Answer:
Newton's Law 2
Hope this helps!
When a charged particle moves along a helical path in a uniform magnetic field, which component determines the pitch of the path? the velocity component perpendicular to the magnetic field vector the velocity component parallel to the magnetic field vector the acceleration component perpendicular to the magnetic field vector the acceleration component parallel to the magnetic field vector the acceleration component radially inward the acceleration component radially outward
Answer:
the velocity component parallel to the magnetic field vector
Explanation:
When a charged particle moves in a helical path, we can decompose its velocity into two parts v_parallel and v_perpendicular to the magnetic field.
Let's analyze which component receives a force
F = q vxB
the bold letters indicate vectors, in the vector product if the two vectors are parallel the angle is zero and the sin 0 = 0 for which there is no force. therefore the velocity parallel to the field remains constant
If the two vectors are perpendicular, the angle is 90º and the sin 90 = 1, for which there is a force, which has a radial direction and consequently a centripetal acceleration that gives a circular path that does not remove the particle from the magnetic field
When checking the different answers, the correct one is: the velocity component parallel to the magnetic field vector
The fastest crossing of the Atlantic Ocean by an ocean
linger was made in July of 1952. The ship, the S.S. United States, traveled 4727 km east by northeast in 3 days, 15 hours, and 20 minutes. Assume that the ship had traveled the same speed, but directly east. What would the velocity of the S.S United States be in km/h?
The rms speed of the molecules in 2.0 g of hydrogen gas is1600 m/s.
(a) What is the total translational kinetic energy of the gasmolecules?
(b) What the thermal energy of the gas?
(c) 500 J of work are done to compress the gas while, in thesame process, 1200 J of heat energy are transferred from the gas tothe environment. Afterward, what is the rms speed of themolecules?
(a) To find the total translational kinetic energy of the gas molecules, we can use the formula: Total kinetic energy = (3/2) * N * k * T, Where: N = Avogadro's number, k = Boltzmann's constant, T = temperature in Kelvin
First, let's convert the given mass of hydrogen gas (2.0 g) into moles: Number of moles = mass / molar mass Number of moles = 2.0 g / (2.016 g/mol) ≈ 0.993 mol. Next, we need to convert the temperature in Kelvin. Since only the rms speed is provided, we can use the following equation to relate it to temperature: v(rms) = sqrt((3 * k * T) / ms. where: v(rms) = rms speed m = molar mass of the gas. Rearranging the equation, we can solve for T: T = (m * v(rms)^2) / (3 * k) Using the given rms speed of 1600 m/s and the molar mass of hydrogen gas (2.016 g/mol), we can calculate the temperature in Kelvin: T = (2.016 g/mol * (1600 m/s)^2) / (3 * (1.381 × 10^-23 J/K)) Calculating T, we find: T ≈ 7309 K. Now, we can substitute the values into the formula for total kinetic energy: Total kinetic energy = (3/2) * N * k * T Total kinetic energy = (3/2) * (0.993 mol) * (1.381 × 10^-23 J/K) * (7309 K) Calculating the total kinetic energy, we find: Total kinetic energy ≈ 2.676 × 10^-19 J, Therefore, the total translational kinetic energy of the gas molecules is approximately 2.676 × 10^-19 J. (b) The thermal energy of the gas is equal to the total translational kinetic energy since we assume the gas is monoatomic and all its energy is in the form of kinetic energy. So, the thermal energy is also approximately 2.676 × 10^-19 J. (c) To find the new rms speed of the molecules after the work and heat transfer, we can use the principle of conservation of energy: Change in thermal energy = Work done + Heat transferred. Since the change in thermal energy is given as 1200 J, we have: 1200 J = 500 J + Heat transferred. Heat transferred = 1200 J - 500 J Heat transferred = 700 J Now, we can use the equation v(rms) = sqrt((3 * k * T) / m) to find the new rms speed. Rearranging the equation, we have: v(rms) = sqrt((3 * k * T') / m) Where T' is the new temperature in Kelvin. We can solve for T' by rearranging the equation: T' = (m * v(rms)^2) / (3 * k) Substituting the values into the equation, we have: T' = (2.016 g/mol * (1600 m/s)^2) / (3 * (1.381 × 10^-23 J/K)) Calculating T', we find: T' ≈ 7309 K, Therefore, the rms speed of the molecules after the work and heat transfer is approximately 1600 m/s, the same as before.
