A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 450 n/m. the block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. the block then executes simple harmonic motion along the horizontal x-axis. the maximum elastic potential energy of the system is closest to

At the top of the giant swing on the gymnastics high bar, candy's total mechanical energy is 1740J.

Given the data in the question;

Candy's total mechanical energy; [tex]M.E_c = \ ?[/tex]

Total Mechanical Energy (M.E) is the sum of both the potential energy and the kinetic energy of an object.

[tex]Mechanical \ Energy = Potential \ Energy + Kinetic \ Energy[/tex]

[tex]M.E = mgh + \frac{1}{2}mv^2[/tex]

Where m is the mass, g is gravitational acceleration( [tex]9.8m/s^2[/tex] ), h is the height and v is the velocity.

We substitute our values into the equation

[tex]M.E_c = ( 50kg * 9.8m/s^2*3.5m) + ( \frac{1}{2}* 50\ *(1m/s)^2)\\\\M.E_c = 1715kg.m^2/s^2 + 25kg.m^2/s^2\\\\M.E_c = 1740 kg.m^2/m^2\\\\M.E_c = 1740J\\[/tex]

Therefore, at the top of the giant swing on the gymnastics high bar, candy's total mechanical energy is 1740J

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With the known value of v (speed of sound in the medium, e.g., 343 m/s) and the desired change in frequency (25% or 0.25), you can calculate the speed you must approach the source of sound to observe a 25% change in frequency.

To observe a 25% change in frequency (Doppler effect) when approaching a source of sound, you need to know the relative velocity between you and the source of sound. The Doppler effect occurs when there is relative motion between the observer and the source of the sound.

The formula for calculating the apparent frequency (f') observed by a moving observer due to the Doppler effect is:

f' = f * (v + vo) / (v - vs)

Where:

f' = Apparent frequency observed by the moving observer

f = Actual frequency of the sound emitted by the source

v = Speed of sound in the medium (approximately 343 meters per second in air at room temperature)

vo = Velocity of the observer (positive if moving towards the source, negative if moving away from it)

vs = Velocity of the source of sound (positive if moving away from the observer, negative if moving towards it)

Since  want to observe a 25% change in frequency, the apparent frequency (f') would be 25% different from the actual frequency (f):

f' = 1.25 * f

Assuming the observer is moving towards the source (vo is positive), we can rewrite the equation as:

1.25 × f = f × (v + vo) / (v - vs)

Now, we can solve for the relative velocity vo:

(v + vo) / (v - vs) = 1.25

Cross-multiply:

v + vo = 1.25 * (v - vs)

Now, isolate vo:

vo = 1.25 × (v - vs) - v

With the known value of v (speed of sound in the medium, e.g., 343 m/s) and the desired change in frequency (25% or 0.25), you can calculate the speed you must approach the source of sound to observe a 25% change in frequency.

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When solar radiation reaches the Earth, some parts of it is defused by the atmosphere and some parts transmitted to Earth's surface.

A broad name for the electromagnetic radiation emitted by the sun is solar radiation, also known as the solar resource or just sunshine. With the use of various technologies, solar radiation may be absorbed and converted into usable forms of energy like heat and electricity. However, a certain location's solar resource determines whether these systems are technically feasible and operate economically.

Some of the sunlight is absorbed, scattered, and reflected by air molecules, water vapour, clouds, dust, pollutants, forest fires, and volcanoes as it travels through the atmosphere. The term for this is diffuse sun radiation.

Direct beam solar radiation is the type of solar radiation that directly reaches the surface of the Earth. Global solar radiation is the total of both diffuse and direct sun radiation. Direct beam radiation can be reduced by atmospheric conditions by 10% on clear, dry days and by 100% on days with heavy clouds.

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The fulcrum in a hammer when removing a nail is at the part where the hammer pivots.

By applying effort to the handle of a claw hammer, the output force at the nail puller end is increased due to the lever principle. Understanding these concepts aids in efficiently removing nails from wood.

The critical angle is the smallest incident angle at which light is no longer refracted into water, but instead is totally internally reflected. This can be calculated using Snell's law, where the sine of the critical angle is the ratio of the indices of refraction for water and glass.

The smallest value of the incident angle θa for which none of the ray refracts into water, and instead exhibits total internal reflection, is known as the critical angle. To find this critical angle, we can apply Snell's law (n1 × sin(θa) = n2 × sin(θb)), where θa is the incident angle and θb is the refracted angle when θb is 90°, the angle of refraction is at the maximum and therefore indicates the critical angle condition. Using the indices of refraction for glass (n1) and water (n2), we can solve for the critical angle which will indicate the threshold above which light will not refract into water but instead be totally internally reflected.

Final answer:

The change in potential energy of the spring is 152.19 J.

