A bullet of mass 20g strikes a block of mass 980g with a velocity u and gets embedded in it. The block is in contact with a spring whose force constant is 100N/m. After the collision the spring is compressed to 10cm. Find: 1. Velocity of the block after the collision. 2. Magnitude of the velocity of the bullet. 3. Loss in kinetic energy due to the collision.

To turn while running, the foot must push off the ground, applying a cutting force while instantaneously supporting the weight of the body. This is a vector addition problem where we must account for the normal force on the foot (from the runner's weight) and the acceleration force. Since the weight of the foot is backing up is vertical and the turning force is horizontal, these two force vectors are perpendicular and will form a right triangle.

Only the magnitude matters, so we need not worry about the sign or angle direction.

Now, what's needed is the hypotenuse of a triangle with legs of

 Fg = (65)(10) = 650 N and F = (65)(5) = 325 N.

This calculation can be approximated as √ (3002 + 7002) = 

√ (90000+490000) = √ (580000) = √ (58 x 104) = √ (58) x 102 = 761

Answer:

Force, F = 715.11 newton

Explanation:

Given that,

Mass of the person, m = 65 kg

Acceleration of man during a running turn, [tex]a=5\ m/s^2[/tex]

We need to find the magnitude of force experienced by the foot due to the ground. It can be calculated using second law of motion as :

F = ma

[tex]F=65\ kg\times 5\ m/s^2[/tex]

F = 325 Newton

Here, the weight of the person and this force force a right angle triangle.

The wight of the person, W = mg

[tex]W=65\ kg\times 9.8\ m/s^2=637\ N[/tex]

So, the resultant for is, [tex]F_r=\sqrt{325^2+637^2}[/tex]

[tex]F_r=715.11\ N[/tex]

So, the f force experienced by the foot due to the ground is 715.11 newtons. Hence, this is the required solution.

A motorboat and a PWC are meeting head-on, the stand-on vessel is generally the motorboat.

The motorboat is typically the stand-on vessel when a motorboat and a personal watercraft (PWC) collide head-on.

The vessel that has the right of way and must maintain its route and speed is referred to as the stand-on vessel. The PWC is the vessel that must surrender or give way.

The PWC should adjust its route or speed to safely pass behind or around the motorboat in order to avoid a collision.

It is crucial to remember that precise laws and guidelines could change depending on the jurisdiction and regional marine laws. It is usually advised to abide by the relevant laws and ordinances of the particular area or waterway.

Thus, the stand-on vessel is generally the motorboat.

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The wavelength of light is given as 463 nm or can also be written as 463 x 10^-9 m. [wavelength = ʎ]

We know that the speed of light is 299 792 458 m / s or approximately 3 x 10^8 m / s. [speed of light = c]

Given the two values, we can calculate for the frequence (f) using the formula:

f = c / ʎ

Substituting the given values:

f = (3 x 10^8 m / s) / 463 x 10^-9 m

f = 6.48 x 10^14 / s = 6.48 x 10^14 s^-1

f = 6.48 x 10^14 Hz

Final answer:

The frequency of blue light with a wavelength of 463 nm is calculated using the speed of light and the formula for frequency, resulting in a frequency of 6.48 × 10¹⁴Hz.

Explanation:

To calculate the frequency of blue light emitted by a laser at a rock concert with a wavelength of 463 nm, we use the formula c = λf, where c is the speed of light (3.00 × 108 m/s), λ is the wavelength in meters, and f is the frequency in Hertz (Hz).

First, convert the wavelength from nanometers to meters: 463 nm = 463 × 10-9 meters.

Next, plug the values into the formula: f = c / λ = (3.00 × 10⁸ m/s) / (463 × [tex]10^-^9[/tex] m) = 6.48 × 10¹⁴ Hz.

Therefore, the frequency of the blue light is 6.48 × 10¹⁴Hz.

