Answers
The magnitude of the vector [tex]\vec C[/tex] is 8.6.
A - B is used to indicate the vector subtraction of two vectors a and b, and it simply involves adding the vector's negative for vector b.
How to Subtract Vectors?To subtract two vectors a and b graphically (i.e., to find a - b), just make them coinitial first and then draw a vector from the tip of b to the tip of a.We can add -b (the negative of vector b which is obtained by multiplying b with -1) to a to perform the vector subtraction a - b.given :
A = 5.7
angle from x axis = 90 -38 = 52
[tex]\vec A =[/tex] ( 5.7 cos 52, 5.7 sin 52)
B = 4.3
[tex]- \vec B[/tex] angle from x axis = 90 +24 = 114
[tex]- \vec B[/tex] = (4.3 cos 114 , 4.3 sin 114)
[tex]\vec A - \vec B = \vec A + ( - \vec B)[/tex]
= ( 5.7 cos 52, 5.7 sin 52) + (4.3 cos 114 , 4.3 sin 114)
=( 5.7 cos 52 +4.3 cos 114 , 5.7 sin 52+ 4.3 sin 114)
= (3.51 - 1.75, 4.49+3.93)
[tex]\vec C[/tex] = (1.76, 8.42)
magnitude of [tex]\vec C[/tex] = [tex]\sqrt{1.76^2+ 8.42^2}[/tex]
=[tex]\sqrt{3.10+70.9}[/tex] =[tex]\sqrt{74}[/tex] = 8.6
The magnitude of the vector [tex]\vec C[/tex] is 8.6.
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Related Questions
Part A Which of the following changes would make the water balloon more likely to pop? (Ignore effects of convection within the fluid.) Select all that apply. View Available Hint(s) Use a liquid that has a higher heat capacity than water Use a thicker balloon. Use a liquid that has a lower heat capacity than water. D Use a thinner balloon. Part A Which of the following changes would make the water balloon more likely to pop? (Ignore effects of convection within the fluid.) Select all that apply. View Available Hint(s) Use a liquid that has a higher heat capacity than water Use a thicker balloon. Use a liquid that has a lower heat capacity than water. D Use a thinner balloon.
Answers
The change that would make the water balloon more likely to pop is:
to use a liquid that has a lower heat capacity than waterto use a thicker balloon.The correct options are B and C
What is heat capacity?Heat capacity or also known as thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature.
So, Using a liquid that has a lower heat capacity than water and using a thicker balloon will make the water balloon more likely to pop.
We know now that heat capacity or specific heat is the amount of heat per unit mass that is required to raise the temperature by 1°C and this is helpful in determining the processing temperatures and amount of heat necessary for processing and can be helpful in differentiating between two polymeric composites.
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Since Finding Nemo came out in theaters, there has been an increased demand for pet clownfish. Now marine biologists are noticing that the sea anemone population is also decreasing. What can we do to help build up the sea anemone population? Explain why your solution would help.
Answers
There are plenty of things we can do to help build up the sea anemone population, but a few ways would be:
A) mate clown-fish to breed,
B) tell people about the problem they're producing, and
C) prohibit the purchase and sale of clown-fish in retailers.
Why sea anemone population is decreasing?The sea anemone is not a threatened species. The effects of climate change and human activities on sea anemone populations, on the other hand, remain mostly unknown. Clown-fish have a thick mucus covering that shields them from the potentially lethal sting of sea anemones.
According to research, clown-fish and other anemone-fish populations are declining in the wild due to over harvesting for the aquarium trade.
Thus,
A) mate clown-fish to breed,
B) tell people about the problem they're producing, and
C) prohibit the purchase and sale of clown-fish in retailers.
This can we do to help build up the sea anemone population.
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PLEASE HURRY!!
Two objects that each have a mass of 10,000 kg are 5.5 m apart. What is the gravitational force between them? (Universal constant of gravitation: 6.67 x 10-11)
a. 2.20 x 10^-4 N
b. 1.51 x 10^-3 N
c. 2.59 x 10^-5 N
d. 1.99 x 10^-4 N
Answers
Answer:
(a) 2.20 x 10^-4 N.
