The car travels approximately 150.65 meter distance to completely stop after applying the breaks.
First we need to consider both its initial velocity and its acceleration. initial velocity is 53km/h and acceleration is 3.4 m/s². If we convert velocity into m/s, 53km/h = 53×5/18 = 14.72 m/s.
So by the end of 40 seconds the final velocity will be 14.722 + (3.4 x 40) = 95.02 m/s . Now we know initial velocity = 14.72 m/s and final velocity = 95.02 m/s.
When the driver applies the brakes, it changes the acceleration to 4.6 m/s². So now acceleration is -4.6 m/s².
The distance that the car travels can be calculated using the equation for average velocity:
distance = (initial velocity + final velocity) / 2 × t
where t is the time taken for car to completely rest.
We know, velocity final= Velocity initial + a × t . So if velocity final is zero and solving for t,
0 = 95.022 - 4.6t
t = 95.022 / 4.6 = 20.67 seconds
Finally, we can use the equation for average velocity to determine the distance traveled:
d = (14.722 + 0) / 2 × 20.67 = 150.65 meters
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suppose you are in a rocket with no windows traveling in deep in space far from other objects. without looking outside the rocket or making any contact with the outside world, explain how you would determine whether the rocket is moving forward at a constant
To determine whether the rocket is moving forward at a constant speed in deep space, without looking outside the rocket or making any contact with the outside world, you could perform a number of experiments inside the rocket.
One such experiment would be to release an object inside the rocket and measure its motion relative to the rocket. If the rocket is moving at a constant speed, the object should fall straight down, relative to the rocket, under the influence of gravity. On the other hand, if the rocket is accelerating or decelerating, the object will experience a horizontal component of motion relative to the rocket.Another experiment would be to perform measurements using instruments such as accelerometers or gyroscopes, which can detect changes in motion. An accelerometer would measure changes in the rocket's acceleration, while a gyroscope would measure changes in the rocket's orientation. If the rocket is moving at a constant speed, these instruments should not detect any changes. If the rocket is accelerating or decelerating, these instruments would detect a change in the rocket's motion.These are a few examples of the types of experiments you could perform inside the rocket to determine whether it is moving at a constant speed in deep space.
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a ball is projected straight up with an initial velocity of 20 m/s. after 3 seconds its velocity will be
The velocity of the ball which is projected straight upward after 3 sec is found to be 49.4m/s.
What is a motion in free fall?When an object falls through with a vacuum, it is solely subject to one external force: gravitational force, which corresponds to the object's weight. Free falling is the term for an item that is only moving due to the pull of gravity, and Newton's second rule of motion describes this motion.
U => 20m/s
t=3s
V= u+gt ; According to law of motion
V= 20 + 9.8x3 (+ve g since the projected straight upward)
=> 49.4m/s
What happens if you throw a ball vertically up in the air?When the body is propelled upward, it rises vertically until both the ball's velocity and the force acting on it are zero. The ball then experiences zero velocity as it accelerates due to gravity it until touches the earth.
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a commuter backs her car out of her garage with an acceleration of 1.40 m/s2. she accelerates until she is moving at 2.00 m/s. if she then brakes to a stop in 0.800s, what is the magnitude of that acceleration, in m/s2? (give your answer as just a number)
It takes her 1.43 s to reach a speed of 2.00 m/s. Therefore, the magnitude of the deceleration of the car is -2.5 m/s^2
Let's call the magnitude of the deceleration a. Then, the final velocity v_f of the car after decelerating for t = 0.800s can be calculated using the equation:
v_f = v_i + a * t
where v_i = 2.00 m/s is the initial velocity of the car. Since the car comes to a stop, v_f = 0.
So, we can solve for a:
0 = 2.00 m/s + a * 0.800s
a = -2.00 m/s / 0.800s = -2.5 m/s^2
Deceleration refers to the slowing down of an object in motion. This can occur due to various reasons such as friction, air resistance, or the application of a force that opposes the direction of motion. Deceleration is expressed as a negative acceleration, as it is opposite in direction to acceleration, which is the rate of change of velocity. The formula for deceleration is expressed as a=-(v-u)/t, where v is the final velocity, u is the initial velocity, and t is the time taken for the deceleration to occur.
In physics, deceleration is a crucial concept that is used to study various aspects of motion. For instance, in automobile engineering, deceleration is used to calculate the braking distance of a vehicle, which is the distance required to bring a vehicle to a stop. This information is crucial in designing safe and efficient vehicles. Deceleration is also important in sports and biomechanics where it is used to study the motion of athletes and the effects of impact on the body.