Explanation:

The potential energy of a spring is given by the equation PE = (1/2)kx², where k is the spring constant and x is the displacement of the spring. In this case, the change in length of the spring is 0.53 m (0.79 m - 0.26 m). We can calculate the potential energy change using the formula and given values:

PE = (1/2)(1140 N/m)(0.53 m)² = 152.19 J

Therefore, the change in potential energy of the spring is 152.19 J.

Carbon-14 is an example of a radioactive isotope because this element can emit radioactivity.

Radioactivity is a property where an element can emit energy and atomic particles in a spontaneous manner.

Isotopes are two or more types of atoms that have the same atomic number and position in the periodic table, and that differ in nucleon numbers due to different numbers of neutrons in their nuclei.

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Answer: Option (B) is the correct answer.

Explanation:

It is known that oxygen, sulfur and selenium are all group 16 elements.

The electronic configuration of oxygen is as follows.

     [tex]1s^{2}2s^{2}2p^{4}[/tex]

The electronic configuration of sulfur is as follows.

     [tex]1s^{2}2s^{2}2p^{6}3s^{2}3p^{4}[/tex]

The electronic configuration of selenium is as follows.

     [tex]1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4p^{4}[/tex]

Hence, we can see that on moving down the group there is increase in energy levels of the atoms from 2p to 4p.

Therefore, we can conclude that when traveling from oxygen to sulfur to selenium, through this group in the periodic table, change is that the number of energy levels increases.

Tycho Brahe

Johannes Kepler

Nicolaus Copernicus

Sir Isaac Newton

Robert Hooke

The scientists contributed to discovering the universal law of gravitation are Tycho Brahe,  Johannes Kepler , Nicolaus Copernicus , Sir Isaac  Newton , and Robert Hooke .

Science is the methodical, empirically-based pursuit and application of knowledge and understanding of the natural and social worlds.

A method of learning about the world is science. Science allows people to participate in the creation of new knowledge as well as use that knowledge to further their goals.

Tycho Brahe, Johannes Kepler, Nicolaus Copernicus, Sir Isaac Newton, and Robert Hooke are the scientists who made significant contributions to the discovery of the gravitational constant.

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Answer:

When different countries use different forms of measurement there is many different mistakes and confusion that can happen.

Explanation:

Final answer:

Different units of measure can cause confusion and serious mishaps in critical fields like medicine and aviation. Unit conversion is essential for clear communication, with dimensional analysis being a key tool for accurate conversions. Appropriate units must be used in context to avoid misunderstandings.

Explanation:

Different units of measure can lead to confusion, miscommunication, and even dangerous situations if not properly managed. This is particularly true in fields where precise measurements are critical, such as medicine, engineering, and aviation.

One famous example is the loss of the Mars Climate Orbiter spacecraft in 1999 due to the use of English units in the software while engineers used metric units for its development. Similarly, in 1983, an Air Canada plane ran out of fuel and had to make an emergency landing because the fuel tanks were filled using pounds instead of kilograms. Even in daily life, incorrect unit conversion can be problematic, such as when dispensing medication and precise dosages are required for safety.

To avoid such missteps, unit conversion is necessary. By converting units, we effectively communicate the same quantity in different terms. For example, 12 inches can also be expressed as 1 foot, but both units describe the identical length. Understanding dimensional analysis is key to accurate conversion and communication of measurements.

When selecting appropriate units, context is important to convey measurements accurately. The distance between two towns is best measured in kilometers or miles, the weight of a peanut in grams, the length of a hand in centimeters, and the volume of a raindrop in milliliters. Using the correct units ensures clarity and avoids confusion.

For an uniformly accelerated motion, the following relationship is used:

[tex]2 a S=v_f^2 -v_i ^2[/tex] (1)

where a is the acceleration, S the distance covered, and vf and vi the final and initial speeds of the motion.

In our problem we are dealing with a rotational motion. Initially, the salad spinner has constant angular speed, which is given by

[tex]\omega _i = 2 \pi f[/tex]

where f is the rotational frequency, which is the number of revolutions per second:

[tex]f=  \frac{20 rev}{5 s}=4 Hz [/tex]

so the initial angular speed is

[tex]\omega _i = 2 \pi (4 Hz)=25.2 rad/s[/tex]

Then, the salad spinner starts to decelerate with constant deceleration [tex]\alpha[/tex], and during its deceleration it spins for other 6 revolutions, so covering a total angle of

[tex]\theta = 2 \pi (6 rev)=37.7 rad[/tex]

until it stops, so until it reaches a final speed of [tex]\omega _f=0[/tex].

To find the angular acceleration, we can use the equivalent of equation (1) for angular motions:

[tex]2 \alpha \theta = \omega_f^2 - \omega_i^2[/tex]

and so, since the final speed is [tex]\omega _f=0[/tex]:

[tex]\alpha = -  \frac{\omega _i^2}{2 \theta}=- \frac{(25.2 rad/s)^2}{2\cdot 37.7 rad}=-8.4 rad/s^2  [/tex]

where the negative sign means the salad spinner is decelerating.

