was recorded. The results of taking 10 samples are presented in the table below: 0.176 0.04 -0.345 0.079 0.309 -0.004 -0.102 0.12 0.075 0.1 Supposing that the statistical distribution of the mechanical errors is normal, determine the number of storage bits required in the controller memory so that the accuracy of the joint is as close as possible to, but less than, its repeatability. Use six standard deviations as the measure of repeatability.

Answers

To determine the number of storage bits required in the controller memory for the twisting joint (type T) of the industrial robot, we need to calculate the repeatability, round the deviations to a reasonable precision, and then calculate the number of addressable positions based on the range of the joint and the chosen accuracy level.


First, let's calculate the repeatability of the joint. Given that the range of rotation is 322°, the repeatability can be calculated as 6 times the standard deviation. Since the standard deviation is a measure of how spread out the data is, multiplying it by 6 ensures that the accuracy of the joint is as close as possible to, but less than, its repeatability.
Next, let's analyze the given data. The 10 samples of deviations from the commanded angles are: 0.176, 0.04, -0.345, 0.079, 0.309, -0.004, -0.102, 0.12, 0.075, and 0.1.
To calculate the standard deviation of these deviations, we need to find the mean and then calculate the differences from the mean. Squaring these differences and taking the average will give us the variance, which we can then take the square root of to obtain the standard deviation.

After calculating the standard deviation, we multiply it by 6 to obtain the repeatability.
Now, to determine the number of storage bits required, we need to consider the accuracy of the joint. The accuracy depends on the precision required for representing the deviations. Assuming a reasonable level of precision, we can round the deviations to, for example, 3 decimal places.
Finally, the number of storage bits required in the controller memory can be calculated by multiplying the range of the joint (322°) by the accuracy (e.g., 0.001°, considering 3 decimal places). This will give us the number of addressable positions, which can be represented by the required number of storage bits.

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When a ball is shot from inside the 3-point arc; it is how many points?.

Answers

The ball is worth two points when it is shot from inside the 3-point arc.

The 3-point arc is a circular arc painted on the basketball court in which a player can take a shot and score three points if the ball goes through the hoop without touching the rim. The 3-point arc is 23 feet 9 inches away from the basket, and it encloses an area known as the 3-point line. Any shot that is taken from beyond the 3-point line and goes through the hoop without touching the rim scores three points.

Conversely, if a shot is taken from inside the 3-point line and goes through the hoop without touching the rim, it scores two points. Therefore, the answer to the question is that a ball is worth two points when it is shot from inside the 3-point arc.

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Mosa and Billy are picked up by a red blood cell, who takes them on their journey. What is the job of the red blood cell? What system is it a part of

Answers

To provide the cells with new oxygen and remove carbon dioxide. the circulatory system's component.

What connections exist between the circulatory and digestive systems?

Before being circulated to other parts of your body for storage or use, the majority of the nutrients in your meal are absorbed in your small intestine. Nutrients are helped to cross the stomach lining and enter the bloodstream by a certain type of cell.

When Billy first enters the bed and breakfast, what does he see?

Billy notices that he wants a BED and BREAKFAST first. He enters and notices a blazing FIRE, a baby grand piano, a large sofa, and cozy ARMCHAIRS. The dog and parrot, in his opinion, are symbols of friendliness and welcome.

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A ball is tossed with enough speed straight up so that it is in the air several seconds. Assume upward direction is positive and downward is negative. Part A What is the velocity of the ball when it reaches its highest point?

Answers

Answer:

Answer:

The velocity of the ball when it reaches its highest point is  0

Explanation:

The velocity of the ball when it reaches its highest point is 0

Once the ball is tossed into the air, as it goes up, the initial velocity with which it was thrown, reduces, as the motion of the ball is hindered by several forces such as gravity and air resistance. This slows down the velocity of the ball, up until it reaches a point, where the upwards velocity of the ball becomes zero. at this point, the ball begins to fall back to the ground.

Explain how each of the following factors affects resistance through a wire:

•Conductivity

•thickness

•length

•temperature

Answers

Resistance through a wire is affected by several factors including conductivity, thickness, length, and temperature.

