Two devices of rating 22 W; 220 V and 11 W; 220 V are connected in series. The combination is
connected across a 440 V mains. The fuse of which of the two devices is likely to burn when
switch is on ? Justify your name. ​

Answers

Answer 1

The 11 W device is likely to burn out when the switch is turned on, due to the higher voltage it will be subjected to compared to its rated voltage. It is important to ensure that the devices used in a circuit have the appropriate voltage rating to avoid damage or failure.

When two devices with different power ratings are connected in series, the voltage across each device is divided according to their power ratings. In this case, the two devices are rated 22 W and 11 W, respectively, and are connected in series across 440 V mains. The voltage across each device can be calculated using the formula V = P/I, where V is the voltage, P is the power rating, and I is the current.

For the 22 W device, the voltage across it is V = P/I = 22/0.1 = 220 V. For the 11 W device, the voltage across it is V = P/I = 11/0.1 = 110 V. Therefore, the 22 W device has a voltage rating of 220 V, which is the same as the voltage of the mains, and the 11 W device has a voltage rating of 110 V.

When the switch is turned on, the voltage across the two devices will be the same, which is 220 V. Therefore, the 22 W device will operate normally, but the 11 W device will be subjected to a higher voltage than its rated voltage. As a result, the 11 W device is likely to burn out before the 22 W device.

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Related Questions

at steady-state, what is the frequency of (displacement) of the mass-spring-damper and will this frequency be in phase with the sinusoidal driving force? explain how you arrived at your answer

Answers

The frequency of displacement of a mass-spring-damper system under sinusoidal driving force is equal to the driving force frequency and in phase with it at steady state.

In a mass-spring-damper system driven by a sinusoidal force, the system will reach a steady-state where the amplitude of the displacement oscillations will remain constant. The frequency of this displacement will be equal to the frequency of the driving force.

Whether the frequency of displacement will be in phase with the driving force depends on the damping ratio of the system. If the damping ratio is zero (i.e. the system is undamped), the displacement frequency will be in phase with the driving force. However, if the system is damped, the displacement frequency will lag behind the driving force frequency.

This is because damping causes energy to be dissipated from the system, resulting in a reduction in the amplitude of the displacement oscillations. As a result, the displacement frequency will be slightly lower than the driving force frequency, and the displacement will lag behind the driving force. The amount of lag will depend on the damping ratio of the system.

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--The complete question is, In a mass-spring-damper system, a sinusoidal driving force is applied. At steady-state, what is the frequency of displacement of the system and will this frequency be in phase with the driving force? Provide an explanation for your answer--

what is the difference between passive and active range of motion

Answers

Answer:

Passive range of motion can be defined as what is achieved when an outside force, such as a therapist, causes movement of a joint. It is usually the maximum range of motion. Active range of motion is what can be achieved when opposing muscles contract and relax, resulting in joint movement

- Parta a BinB8 The crank AB has a constant angular velocity ω. (Figure 1 ) Determine the velocity of the slider at C as a function of θ. Suggestion: Use the x coordinate to express the motion of C and the ϕ coordinate for CB. x=0 when ϕ=0. Express your answer in terms of the variables b,l,ω, and θ. Enter the arguments of trigonometric functions in parenthesis. Determine the accelerotion of the sidet at C as a tunction of θ. Suggestion: Une the x coordinato fo express tho motion of C and the ϕ coordinale for CB. x=0 whin ϕ=0. Express your answer in ferms of the variables b,1,w
1

and θ. Enter the arguments of trigonometric functions in parenthesis, Enter the powers of trigonometic functions parenthesis, e.g. (sin(θ))
3
,(cos(θ))
4
, etc.

Answers

The specific numerical values for the variables b, l, and ω will depend on the dimensions and angular velocity of the system as shown in Figure 1.

To determine the velocity of the slider at point C as a function of θ, we need to analyze the motion of point C and the connecting rod CB.Let's consider the position of point C along the x-axis and the angle ϕ as the angle between the

connecting rod CB and the x-axis. When ϕ = 0, point C is at the origin of the x-axis.

Using basic trigonometry, we can express the x-coordinate of point C as:

x = b + l * cos(ϕ)

Differentiating both sides of the equation with respect to time (t), we obtain the velocity of point C (v_c) as:

v_c = dx/dt = -l * ω * sin(ϕ)

Substituting ϕ = θ - π/2 (since ϕ = 0 corresponds to θ = π/2), we get:

v_c = -l * ω * sin(θ - π/2)

The negative sign indicates that the velocity of point C is in the opposite direction to the positive x-axis.

