the spring constant for a spring-mass system undergoing simple harmonic motion is doubled. if the total energy remains unchanged, what will happen to the maximum amplitude of the oscillation? assume that the system is underdamped.

Answer:

the potential energy is 114 J.

Explanation:

Given;

total mechanical energy, E = 400 J

kinetic energy, K.E = 286 J

The potential energy is calculated as follows;

E = K.E +  P.E

where;

P.E is the potential energy

P.E = E - K.E

P.E = 400 J - 286 J

P.E = 114 J

Therefore, the potential energy is 114 J.

The electric potential at the given point is approximately 12 mV.

An electric dipole consists of two equal and opposite charges, in this case ±12 nC, separated by a distance, which is 1.0 mm in this scenario. The electric potential (V) at a point located at a distance (r) from the dipole and at an angle (θ) from the direction of the dipole moment vector can be calculated using the following formula:

V = (1 / 4πε₀) * (p * cosθ) / r²

where:
- V is the electric potential
- ε₀ is the vacuum permittivity (8.854 x 10⁻¹² F/m)
- p is the dipole moment (charge * distance between charges)
- θ is the angle (in radians) between the dipole moment vector and the point's position vector
- r is the distance from the dipole to the point

For this problem, we have:
- p = (12 x 10⁻⁹ C) * (1.0 x 10⁻³ m) = 12 x 10⁻¹² C*m
- θ = 0° (0 radians since cos(0) = 1)
- r = 25 cm = 0.25 m

Plugging these values into the formula:

V = (1 / 4πε₀) * (12 x 10⁻¹² C*m) / (0.25 m)²
V ≈ 12 x 10⁻³ V
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The momentum of the bowling ball at the point where it reaches a speed of 3.6 m/s is 22.3 Kg.m/s (Option C)

Momentum is defined as the product of mass and velocity. It is represented mathematically as:

Momentum = mass × velocity

Now, we can obtain the momentum of the bowling ball at the point where it reaches a speed of 3.6 m/s. Details below:

Momentum = mass × velocity

Momentum =  6.2 × 3.6

Momentum = 22.3 Kg.m/s

Thus, the momentum at the point is 22.3 Kg.m/s (Option C)

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Answer:

electromagnetic waves can travel through a vacuum where as mechanical waves have to have a medium to travel

Explanation:

The change in speed of the body is 25 meters per second.

To calculate the change in speed of an object, we need to use the formula:

Δv = (Fnet/m) * t

Where:

Δv is the change in speed

Fnet is the net force acting on the object

m is the mass of the object

t is the time for which the force is applied

Given that a net force of 15N acts upon a body of mass 3kg for 5 seconds, we can plug in the values into the formula:

Δv = (15N/3kg) * 5s

Simplifying this, we get:

Δv = 25 m/s

Therefore, the change in speed of the body is 25 meters per second.

It is important to note that speed is a scalar quantity, which means it only has magnitude & no direction.

In this case, the speed of the object increases by 25 m/s, but we do not know in which direction it moves.

If we want to calculate the change in velocity, which is a vector quantity that includes both magnitude & direction, we need to know the initial velocity & the direction of the net force.

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Answer:

0.2

Explanation:

0.5 - 0.3 = 0.2

Answer: I think a

Explanation:

Answer:

D

Explanation:

Temperature is a measure of the particles of a mass's  energy/motion

Answer:

0.16 A

Explanation:

V = IRtotal

24V = I(100 + 40 + 10)

I = 0.16 A

Answer: 0.16 is correct

Explanation:

(i) The generator delivers a greater rms current when only the resistor is present.

(ii) The greater average power is consumed by the circuit when both the inductor and the resistor are present.

The average power consumed in the inductor-resistor series circuit is 0.0216 A.

(i) In the case where both the inductor and the resistor are present, the generator delivers a greater rms current. This is because the presence of the inductor introduces reactance, which affects the overall impedance of the circuit. The reactance of an inductor is frequency-dependent, and since the generator has a frequency of 1160 Hz, the inductor will have a significant impact on the current flow. (ii) In the case where both the inductor and the resistor are present, the greater average power is consumed by the circuit. This is because the inductor introduces reactive power to the circuit, which does not contribute to useful work but rather oscillates between the inductor and the generator. Therefore, the combination of the resistor and the inductor results in a higher total power consumption compared to when only the resistor is present.

