The required magnitude of velocity and acceleration are calculated to be 2 m/s and 12 m/s² respectively.
The position of the particle is given as, x = 4t⁴
We know the velocity, V = dx/dt
dx/dt = d/dt (4t⁴) = 16 t³
The velocity at t = 0.5 s is given as,
V = 16 t³ = 16 × 0.5³ = 2 m/s
Acceleration function A = dV/dt
dV/dt = d/dt(16 t³) = 48 t²
A = 48 t² = 48(0.5)² = 12 m/s²
Thus, the magnitude of velocity and acceleration are calculated to be 2 m/s and 12 m/s² respectively.
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a seconds pendulum in chicago has a length of 0.9933 m . what is the acceleration due to gravity in chicago?
The acceleration due to gravity in Chicago is [tex]9.803 m/s^2[/tex].
Let us assume that the acceleration due to gravity in Chicago is [tex]g[/tex] [tex]m/s^2[/tex].
It is given that,
The length of the second pendulum is [tex]l=0.9933 m[/tex].
It is known that,
The time period of a second pendulum is [tex]T=2s[/tex].
The time period of a simple pendulum, [tex]T=2\pi\sqrt{\frac{l}{g}}[/tex].
[tex]\Rightarrow (2)=2\pi \sqrt{\frac{0.9933}{g}}[/tex]
[tex]\Rightarrow \frac{2}{2\pi}=\sqrt{\frac{0.9933}{g}}[/tex]
[tex]\Rightarrow \frac{0.9933}{g}=(\frac{1}{\pi})^2[/tex]
[tex]\Rightarrow g=0.9933\times(\pi)^2[/tex]
[tex]\Rightarrow g=9.803 m/s^2[/tex]
Hence, the acceleration due to gravity in Chicago is [tex]9.803 m/s^2[/tex].
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A toy rocket has a mass 0f 350g at launch. The force it produces is 15N and it is fired at an angle of 65° to the horizontal. What is the initial acceleration of rocket as a vector?
Answer:
250 g
Explanation:
it has the weight of the angle
Answer:
break the launch vector into two components, vertical and horizontal
Force Net Vertical=-9.8*.350+15cos65 N
force net horizonal=15sin65
initial acceleration= force/mass= (-9.8+15/.350*cos65)j+(15/.350*sin65)i
using i,j vectors..
Select the correct answer. It is more fun to play when you have good sportsmanship OA B. True False
It is more fun to play when you have good sportsmanship is true.
What is Sportsmanship?Sportsmanship can be thought of as a persistent and largely constant trait or disposition that allows people to differ in how they are typically expected to respond in sporting situations.
Sportsmanship has been linked to interpersonal notions of treating others equally, retaining self-control when interacting with others, and respecting both authority figures and opponents. It mostly refers to virtues like fairness, self-control, courage, and perseverance.
The four components of sportsmanship—good form, the desire to triumph, equity, and fairness—are frequently displayed. For true sportsmanship to be demonstrated, a balance between all four components must be achieved.
Therefore, It is more fun to play when you have good sportsmanship is true.
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jane is using a 14 cm long screwdriver to assemble a bookcase. she applied a force of 45 n to rotate the screw 180 degrees. how much work did she do?
The amount of work done by Jane in applying the force and rotating through certain angle is calculated to be -6.3 J.
The force applied on the screw is given as 45 N.
The angle through which screw is rotated is given as 180°.
The length of the screw driver is given as 14 cm = 0.14 m.
The expression for work is given as,
W = F s cosθ
where, W is the work done
F is the force
s is the displacement
θ is the angle of rotation
Putting the values in the above equation, we have,
W = F s cosθ = 45 × 0.14 × cos180 = 45 × 0.14 × (-1) = -6.3 J
When the displacement occurs in the direction opposite to the force applied, negative work is done.
Thus, the work done is -6.3 J.
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determine the magnitude of the resultant force of the two forces acting on the sign at point a .
The magnitude of the resultant force of the two forces acting on the sign at point a is 759.46N.