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the test tubes shown below contain equal amounts of the specified motor oils. identical metal spheres were dropped at the same time into each of the tubes, and a brief moment later, the spheres had fallen to the heights indicated in the illustration. which motor oil has the least viscosity?
The motor oil, where the metal sphere takes least time to fall, has the least viscosity.
What is viscosity?We refer to this resistance to motion that most fluids provide as "viscosity." When there is relative motion between the fluid's layers, viscosity develops.
More specifically, it measures flow resistance brought on by internal friction between fluid layers that occur when they pass one another during fluid flow.
Strong intermolecular forces provide a lot of internal friction in a fluid with a high viscosity, which makes it difficult for layers to move past one another.
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A roller coaster climbs up a hill at 4 m/s and then zips down the hill at 30 m/s what is the momentum of the roller coaster a. zero throughout the ride
b. the same throughout the ride
c. the greater down the hill than up the hill
d. greater up the hill than down the hill
Answer:
Greater down the hill than up the hill.
Explanation:
the table shows the position of a motorcyclist after accelerating from rest. t (seconds) 0 1 2 3 4 5 6 s (feet) 0 4.9 10.6 23.1 50.2 109.4 238.3 (a) find the average velocity (in ft/s) for each time period.
The average velocity for each time period is as follows: t = 1 sec: 4.9 ft/s, t = 2 sec: 5.3 ft/s, t = 3 sec: 7.7 ft/s, t = 4 sec: 12.5 ft/s, t = 5 sec: 21.9 ft/s, t = 6 sec: 39.7 ft/s
To find the average velocity for each time period, we need to calculate the change in position (displacement) and divide it by the change in time. The formula for average velocity is:
v = Δs / Δt
Where Δs is the change in position (displacement) and Δt is the change in time.
Here's the calculation for each time period:
t = 1 sec: Δs = 4.9 ft, Δt = 1 sec, v = Δs / Δt = 4.9 ft/s
t = 2 sec: Δs = 10.6 ft, Δt = 1 sec, v = Δs / Δt = 5.3 ft/s
t = 3 sec: Δs = 23.1 ft, Δt = 1 sec, v = Δs / Δt = 7.7 ft/s
t = 4 sec: Δs = 50.2 ft, Δt = 1 sec, v = Δs / Δt = 12.5 ft/s
t = 5 sec: Δs = 109.4 ft, Δt = 1 sec, v = Δs / Δt = 21.9 ft/s
t = 6 sec: Δs = 238.3 ft, Δt = 1 sec, v = Δs / Δt = 39.7 ft/s
So the average velocity for each time period is as follows:
t = 1 sec: 4.9 ft/s
t = 2 sec: 5.3 ft/s
t = 3 sec: 7.7 ft/s
t = 4 sec: 12.5 ft/s
t = 5 sec: 21.9 ft/s
t = 6 sec: 39.7 ft/s
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imani is in a specialty clinic, sitting in a chair. she is about to receive a treatment that scientists believe will produce less side effects by targeting specific brain areas using short magnetic pulses from a coil held next to her head. anesthesia will also be unnecessary, further reducing negative side effects. what treatment will imani be receiving?
Imani is likely to be receiving Transcranial Magnetic Stimulation (TMS) treatment.
What is magnet?Magnetism is a physical quality mediated by a magnetic field that refers to the ability to create attracted and repulsive occurrences in other substances. Diamagnetic materials are those that magnetize freely when put in a magnetic field. However, the magnetization is oriented in the opposite direction as the magnetic field. These materials' magnetism is referred to as diamagnetism. Magnetism is a component of the broader phenomenon of electromagnetic. The most well-known effects occur in ferromagnetic materials, which are highly attracted by magnetic fields and may be magnetized to become permanent magnets, hence creating magnetic fields. It is also feasible to demagnetize a magnet.
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what is the magnitude of the electric field, in newtons per coulomb, at point p, in the center of the semicircle?
The magnitude of the electric field at a point can be calculated using the equation: [tex]E = k *\frac{Q}{ r^2}[/tex].
where E is the electric field, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), Q is the charge generating the field, and r is the distance from the point to the source of the field.