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Imagine carefully weighing a metal can, leaving it out in the rain for weeks and weeks
until it was very rusted, and then carefully weighing it again. Would the can be heavier or lighter after it was rusted? Why?
Answer:
The can would be heavier.
Explanation:
The more rust is on the can, (Or object) the more it weights it down.
Answer:
The answer would be heavier, though it depends upon the type of metal. Rusting is essentially corrosion. Rust is often caused by a piece of metal getting soaked in water and then being exposed to oxygen. The rust will add more weight to the can so it becomes heavier.
draw all stereoisomers formed when the following alkene is treated with mcpba. be sure to answer all parts.
When the given alkene is treated with MCPBA (meta-chloroperoxybenzoic acid), four stereoisomers are formed due to the presence of a double bond.
These stereoisomers can be classified as cis-trans isomers and enantiomers. When an alkene reacts with MCPBA, it undergoes an epoxidation reaction, resulting in the formation of an epoxide. The given alkene has a double bond between two carbon atoms, and MCPBA adds an oxygen atom across this double bond, forming an epoxide.
The first type of stereoisomer formed is the cis-trans isomers. The cis isomer refers to the arrangement where the two substituents on the same side of the double bond in the alkene remain on the same side in the resulting epoxide. The trans isomer refers to the arrangement where the substituents on the alkene's two carbons switch sides in the resulting epoxide. Thus, two cis-trans isomers are formed.
The second type of stereoisomer formed is enantiomers. Enantiomers are non-superimposable mirror images of each other. In the case of the given alkene, if the substituents attached to the double bond are different, two enantiomers are formed as a result of the epoxidation reaction.
In total, four stereoisomers are formed when the given alkene is treated with MCPBA. These stereoisomers can be identified by their different arrangements of substituents around the newly formed epoxide group.
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In this reaction, how many miles of CO2 would be produced when methane (CH4) fully reacts with 6 moles of O2? CH4 + 2O2 - 2H2O + CO2
Answer:
3 moles
Explanation:
Ratio of O2 to CO2 = 2 : 1 = 6 : 3
Which of the following equations is balanced correctly and has the correct products for the reactants RbNO3 and BeF2?
A balanced equation is a chemical equation in which the number of atoms of each element on both sides of the equation is equal. It represents a chemical reaction, indicating the reactants and products involved and the stoichiometric relationship between them.
The balanced equation for the reaction between RbNO3 and BeF2 is: 2RbNO3 + BeF2 → Be(NO3)2 + 2RbF.
To check if the equation is balanced or not, we can count the number of atoms of each element on both sides of the equation.
Here, we have Rb: 2 on both sides, N: 2 on both sides, O: 6 on both sides, Be: 1 on both sides, F: 2 on both sides.
Therefore, the balanced equation for the reaction between RbNO3 and BeF2 is 2RbNO3 + BeF2 → Be(NO3)2 + 2RbF, which has the correct products for the given reactants.
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HELP ME
PLZZZ
ASAP
HELP
LIFE
OR
DEATH
SITUATION
The half-life of carbon-14 is 5730 years.
Carbon-14 is used for carbon dating. Carbon dating can tell us how old some
objects are
A skeleton was carbon dated. The results showed that there was only 12.5% of the
original amount of carbon-14 left in the skeleton.
Calculate the age of the skeleton.