Explanation:
To solve this problem, you can use the formula for the gravitational force between two objects:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the universal constant of gravitation, m1 and m2 are the masses of the two objects, and r is the distance between them.
Plugging in the given values, we get:
F = (6.67 x 10^-11) * (10,000 kg) * (10,000 kg) / (5.5 m)^2
= 2.20 x 10^-4 N
So the answer is (a) 2.20 x 10^-4 N.
Tell me if this helps :)
Wich is faster this is for a project so pls don't guess
1.328m/s
or
1.351 m/s
Answers
Answer:
1.328m/s
Explanation:
Because it takes less meters per second compared to 1.351 m/s. Hope it helps!
A teacher wants to determine how well students can discuss ways in which related concepts differ. Which of the following is most appropriate for this objective?
Group of answer choices
True-false
Matching
Multiple choice
Short essay
Answers
Short essay is most appropriate for this objective because it allows
students to discuss ways in which related concepts differ in their own
words. True-false, matching, and multiple choice formats do not
typically provide as much opportunity for in-depth discussion.
(a) Find an equation for the length L of a refracting telescope in terms of the focal length of the object Fo and the magnification m. (b) A knob adjusts the eyepiece forward and backward. Suppose the telescope is in focus with an eyepiece giving a magnification of 50.0. By what distance must the eyepiece be adjusted when the eyepiece is replaced, with a resulting magnification of 1.00x10^2? Must the eyepiece be adjusted backward or forward? Assume the objective lens has a focal length of 2.00m.
Answers
The equation of length is fo(1-1/M) and distance used for adjustment of eye piece is 20cm.
A refracting telescope's magnification is calculated by dividing the objective's focal length by the eyepiece's focal length.
e. g. A reflecting telescope has a 5 cm eyepiece and an objective with a focal length of 70 cm. It will be magnified by 70 / 5 = 14.
a) L = fo + fe
M = -fo / fe========> fe = -fo / M
L = fo - fo/M = fo*(1-1/M)
b) M = 50 = -fo/fe
L1 = fo*(1-(1/50)) = 2*(1-(1/50)) = 1.96 m
L2 = fo*(1-(1/50)) = 2*(1-(1/100)) = 1.98 m
d = L2 - L1 = 0.02m = 20 cm
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During a storm, a car traveling on a level horizontal road comes upon a bridge that has washed out. The driver must get to the other side, so he decides to try leaping the river with his car. The side of the road the car is on is 21.3 meters above the river, while the opposite side is only 1.8 meters above the river. The river itself is a raging torrent 48.0 meters wide.
Answers
The speed of the car to land safely on the opposite side will be 24.0 m/s. The speed of the car just before it lands on the other side will be 31.0 m/s.
(a) Speed is defined as the rate of change of the distance attained. it is a time-based quantity.
The equation for the position vector will be;
= r = x₀ + v₀xt,y₀ + v₀yt + (1/2)gt²
where,
r = the vector position of the car
vₓ = the initial horizontal velocity
vₐ = initial vertical velocity
t = time
y₀ =the initial vertical position
g =the acceleration due to gravity
v = the velocity at time t
From the figure, the origin of the frame of reference is located at y₀ = 0 and x₀ = 0.
The given position vector from the figure;
= r(final) = (48 -19.5) m
Then, employing the equations for the x and y-components of the vector r final, we will obtain;
= y = y₀ + v₀yt + (1/2)gt²
= y = (1/2)gt²
= -19.5 m = (1/2) X 9.8 X t²
= t = 2 s
By estimating the initial velocity at t = 2.00
The value is x-component of the vector r final is 48.0 m.
= x = x₀ + v₀xt [x₀ = 0]
= 48 = v₀x X 2
= v₀x = 24 m/s
Hence the speed of the car to land safely on the opposite side will be 24.0 m/s.
(b) The speed of the car just before it lands on the other side will be 31.0 m/s.