Answer:

Sample Response: All elements in the same group of the periodic table have the same number of valence electrons. This made it possible to compare the valence of the alien elements to the valence of elements from our periodic table, and match the alien elements to the correct group. For example, our group 14 elements all have 4 valence electrons, so the alien element with 4 valence electrons had to be part of group 14 also.

Explanation:

The existence of quantized energy levels in an atom can be inferred from observations related to radiation, atomic spectra, and principles of quantum mechanics. For example, distinct lines in atomic spectra represent transitions between these energy levels, and Bohr's model suggests each orbit around the nucleus reflects a distinguished energy level.

The existence of quantized energy levels in an atom can be inferred from the concept of radiation and atomic spectra. Atomic spectra are the electromagnetic emissions of individual atoms and molecules. They form in distinct lines, which from the concept of quantum mechanics, signify the transition of electrons between discrete energy levels, otherwise known as 'quantized' energy levels.

These energy levels are quantized, meaning they are represented by quantum numbers, which are integer values corresponding to particular energy levels, or orbits, of an electron in an atom. The energy levels are not continuous and an electron can only occupy these definite levels.

The Bohr model provides a picture of this, presenting the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus, similar to planets revolving around the Sun. Each orbit corresponds to a particular energy level, and the electron can transition from one level to another by absorbing or emitting energy.

The energy of an electron in an atom is labeled with the principal quantum number (n), which varies as n = 1, 2, 3...

Therefore, the observations related to radiation, atomic spectra, and the principles of quantum mechanics can imply the existence of quantized energy levels in an atom.

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Answer:

Wake

Explanation:

As a boat moves through a water body (sea, river or ocean), the propeller causes the water to be separated as the boat moves. This separated water forms a new pattern based on the disturbance conferred by the boat. The disturbed water forms a visible huge flow of water sideways and backwards (based on the speed, size and weight of the boat). This disturbed water is referred to as the wake of the boat.    

Alcohol affects the brain shortly after consumption, with BAC being a key factor in the extent of these effects, which include impaired motor skills and judgment. Chronic consumption can lead to tolerance and withdrawal, and during pregnancy, there's a risk of FASD. The liver metabolizes alcohol steadily, unaffected by external remedies like coffee.

Alcohol begins to affect your brain shortly after consumption, with effects ranging from social disinhibition to impaired motor control and decision-making. The immediate effects of alcohol on the brain depend on the individual's blood alcohol concentration (BAC), which is influenced by age, sex, health condition, and the quantity of alcohol consumed. Acute alcohol ingestion can result in decreased reaction time, visual acuity, alertness, and behavioral control, leading to consequences such as lack of coordination, blurred vision, and impaired judgment. It is worth noting that chronic exposure to alcohol may cause adaptations in the brain's reward circuitry, increased tolerance, and potential withdrawal effects. Additionally, alcohol consumption during pregnancy can lead to fetal alcohol spectrum disorder (FASD) or fetal alcohol syndrome (FAS), with their respective long-term effects on the child.

Alcohol metabolism is a critical aspect of managing intoxication. The liver metabolizes alcohol at a rate of about 3.3 mmol/L (15 mg/dL) per hour, and no amount of coffee or a cold shower can speed up this process. Therefore, to avoid alcohol toxicity and its associated risks – such as road accidents and physiological disorders – it is essential to drink responsibly and allow sufficient time for the body to metabolize alcohol.

Answer:

It will become a neutron star

Explanation:

For the solar mass of anything above 1.4, the mass will automatically become a neutron star. This is according to the Chandrasekhar limit. This limit determines that 1 solar mass will collapse to form a white dwarf of a solar mass above 1.4 .

The weight of a 255-kg object on Jupiter is approximately 1421.6 pounds, after converting kilograms to pounds and adjusting for Jupiter's greater gravitational force.