Now, b=3.4m
The overall force acting on the item or body, along with the direction in which the body is moving, is referred to as the resultant force. When the object is stationary or moving at the same speed as the object, the resultant force is zero. Since all of the forces are acting in the same direction, the combined force should be equal for all of the forces.
Now, force is [tex]F_{c}=F_{c}u_{c}[/tex]
[tex]F_{c}=400\times\frac{(0-5)i+(-2-0)j+(3.4-0)k}{\sqrt{5^{2} +2^{2} +3.4^{2} } }[/tex]
which gives, [tex]F_{c}=-314i-125.6j+213.54k[/tex]
Force [tex]F_{B}=F_{B}u_{c}[/tex]
[tex]F_{B}=400\times\frac{(0-5)i+(2-0)j+(3.4-0)k}{\sqrt{5^{2} +2^{2} +3.4^{2} } }[/tex]
which gives,[tex]F_{B}=-314i+125.6j+213.54k[/tex]
Resultant Force is given by,
[tex]F_{R} =F_{B} +F_{C}[/tex]
[tex]F_{R}=-314i-125.6j+213.54k-314i-125.6j+213.54k[/tex]
[tex]F_{R}=-628i+427.08k[/tex]
Magnitude of the resultant force,
[tex]F_{R}=\sqrt{628^{2} +427.08^{2} }[/tex]
[tex]F_{R}=759.46N[/tex]
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Question)- Determine The Magnitude Of The Resultant Force Of The Two Forces Acting On The Sign At Point A.Express your answer to three significant figures and include the appropriate units.which of the following statements is true? question 1 options: a) uv light has higher energy than x-ray radiation. b) the higher the frequency of a wave, the lower its energy. c) uv light has higher energy and higher frequency than visible light. d) uv light has longer wavelength and higher energy than visible light.
Answer:
c) UV light has higher energy and higher frequency than visible light.
Explanation:
The statement "c) UV light has higher energy and higher frequency than visible light" is true because UV light is a type of electromagnetic radiation with a higher frequency than visible light. The frequency of a wave is a measure of how many oscillations or cycles it completes in one second and is typically measured in hertz (Hz). The higher the frequency, the more energy it contains. UV light has a higher frequency than visible light, which means it has more energy. Additionally, ultraviolet radiation is also considered to have higher energy than visible light as well.
An atom travelling away from a light detector at 0.8c emits a photon of light of wavelength 600 nm. The wavelength received by the detector is
So the wavelength received by the detector is 375 nm.
How to calculate the wavelength?In this case, the atom is travelling at 0.8 times the speed of light away from the light detector (c). This means that the observed wavelength of light emitted by the atom will be longer than the wavelength of light emitted by the atom.
Where _observed is the observed wavelength, _emitted is the wavelength emitted by the object, c is the speed of light, v object is the velocity of the object relative to the observer, and v observer is the velocity of the observer relative to the object.
The effective wavelength is = [v -/+ vs]/f / = v/f -/+ vs/f
When the source travels toward the observer, use the first sign (-), and when it goes away, use the second sign (+).
The frequency discovered
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for quantities of power, electrical voltage, frequency (clock speeds), is it more common to see prefixes represent powers-of-2 or powers-of-10?
For quantities like power electric voltage frequency it is more common to see prefixes represent the power of minus 2 and minus 10 because it makes the data more accurate.
When you measure the quantities which are very difficult to measures and at the same time getting high Precision and accuracy we use the concept of using the prefixes to represent the power of -2 and -10.
Usually for frequencies we use the powers of -10 and 4 quantities like power and electric voltage we use the prefixes like the power of -2.
The reason for this is very simple because it makes the data accurate and easy to understand for the person operating on the devices.
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the imaginary plane in which all objects project to corresponding points in the left and right retina is called
The imaginary plane in which all objects project corresponding points in the left and right retina is called the Horopter.
The horopter is a concept in visual perception that refers to the plane that contains all points that produce the same retinal disparity (the difference in the position of an object as seen by the two eyes).
The horopter is used to explain why some objects appear to be in front of or behind the plane of the screen in stereo vision.