HELP ASAP PLZZZ I BEG YOUUUU
Answer:
13,308 MAYBE IF IT ISN'T IM SO SORRY
Explanation:
El monoxido de carbono reacciona con el hidrogeno gaseoso para producir metanol (ch3oh) calcule el reactivo limite y el reactivo en exceso si la reaccion inicia con 2,0 g de cada reactivo calcule cuantos gramos de metanol se obtiene
Answer:
Se obtienen 2,27 gramos de metanol.
Explanation:
La reacción entre monóxido de carbono e hidrógeno para producir metanol es la siguiente:
CO + 2H₂ → CH₃OH
Para encontrar el reactivo limitante y el reactivo en exceso, debemos calcular el número de moles de CO y H₂:
[tex]\eta_{CO} = \frac{m}{M} [/tex]
En donde:
m: es la masa
M: es el peso molecular
[tex]\eta_{CO} = \frac{m}{M_{CO}} = \frac{2,0 g}{28,01 g/mol} = 0,071 moles [/tex]
[tex]\eta_{H_{2}} = \frac{2,0 g}{2,02 g/mol} = 0,99 moles [/tex]
Dado que la relación estequiométrica entre CO y H₂ es 1:2, el número de moles de hidrógeno gaseoso que reaccionan con el monóxido de carbono es:
[tex] \eta_{H_{2}} = \frac{2}{1}*0,071 = 0,142 moles [/tex]
Entonces, se necesitan 0,142 moles de H₂ para reaccionar con 0,071 moles de CO y debido a que se tienen más moles de H₂ (0,99 moles) entonces el reactivo limitante es CO y el reactivo en exceso es H₂.
Ahora podemos encontar la masa de metanol obtenida usando el reactivo limitante (CO) y sabiendo que la realcion estequiométrica entre CO y CH₃OH es 1:1.
[tex] \eta_{CH_{3}OH} = \eta_{CO} = 0,071 moles [/tex]
[tex] m = 0,071 moles*32,04 g/mol = 2,27 g [/tex]
Por lo tanto, se obtienen 2,27 gramos de metanol.
Espero que te sea de utilidad!
as light travels from air into the water through the oil film,
When light travels from air into water through an oil film, several optical phenomena come into play: refraction, reflection, and interference.
First, refraction occurs at the air-water interface. As light enters the water, it undergoes a change in speed and direction due to the change in the refractive index between the two mediums. This causes the light to bend or deviate from its original path. Next, reflection occurs at the interface between the water and the oil film. A portion of the light is reflected back into the water, following the law of reflection. The angle of incidence is equal to the angle of reflection.
Interference also plays a role in this scenario. When the light waves reflect off the oil film, they can interfere constructively or destructively depending on their phase relationship. This interference can result in the appearance of colorful patterns, commonly known as thin-film interference. The colors observed in the oil film are due to the constructive and destructive interference of different wavelengths of light. The thickness of the oil film determines which wavelengths interfere constructively and produce visible colors.
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What are two main types of friction
Answer:There are two main types of friction, static friction and kinetic friction. Static friction operates between two surfaces that aren't moving relative to each other, while kinetic friction acts between objects in motion.
determine the pressure drop per 100-m length of horizontal new 0.35-m-diameter cast iron water pipe when the average velocity is 2.9 m/s.
When the average velocity is 2.4 m/s, the horizontal 0.35 meter diameter cast iron water pipe experiences a pressure drop (P) of roughly 16457.14 kPa every 100 meters.
To determine the pressure drop per 100-meter length of a horizontal 0.35-meter diameter cast iron water pipe, we can use the Darcy-Weisbach equation. The equation is as follows:
[tex]\begin{equation}\Delta P = \frac{f \cdot \frac{L}{D} \cdot (\rho \cdot V^2)}{2}[/tex]
where ΔP is the pressure drop, f is the Darcy friction factor, L is the length of the pipe (100 meters in this case), D is the diameter of the pipe (0.35 meters), ρ is the density of water, and V is the average velocity of water.