Next, to determine the acceleration of the slider at point C as a function of θ, we differentiate the velocity equation with respect to time:

a_c = dv_c/dt = -l * ω * cos(θ - π/2) * d(θ - π/2)/dt

Since ϕ = θ - π/2, we have d(θ - π/2)/dt = dϕ/dt = ω.

Therefore, the acceleration of point C (a_c) is given by:

a_c = -l * ω^2 * cos(θ - π/2)

The negative sign indicates that the acceleration is directed towards the origin of the x-axis. The specific numerical values for the variables b, l, and ω will depend on the dimensions and angular velocity of the system as shown in Figure 1.

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Is there an equal and opposite reaction for every action?

Answers

Answer: Yes it is true according o newton third law of motion

What is Newton Third Law of motion ?

--According to Newton's third law of motion, every action has an equal and opposite reaction.

--These two forces act on two different bodies.

-- Example,

1-  while swimming, you push the water backward. The water, in turn, pushes you forward.

--Similarly, while walking, you push the ground backward.

-- The ground then exerts a reaction force on you in the forward direction.

What is Newton Second Law of motion ?

--Newton's second law of motion states that “Force is equal to the rate of change of momentum.

--For a constant mass, force equals mass times acceleration.

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Which of the following requires the most work done by the brakes of a car?
A. slowing down from 80 mph to 55 mph
B. Stopping from 55 mph
C. equal amounts of work for both

Answers

Stopping from 55 mph requires the most work done by the brakes of a car.

Hence, the correct option is B.

When a car slows down or comes to a complete stop, the work done by the brakes is directly related to the change in kinetic energy of the car. The kinetic energy of an object is given by the equation:

Kinetic energy = (1/2) * mass * \(velocity^2\)

Comparing the options:

A. Slowing down from 80 mph to 55 mph: In this case, the car is experiencing a decrease in velocity, resulting in a decrease in kinetic energy. However, the change in kinetic energy is less compared to option B.

B. Stopping from 55 mph: In this case, the car comes to a complete stop, resulting in a significant decrease in velocity and a substantial change in kinetic energy. The brakes need to dissipate the entire kinetic energy of the car, requiring the most work.

C. Equal amounts of work for both: This option is incorrect. Slowing down from a higher speed to a lower speed (option A) requires less work than coming to a complete stop (option B). The work done by the brakes is directly proportional to the change in kinetic energy, and stopping from a higher speed involves a greater change in kinetic energy.

Therefore, Stopping from 55 mph requires the most work done by the brakes of a car.

Hence, the correct option is B.

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Write 3 – 4 sentences explaining why a nucleus tends to become less stable if the number of neutrons is decreased.

Answers

The stability of a nucleus depends on the balance between the strong nuclear force that holds the nucleus together and the repulsive electromagnetic force between the positively charged protons. When the number of neutrons in a nucleus is decreased, the balance between these forces is disrupted, which can lead to a less stable nucleus. This is because the strong nuclear force between the protons and neutrons is weakened, and the repulsive electromagnetic force between the protons becomes stronger, making the nucleus more likely to decay into a more stable configuration.

Select all statements below that are true about sound waves.

A(Sound is caused when something vibrates.

B(Sound moves by longitudinal waves.

C(Sound is a type of mechanical energy.

D(A medium is not required for sound to travel, but sound can move through a vacuum (empty space).

E(Pitch and loudness are not characteristic of sound waves

Answers

The true statement about sound waves include;  Sound is caused when something vibrates, and  Sound moves by longitudinal waves.

option A and B are the correct answers.

What is a mechanical wave?

A mechanical wave is a type of wave that requires material medium for its propagation.

A mechanical wave can be of two types based on mode of propagation;

longitudinal wavetransverse wave

A longitudinal wave travels parallel to the direction of the wave's vibration, while transverse wave travels perpendicular to the direction of the wave's vibration.

An example of longitudinal wave is sound wave. Pitch and loudness are basic characteristic of sound waves because they determine the quality of the sound.