= v = (v₀x,v₀y + gt)
The y-component of v is given by;
= vₐ = v₀y + gt [v₀y = 0]
= vₐ = -9.8 X 2
= vₐ = -19.6 m/s
The resultant speed of the vector v will be :
= v² = 24² + (-19.6)²
= v = √ (24² + (-19.6)²)
= v = 31 m/s
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The complete question:
During a storm, a car traveling on a level horizontal road comes upon a bridge that has washed out. The driver must get to the other side, so he decides to try leap- ing the river with his car. The side of the road the car is on is 21.3 m above the river, while the opposite side is only 1.8 m above the river. The river itself is a raging torrent 48.0 m wide. (a) How fast should the car be traveling at the time it leaves the road in order just to clear the river and land safely on the opposite side? (b) What is the speed of the car just before it lands on the other side?
This graph shows the changes in energy of a box as it moves down a ramp. The x-axis represents the distance the box travels from its starting point at the top of the ramp. How do the height and velocity of the box change as it moves down the ramp?
The height and the velocity both decrease.
The height and the velocity both increase.
The height increases and the velocity decreases.
The height decreases and the velocity increases.
Answers
The height of the box decreases and the velocity of the box increases.
What is law of conservation of energy?Energy cannot be created or destroyed according to the rule of conservation of energy. However, it is capable of changing its form. The total energy of an isolated system is constant for all forms of energy.
The law of energy conservation is observed by all energy forms. In a nutshell, the law of conservation of energy asserts that: The whole energy of the system is preserved in a closed system, or a system that is cut off from its surroundings.
As the total mechanical energy of the box is conserved, the potential energy of the box transfers into kinetic energy which refers that the height of the box decreases and the velocity of the box increases.
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reactive power flow through a transmission line is proportional to the cosine of the phase angle difference between the sending and receiving end voltages
Answers
Capacitors and inductors (which might be from time to time known as reactors) are passive gadgets that generate or soak up reactive strength.
They accomplish this with out widespread real-strength losses or running expense. The output of capacitors and inductors is proportional to the rectangular of the voltage. Voltage magnitudes are in large part decided via way of means of reactive strength flows;
Reactive strength go with the drift on the road will increase the voltage distinction among sending and receiving buses; • The more potent the short-circuit strength in a given bus, the much less reactive strength go with the drift from the road reduces its voltage with appreciate to the sending bus reactive strength go with the drift thru a transmission line is proportional to the cosine of the section perspective distinction among the sending and receiving give up voltages.
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A mechanic uses a crowfoot wrench to loosen a bolt at E. Knowing that the mechanic applies a vertical 24-lb force at A, determine using Mohr's circle method the principal stresses and the maximum shearing stress at point H located as shown as on top of the 3/4-in. diameter shaft (this is the problem of 7.47 in the 7th edition).
Answers
As a result, the diameter of the shaft, as determined by Mohr's circle method, is 3.4 ksi.
What is Mohr's circle method?The transformation equation for issues involving plane stress are shown graphically by Mohr's circle. It helps to visualize the relationship between normal and shear loads acting on a stress component at any required direction. This process was developed by a German scientist by the name of Karl Friedrich Mohr. As a result, this procedure was given the moniker Mohr's method. Direct titration is a part of the procedure. Chloride ion solution serves as the analyte in this process, while silver nitrate is utilized to prepare titrants.
What is Mohr equation?The major stress and maximum shear stresses are identified, along with their planes, using Mohr's circle, which also aids in visualizing the normal stress and shear stress acting on the plane. Maximum shear stress (max) equals (σ1-σ2). Mohr's Circle coordinate is represented by the symbols σx,σy. Mohr's Circle Center (C) = ((σ1+2)/2, 0)
Briefing:J=0.0310 in^4
I=J/2=0.0310/2
I=0.0155 〖in〗^4
T=Tr/J=(240×0.375)/0.031
=2.9ksi
σ=Mr=144×(0.375)
=3.5ksi
σA=σmax=σ avg+R
=1.75+3.4
=5.15ksi
σB=σ min=σ avg-R
=1.75-3.4
=-1.65ksi
T max.=R=3.4ksi
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part 1 of 2
Given: G = 6.67259 x 10-11 Nm' /kg'
A 588 kg geosynchronous satellite orbits a planet similar to Earth at a radius 2.01 × 105 km from the planet's center. Its angular speed at this radius is the same as the rotational speed of the Earth, and so they appear stationary in the sky. That is, the period of the satellite is 24 h.
What is the force acting on this satellite?
Answer in units of N.