To calculate the pressure drop, we need to determine the Darcy friction factor. For a rough cast iron pipe, we can estimate the friction factor to be around 0.02.
Using the given values and the estimated friction factor, the calculation becomes:
[tex]\begin{equation}\Delta P = \frac{0.02 \cdot \frac{100}{0.35} \cdot (\rho \cdot 2.4^2)}{2}[/tex]
Since the density of water (ρ) is approximately 1000 kg/m³, we can substitute this value and calculate the pressure drop:
ΔP = [tex]\frac{0.02 \times \frac{100}{0.35} \times 1000 \times 2.4^2}{2}[/tex]
Let's solve the expression to calculate the pressure drop (ΔP) in kilopascals (kPa):
ΔP = [tex]\frac{0.02 \times \frac{100}{0.35} \times 1000 \times 2.4^2}{2}[/tex]
First, let's simplify the expression:
ΔP = [tex]\frac{0.02 \times (285.714) \times (1000 \times 5.76)}{2}[/tex]
= 16457.14
Therefore, the pressure drop (ΔP) per 100-meter length of the horizontal 0.35-meter diameter cast iron water pipe, when the average velocity is 2.4 m/s, is approximately 16457.14 kPa.
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Complete question :
Determine the pressure drop per 100 -m length of horizontal new 0.35−m-diameter cast iron water pipe when the average velocity 2.4 m/s. Δp= kPa
Hello everyone, Can you help me please I have to hand it in today and I can't do my calculation. Thank you in advance The sound emitted by blue whales has a speed in water of about 1,500 m/s. A male whale looking for a mate emits a sound that returns to him after 4 sec. How far away is the female whale? Give details of your calculation.
The female whale is approximately 3,000 meters away from the male whale.
To calculate the distance between the male and female blue whales, we can use the formula:
Distance = (Speed of sound in water × Time) / 2
Given that the speed of sound in water is approximately 1,500 m/s and the time taken for the sound to return is 4 seconds, we can substitute these values into the formula:
Distance = (1,500 m/s × 4 s) / 2
Simplifying the equation:
Distance = (6,000 m) / 2
Distance = 3,000 m
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The gravitational field strength on the moon is 1.63 N/kg. If a rock on the moon weighs 2000N, how
much does the same rock weigh on the earth?
Answer:
12000N
Explanation:
gravity on earth is six times one on the moon
microwaves travel with the speed of light, c = 3 × 108 m/s. at a frequency of 10 ghz these waves cause the water molecules in your burrito to vibrate. what is their wavelength?
The wavelength of microwaves with a frequency of 10 GHz is 0.03 meters or 3 centimeters. These microwaves cause the water molecules in the burrito to vibrate due to the absorption of their energy, resulting in the heating of the food.
The wavelength of microwaves with a frequency of 10 GHz can be calculated using the formula λ = c/f, where λ represents wavelength, c is the speed of light (3 × 10^8 m/s), and f is the frequency (10^10 Hz). Therefore, the wavelength of these microwaves is 0.03 meters or 3 centimeters.
The relationship between wavelength, frequency, and the speed of light is given by the equation λ = c/f, where λ represents wavelength, c is the speed of light, and f is the frequency. In this case, we have a frequency of 10 GHz, which is equivalent to 10^10 Hz. Plugging these values into the equation, we get:
λ = c/f
= (3 × 10^8 m/s) / (10^10 Hz)
= 3 × 10^(-2) meters
= 0.03 meters
= 3 centimeters
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what is the frequency (in hz) of light that has a wavelength of 400 nm? (you can enter your answer in scientific notation using e. include three significant figures.)
The frequency of light with a wavelength of 400 nm is approximately [tex]7.494 * 10^{14} Hz[/tex] (or 749.4 THz).
To calculate the frequency of light, you can use the equation:
Frequency = Speed of light / Wavelength
The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s). We need to convert the given wavelength of 400 nm to meters.