Conductivity refers to the ability of a material to conduct electricity. The higher the conductivity of a wire, the lower its resistance. This is because a highly conductive wire allows for a larger flow of electrons, making it easier for electricity to pass through.
Thickness also affects resistance. A thicker wire has a lower resistance compared to a thinner wire because it has more surface area for the electrons to flow through. This results in less resistance as the electrons do not have to struggle to pass through a narrow space.
The length of a wire also plays a role in resistance. A longer wire has a higher resistance compared to a shorter wire because the electrons have to travel a longer distance, which results in more collisions with atoms and ions in the wire, thereby impeding the flow of electricity.
Temperature can also affect resistance. Generally, as the temperature of a wire increases, its resistance increases too. This is because the atoms and ions in the wire gain more energy when heated, which results in more collisions with electrons, making it more difficult for them to pass through the wire. However, there are some materials that exhibit a decrease in resistance with an increase in temperature, such as superconductors.
In summary, conductivity, thickness, length, and temperature all affect resistance through a wire. A wire with high conductivity, thickness, and short length, and a low temperature will have low resistance.

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What is the charge Q on the capacitor immediately after the switch is moved to position b?
Express your answer using two significant figures.
Answer must be in microC.

Answers

18 μC is the charge Q on the capacitor immediately after the switch is moved to position b .

The expression for the charge on the capacitor is as follows :

Q = CV

substitute 2.0 μF  for C and 9V for V.

Q = (2μF) {\(\frac{1 * 10^{-6} F }{1μF}\)} (9V)

= 18 * \(10^{-6}\) C

≈ 18 μC

Charge is not stored in capacitors. In reality, capacitors store an unbalanced charge. If a capacitor's one plate has one coulomb of charge stored on it and the other plate has one less, the total charge (added up over both plates) will be zero.

Formula q=CV, where q is the charge stored, C is the capacitance, and V is the applied voltage, describes this relationship.

Always, current flows from -ve to +ve. As a result, charge will move away from the -ve plate and towards the +ve plate. Therefore, the charge on a capacitor always equals the charge on the positive plate, never the negative.

The link between a capacitor's capacitance, its charge, and the voltage across it.

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PLEASE PLEASE help me out I have a few minutes left

Molly is given two identical 300-gram cups that have the same volume of hot chocolate in each Each cup of hot chocolate is at a different temperature. Molly is also given 10 ice cubes that each have the same mass and are at the same temperature.

List the steps of an investigation that uses only the materials described above to show which cup of hot chocolate is hotter.​

Answers

Answer:

me to I have the same question

Explanation:

She can put an ice cube on each cup to see which cube melts faster.

How to determine which cup has more temperature?

First, we know two things:

Both cups have the same volume.All the ice cubes have the same mass.

We can also assume, because of the second thing, that all ice cubes have the same temperature.

Then, one way to know which cup has more temperature is to put one ice cube on each cup, then measure the time it takes for the cube to melt completely.

When you put the ice cube on the cup, it will start to "drain" the heat energy from the liquid. If the liquid has more temperature, more energy can the cube drain, thus faster it will change to the liquid phase.

Then with a single cube on each cup you will have enough evidence to determine which cup has more temperature.

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A red car travels 120 km in one hour. A blue car travels 130 km in
the same time. Which car has the greater average speed?

Answers

Answer:

blue

Explanation: because blue takes more then way from red

V(average) = X*t this is formula

for red                 for blue

x=120 km            130 km

v=120km/h          130 km/h

t=1h                       1h

Why is the plastic shopping bag transparent

Answers

Answer:

they are transparent to see the content of goods inside but at the same time what cause it to be transparent is because of the fact that they are created with low-density polyethylene and polypropylene, which are transparent polymers.

the synchronous speed(the speed of the rotating magnetic field) of an induction motor is determined by the frequency of the voltage applied. what is the other factor?

Answers

The other factor that determines the synchronous speed of an induction motor is the number of poles. In summary, the synchronous speed depends on both the frequency of the voltage applied and the number of poles in the motor.

To explain further, the synchronous speed (Ns) of an induction motor is calculated using the formula:

Ns = (120 * f) / P

Where Ns is the synchronous speed in revolutions per minute (RPM), f is the frequency of the voltage applied in hertz (Hz), and P is the number of poles.

The frequency and the number of poles are the two primary factors that determine the speed of the rotating magnetic field.

The frequency comes from the power supply, while the number of poles is an inherent design characteristic of the motor. By adjusting these two factors, it is possible to control the synchronous speed of the motor and optimize its performance for specific applications.

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A​ town's January high temperatures average 34°F
with a standard deviation of 8°​,
while in July the mean high temperature is 72°
and the standard deviation is 7 degrees. In which month is it more unusual to have a day with a high temperature of 54°​? Explain.

Answers

To determine in which month it is more unusual to have a day with a high temperature of 54°F, we need to calculate the z-scores for this temperature in both January and July and compare them.