Answers
The force acting on satellite is 6.15 × [tex]10^{26}[/tex] kg.
What is force?
An object having mass differs its velocity in response to a push or pull. Force is an external agent that has the power to alter a body's resting or moving condition. It has a size and a movement.
Given,
F= [tex]M_{satellite}[/tex] × [tex]v^{2}[/tex]/r
v = 2[tex]\pi[/tex]r/T
F= [tex]M_{satellite}[/tex] × [4[tex]\pi[/tex][tex]r^{2}[/tex]/[tex]T^{2}[/tex]]
= 602 × 4[tex]\pi^{2}[/tex] × 1.98 × [tex]10^{8}[/tex] /[tex]86400^{2}[/tex]
= 630.37 N
[tex]M_{planet}[/tex] = 4[tex]\pi[/tex][tex]r^{2}[/tex][tex]r^{3}[/tex]/[tex]GT^{2}[/tex]
= (4[tex]\pi^{2}[/tex] × (1.98 × [tex]10^{8}[/tex][tex])^{3}[/tex])/ (6.67 × [tex]10^{-11}[/tex] × [tex]86400^{2}[/tex])
= 6.15 × [tex]10^{26}[/tex] kg.
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the following is the electron configuration for an element that combines with magnesium to form an ionic compound. what are the correct subscripts for the formula of this compound?
Answers
Magnesium oxide is created by the ionic bonding of magnesium (Mg) and oxygen (O2). While oxygen has six valence electrons and an of 3,44, magnesium only has two valence electrons and a value of 1,31.
What is in a electron?A opposite charges subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of components within an atom is an e that is bonded to it; the other couple are protons и neutrons.
What gives electrons their energy?When sufficiently stimulated, atoms in these materials transition from one energy level to another and inhabit a new orbital. These higher-energy electrons eventually return to their initial energy level after releasing their "excess" energy in form of a light photon.
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I need help with this question please.
Answers
The frequency heard by the person is 493.78Hz.
When the train moves toward the stationary observer then:
[tex]F=n(V/V-V_{s})[/tex]
Given:[tex]n=472,V=340m/s,V_{s}=15m/s[/tex]
[tex]F=472(340/340-15)\\F=493.78Hz[/tex]
What are the frequency and pitch of sound?
Sounds are higher or lower in pitch according to the frequency of vibration of the sound waves producing them. A high frequency (e.g., 880 hertz [Hz; cycles per second]) is perceived as a high pitch, and a low frequency (e.g., 55 Hz) as a low pitch.
How does the frequency of sound change with distance?
The frequency of sound doesn't decrease with distance, but it does decrease with increasing distance, meaning it does go through the doppler shift, the same as light. This is why the sound of a car driving by at high speeds drops in frequency as the car passes you.
Thus, the frequency at which the whistle is heard is 493.78Hz
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452.05 Hz is the frequency at which whistle is heard when the frequency (Hz) a person hears as a train blows its whistle at 472Hz while moving 15m/s toward this person on a freezing cold day.
What is frequency ?The No. of oscillations of a wave in fixed unit of time is termed as frequency. f=1/T .
The S.I unit of frequency is hertz (Hz). One hertz is = to one cycle per second.Given:
Frequency of whistle is =472Hz
The speed of train = 15m/s
Speed of air =340m/s
Solution:We use the given formula nA=n( V/V+Vs)
nA= 472(340/340+15)
nA=452.05 Hz
Hence, 452.05 Hz is the frequency at which whistle is heard when the frequency (Hz) a person hears as a train blows its whistle at 472Hz while moving 15m/s toward this person on a freezing cold day.
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creep i. is the plastic deformation of a material under a stress. ii. is the time dependent degradation of material. iii. is a measure of the amount of energy a material can absorb. iv. is the fracture of material under cyclic stress.
Answers
The plastic deformation of a material under a stress is the permanent deformation.
Plastic deformation is the permanent deformation of a material that occurs when the material is subjected to a stress that is above its yield strength. When a material undergoes plastic deformation, the bonds between the atoms or molecules that make up the material are broken and reformed in a new configuration, resulting in a permanent change in the shape of the material.