The horopter is the plane in which objects are seen as having the same depth by both eyes, which is why objects on or near the horopter appear to be in the same plane as the screen.
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a hurricane wind blows across a 5.90 mm ×× 13.2 mm flat roof at a speed of 110 km/hrkm/hr .
The pressure difference is 562.1 Pa.
The pressure difference can be calculated using the equation:
[tex]ΔP = 1/2 * ρ * v^2[/tex], where [tex]ρ[/tex] is the air density and [tex]v[/tex] is the wind speed.
Air density at sea level = 1.225 kg/m^3.
To convert the wind speed from km/hr to m/s, divide by 3.6.
The pressure difference can then be calculated as follows:
[tex]ΔP = 1/2 * 1.225 kg/m^3 * (110 km/hr / 3.6)^2[/tex]
[tex]ΔP = 1/2 * 1.225 kg/m^3 * (30.56 m/s)^2[/tex]
[tex]ΔP = 1/2 * 1.225 kg/m^3 * 935.24 m^2/s^2[/tex]
[tex]ΔP = 562.1 Pa[/tex]
So, the pressure difference is approximately 562.1 Pa.
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The given question is incorrect. The correct question is given as:
A hurricane wind blows across a 5.90 mm ×× 13.2 mm flat roof at a speed of 110 km/hr. What is the pressure difference?
why do astronomers use the word dark when referring to dark energy and dark matter?
The astronomers use the work dark in dark matter as it does not appear to interact with the electromagnetic field, which means it does not absorb, reflect, or emit electromagnetic radiation and is, therefore, difficult to detect.
Unseen matter is referred to as dark matter. Because of the impact it has on items that we can directly view, we are aware that dark matter exists.
Dark matter slows down the expansion of the universe, while dark energy speeds it up. Dark matter works like an attractive force, a kind of cosmic cement that holds our universe together.
So, the term dark is used in both dark energy and dark matter.
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(a) what is the electric field 4.2 m from the center of the terminal of a van de graaff with a 8.20 mc charge, noting that the field is equivalent to that of a point charge at the center of the terminal?
The electric field 4.2 m from the center of the terminal of a van de Graaff with an 8.20 mc charge, noting that the field is equivalent to that of a point charge at the center of the terminal is 4.18×10⁶ N/C.
An electric field is set up when a specific point charge lies at a particular point in the field. The electric field is obtained by the Coulomb's equation. So as the distance increases, the value of the electric field decreases.
The distance from the center of the terminal of a Van de Graff is r=4.2m. The electric charge is q=(8.20 mC × 10⁻³/1mC) =8.20 ×10⁻³ C. The electric field is E=kq/r², where E is the electric field and k is Coulomb's constant, k=9×10⁹ N.m²/C². So, E=(9×10⁹×8.20×10⁻³)/(4.2)² = 4.18×10⁶ N/C.
So the electric field at a distance of 4.2m is 4.18×10⁶ N/C.
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what particle is transferred from one reactant to another in oxidation-reduction reactions?
Electrons are transferred from one reactant to another in oxidation-reduction reactions.
Oxidation-reduction (redox) reactions are chemical processes that involve the transfer of electrons from one reactant to another. In a redox reaction, one reactant is oxidized, meaning it loses electrons, while the other reactant is reduced, meaning it gains electrons.
These electron transfers are essential for energy production in cells and for a variety of chemical processes. Redox reactions are also responsible for the corrosion of metals, the tarnishing of silver, and many other everyday occurrences.
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what energy is produced by a 200 w lightbulb lit for 2.5 hours? answer in units of j.
The energy produced by a 200 W light bulb after 2.5 hours of use is 1,800,000 J.
Energy (J) = Power (W) x Time is the formula for computing energy from power and time (s). Power is the rate of energy production or consumption, commonly expressed in watts (W), and time is the length of time.
The following formula can be used to determine how much energy a 200 W light bulb produces over the course of 2.5 hours:
Energy (J) equals Power (W) times Time (s)
We must first translate 2.5 hours into seconds:
2.5 hours equals 9,000 seconds (2.5 × 60 x 60).