To calculate the average power consumed in the inductor-resistor series circuit, we need to determine the total impedance of the circuit and use it to calculate the average power.

Given:

Resistance, R = 495 Ω

Inductance, L = 0.085 H

Frequency, f = 1160 Hz

Average power consumed by the resistor, P_resistor = 0.25 W

First, we calculate the reactance of the inductor using the formula X_L = 2πfL:

X_L = 2π(1160 Hz)(0.085 H) ≈ 200.34 Ω

Next, we calculate the total impedance of the circuit using the resistance and reactance:

Z = √(R^2 + X_L^2) = √(495^2 + 200.34^2) ≈ 535.23 Ω

Finally, we can calculate the average power consumed in the inductor-resistor series circuit using the formula P = I^2Z, where I is the rms current:

P = I^2Z

0.25 W = I^2(535.23 Ω)

I^2 = 0.25 W / 535.23 Ω

I ≈ √(0.000468 A)

I ≈ 0.0216 A

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The half-life of 40K is approximately 1.3 billion years. Given a ratio of 40Ar/40K as 3/1 in a granite sample, we can estimate the age of the sample by understanding the decay process.  Based on the given 40Ar/40K ratio, the age of the sample is approximately 650 million years.

Since the half-life of 40K is 1.3 billion years, this means that after each half-life, half of the 40K atoms will have decayed into 40Ar. Therefore, if the ratio of 40Ar/40K is 3/1, it suggests that three-quarters (or 75%) of the original 40K atoms have decayed into 40Ar.

To determine the age, we can calculate the number of half-lives that have occurred based on the remaining 25% of 40K. Since each half-life is 1.3 billion years, dividing the remaining 25% by 50% (half) gives us 0.5. Thus, the sample has undergone 0.5 half-lives.

Multiplying 0.5 by the half-life of 1.3 billion years gives us an estimated age of 0.65 billion years, or 650 million years, for the granite sample.

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Answer:

I believe it's called a diatomic atom

Answer:

The two philosophers furthermore seem to share the same conception of the conditions of human freedom. For Hegel as well as Kant, a theory of morality and political right devoted to advancing the cause of freedom must require more than just the absence of obstacles preventing the satisfaction of our animal passions.

Explanation:

Hope that help ;)

Answer:

V≈0.034m³

Explanation:

Review:

Every point on the surface of a sphere's three-dimensional, perfectly round shape is equally spaced from the object's center. Spheres are a frequent type of item, including balls and globes. You only need to know a sphere's radius and enter it into a straightforward formula (V = 4⁄3πr³) to get its volume.

The volume of a sphere is calculated as 4/3 times pi times the cube of the radius. A number is cubed when it has been multiplied three times, in this example, three times the radius.

V = 4⁄3πr³

The ratio of a circle's circumference to its diameter is 4/3; this formula is used to calculate the volume of a sphere.

Given:

400 mm diameter

To find:

Volume in m^3

Steps:

Unit Conversion:

\(d=0.4m\)

Using the formulas

\(V=\frac{4}{3} \pi r^3\\d=2r\)

Solving for \(V\)

\(V=\frac{1}{6} \pi d^3=\frac{1}{6} *\pi *0.4^3\) ≈ \(0.03351m^3\)

Answer:

Explanation:

Hello!

The sphere has a diameter of 400mm which is equivalent to 40 cm.

The volume of a sphere equals to V = 4/3 π r^3

That is Pi multiplied by the radius of the sphere to the power of three, all multiplied by 4 and divided by 3.

The sphere has a diameter to 40 cm, and to get its radius we need to divide diameter by 2.

radius = 20 cm

Volume = 4/3 π 20cm^3

Volume = 4/3 * 3.14 * 20cm^3

Volume = 4/3 * 62.8 cm^3

Volume = 251.2 / 3 cm^3

Volume = 83.7(3) cm^3

let's make the number into a fraction, and then convert it into meters cubed:

83.7(3) = \(\frac{8373-837}{90}\) cm^3

Volume = \(\frac{7536}{90}\) cm^3

Now, because the measurement is cubed, we gotta divide centimeter by 100 cubed, to get meters cubed.

that will be our Volume divided by 1.000.000 (million).