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(a) an endothermic reaction for which the system exhibits an increase in entropy. ΔG will be positive. 。ΔG will decrease with raising the temperature. 。ΔG will increase with raising the temperature.

Answers

In an endothermic reaction where the system exhibits an increase in entropy, the change in Gibbs free energy (ΔG) will be negative.

According to the equation ΔG = ΔH - TΔS, where ΔH is the enthalpy change, T is the temperature, and ΔS is the entropy change, the negative ΔS term dominates the equation, leading to a negative ΔG.

As for the effect of temperature on ΔG, if ΔH is positive (as in an endothermic reaction), increasing the temperature will decrease ΔG. This is because the TΔS term in the equation becomes relatively larger, making the overall ΔG more negative. Conversely, decreasing the temperature will increase ΔG, as the TΔS term becomes relatively smaller.

Therefore, the correct statements are:

- ΔG will be negative for an endothermic reaction with an increase in entropy.

- ΔG will decrease with raising the temperature.

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Two dimensions. In Figure 13-34, three point particles are fixed in place in an xy plane. Particle A has mass mA = 3 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. What (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero (d = 22 cm)?

Answers

To make the net gravitational force on particle A from particles B, C, and D zero, particle D should be placed at the x coordinate of -11 cm and the y coordinate of 0 cm.

The net gravitational force on particle A from particles B, C, and D can be calculated using the formula for gravitational force:

F = G * (m₁ * m₂) / r²

Where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of the two particles, and r is the distance between them.

Since the net gravitational force on particle A should be zero, we can set up an equation:

FAB + FAC + FAD = 0

Using the given information that the distance d is 22 cm and the masses of particles B, C, and D are known in terms of mA, we can calculate the x and y coordinates for particle D.

By applying the principle of superposition, we can calculate the net gravitational force on particle A from particles B, C, and D at the x coordinate and y coordinate of particle D. By adjusting the position of particle D, we can find the coordinates that result in a net gravitational force of zero on particle A.

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Two dimensions. In Figure 13-34, three point particles are fixed in place in an xy plane. Particle A

What is the resistance of a 60 Watt light bulb that allows 500 mA to flow when 120 V is applied to it?

Answers

Answer:

The resistance of the 60 Watt light bulb is 240 ohms.

Explanation:

To calculate the resistance of the light bulb, we can use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I). In this case, we are given the voltage (V = 120 V) and the current (I = 500 mA = 0.5 A). However, we first need to convert the power (60 Watts) into current using the equation P = IV.

P = IV

60 W = (0.5 A) * V

Now, we can rearrange the equation to solve for voltage:

V = (60 W) / (0.5 A)

V = 120 V

Now, we have the voltage (V = 120 V) and the current (I = 0.5 A). We can substitute these values into Ohm's Law to calculate the resistance:

R = V / I

R = 120 V / 0.5 A

R = 240 Ω

The mass of the beam is 3480kg
Calculate the weight of the beam. Remember that a mass of 1 kg has a
weight of 10 N.

Answers

Answer:

34800N

Explanation:

weight = mass × gravitational field strength

w=mg

w= 3480×10. (Gravitational field strength is constant at the value of 10)

w=34800N

two identical speakers that face each other and that are separated by a distance of emit a constant tone in phase. you stand in line with the speakers such that your right ear is exactly halfway between the two speakers, resulting in your left ear being closer to one speaker than the other. you notice that what you hear in your right ear is loud, but in your left ear you hear almost nothing. given that your hearing is fine in both ears and the distance between your ears is , what are the two lowest frequencies that the speakers could possibly be emitting?

Answers

This is an example of a standing wave interference pattern, where sound waves interfere constructively at certain points and destructively at others.

The distance between the speakers is not given, so we'll call it d. We'll also call the distance from each speaker to your ears x and y, respectively. Using the formula for the path difference for constructive interference, we have:

path difference = mλ, where m is an integer and λ is the wavelength of the sound wave.

For the first case, m = 0 (since the distance from the midpoint between the speakers to your right ear is an exact multiple of the wavelength), so the path difference is zero. For the second case, m = 1 (since the distance from the midpoint between the speakers to your left ear is one-half of a wavelength more than an exact multiple of the wavelength), so the path difference is λ/2. Equating these two expressions for the path difference, we get:

λ/2 = d sinθ, where θ is the angle between the line connecting the two speakers and the line connecting your left ear to the midpoint between the speakers.