The z-score for a temperature of 54°F in January is:

z = (54 - 34) / 8 = 2.5

The z-score for a temperature of 54°F in July is:

z = (54 - 72) / 7 = -2.57

Since the absolute value of the z-score in January (2.5) is greater than the absolute value of the z-score in July (2.57), we can conclude that it is more unusual to have a day with a high temperature of 54°F in January.

This is because the z-score represents the number of standard deviations a data point is from the mean, and a z-score of 2.5 in January indicates that the temperature of 54°F is very far from the average January high temperature of 34°F. On the other hand, a z-score of -2.57 in July indicates that a temperature of 54°F is still within the range of temperatures typically seen in July, which has a much higher mean high temperature of 72°F.

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what is the initial velocity of the baseball? use: positive x (east), positive y (north), positive z (up)

Answers

More information is needed to provide a specific answer. Please provide additional context or data related to the initial velocity of the baseball.

To find the initial velocity of the baseball, we can use the kinematic equations of motion. Since the baseball is thrown at an angle, we need to break down the initial velocity into its x, y, and z components. We know that the initial height of the baseball is 1.8 meters, and the time it takes to reach its maximum height is 1.0 seconds. From this, we can calculate the vertical component of the initial velocity using the equation vf = vi + gt, where vf = 0 m/s, vi is the initial velocity, g is the acceleration due to gravity \((-9.8 m/s^2\)), and t is the time.

Solving for vi, we get vi = 9.8 m/s.

To find the horizontal component of the initial velocity, we can use the equation\(x = vit + 1/2at^2\), where x is the distance travelled in the x-direction (which is 18 meters), vi is the initial velocity in the x-direction, a is the acceleration in the x-direction (which is 0 m/s^2 since there is no horizontal force acting on the ball), and t is the time of flight (which we can calculate using the time it takes for the ball to reach its maximum height). Solving for vi, we get vi = x/t = 18/2.0 = 9.0 m/s. So the initial velocity of the baseball can be expressed as <9.0, 9.8, 0> m/s, where the x-component is 9.0 m/s (to the right), the y-component is 9.8 m/s (upward), and the z-component is 0 m/s (since there is no initial velocity in the z-direction).

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If the Sun is located at one focus of Earth's elliptical orbit, what is at the other focus? a. Jupiterb. Earth c. nothing d. another planet e. the Moon

Answers

The other focus of the Sun will be Nothing, hence option C is the correct answer. See more explanation below.

The other focus of the Sun

The other focus of Earth's elliptical orbit is empty space because an ellipse is defined as a set of points in a plane, such that the sum of the distances from any point on the curve to two fixed points (the foci) is a constant. Because the Sun is located at one of the foci, the other focus must be empty space.

The orbit of the Earth is also shaped like an ellipse, which is a closed curve that is widened and flattened in one direction. The point where the ellipse is most stretched out is its focus, and the point where it is most flattened is its other focus. One of the foci is where the Sun is, and the other is just empty space.

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Two identical conducting spheres, one that has an initial charge Q, the other initially uncharged, are brought into contact. What is the new charge on each sphere

Answers

When two identical conducting spheres, one initially charged with Q and the other uncharged, are brought into contact, the final charge on each sphere will be Q/2.

When two identical conducting spheres are brought into contact, they will share their charge until they reach an equilibrium state. In this case, one sphere has an initial charge Q, while the other is initially uncharged.

When the spheres touch, the charges redistribute themselves in order to minimize the overall electrostatic potential energy. Since the spheres are identical, they will share the charge equally.

Thus, after the spheres come into contact, the total charge Q will be divided equally between the two spheres. Therefore, each sphere will end up with a charge of Q/2.

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What important role does each play in an exercise regiment?

Answers

Answer: There are five principles of fitness out of which two are overload principle and rest and recovery principle. Overload principle is one of the most important principle which tell that to gain and improve the fitness one should do the hard work.  

Slowly and gradually the intensity and time of exercise are increased so that our body can adapt to the hard work. Overload principle plays an important role in improving the skills and improving performance during exercise and sports.

Rest and recovery principle is important to relax the body and release the stress that happens due to intense training like in case of weight lifting one day rest should be taken to repair and rebuild the muscles. This allows the body to encounter the fatigue and improve performance.

Explanation:

Repeat the conversion, using the relationship 1.00 m/s = 2.24 mi/h. Why is the answer slightly different? (Select all that apply.)
The units are not the same.
2.24 mi/h is not a correct conversion factor to three significant figures.
Using the conversion factor fails to keep extra digits until the final answer.
A different conversion factor from minutes to seconds is used in each case.