Answer:

[tex] \alpha = -\frac{(25.132 rad/s)^2}{2* 37.7 rad}= -8.377 rad/s^2[/tex]

And we can convert this into degrees like this:

[tex] \alpha= -8.377 rad/s^2 * (\frac{180}{\pi rad}) =-479.967 rad/s^2[/tex]

Explanation:

For this case we assume that the angular acceleration is constant and the spinner slows down and come to rest at the end

We can calculate the distance traveled each revolution with this formula:

[tex] \theta= 20 rev * \frac{2\pi rad}{1 rev}= 40 \pi rad[/tex]

And since we know that the time to reach the velocity 0 is 5 s we can find the angular velocity like this:

[tex] w_o= \frac{\theta}{t}= \frac{40 \pi rad}{5 s}= 25.132 rad/s[/tex]

We know that the spinner rotates 6 more times before come rest, so the total distance traveled is:

[tex] \theta= 6* 2\pi = 37.699 rad[/tex]

[tex] w_f = 0 rad/s[/tex]

And we have the following formula :

[tex] w^2_f = w^2_i + 2\alpha \theta[/tex]

Since we know that the final angular velocity is 0 we can solve for [tex] \alpha[/tex] the angular acceleration and we got:

[tex] \alpha = -\frac{w^2_o}{2 \theta}[/tex]

And replacing the values that we found before we have this:

[tex] \alpha = -\frac{(25.132 rad/s)^2}{2* 37.7 rad}= -8.377 rad/s^2[/tex]

And we can convert this into degrees like this:

[tex] \alpha= -8.377 rad/s^2 * (\frac{180}{\pi rad}) =-479.967 rad/s^2[/tex]

Using the principles of energy conservation and kinetic energy, the distance the spring compresses when the block comes to rest is found through the equation x = sqrt((m*v*v)/k), where m is the mass, v is the velocity, k is the spring constant, and x is the distance of compression.

To compute the distance the spring is compressed when the block comes to rest, we need to consider both kinetic energy conservation and energy conservation through potential energy of the spring. Our initial kinetic energy supplied by the block sliding down the plane (K1) will turn into a potential energy in the spring when it's compressed (U2). Hence, we have K1 = U2.

Assuming initial kinetic energy (K1) given by 0.5*m*v*v, and potential energy in the spring (U2) equals to 0.5*k*x*x where x is the distance in which spring is compressed.

From the conservation of energy principle, 0.5*m*v*v = 0.5*k*x*x. By simplifying the equation, we get x = sqrt((m*v*v)/k). This equation provides us the distance the spring is compressed when the block comes to rest.

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Answer:

  0.125 J/(g·k)

Explanation:

Specific heat has units of J/(g·K), so we find the value by dividing the energy by the product of mass and temperature change.

  (10^4 J)/(2·10^3 g·(60 -20)K) = 10/(2·40) J/(g·K) = 0.125 J/(g·k)

If the speed of an object increases, then its kinetic energy will increase proportionally because speed and kinetic energy have a linear relationship when graphed.

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The question involves physics and vector subtraction to determine the wind's speed and direction affecting an airplane's travel based on its heading and ground velocity.

The student is asking about determining the wind's speed and direction based on an airplane's velocity relative to the ground and its intended heading. To solve for this, we need to use vector subtraction since the airplane's ground velocity can be thought of as a combination of its own speed and the wind's influence. Given that the airplane is heading north at 45.0 m/s and its ground speed is 38.0 m/s at an angle west of north, the wind's speed and direction are the vectors that need to be added to the airplane's heading to equal the ground speed vector. A vector diagram would need to be drawn, and trigonometry would be used to calculate the magnitude of the wind's vector and its angle relative to the west.

Answer:

when electron jump from n=3 to n=1 then the photon coming out is of Lyman series. Here Lyman series photon is also known as Ultraviolet range of photon

Explanation:

As per Bohr's theory we know that when electron make transition from higher energy level to lower energy level then it emits photons of different energy range.

Here we know that when electron makes transition from any higher level to n=1 then it is ultraviolet range of photons.

While if electron makes transition from any higher energy range to n= 2 then it is visible range of photons

and for any higher energy level to n=3 then it is infrared range of photon

So here the spectrum received in this case is of ultraviolet range

Layer masks are a non-destructive image editing technique that allows changes to be applied without altering the original image data, providing safety and flexibility in editing.

One accurate fact about layer masks in image editing is that they are non-destructive. This means that when Jack works with layer masks, he is not directly altering or damaging the original image data. Instead, layer masks allow him to apply changes, such as hiding or revealing parts of the layer, without permanently affecting the image. These masks can be edited at any time to adjust the visibility of different portions of the layer. If a mistake is made, Jack can simply edit the mask to correct the issue, rather than having to restore the original image from a separate file. Therefore, layer masks provide flexibility and safety for image editing, ensuring the original data remains intact.