We can now determine how much energy the lightbulb produces:
= 200 W x 9,000 seconds.
= 1,800,000 J
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uranus was not considered a planet by ancient greeks because it is too faint to be seen without the aid of a telescope. group of answer choices true false
True. Uranus is too faint to be seen without the aid of a telescope, and was not considered a planet by the ancient Greeks.
What is telescope?A telescope is an instrument used to observe distant objects by collecting and magnifying the visible light they emit. Telescopes are used to observe a wide variety of celestial objects, including stars, galaxies, planets, and comets. Telescopes come in a variety of shapes and sizes, ranging from small handheld models to huge observatories. Telescopes are also used in astronomy and other scientific fields to study the universe, as well as in military and law enforcement applications to survey and observe terrestrial objects. Telescopes are typically built with one or more curved mirrors or lenses which collect and focus the incoming light, allowing for a magnified image to be viewed. Many modern telescopes are equipped with sophisticated technology, such as digital cameras, computer-controlled tracking systems, and spectrographs to allow for detailed analysis and observation of distant objects.
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when carts of unequal mass push away from each other, which cart has more momentum, the heavy or the light cart? explain your answer in 1-2 sentences
The correct answer is both carts have the same momentum, though the cart that has larger mass will move slower than the cart that has smaller mass.
How momentum and mass are connected?
The initial and final momentums will equal one another in accordance with the law of conservation of momentum. As a result, the momentum of both carts should be equal. Since the beginning value is zero, the momentum of the two carts should be identical. Both carts are moving at the same speed, but the one with more mass will go more slowly than the one with less mass. The result is a balance between the two masses.
Hence , both carts have the same momentum, though the cart that has larger mass will move slower than the cart that has smaller mass.
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correct answerrr is a ?
Answer:
2 A
Explanation:
Remember V= IR
Then V/R = I
12 v / 6 ohm = 2 A
at what latitude is the sun directly overhead on april 22
The latitude where the sun is directly overhead on April 22nd is called the subsolar point.
The sun is directly overhead at the equator on the spring and autumn equinoxes, which occur around March 20th and September 22nd respectively. On April 22nd, the sun is not directly overhead at the equator, but it is overhead at a latitude in the tropics, close to the equator.
To be more precise, the latitude where the sun is directly overhead on April 22nd is called the subsolar point, and it changes slightly from year to year due to the elliptical shape of Earth's orbit around the sun. On average, the subsolar point on April 22nd is around Latitude 10° N. However, to get an exact value for a specific year, you would need to perform calculations based on the exact position of the Earth in its orbit.
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what is the magnitude of the buoyant force fb on the balloon?
The buoyant force an object experiences when floating is proportional to its weight. The weight w, liquid of the displaced liquid has the same magnitude as the buoyant force.
The formula for buoyant force is (B) = ρVg, where g = 9.8 (gravity), V = Displaced Volume, and = Density of Fluid (we used air density because the balloons were afloat, not submerged). Thus, buoyant force is directly influenced by the volume of the fluid displaced, the fluid's density, and the acceleration caused by gravity at the location. As is common knowledge, buoyant force equals the weight of the fluid displaced by the body part submerged in it.
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a roller coaster car of mass 250kg is atop a hill that has a height of 30m. the cart, starting from rest, proceeds down the hill and then up an adjacent hill that has a height of 10m. at the top of the second hill, the cart has a velocity of 17m/s. determine the work done by friction.
The work done by friction can be calculated using the equation W = F * d, where F is the force of friction and d is the distance traveled. In this case, the distance traveled is 30m (the height of the first hill) + 10m (the height of the second hill).
The force of friction can be calculated using the formula F = µmg, where µ is the coefficient of friction and m is the mass of the roller coaster car (250kg).
Assuming the coefficient of friction is 0.2, the force of friction would be 50N. Therefore, the work done by friction would be W = 50N * 40m = 2000J.