[tex]1 nm = 1 * 10^{-9}[/tex] meters
Converting 400 nm to meters:
[tex]400 nm = 400 * 10^{-9} meters = 4 * 10^{-7} meters[/tex]
Now, we can calculate the frequency:
Frequency = (Speed of light) / (Wavelength)
[tex]= 299,792,458 m/s / (4 * 10^{-7} meters)\\ =7.494 * 10^{14} Hz[/tex]
Therefore, the frequency of light with a wavelength of 400 nm is approximately [tex]7.494 * 10^{14} Hz[/tex] (or 749.4 THz).
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PLEASE HELP ME I AM TIMED!
Answer:
they all need a source of oxygen
Answer:
B
Explanation:
true or false
two different notes can have the same fundamental frequency
Answer:
true:)
Explanation:
I will mark you brainlist!
What mythical creature do you think is possibly real, and not actually a myth? Why?
Examples of mythical creatures: Mermaids/Merman, Fairies/ Pixie, Nymphs, Dragons, Unicorn, Leprechauns, Werewolf, Loch Ness Monster, Sphinx, Centaur, Griffin, Yeti, Pegasus, Basilisk, Chimera, Ghoul, Imp, Gnome, Manticore, Troll, Bigfoot, Phoenix, Vampire etc.
You can choose one that is listed or not listed.
Explanation:
With most of our blue planet covered by water, it's little wonder that, centuries ago, the oceans were believed to hide mysterious creatures including sea serpents and mermaids. Merfolk (mermaids and mermen) are, of course, the marine version of half-human, half-animal legends that have captured human imagination for ages. One source, the "Arabian Nights," described mermaids as having "moon faces and hair like a woman's but their hands and feet were in their bellies and they had tails like fishes."
C.J.S. Thompson, a former curator at the Royal College of Surgeons of England, notes in his book "The Mystery and Lore of Monsters" that "Traditions concerning creatures half-human and half-fish in form have existed for thousands of years, and the Babylonian deity Era or Oannes, the Fish-god ... is usually depicted as having a bearded head with a crown and a body like a man, but from the waist downwards he has the shape of a fish." Greek mythology contains stories of the god Triton, the merman messenger of the sea, and several modern religions including Hinduism and Candomble (an Afro-Brazilian belief) worship mermaid goddesses to this day.
at what speed does a 1800 kg compact car have the same kinetic energy as a 1.80×104 kg truck going 25.0 km/hr ?
Kinetic energy refers to the energy possessed by an object due to its motion. The formula for kinetic energy is given as follows: Kinetic energy = 1/2 × mass × velocity², Where: mass = the mass of the object, velocity = the speed of the object.
We can equate the kinetic energies of the car and truck using the formula above. Let's assume that the speed of the car is v. Therefore, we can write:1/2 × 1800 × v² = 1/2 × 1.80×10⁴ × (25/3.6)², Where:25/3.6 is used to converting the speed of the truck from km/h to m/s.
Simplifying the right-hand side of the equation, we get:1/2 × 1.80×10⁴ × (25/3.6)² = 781250 J.
Now, we can solve for v by dividing both sides of the equation by 1/2 × 1800:1/2 × 1800 × v² = 781250v² = 781250 ÷ 900v² = 868.056v ≈ 29.47 m/s.
Therefore, the speed at which an 1800 kg compact car has the same kinetic energy as a 1.80×10⁴ kg truck going 25.0 km/h is approximately 29.47 m/s.
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A 7.7 mW laser produces a narrow beam of light. How much energy is contained in a 1.0 m length of its beam? Please show step by step
The energy contained in a 1.0 m length of the beam from a 7.7 mW laser is 7.7 μJ (microjoules).
To calculate the energy contained in the length of the laser beam, we need to use the power of the laser and the formula:
Energy = Power × Time
However, we don't have the time information here. To proceed, we'll assume a continuous wave laser where the power remains constant over time.