To calculate the weight of a 255-kg object on Jupiter, we need to convert the mass in kilograms to pounds and then consider Jupiter's stronger gravitational pull. The weight calculation on Earth uses the conversion where 1 kg is equivalent to 2.205 pounds. However, since Jupiter's gravity is approximately 2.53 times that of Earth, we must multiply the Earth weight by this factor. Using the provided conversion factor, 255 kg on Earth is equivalent to 255 kg × 2.205 lb/kg which is approximately 561.975 lb. To find the weight on Jupiter, multiply this result by Jupiter's gravity factor: 561.975 lb × 2.53 = 1421.59725 lb. Considering significant figures based on the conversion factor of pounds and tenths place rounding, the weight would be reported as 1421.6 lb.

Answer:

I think is 8.5" x 11"

Explanation:

 
The needle of a compass will always lies along the magnetic field lines of the earth. 
A magnetic declination at a point on the earth’s surface equal to zero implies that 
the horizontal component of the earth’s magnetic field line at that specific point lies along 
the line of the north-south magnetic poles. 

The presence of a current-carrying wire creates an additional 
magnetic field that combines with the earth’s magnetic field. Since magnetic 
fields are vector quantities, therefore the magnetic field of the earth and the magnetic field of the vertical wire must be combined vectorially. 

Where:

B1 = magnetic field of the earth along the x-axis = 0.45 × 10 ⁻ ⁴ T

B2 = magnetic field due to the straight vertical wire along the y-axis

We can calculate for B2 using Amperes Law:

B2 = μ₀ i / [ 2 π R ]

B2 = [ 4π × 10 ⁻ ⁷ T • m / A ] ( 36 A ) / [ 2 π (0.21 m ) ] 
B2 = 5.97 × 10 ⁻ ⁵ T = 0.60 × 10 ⁻ ⁴ T 

The angle can be calculated using tan function:
tan θ = y / x = B₂ / B₁ = 0.60 × 10 ⁻ ⁴ T / 0.45 × 10 ⁻ ⁴ T
tan θ = 1.326

θ = 53°

The compass needle points along the direction of 53° west of north.

The compass needle near a current-carrying wire aligns northwest due to the combined influence of the Earth's northward magnetic field and the wire's westward magnetic field at that location.

A compass needle, which is a tiny bar magnet, aligns with the magnetic field it experiences. In this scenario, both the Earth's magnetic field and the magnetic field created by a vertical current-carrying wire influence the needle.

The magnetic field produced by a straight current-carrying wire is given by the right-hand rule: point your thumb in the direction of the current (downward) and curl your fingers around the wire.

Your fingers show the direction of the magnetic field; moving in circles around the wire.

Therefore, the compass needle will align with this resultant field, pointing in a direction northwest.

The magnetic force on a proton falling towards Earth at the equator, with the Earth's magnetic field directed north, will be towards the west due to the right-hand rule for magnetic forces on charged particles.

If a proton is released at the equator and falls towards Earth under the influence of gravity, and assuming the magnetic field is directed toward the north at this location, the magnetic force on the proton will be towards the west. This assertion is based on the right-hand rule for magnetic force, which states that if you point the fingers of your right hand in the direction of the proton's velocity (downward towards Earth), and bend your fingers in the direction of the magnetic field (north), your thumb will point in the direction of the magnetic force on a positively charged particle, which in this case is to the west.

This scenario exemplifies the interaction between charged particles and magnetic fields. The force on a charged particle moving through a magnetic field is always perpendicular to both the velocity of the particle and the magnetic field, which can result in circular or helical motion depending on the context.