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a satellite is orbiting the earth a distance re above its surface. what is the acceleration due to gravity in this orbit? (re is the radius of the earth)
The acceleration due to gravity in this orbit is 9.81 m/s2.
What is gravity?Gravity is a natural force of attraction that exists between any two objects with mass. It is the force that keeps us grounded to the Earth and causes objects to fall to the ground when released. Gravity is strongest at the surface of the Earth, and its effects diminish with distance. In the universe, gravity is responsible for maintaining the orbits of planets and stars, and for the formation of galaxies.
The acceleration due to gravity (g) at a distance r from the centre of the Earth is given by:
g = GM/r2
Where G is the gravitational constant and M is the mass of the Earth.
Therefore, the acceleration due to gravity at a distance re above the Earth's surface is given by:
g = GM/re2
= (6.67 x 10-11 Nm2/kg2) x (5.98 x 1024 kg) / (6.37 x 106 m)2
= 9.81 m/s2.
Therefore, the acceleration due to gravity in this orbit is 9.81 m/s2.
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where could the needle puncture the balloon with the least amount of effort
The needle puncture the balloon with the least amount of effort where the surface tension is highest i.e. at the middle widest part.
Surface tension is the tendency of a fluid to acquire the minimum surface area possible.
A balloon has a difference in internal and external pressure because of the surface tension. While the increased internal pressure in the balloon exerts a push to expand it, the surface tension in the stretched rubber tends to constrict it.
Hence the tension is highest at the broadest part and the balloon will pop easily if one punctures it around that region.
Therefore, the needle punctures the balloon with the least amount of effort at the broadest part.
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which conditions would not typically be considered a safety concern relative to grounds?
Grounds that are isolated or insulated are typically not considered a safety concern.
Grounds refer to the electrical connection between a conductor and the earth. In electrical systems, a ground is used to provide a reference point of zero potential, which helps to maintain electrical safety.
However, not all grounds are equal and some conditions can pose a safety concern. For example, a ground that is in direct contact with a source of electrical energy, such as a live wire, can be dangerous because it can cause electrical current to flow into the ground, potentially causing an electrical shock or fire.
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In order to convert temperature from Celsius to Fahrenheit, one can use the following equation F=1.8C+32, where C is the temperature in Celsius and F is the temperature in Fahrenheit. What is the temperature in Fahrenheit when C is 15 degrees?
The temperature is 57 degrees Fahrenheit while C is 15 degrees.
What does 32 F mean on the Fahrenheit scale?Water has a freezing point of 32° and a boiling point of 212° on the Fahrenheit temperature scale. The difference between the two is divided into 180 equal parts.
Is 37.0 degrees Celsius a fever?Your body temperature is usually around 37 °C. When your body temperature is 37.8°C or greater, you typically have a fever. You might feel hot, cold, or shaky. By taking your temperature using a thermometer, you can determine whether you have a fever.
How do you convert between Fahrenheit and Celsius?The conversion of a degree in Fahrenheit to a degree in Celsius is represented by the Fahrenheit to Celsius formula. Fahrenheit to Celsius conversion formula: °C = [(°F-32)×5]/9
Given:
C = 15 degree
We know that,
F = 1.8C+32
F = 1.8*15+ 32
F = 27 +32
F = 57 degrees Fahrenheit
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A bicyclist accelerates at 1 m/s2 during a 4.0 s interval. What is the change in the speed of the bicyclist and the bicycle?
The change in the speed of the bicyclist and the bicycle is 4 meters per second.
What is Speed?Speed is the distance covered by an object in a particular time period. Speed is different from velocity, as it is a scalar quantity due to no direction. Whereas, velocity is a vector quantity due to both direction and magnitude.
Acceleration = Rate of change in velocity
Acceleration = Change in velocity/ Time taken
a = (v-u)/t
a = 1m/s²
t = 4 seconds
(v-u) = ΔV = ?
a = ΔV/ t
1 = ΔV/ 4
ΔV = 1×4
ΔV = 4 meters per second.
The change in the speed is 4 meter per second.
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the electric field at a point in space is e⃗ e→e_vec =(=( 400 i^ i^ 200 j^)n/cj^)n/c.