Given:
Power of the laser = 7.7 mW (milliwatts)
Length of the beam = 1.0 m
First, we need to convert the power from milliwatts to watts:
7.7 mW = 7.7 × 10^(-3) W
Next, we can calculate the energy using the formula:
Energy = Power × Time
Since we assume a continuous wave laser, we can rearrange the formula as:
Energy = Power × Time = Power × (1 second)
Plugging in the values:
Energy = (7.7 × 10^(-3) W) × (1 second)
The time in this case is 1 second because we assume a continuous beam over that duration. Multiplying the power by 1 second doesn't change the value.
Finally, we can calculate the energy:
Energy = (7.7 × 10^(-3) W) × (1 second)
= 7.7 × 10^(-3) J (joules)
Since the joule is a relatively large unit, it's common to express small energy values in smaller units such as microjoules (μJ).
Converting from joules to microjoules:
1 J = 10^6 μJ
Therefore,
Energy = 7.7 × 10^(-3) J
= 7.7 × 10^(-3) × 10^6 μJ
= 7.7 × 10^(3) μJ
= 7.7 μJ
The energy contained in a 1.0 m length of the beam from a 7.7 mW laser is 7.7 μJ (microjoules).
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) A 1.0kW kettle contains 500g of boiling waterCalculate the time needed to evaporate all the water
in the kettle (specific latent heat of vaporization2.26 MJ kg-1
Answer:
t = 1130 s = 18.83 min
Explanation:
First, we will calculate the energy required to evaporate 500 g of water:
[tex]E = mL[/tex]
where,
E = Energy Required for evaporation of water =?
m = mass of water = 500 g = 0.5 kg
L = Latent heat of vaporization of water = 2.26 MJ/kg = 2260 KJ/kg
Therefore,
[tex]E = (0.5\ kg)(2260\ KJ/kg)\\E = 1130\ KJ[/tex]
Now, we will calculate the time required:
[tex]P = \frac{W}{t}\\\\t = \frac{W}{P}[/tex]
where,
t = time = ?
P = Power of kettle = 1 KW
Therefore,
[tex]t = \frac{1130\ KJ}{1 KW}\\\\[/tex]
t = 1130 s = 18.83 min
A force is applied to the rim of a disk that can rotate like amerry-go-round, so as to change its angular velocity. Its initialand final angular velocities, respectively, for four situationsare: (a) -3 rad/s, 7 rad/s; (b) 3 rad/s, 7 rad/s; (c) -3 rad/s, -7rad/s; (d) 3 rad/s, -7 rad/s. Rank the situations according to thework done by the torque due to the force, greatest first (use onlythe symbols > or =, for example, a>d=b>c).
The ranking of the work done by the torque is a > b > c > d.
What is the work done by the torque?The work done by the torque is equal to the change in rotational kinetic energy of the body.
Mathematically, the formula for torque is given as;
τ = r.F sinθ = Iα
where;
r is the radius of the force actionF is the applied forceI is the moment of inertiaα is the angular accelerationThe formula for angular acceleration is given as;
α = Δω / Δt
where;
Δω is the change in angular speedΔt is the change in time of motionThus, the greater the change in angular speed, the greater the work done by the applied torque.
(a) Δω = 7 rad/s - (-3 rad/s) = 10 rad/s
(b) Δω = 7 rad/s - 3 rad/s = 4 rad/s
(c) Δω = -7 rad/s - (-3 rad/s) = -4 rad/s
(d) Δω = -7 rad/s - 3 rad/s = -10 rad/s
The ranking, a > b > c > d
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The brick wall (of thermal conductivity
1.16 W/m ° C) of a building has dimensions
of 5 m by 7 m and is 18 cm thick.
How much heat flows through the wall in
a 17.2 h period when the average inside and
outside temperatures are, respectively, 24°C
and 8°C?
Answer in units of MJ.