The solution would be like this for this specific problem:

The force on m is:

GMm / x^2 + Gm(2m) / L^2 = 2[Gm (2m) / L^2] -> 1

The force on 2m is:

GM(2m) / (L - x)^2 + Gm(2m) / L^2 = 2[Gm (2m) / L^2] -> 2

From (1), you’ll get M = 2mx^2 / L^2 and from (2) you get M = m(L - x)^2 / L^2 

Since the Ms are the same, then 

2mx^2 / L^2 = m(L - x)^2 / L^2 

2x^2 = (L - x)^2 

xsqrt2 = L - x 

x(1 + sqrt2) = L 

x = L / (sqrt2 + 1) From here, we rationalize. 

x = L(sqrt2 - 1) / (sqrt2 + 1)(sqrt2 - 1) 

x = L(sqrt2 - 1) / (2 - 1) 


x = L(sqrt2 - 1)

= 0.414L

Therefore, the third particle should be located the 0.414L x axis so that the magnitude of the gravitational force on both particle 1 and particle 2 doubles.

Using Newton's law of universal gravitation, we can set up equations to find the location of the third particle such that the gravitational force exerted on both particle 1 and particle 2 doubles. The third particle should be placed at the position solved from these equations, either closer to particle 1 or further away.

The location of the third particle that could double the gravitational force on both particle 1 and 2 can be achieved by using Newton's law of universal gravitation. This law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

For particle 1 and the third particle, if we denote the mass of the third particle as m3 and its position as x3, the gravitational force F1 on particle 1 is given by F1 = G*m*m3/x3^2. Similarly, for particle 2 and the third particle, the gravitational force F2 on particle 2 is also given by F2 = G*2m*m3/(l-x3)^2.

According to the question, both the gravitational force on particle 1 and particle 2 doubles when the third particle is added. Therefore, we can set up the following equations: 2F1 = G*m*m3/x3^2 and 2F2 = G*2m*m3/(l-x3)^2. From the equations, we could solve for x3 to find the location of the third particle.

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The gravitational force between them changes by a factor if, the distance between two masses is tripled, is 1 / 9.

In mechanics, the force of attraction that acts on all matter is known as gravity, also known as gravitation. It does not affect how daily stuff behaves internally because it is by far the weakest known force in nature. In contrast, it regulates the paths of objects in the solar system and elsewhere in the universe, as well as the architecture and evolution of stars, galaxies, and the entire universe, through its extensive and universal action.

Given:

If the distance between two masses is tripled,

Calculate the initial gravitational force as shown below,

Initial gravitational force = Gravitation constant × m₁ × m₂ / d²

Here, d is the distance between objects,

Final gravitational force = Gravitation constant × m₁ × m₂ / d²

Final gravitational force = Gravitation constant × m₁ × m₂ / (3d)²

Final gravitational force = Gravitation constant × m₁ × m₂ / 9d²

Thus, the gravitational force between them changes by a factor of 1 / 9.

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If 3.5 paper clips = 1.0 pencils and your paper is 1.5 pencils long, then your paper would be 5.25 paper clips long.

It is defined as the multiplication factor used for the design of an object with respect to some other object. the scale is generally used to design prototype designs of large objects. It is also used in interior design planning rooms.

It is multiplied by the design dimension to get the actual size of the object or product.

As given in the problem If 3.5 paper clips = 1.0 pencils and your paper is 1.5 pencils long, this means the scale factor of the pencil as a paper clip is 3.5

1 pencil = 3.5 paper clips

1.5 pencils = 1.5 × 3.5 paper clips

                 = 5.25 paper clips

Thus, If 3.5 paper clips = 1.0 pencils and your paper is 1.5 pencils long, then your paper would be 5.25 paper clips long.

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Answer:

Steering control

Explanation:

If you lose Steering control , braking may cause the vehicle to steer left or right unpredictably.  Steering is collection components and linkages that control the direction of wheel of vehicle on road. Once the steering control is lost , the driver is not able to guide the vehicle and on braking, the vehicle can move in any direction unpredictably.

Answer:

Explanation:

Noise which falls under human hearing range means from 20 Hz to 20,000 hz has sound at every frequency. The audible range from human is 20-20,000 hz so every noise within this range is audible to humans. Some animals such as whale, dolphin, bat communicate( to get their prey) beyond this range.