Plastic deformation can occur in a variety of materials, including metals, plastics, and ceramics. It is typically characterized by a decrease in the strength and an increase in the ductility of the material, as the material becomes more pliable and able to undergo significant deformation without breaking. The amount of plastic deformation that a material can undergo depends on a variety of factors, including the material's yield strength, the type of stress it is subjected to, and the duration of the stress. Some materials, such as steel, are able to undergo significant plastic deformation before breaking, while other materials, such as glass, are prone to brittle failure and can undergo little or no plastic deformation before breaking.
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A mass m is suspended by a massless string forming a simple pendulum of length 2.0 m. The string of the pendulum is initially at an angle of 60° with the vertically downward direction when the mass is released from rest.
Answers
The centripetal acceleration of the mass is 10 m/s².
What is the centripetal acceleration of the mass?
The centripetal acceleration of the mass when it is at the lowest position is calculated as follows;
Tsinθ = ma - mg
where;
θ is the angle of inclination of the stringT is the tension in the stringm is mass suspendeda is centripetal acceleration of the massg is acceleration due to gravitywhen the mass is at the lowest position, θ = 0
The centripetal acceleration of the mass is calculated as follows;
T sin (0) = ma - mg
0 = ma - mg
ma = mg
a = g
Given that g, acceleration due to gravity = 10 m/s²
Hence, a = 10 m/s²
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The complete question is below:
A mass m is suspended by a massless string forming a simple pendulum of length 2.0 m. The string of the pendulum is initially at an angle of 60° with the vertically downward direction when the mass is released from rest. Calculate the centripetal acceleration of the mass when it is at the lowest position ( take g = 10 m/s²).
The CN Tower in Toronto, Canada, is 553 m tall, making it the tallest free-standing structure in the world. Suppose a chunk of ice with a mass of 25.0 g falls from the top of the tower. The speed of the ice is 30.0 m/s as it passes the restaurant, which is located 353 m above the ground. What is the magnitude of the average force due to air resistance?
Answers
The magnitude of the average force due to air resistance be 188.75 N.
What is law of conservation of energy?Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms. The law of conservation of energy essentially says that
The total energy of the system is conserved in a closed system, also known as an isolated system.
Total energy of the chuck of ice at 553 m tall tower: E = mgh
= 25.0 × 9.8 × 553 Joule = 135485 joule.
If the average force due to air is W the, total energy of the ice at 353 m above the ground:
E = mgh + 1/2mv² + W(553-353)
= 25.0 × 9.8 × 353 + 1/2×25×30² + 200 W
= 97735 + 200 W joule
According to conservation of energy:
135485 = 97735 + 200 W
⇒ 200 W = 37750
⇒ W = 188.75 N.
Hence, the magnitude of the average force due to air resistance be 188.75 N.
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g determine how fast the top of the ladder is sliding down along the vertical wall when the base is 6 ft from the wall
Answers
The top of the ladder is sliding down the vertical line with a vertical speed of 0.75ft/s when the bottom of the ladder is 6ft from the wall.
Please refer to the image below.
We know from the case, that:
x = 6ft
l = 10ft
dx/dt = 1ft/s
Using the phytagoras theorem, we know that:
y² = 10² - x² ... (i)
Since the speed is the derivative of distance with respect to time, we could use the same concept to the equation (i) above:
2y.dy/dt = (0 - 2x) dx/dt
dy/dt = (x/y) dx/dt ... (ii)
When the ladder slides down and its bottom reach 6ft from the wall, the height of the ladder on the wall is:
y² = 10² - x²
y² = 10² - 6²
h = 8ft
The vertical speed of the ladder is:
dy/dt = (8/6) dx/dt
dy/dt = (8/6) (1)
dy/dt = 0.75 ft/s
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Complete Question:
A ladder 10ft long rest afainst a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6ft from the wall?
A box with a mass of 1.5 kg is pulled across the floor with a constant velocity by a force of 37 N. What is the coefficient of friction? Show
work for full credit.
Answers
A box with a mass of 1.5 kg is pulled across the floor with a constant velocity by a force of 37 N, the coefficient of friction is 2.52
What is friction?The force that resists the motion of one solid object over another is known as friction. The four basic forms of friction are fluid friction, rolling friction, sliding friction, and static friction.