\(\frac{7536}{90*1.000.000}\) meters^3

Volume = \(\frac{7536}{90,000,000}\) meters^3

Hope I helped!

Explanation:

9.

Given parameters:

     Net force on object  = 200N

      Acceleration  = 500m/s²

Unknown:

Mass of the object = ?

Solution:

According to newton's second law of motion, force is the product of mass and acceleration;

      force  = mass x acceleration

Insert the parameters and solve;

         200  = mass x 500

             mass  = \(\frac{200}{500}\)   = 0.4kg

10:

Given parameters:

           Mass of dummy = 75kg

             Net force on dummy  = 825N

Unknown:

Dummy's deceleration = ?

 Solution:

Deceleration is the negative form of acceleration;

    Force  = mass x acceleration

       Acceleration  = \(\frac{force }{mass}\)  

       Acceleration  = \(\frac{825}{75}\) = 11m/s²

The deceleration is -11m/s²

Orange, Blue, and Red are the three filters. They are easy to attach and cover the lens and flash on the front of the Polaroid Go camera.

The primary benefit of Polaroid photography is the immediate visual feedback. Sharing Polaroid photos is one of the simplest things you can do with them.

An image of a friend is taken and given to the friend. Being one-to-one rather than one-to-the-world makes it a little different from other forms of sharing. Polaroid started to lose some of its major clients in the real estate, insurance, and photo identi-fication industries as digital cameras proliferated on the market.

As film sales collapsed, Polaroid declared bankruptcy in October 2001. A series of chemicals and dyes are sandwiched between layers to make up a Polaroid;

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0.36 m of a 4.0 g string that is under stress. The third harmonic of the string vibrates at 500 Hz. The standing wave in the string has a wavelength of 0.24 m.

To calculate the wavelength of the standing wave in the string, we need to use the relationship between the frequency of the standing wave, the tension in the string, and the linear density of the string.

The formula to calculate the wavelength (λ) of the standing wave in the string is given by:

λ = (2L/n) where L is the length of the string and n is the harmonic number.

In this case, the harmonic number is 3 (as it is vibrating at its third harmonic), the length of the string is 0.36 m and the frequency of vibration is given as 500 Hz.

So, the wavelength of the standing wave in the string can be calculated as:

= λ

= (2L/n)

= (2 x 0.36 m / 3)

= 0.24 m

Therefore, the wavelength of the standing wave in the string is 0.24 m.

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Answer:

Some of the disadvantages are: The normal design of a belt conveyor is opened. If your product needs to be contained, covers and or drip pans can become expensive and cumbersome. If the material is sticky, belt cleaning can be difficult and generally not very successful.

Explanation:

Answer:

B.

Explanation:

B. is correct because every time usually when a hurricane hits it causes flooding causing multiple homes to be ruined. It is a known fact that usually hurricanes start close or in along with tornadoes, the water, meaning once they hit land they have some water to flood that land with.

C. is absolutely false hurricanes have VERY strong wind gusts.

D. is absolutely wrong they do alter landscapes by ripping trees and plants and houses out of the ground making the landscapes look different.

A. is wrong they tend to deposit and remove sediment evenly.

~ LadyBrain

Answer:

B

Explanation:

The equilibrium height to which the wire CD will rise is given by the expression h = μ₀I² / 2π λg

A region in which the force of magnetism acts is known as the magnetic field, and it surrounds magnetic materials or a moving electric charge. Moving magnetic dipoles and electric charges produce a magnetic field, which acts as a force field on other nearby magnetic dipoles and moving charges.

Magnetic field at a distance h produced by a current carrying wire

B = μ₀I/ 2πh

Magnetic force due to the present current carrying wire can be calculated by the formula

F = B I  L

And we also know that F = mg

On equating these mg = B I L

( μ₀I/ 2πh ) I = ( m/ I ) g = λg

thus we get the value of h as

h = μ₀I² / 2π λg

Thus, the equilibrium height to which the wire CD will rise is given by the expression h = μ₀I² / 2π λg .