Since the speakers are facing each other, the angle between them is 180 degrees, so sinθ = sin(180 - θ) = sinθ. Therefore:

λ = 2d sinθ.

The two lowest frequencies correspond to the longest wavelengths that fit between the speakers, which occur when the wavelength is twice the distance between the speakers (i.e., one full wavelength fits between them) and four times the distance between the speakers (i.e., two full wavelengths fit between them). Therefore:

λ1 = 2d, f1 = v/λ1 = v/2d,

λ2 = 4d, f2 = v/λ2 = v/4d,

where v is the speed of sound.

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what colour will a yellow banana appear to be when illuminated by white light

Answers

Any object that's illuminated by the white light will reflect the same color to our eye, which means the yellow banana will appear yellow.

Which of the following is likely to indicate a chemical change?
O A. A decrease in size
O B. The disappearance of a solid stirred in water
C. A change of temperature in sunlight
O D. Production of gas bubbles

Answers

i think it’s A but i might be wrong

A hiker has determined which hiking path to take through a national forest (A is the starting point and B is the final destination). Below is the map of that trail. What does the red line most likely represent?
Total displacement from A to B
Total distance of the path from A to B
Both Total displacement and distance of path from A to B
The shortest path between A and B


In the following equation, Vi represents initial velocity and Vf represents final velocity. The equation for average acceleration is a = (Vf - Vi)/t. Solve this formula for t.
t = a/(Vf - Vi)
t = (Vf - Vi)/a
t = a(Vf - Vi)
t = (Vf - Vi)a

Select the 2 equations that show the same correct relationship between Average Velocity, Distance, and Time.
d = vt
t = v/d
v = t/d
v = d/t

NEED HELP ASAP PLEASE HELP

Answers

Haisjdbdjidwjsnididjhsuwiwkbicidjjss djdjdjbe djdisjs disioqke Baud je eifjenjeoe Didier ejdisjjw ejdisjnw ejdogolwmw. Fjivodkebrjivkenei rjridiwjw tjcijdnfuieiowjfn

200 meters in 20 seconds

Answers

The speed of the object is 10 meters/second.

Speed is defined as the rate at which an object covers distance. It is a scalar quantity, which means that it only has a magnitude (i.e., size) and no direction. The SI unit for speed is meters per second (m/s).

To calculate speed, we need to know the distance traveled and the time it took to cover that distance. In this case, we were given that the object traveled 200 meters and took 20 seconds to do so. We then used the formula:

speed = distance / time

To calculate the speed of the object. We divided the distance traveled by the time it took to travel that distance to find the speed.

Substituting the given values into the formula, we get:

speed = 200 meters / 20 seconds

This simplifies to:

speed = 10 meters/second

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The tools to distinguish the thickness of two objects of thickness of 1.92mm and the other with thickness of 1.93mm is ?

Answers

Answer:

the instrument that gives this precision is the micrometer screw

Explanation:

The high precision measurements of small parts are the general vernier and the micrometer screw.

In these two instruments the same principle is used: there is a fixed rule and a mobile one that increases precision.

Let's analyze the absolute error or precision of each instrument

* For the vernier, the precision of the fixed rule is 1 mm and there are 20 divisions (the most common); therefore the precision of the instrument is

            Δx = 1 mm / 20

            Δx = 0.05 mm

* For the micrometer screw, the precision of the fida rule is 0.5 mm and the number of divisions is 50, therefore the precision of the screw is

            Δx = 0.5mm / 50

            Δx = 0.01 mm

consequently the instrument that gives this precision is the micrometer screw

HOW TO PROTECT OUR SELF FROM THUNDER STORM

Answers

Cover yourself by a cover or blanket I think

a beetle runs an erratic pattern on a square kitchen table that is 1.5 m on a side. the sides are arranged along the directions north/south and east/west. it begins at the southwest corner and travels east along one side to the adjacent corner in 20.0 s. it then turns north and reaches the northeast corner 12.5 s later. what is the magnitude of the beetle's average velocity for the whole trip?

Answers

The magnitude of the beetle's average velocity for the whole trip is approximately 0.106 m/s.


To find the magnitude of the average velocity, we'll need to calculate the total displacement and total time.

The table is 1.5 m on each side.

The beetle travels along two sides, so its total displacement is 1.5 m + 1.5 m = 3.0 m.