Friction is a sort of contact force. It exists between surfaces that are in touch with one another.
Given that,
Mass (m) = 1.5 kg
force (F) = 37 N
As we know,
co-efficient of friction (μ) = F/mg
μ = 37 N / (1.5 kg × 9.8 m/sec)
μ = 2.52
Thus, co-efficient of friction = 2.52
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Answer:
ok the final answer is μ = 2.52
Explanation:
I did the question on the flvs the first explanation is correct
The speed of sound (velocity) is 343 m/s and a burglar alarm on a car has a frequency of 1200hz. What is the wavelength of the burglar alarm on the car? Formula is Wavelength=Velocity/Frequency
PLEASE HELP!!
Answers
The speed of sound (velocity) is 343 m/s and a burglar alarm on a car has a frequency of 1200hz. 0.286 m/sec is the wavelength of the burglar alarm on the car.
What is frequency?Frequency is a unit of measurement for how frequently a recurrent event, like a wave, takes place over a specified period of time. A cycle is one repetition of the repeating pattern. Frequency only exists in moving waves that change their places throughout time. One method to describe how quickly a wave moves is by its frequency.
Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 times per hour if it takes 1/100 of an hour.
Given that,
speed of sound (velocity) is 343 m/s
frequency of 1200 Hz.
Now as we know,
v = n × λ
or, λ = v/n
or, λ = (343 m/sec) / 1200 Hz.
or, λ = 0.286 m/sec
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If Impulse is the change in momentum using forces, how would you have to change a large amount of force with a small force?
a .You will have to apply the force over a longer period of time
b. You will have to apply the force at a different direction
c. You will have to have more than one force present
d. You will have to decrease the total impulse acting on the object
Answers
To change a large amount of force with a small force, you will have to apply the force over a longer period of time. So, option (a) is correct.
What is impulse?In physics, the term "impulse" is used to characterize or measure the impact of force operating gradually to alter an object's motion. It is often stated in Newton-seconds or kilograms per second and is denoted by the symbol J.
Product of the average force applied to an object throughout time and the time period during which it is applied is impulse. The change in momentum is the same as impulse.
You will have to apply the force over a longer period of time to create large amount of impulse with a small force.
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The graph in Figure 13 represents the motion of a car moving along a straight highway. Describe in words the car’s motion.
Answers
Answer: decreasing diagnol lines are constant dpeed moving toward the origin
Explanation:
If you live in a place that gets its electricity from a coal plant, it is better to drive a(n) ____ car.
Answers
Driving an electric vehicle is preferable if you reside somewhere where coal plants are used to generate power.
Coal-fired power plants generate steam in order to generate electricity. These facilities generate almost 40% of the power used worldwide. Coal plants require enormous amounts of coal. The coal plant uses 9000 tonnes of coal per day. Coal is a flammable sedimentary rock with a colour that is either black or brownish-black, and it is sometimes referred to as coal seams. Coal is essentially made of carbon, with different amounts of other elements, including hydrogen, sulphur, oxygen, and nitrogen. Dead plant matter decomposes into peat, which under the heat and pressure of deep burial for millions of years eventually turns into coal. Coal mining and consumption result in early mortality and disease. The biggest anthropogenic source of carbondioxide causing climate change is coal burning, which harms the ecosystem.
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A 0.321 kg, 0.27 m radius thin shelled ball rolls (starting at rest) 3.82 m from the top down a 35 degree 10.0 m long incline without slipping. After the 3.82 m, the incline becomes frictionless for the rest of the board. After 0.8 m of the frictionless unencumbered movement, the ball reaches a frictionless, massless spring with a spring constant of 20 N/m.
a) How fast is the center of mass of the ball going after 3.82 m? (linear speed)
b) How fast is the ball rolling after the 3.82 m? (angular speed)
c) How much does the spring compress?
d) What is the ball's maximum linear speed?
e) What is the balls angular speed with the spring is fully compressed?
I need this answered by tomorrow night, so please don't rush this one too bad... I would like step-by-step solutions not just answers.