Answer:223.46 MJ
Explanation:
Given
The thermal conductivity of brick wall is [tex]k=1.16\ W/m.^{\circ}C[/tex]
Cross-section of Wall [tex]A=5\m \times 7\ m[/tex]
time period [tex]t=17.2\ h=17.2\times 60\times 60=61,920\ s[/tex]
Inside temperature [tex]T_i=24^{\circ}C[/tex]
Outside temperature [tex]T_o=8^{\circ}C[/tex]
Heat transfer through the bricks
[tex]\dot{Q}=kA\dfrac{dT}{dx}[/tex]
[tex]\dot{Q}=1.16\times 35\times \dfrac{16}{0.18}\\\\\dot{Q}=3608.88\ W[/tex]
Heat flow for 17.2 h
[tex]Q=3608.88\times 61,920=223.46\ MJ[/tex]
Which of the following activities can be done thanks to observing asteroids?
[mark all correct answers]
A. Calculate and improve current calculations of their orbits.
B. Know more about the composition of asteroids
C. Identify characteristics of asteroids such as if they have rings or tails
D. Take samples of materials from asteroids
E. Identify asteroids that represent a threat to life on earth
To observe asteroids: Calculate and improve orbits. Know about asteroids. Identify characteristics of asteroids. Take samples from asteroids. Identify asteroids a threat to life on earth. The correct answers are A, B, C, D, and E.
Observing asteroids allows us to:
A. Calculate and improve current calculations of their orbits: By observing their positions and movements over time, we can refine our understanding of their orbits, predict future positions, and assess potential collision risks.
B. Know more about the composition of asteroids: By analyzing their reflected light, emission spectra, and studying meteorites that originate from asteroids, we can gain insights into their mineralogical and chemical compositions, helping us understand the formation and evolution of the solar system.
C. Identify characteristics of asteroids such as if they have rings or tails: Through careful observations, we can detect features like rings or tails associated with certain asteroids, providing valuable information about their structure and behavior.
D. Take samples of materials from asteroids: By sending spacecraft missions to asteroids, we can collect samples from their surfaces or even perform asteroid deflection experiments, enabling us to study their physical properties and potential resources.
E. Identify asteroids that represent a threat to life on Earth: Continuous monitoring and observation of asteroids allow us to identify and track potentially hazardous asteroids that may pose a risk of impacting Earth, enabling us to plan and develop mitigation strategies if necessary.
Therefore, observing asteroids contributes to a wide range of activities, from refining orbital calculations and understanding their composition and characteristics to assessing potential threats and even collecting samples from them.The correct answers are A, B, C, D, and E.
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a particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds. its maximum velocity is:
The maximum velocity of the particle is 100 m/s. Negative sign indicates that the velocity is in the opposite direction of the displacement at that particular point in time.
To find the maximum velocity of a particle in simple harmonic motion, we need to differentiate the position function with respect to time and then find the maximum value of the resulting velocity function.
Given the position function x = 2cos(50t), we can find the velocity function v(t) by taking the derivative of x with respect to t:
v(t) = dx/dt = -2(50)sin(50t) = -100sin(50t)
The maximum velocity occurs when the sine function has a maximum value of 1. Therefore, the maximum velocity can be found by evaluating the velocity function at that point. In this case, the maximum value of sin(50t) is 1 when 50t = π/2 or t = π/100.
Substituting t = π/100 into the velocity function:
v_max = -100sin(50(π/100)) = -100sin(π/2) = -100(1) = -100 m/s
Therefore, the maximum velocity of the particle is 100 m/s. Note that the negative sign indicates that the velocity is in the opposite direction of the displacement at that particular point in time.
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A longitudinal wave is observed. Exactly 6 crests are observed
to move past a given point in 9.1 s. Its wavelength is 2.4 m and
its frequency is 0.66 HZ. What is the speed of the wave?
The decay of uranium isotopes is used to provide what information about Earths history?
The decay of uranium isotopes is used to provide information about the age of earth.
Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle. Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius R with angular velocity ω, r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^] =Rcos(ωt)i^+Rsin(ωt)j^. The main point of the problem is to compute the acceleration using geometric arguments. (Figure 1) Part A What is the velocity of the mass at a time t? You can work this out geometrically with the help of the hints, or by differentiating the expression for r⃗ (t) given in the introduction. (Figure 2) Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (t) = Part Assume that the mass has been moving along its circular path for some time. You start timing its motion with a stopwatch when it crosses the positive x axis, an instant that corresponds to t=0. [Notice that when t=0, r⃗ (t=0)=Ri^. ] For the remainder of this problem, assume that the time t is measured from the moment you start timing the motion. Then the time − t refers to the moment a time t before you start your stopwatch. Part B What is the velocity of the mass at a time − t? Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (−t) = SubmitMy AnswersGive Up Part C What is the average acceleration of the mass during the time interval from − t to t? (Figure 3) Express this acceleration in terms of R, ω, t, and the unit vectors i^ and j^.
Part A :The position of the particle in vector form is given by[tex]r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^][/tex]where R is the radius of the circle and ω is the angular velocity.The velocity of the particle is given by taking the derivative of the position vector with respect to time.
Taking derivative with respect to time on both side we get [tex]v⃗ (t)=d/dt R[cos(ωt)i^+sin(ωt)j^]= R[-in(ωt)ωi^+cos(ωt)ωj^]=ωR[-sin(ωt)i^+cos(ωt)j^]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^][/tex]Thus the velocity of the mass at a time t is given by [tex]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^][/tex].
Part B :
We have to find the velocity at time -t. The velocity of the particle is given by taking the derivative of the position vector with respect to time. Thus the velocity of the mass at a time -t is given by [tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]
[tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]Part C :
The average acceleration of the particle can be computed using the formulaa = [tex]Δv/Δt[/tex]The velocity at time t is given by[tex]v⃗ (t) = ωR[-sin(ωt)i^+cos(ωt)j^][/tex]
The velocity at time -t is given by [tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]
[tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]The change in velocity over the interval from -t to t is therefore
[tex]Δv = v(t) - v(-t) = 2ωR[sin(ωt)i^ + cos(ωt)j^][/tex]
The time interval over which this change occurs is[tex]Δt = 2t[/tex]Thus the average acceleration of the particle is given by a = [tex]Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex]
[tex]a = Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex]
The acceleration can be expressed in terms of R, ω, t, and the unit vectors [tex]i^ and j^[/tex] as [tex]a = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex].
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Match the phrase with word please help!
Phrases:
1.) The amount of work done when jerry carries a box from his house to the moving truck . He exerts a force of 35 N while carrying the box 4 meters
2.) The power resulting from 420 Nm of work being completed in 3 seconds
3.) The amount of work done when Fido carries his toy from the backyard to his crate. He exerts a force of 1.2 N over a distance of 15 m
4.) The power resulting from 120 Nm of work being completed in 20 seconds
A.) 140 joules
B.) 140 Newton-meters
C.) 6 joules
D.) 6 Newton-meters
Answer:
1-B, 2-A, 3-D, 4-C
Explanation:
1. The force exerted is, F = 35 N
Distance the box is moved, d = 4 m
So the amount of work done is, W = F x d
= 35 x 4
= 140 Newton-meters
2. Work done, W = 420 Nm
Time, T = 3 seconds
Therefore, the power required is,
[tex]$P=\frac{W}{T}$[/tex]
[tex]$P=\frac{420}{3}$[/tex]
= 140 joules
3. The force exerted is, F = 1.2 N
Distance the box is moved, d = 5 m
So the amount of work done is, W = F x d
= 1.2 x 5
= 6 Newton-meters
4. Work done, W = 120 Nm
Time, T = 20 seconds
Therefore, the power required is,
[tex]$P=\frac{W}{T}$[/tex]
[tex]$P=\frac{120}{20}$[/tex]
= 6 joules