The total time taken is 20.0 s + 12.5 s = 32.5 s.

The average velocity can be calculated as:
Average velocity = Total displacement / Total time
Average velocity = 3.0 m / 32.5 s ≈ 0.092 m/s


Summary: The magnitude of the beetle's average velocity for the whole trip on the square kitchen table is approximately 0.092 m/s.

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Final answer:

The beetle's average velocity for the trip is calculated by finding the total displacement (2.12 m) and dividing it by the total time (32.5 s). This results in an average velocity of 0.065 m/s.

Explanation:

The subject of this question is Physics, particularly dealing with concepts of displacement, average velocity, and vector quantities. The average velocity, in this case, is the total displacement (change in position) divided by the total time. The beetle's trip consists of two legs: first, it travels east for 1.5 m, then turns north and travels for another 1.5 m. This makes the total displacement of the beetle to be 1.5 m east + 1.5 m north = 2.1 m in a northeast direction. The total time of this trip is 20.0 s + 12.5 s = 32.5 s.

When it comes to calculating the magnitude of this displacement (ignoring the north/east directions and focusing only on the total distance), we need to consider that the beetle has essentially moved diagonally across a square table. If we treat this as a 45-degree right triangle, where the legs are each 1.5 m, the hypotenuse (total displacement) can be found using the Pythagorean theorem: hypotenuse = √(1.5^2 + 1.5^2) ≈ 2.12 m.

The average velocity of the beetle is now found by dividing this total displacement by the total time: average velocity = total displacement / total time = 2.12 m / 32.5 s = 0.065 m/s. So, the magnitude of the beetle's average velocity for the entire trip is 0.065 m/s.

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if a ball is thrown straight up with an initial velocity of 15 m/s, what will its velocity be after 2.0 s?

Answers

If a ball is thrown straight up with an initial velocity of 15 m/s, its velocity be after 2.0 s will be 34.6 m/s

In Newtonian mechanics, equations of motion specify how a physical system will behave in terms of how it will move over time. Equations of motion are mathematical formulas that describe a body's position, velocity, or acceleration in respect to a certain frame of reference.

The ball would accelerate due to gravity,

a = g = 9.8 m/s²

Using first equation of motion:

v = u + a t

where

Initial velocity of the ball, u = 15 m/s

final velocity of ball, v

Time, t = 2.0 s

v = u + a t

v = 15 m/s + 9.8 m/s² × 2.0 s = 34.6 m/s

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which two criteria are least important for engineers to consider when developing a process to produce an important chemical

Answers

Answer:

Chemical engineering is a multi-disciplinary branch of engineering that combines natural and experimental sciences such as chemistry and physics, along with life sciences such as biology, microbiology and biochemistryplus mathematics and economics to design, develop, produce, transform, transport, operate

Explanation:

Answer:

A. the process needs to produce significant amounts of ammonia

C. the process needs to be able to be performed safely

Explanation:

a p e x

What would be the weight (in Newtons) of a person with a mass of 80 kg on Earth, where the acceleration due to gravity is approximately 9.8 m/s/s? *
please help asap

Answers

Answer:

ml tayo 1v1 durugin kita

Explanation:

ano takot ml 1v1

Important!
New drivers who are 18 don't have to complete all the steps of the graduated licensing system.

A. True

B. False

Answers

Answer:

b

Explanation:

An emf of 99 mv is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of 1.20A/s. What is the mutual inductance (M) of the two coils?

Answers

The mutual inductance of the two coils given is 82.5 microhenries.

To solve this problem, we can use Faraday's Law which states that the emf induced in a coil is proportional to the rate of change of magnetic flux through the coil. The formula for calculating mutual inductance (M) is:

M = emf / (dI/dt)

where emf is the induced emf in the coil and (dI/dt) is the rate of change of current in the nearby coil.

Substituting the given values, we have:

M = 99mV / (1.20A/s)

M = 82.5 μH

Therefore, the mutual inductance (M) of the two coils, based on the information, is 82.5 microhenries.

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A container gas expands to fill a 3l container has a mass of 129g what is its density

Answers

A container gas expands to fill a 3l container and has a mass of 129g its density is equal to 0.043 \(kgm^{-3}\)

Let's understand the answer in detail

Density is equal to the mass of a substance divided by its volume. The SI unit of density is Kg/m3. Other units of density are g/cm3, g/mL, kg/L

The formula we are using is going to be

D=m/v, where

D= density

m=mass

V=volume

The data that is given to us states that

mass = 129g

volume= 3 L

density = ?