Answers
Answer:
Explanation:
Hope you can give me "Brainliest" answer is will help a lot! Thank you
To solve this problem, we can use the following equations:
Linear speed: v = d/t
Angular speed: w = v/r
Spring compression: x = (1/2)kx^2
Conservation of energy: KE = PE
a) To find the linear speed of the center of mass after 3.82 m, we can use the equation v = d/t. We know that d = 3.82 m and t = 1 s (since the ball is starting from rest). Plugging these values into the equation gives us:
v = 3.82 m / 1 s = 3.82 m/s
This is the linear speed of the center of mass after 3.82 m.
b) To find the angular speed after 3.82 m, we can use the equation w = v/r. We know that v is 3.82 m/s (the linear speed we just found) and r is 0.27 m (the radius of the ball). Plugging these values into the equation gives us:
w = 3.82 m/s / 0.27 m = 14.15 rad/s
This is the angular speed of the ball after 3.82 m.
c) To find the spring compression, we can use the equation x = (1/2)kx^2. We know that k is 20 N/m (the spring constant) and x is the spring compression (which we are trying to find). Plugging these values into the equation gives us:
x = (1/2)(20 N/m)(x^2)
To solve for x, we can rearrange the equation to get:
x^2 = (2/k)x
Substituting in the value for k gives us:
x^2 = (2/20 N/m)x
Solving for x gives us:
x = sqrt(2/20 N/m) = 0.2 m
This is the spring compression.
d) To find the maximum linear speed, we can use the conservation of energy equation KE = PE. We know that KE is the kinetic energy of the ball (which is equal to (1/2)mv^2) and PE is the potential energy of the ball (which is equal to mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the incline). We also know that the ball starts at the top of the incline with a height of h = 10 m and that it rolls down the incline a distance of d = 3.82 m. We can use these values to find the final height of the ball, h2, using the equation h2 = h - d = 10 m - 3.82 m = 6.18 m.
Substituting these values into the conservation of energy equation gives us:
(1/2)mv^2 = mgh2
Solving for v gives us:
v = sqrt(2gh2/m) = sqrt(2(9.8 m/s^2)(6.18 m)/0.321 kg) = 6.58 m/s
This is the maximum linear speed of the ball.
e) To find the angular speed with the spring fully compressed, we can use the equation w = v/r. We know that v is the maximum linear speed we just found (6.58 m/s) and r is the radius of the
11.15 in the circuit of fig. 11.46, find the value of zl that will absorb the maximum power and the value of the maximum power.
Answers
The value of x =3.
What is value?Value is regard that something is held to deserve the important worth or usefullness of something .
In ∆ ABC
<A= <B=<C
Triangle is equilibrium triangle.
All the triangle side will be equal
6x-3=3x+6=5x
=6x-3 =3x+6
=3x=g
X=3
Thus, X = 3
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The current in one part of a series circuit is 5 - 3f amps. The current in another part of the circuit is 7 + 9j amps. Add these complex numbers to find the total current in the circuit.
Answers
The overall current in the circuit, according to the stated assertion, is 12 -2f + 9j.
What does current in electrical terms mean?When describing however much electricity flows through a connection and how it moves in an electronic circuit, the phrase "electric current" is often employed. It is measured in amperes (A). The ampere number rises as more electricity flows through the circuit.
Briefing:
Since all current in a series circuit travels in the same direction.
We can evaluate the total current that flows in the circuit as follows;
Total current = 1st part current + 2nd part current
Total current =5 – 2f + 7 + 9j
Total amps = 12 –2f + 9j.
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which of the following are advantages of deformation processes compared to other metal manufacturing processes? [select all that apply]
Answers
The advantages of deformation processes are surface qualities, strength, and durability. Cold processing of metals has numerous advantages.
In cold settings, metals are distorted to achieve the desired forms. Cold processing of metals has numerous advantages.
The most significant advantage of cold working is the absence of the need for heating equipment and heat energy to raise the temperature of the metal. This is a highly valuable advantage of cold-working metals over heat-working processes.
Because the dimensions do not vary as the temperature rises, greater surface qualities, and dimensional tolerances can be produced.
Because of grain flow, when metal parts are deformed at high temperatures, the desired mechanical characteristics can be acquired in the desired directions.
The strain-hardening phenomenon occurs during the cold deformation of metal parts, resulting in increased strength.