The x component of an electric force is 6.41 × [tex]10^{-17}[/tex] N and the y component of an electric force is 3.20 x [tex]10^{-17}[/tex]N.
E=(400 )i+(200 )j is the electric field vector
q=1.602 × [tex]10^{-19}[/tex]C is the charge of a proton
The electric force is calculated using:
F = qE
and we substitute:
F =(1.602 × [tex]10^{-19}[/tex]C)× ((400)i+(200)j)
we distribute the charge to both components of the vector to obtain:
F= (6.41 × [tex]10^{-17}[/tex] N)i+ (3.20 x [tex]10^{-17}[/tex]N)j
(a) Vector parts are represented by unit vectors. The unit vector I in the "hat" convention stands in for a vector's x-component. In this instance, the x-component of our electric force vector is as follows:
F=6.41 x [tex]10^{-17}[/tex]N
(b) Similar to our earlier response, the unit vector typically denotes a vector's y-component. Therefore, the y-component of our electric force vector is:
F=3.20× [tex]10^{-17}[/tex]N
We observe that our vector components' directions, which are their magnitudes, are represented by the unit vectors (or the numbers aside from the hat unit vectors).
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3 parts....challenging......
-Mitchell is making a diagram that compares balanced and unbalanced forces. Which of these characteristics would most likely describe unbalanced forces in Mitchell's diagram?
A. They cause an object to move.
B. They create a net force of 0 Newtons.
C. They result when no forces are acting on the object.
D. They result when equal and opposite forces act on an object.
Kyson enjoys doing many hobbies. If Kyson is experiencing a balanced force on his body doing one such hobby, which of these activities might he be doing?
A. walking his dog
B. running in a race
C. sitting and reading
D. swimming laps in a pool
A student is writing a short essay about forces for her science class. Which of the following statements can she use to describe the characteristics of all types of forces?
A. Forces act in pairs.
B. Forces only pull objects together.
C. Only one force can act on an object at a time.
D. Forces cause objects to move faster, but not slower.
In Mitchell's diagram, unbalanced forces cause an object to move.
Kyson is sitting and reading. The characteristics of all types of forces is: Forces act in pairs.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
A spring balance can be used to calculate the Force. The Newton is the SI unit of force.
For balanced force net force is zero and unbalanced force causes motion.
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if a juggler throws a ball straight up at a speed of 25 m/s, how long will it take to come back down?
If a juggler throws a ball straight up at a speed of 25 m/s, it will take 5.10 second to come back down.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Initial upward speed of the ball: v = 25 m/s.
Acceleration due to gravity: g = 9.8 m/s²
Hence, time taken by the ball = 2v/g
= ( 2 × 25)/9.8 second
= 5.10 second.
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the diameter of the he nucleus is about 2.0 fm f m . assuming the nucleus to be a sphere, calculate its density in g/cm3 g / c m 3 . express your answer in grams per cubic centimeter.
The density of the helium nucleus which has a diameter of 2 fm is 1.59 x 10¹² g/cm³
The diameter of the helium nucleus = 2.0 x 10⁻¹⁵ m
= 2 x 10⁻¹² cm
The radius of the helium = 1 x 10⁻¹² cm
The volume of the helium nucleus can be found using the formula,
V = 4/3πr³
= 4/3 x 3.14 x (1 x 10⁻¹²)³
= 4.17 x 10⁻³⁶ cm³
The density of the helium nucleus can be found using the formula,
d = m/v
where d is the density of the helium nucleus
m is the mass of the nucleus
v is the volume of the nucleus
Let us substitute the known values in the above equation, we get
d = 6.64 × 10⁻²⁴ / 4.17 x 10⁻³⁶
= 1.59 x 10¹² g/cm³
Thus, the density of the helium nucleus is 1.59 x 10¹² g/cm³
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The kinetic energy of the dark Throne would be w=2.38, the speed of the dart would be 12 m/s. If the dart were thrown straight upwards, what maximum height would it reach?
Answer:
2.38×12 = 28.56
w×v = height