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C) A small amount of mass can be turned into a large amount of energy. This is the principle behind nuclear reactions and the development of nuclear energy.

E=mc2 is Einstein's equation that connects energy (E) to mass (m) and light speed (c). According to this definition, energy is determined by multiplying an object's mass by its square of the speed of light. This formula emphasises the relationship between mass and energy.

The equation demonstrates how a little bit of mass may yield a lot of energy. The figure "c," which stands for the speed of light, is enormous—it is roughly 3 x 108 metres per second. This value gains considerably more significance when squared.

Because the speed of light is such a huge number, it produces a massive quantity of energy when multiplied by the mass of an object, even a modest amount of mass. This phenomenon is seen in nuclear reactions, where a sizable amount of energy is released but only a small portion of the mass of the atomic nuclei is changed. This idea underlies the operation of nuclear power plants and nuclear weapons.

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Answer:

O N

Explanation:

Upthrust = Volume of object * density of fluid * acceleration due to gravity

Upthrust = 4.0 m3 *  1000 kg/m3 * 10 m/^2

Upthrust = 40, 000 N

Upthrust = Weight in air - Weight in water

Weight in air = 40,000 N

Weight in water = Weight in air - Upthrust

Weight in water = 40,000 N - 40,000 N

Weight in water = 0 N

4.74 m/s is the speed in crown glass m/s.

λ= 632.8 nm= 6.328×10^-7m

ν=c/λ

v=3×10^8/6.328×10^-7

v=4.74 m/s

When describing how quickly something moves or how much its location changes over time, the scalar variable speed can be utilized. It is frequently abbreviated to "s." By dividing the entire distance traveled by the period's duration, the average speed of an object is determined.

The unit of measurement for speed is time divided by distance. Although the unit of speed most frequently employed in daily life is the kilometer per hour (kph), the meter per second (m/s) is the SI unit of speed.

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Option C, It would take 50 m³ of Mars' atmosphere to collect the same mass of air as one m³ on Earth. To calculate the volume of Mars' atmosphere required to collect a mass of 1kg, we need to use the density of the Martian atmosphere and the mass of the air on Earth.

The density of air at moderate altitude on Earth is given as 1 kg/m3. This means that 1 cubic meter of air on Earth has a mass of 1 kg. To convert this to grams per cubic centimeter, we can divide by 1000, which gives 0.001 g/cm3.

The mass of air in one m³ on Earth is 1 kg, while the density of the atmosphere near Mars' surface is 0.02 kg/m³. Therefore, to collect 1 kg of Mars' atmosphere, we need:

1 kg / 0.02 kg/m³ = 50 m³

So, it would take 50 m³ of Mars' atmosphere to collect the same mass of air as one m³ on Earth.

Complete question -

The density of air at moderate altitude on earth is 1 kg/m3 (this can be converted to 0.001 g/cm3). the density of the atmosphere near mars' surface is 0.02 kg/m3. how many m3 of mars atmosphere would it take to collect a mass of 1kg, the same mass as in one m3 on earth?

A. 1

B. 10

C. 50

D. 100

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Explanation:

work = 0

Work is zero because it remains in its place x=0

The largest possible distance between speaker B and the observer at C is 1.37 m.

The largest possible distance between speaker B and the observer at C occurs when the difference in travel distances is just one half wavelength.

λ = v/f

λ = (343)/125

λ = 2.744

¹/₂λ = ¹/₂(2.744) = 1.37 m

Thus, the largest possible distance between speaker B and the observer at C is 1.37 m.

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The displacement of Curiosity is 2.334 m

The given parameter:

maximum speed of Curiosity, v = 0.14 km/hr

time of motion of Curiosity = 60 s

To find:

The displacement of Curiosity is calculated as follows;

The displacement of Curiosity = speed x time

The displacement of Curiosity = 0.0389 m/s x 60 s

The displacement of Curiosity = 2.334 m

Thus, the displacement of Curiosity is 2.334 m

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