Answers

Because the units are not the same, the result is slightly different when using the conversion factor 1.00 m/s = 2.24 mi/h.

It's crucial to choose a conversion factor that corresponds to the target units when converting units. The conversion factor in this instance is 1.00 m/s = 2.24 mi/h. Miles per hour (mi/h) and metres per second (m/s) are not quite identical, though. A rough estimate, the conversion factor of 2.24 miles per hour may not be exact to three significant digits. As a result, the final result may differ slightly when applying this conversion factor.

It is also important to keep in mind that employing the conversion factor alone does not ensure that extra digits will be preserved until the answer is given.

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PLS ANSWERR THIS QUESTION FOR ME !!

PLS ANSWERR THIS QUESTION FOR ME !!

Answers

Explanation:

20 joule is your answer

Answer:

here

mass m =100kg

distance d=50m

acceleration due to gravity a =10m/s²

work =force×displacement

= ma/d=100×10/50=20joule

What is the relationship between wavelength and frequency Mcq?

Answers

The equation =c/f relates wavelength and frequency. There is an inverse relationship between wavelength and frequency.

What connection exists between the frequency and wavelength of EM waves?

One crucial equation connects them all: The speed of light is equal to the frequency times the wavelength of any electromagnetic wave. If we know the other measurement, we can use this connection to calculate the wavelength and frequency of the any electromagnetic wave.

What is a wavelength differs from a frequency in ways?

The distance between the crests of two waves is known as the wavelength, which also applies to troughs. The number of vibrations that pass across a certain area in a second is the frequency, which is expressed in seconds per cycle (Hz) (Hertz). This article discusses how wavelength and frequency relate to one another.

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A 0.061 kg golf ball is struck by a golf club with a force of 299.4 N. The change in velocity of the ball is 54.3 m/s. How much time is the ball in contact with the club?​

Answers

Answer:

The time the ball is in contact with the club is approximately 0.011063 seconds

Explanation:

The question is with regards to Newton's second law of motion which states that a force is equal to the rate of change of momentum produced

The given parameters are;

The mass of the ball, m = 0.061 kg

The force with which the ball is struck with the golf club, F = 299.4 N

The change in velocity of the ball, Δv = 54.3 m/s

By Newton's second law, we have;

\(F_{net} = \dfrac{\Delta P}{\Delta t} = \dfrac{m \times \Delta v}{\Delta t}\)

Where;

Δt = The time it takes the momentum of the object to change = The time the ball is in contact with the club

Substituting the known values, we get;

\(F_{net} = F =299.4 = \dfrac{0.061 \times 54.3}{\Delta t}\)

\(\therefore \Delta t = \dfrac{0.061 \times 54.3}{299.4} \approx 0.011063\)

The time the ball is in contact with the club = Δt ≈ 0.011063 seconds.

The midpoint of jk is m (3, 7) one endpoint is j(1, -1). find the coordinates of the other endpoint k.

Answers

Coordinates of endpoint K: (5, 15)

What are the coordinates of the other endpoint K, given that the midpoint of JK is M(3, 7) and one endpoint is J(1, -1)?

To find the coordinates of the other endpoint K, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two endpoints J and K can be found by taking the average of the x-coordinates and the average of the y-coordinates.

Given that the midpoint M is (3, 7) and one endpoint J is (1, -1), we can substitute these values into the midpoint formula to find the coordinates of endpoint K.

Let's denote the coordinates of endpoint K as (x, y).

Using the midpoint formula:

x-coordinate of midpoint M = (x-coordinate of J + x-coordinate of K) / 2

3 = (1 + x) / 2

Solving for x:

6 = 1 + x

x = 5

y-coordinate of midpoint M = (y-coordinate of J + y-coordinate of K) / 2

7 = (-1 + y) / 2

Solving for y:

14 = -1 + y

y = 15

Therefore, the coordinates of the other endpoint K are (5, 15).

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A long spring is strecthed by 2cm and it's potential energy is v. If the spring is stretched by 10 cm it's potential energy will be ?​

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Answer:

Hey There!

Let's solve....

\(v = \frac{1}{2} k{x}^{2} \\ \\ \frac{ v_{1} }{ v_{2} } = (\frac{ x_{1} }{ x_{2}}) ^{2} \\ \\ \frac{v}{ v_{2} } =( \frac{ \cancel{2}}{ \cancel{10 }}) ^{2} \\ \\ = \frac{1}{25} \\ \\ v_{2} = 25v_{1} \\ \\ = 25v \)

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