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MgBr2 + 2 NaCl → MgCl2 + 2 NaBr
is this double replacement or single replacement or something else
Answers
The reaction depicted by the equation is a double replacement reaction.
What are double replacement reactions?Double-replacement reactions are chemical reactions during which the reactants exchange ions to form two new products entirely. The two compounds participating in double-replacement reactions are usually ionic compounds.
Unlike double-replacement reactions, single-replacement reactions involve the displacement of an atom from a compound by another atom.
Thus, a double-replacement reaction is in the form: [tex]AB + CD --- > AD + CB[/tex]
While a single-replacement reaction is usually in the form: [tex]AB + C --- > AC + B[/tex]
Thus, the reaction [tex]MgBr_2 + 2 NaCl --- > MgCl_2 + 2 NaBr[/tex] is a double replacement reaction.
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Which statement is true about the motion of a planet in its orbit around the Sun?
A: The orbital speed increases as the planet approaches apogee.
B: The orbital speed of the planet remains constant as it orbits the Sun.
C: The planent's orbital speed changes as it moves closer and farther from the Sun.
D: Perigee is when the orbital speed is at its least.
Answers
The statement that is true about the motion of a planet in its orbit around the Sun is the planet's orbital speed changes as it moves closer and farther from the Sun. The correct option is C.
What is the motion of planets?The motion of a planet is explained by Kepler's law of motion. Kepler's laws of planetary motion are physics rules that govern the motions of the planets in the solar system. They were developed by the German astronomer Johannes Kepler.
According to Kepler's first law of planetary motion, the path that the planets take around the sun is elliptical, with the sun's center at one focus. The distance between the Sun and the planets changes as they orbit the Sun.
Therefore, the correct option is C: The planet's orbital speed changes as it moves closer and farther from the Sun.
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14C is produced in the upper atmosphere by cosmic rays. Living organisms uptake 14C. Assume we isolate the same quantity of 14C from a 1000 year old fossil and from a recently harvested tomato. We monitor the decay of these quantities.
A. The carbon islated from the tomato plant will have more decays per second that the carbon isolated from the fossil
B. The two samples will have approximately the same number of decays per second.
C. The carbon isolated from the fossil will have more decays per second that the carbon isolated from the tomato plant.
D. It is impossible to compare the decay rates, since nuclear decay is a random process.
Answers
The average decay rate for the two samples will be about the same.
The correct option is B.
What happens if cosmic rays hit the Earth?Cosmic rays that reach Earth have the potential to interact with atom nuclei in the atmosphere, producing billions of fission fragments in the process. Cosmic rays were the sole technique to examine subatomic particles before people created the first photon accelerators in the 1950s.
What examples of cosmic rays?HZE ions are the name for these high-mass, high-charged particles. Numerous sources produce primary cosmic rays. They may originate from sunspots or solar explosions, for instance. The term "solar energetic particles" is frequently used to describe the particles released by the sun.
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Conservation of Momentum - A 5 kg mass has a speed of 3 m/s to the right when it hits and sticks to a 4 kg mass. If the final combined speed is 2 m/s to the right, what was the initial velocity of the second object. Pick the closest answer. A) 1.2 to the right B) 1.2 to the left C) 0.75 to the right D) 0.75 to the left
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The system is working based on the Conservation of Momentum: A 5kg mass has a speed of 3m/s to the right when it hits and sticks to a 4 kg mass that moves with speed of 0.75m/s to the right (C). Both mass then move together with 2m/s to the right.
Conservation of momentum states that the total momentum of a system remains constant.
P = P'
Momentum is the product of a particle's mass and velocity. Momentum could be formulized as:
P = m.v
From the case, we know that:
m1 = 5kg
m2 = 4kg
v1 = 3m/s to the right
v1' = v2' = v' = 2m/s to the right
v2 = ?
Based on the conservation of momentum concept, we know that:
P = P'
where:
P = m.v
Hence:
P = P'
m1.v1 + m2.v2 = (m1 + m2)v'
5 (3) + 4 (v2) = (5+4) 2
15 + 4v2 = 18
4v2 = 3
v2 = 0.75 m/s --> because v2 positive, hence m2 is moving to the right
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