Now we will put the values in the formula,

d= m/v

d = 0.129 Kg / 3L

d = 0.043 Kg / L

Therefore the density of the gas is 0.043 Kg / L.

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Why does Ice melt in an open space?

Answers

It’s important to understand how thermodynamics works.

The state of “cold” is a state without heat, so when removed from a freezer, the ice is exposed to heat. Heat always moves from warm to cold, so heat from outside of the ice moves inside of it, causing it to melt.

A rocket has an acceleration of 45 m/s2. If the rocket begins its take off from rest, how long does it take to reach a final velocity of 1,000 m/s?.

Answers

F = m * a. Algebra can be used to find the acceleration (a = F/m). The following formula is used to determine  the final velocity; if 1000 = 0 + 45t, then 45t = 1000, then t = 1000 / 45, then t = 22.2 seconds

How much time does a rocket need to accelerate?

The space shuttle must accelerate from zero to 8,000 meters per second (almost 18,000 miles per hour) in eight and a half minutes in order to reach the minimum height needed to orbit the Earth. To do this, a very special vehicle is required.

What is the rocket's speed in seconds?

A rocket must travel at least 7.9 kilometers per second (4.9 miles per second) in order to reach space if it is launched from the surface of the Earth. The orbital velocity, which is 7.9 km/s and more than 20 times the speed of sound, is measured in this manner.

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True or false? If the line of action of the weight of an object lies outside the base of the object, there will be a resultant moment.

Answers

The answer is true that if the line of action of the weight of an object lies outside then the base of the object, then there will be a resultant moment.

What is Moment?

A force's moment is a measurement of how likely it is to make a body rotate around a certain point or axis. This differs from a body's propensity to translate or move in the direction of the force.

A body must experience the force in such a way that it starts to twist before a moment may emerge.

This happens each time a force is applied so that it misses the body's centroid. When a force does not have an equal and opposing force acting immediately across its path of action, a moment results.

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An Object with a mass o 5.13kg placed on top of a spring compresses it by 0.25m (a) what is the force constant of the spring (b) How high will this object go when the spring releases its energy?

Answers

The force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

The spring constant is the force needed to stretch or compress a spring, divided by the compressive or expansive distance. It's used to determine stability or instability in the spring, and therefore the system it's intended for. we know,

F = kx

Therefore,

k = F/x

We also know that the force being exerted on the spring is equal to the mass of the object. Hence, F = mg = 5.13 * 9.8 N = 50.174 N and we know compression due to the mass is 0.25m. Therefore,

K = 50.174/0.25 N/m

K = 200.696 N/m

Therefore, The Spring Constant is 200.696 N/m

On release, the spring potential energy gets converted to kinetic energy. Hence, on release, the height attained by the object is given by:

h = \(1/2 kx^{2}\)

We know that k=200.696 N/m and x=0.25 m. Therefore the height is:

h = \(1/2 (200.696 N/m)(0.25 m)^{2}\)

h = 2.5087 m

Therefore, the force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

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A mother spins her son in a circle of radius R at angular
speed wi. Then the mother pulls in her arms and spins
1
him in a circle of radius R with the same angular speed.
2
How does the magnitude of the child's centripetal
acceleration change when the mother pulls her arms
in?
Choose 1 answer:

A mother spins her son in a circle of radius R at angularspeed wi. Then the mother pulls in her arms

Answers

A body has centripetal acceleration with magnitude a such that

a = v ² / R

where v is the body's tangential speed and R is the radius of the circular path the body takes.

Convert the child's angular speed ω into linear/tangential speed. Assume angular speed is measured in rad/s and tangential speed in m/s. For every 2π rad that he revolves around his mother, the child travels a distance of 2πR m, so that

ω = (ω rad/s) • (2πR/(2π) m/rad) = = v

Then the child's acceleration is

a = ()² / R = ²

When the mother pulls her arms in, the distance R gets halved and changes to R/2, so that the child's new acceleration is

a = (R/2 • ω)² / (R/2) = (1/4 • ()²) / (1/2 • R) = 1/2 ²

so the child's centripetal acceleration decreases by a factor of 2.

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