Without more information on the charge distribution, it is not possible to calculate the electric field at point P in the center of the semicircle. When Q is the charge producing the field, k is Coulomb's constant (8.99 x 109 N m2/C2), and r is the distance between the point and the source of the field.
The magnitude of the electric field at a point can be calculated using the equation: [tex]E = k *\frac{Q}{ r^2}[/tex]
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calculate the energy (in j) stored in a fully charged battery if the phone requires charging after 8.03 hours of use.
58,741.1 joules.the energy (in j) stored in a fully charged battery if the phone requires charging after 8.03 hours of use.
The energy stored in the battery is equal to 8.03 hour x battery voltage x battery capacity.
The total energy (in joules) is equal to 8.03 x battery voltage x battery capacity.
if the battery voltage is 3.7V
the battery capacity is 2100mAh,
the energy stored in the battery is
8.03 x 3.7V x 2100mAh
= 58,741.1 joules.
the energy (in j) stored in a fully charged battery if the phone requires charging after 8.03 hours of use is 58,741.1
To calculate the energy (in joules) stored in a fully charged battery, you need to know the battery's capacity and voltage. The capacity of the battery is the amount of energy (in joules) it can store. The voltage is the amount of energy (in volts) that the battery is able to produce.
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the all-or-nothing principle maintains that once the electrical impulse reaches a _____, the impulse will fire.
if we could observe background stars in daylight, how would the sun appear to move against this background because of our motion on an orbiting earth?
Star parallax is the apparent shift in the position of a distant star as seen from two different locations (the Earth's surface) due to the Earth's orbit around the Sun.
If we could observe background stars during the day, the Sun would appear to remain fixed in one position while the background stars would seem to move in circular paths around it.
The amount of apparent shift depends on the distance of the star from the Earth and the position of the Earth in its orbit.
This effect can be imagined by holding your thumb up at arm's length and alternately closing and opening each eye. Your thumb appears to shift against the background because of the different perspective each eye provides.
Similarly, the apparent shift of the background stars against the Sun is caused by the difference in perspective of the Earth at two points in its orbit.
Star parallax is a key principle used in astronomy to measure the distances to nearby stars, as it provides a direct method to determine their distances.
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if a mass undergoes a temperature change without the input or removal of heat from the surrounding environment, the process is known as
By providing shade and evapotranspiration cooling, planting trees and other plants lower surface and air temperatures. Directly shady trees and other greenery can reduce the amount of air conditioning in your home.
When heat is removed, what is it known as?Exothermic reactions are those in which heat is removed from a substance. As the heat decreases, molecules' speeds also do so. This causes them to move more slowly, which changes their phase.
What impact does temperature have on mass?Mass is just the quantity of substance that exists. As a result, modifying the temperature has had no direct effect on mass because there is always the same quantity of matter present. Mass every unit volume is the definition of density for a substance.
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which moon phases are associated with the highest tides
As stated in the preceding statement The highest tides occur during new moon nor low moon phases.
How will the moon end?The Moon will finish moving away from Earth at present rate of separation in around 15 billion years, according to calculations of the development of the Earth/Moon system. In around 6 to 700 million years, our Sun is predicted to enter his Red Giant phase.
Were we able to endure without the Moon?The stability of the climate is maintained by the moon's gravitational pull, which reduces Earth's tremor. A blessing for life, that. Without it, the climate may change dramatically over millennia, with certain regions being extremely hot before going through protracted ice ages.
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the electric potential of a charge distribution is given by v(x, y) = 2xy - x2 - y. at which point is the electric field equal to zero?
The electric field is equal to zero at the point [tex](x, y) = (1/2, 1/2)[/tex].
What is electric potential?
The electric potential, is a scalar field that represents the potential energy per unit charge at a given point in space. It is a measure of the amount of work required to move a unit positive charge from a reference point (typically taken as infinity) to a particular point in space. The electric potential is often used to describe the behavior of electric fields in a region and to calculate the force experienced by charges in that region.
Calculation to find the points where the electric field is equal to zero.
The electric field at a point (x, y) is given by the gradient of the electric potential, which is a vector pointing in the direction of the maximum rate of increase of the potential.
The electric potential[tex]v(x, y) = 2xy - x^2 - y[/tex] can be written as:
[tex]v(x, y) = 2x y - x^2 - y[/tex]
So the gradient of the electric potential is:
[tex]∇v(x, y) = < ∂v/∂x, ∂v/∂y > = < 2y - 2x, 2x - 1 >[/tex]
The electric field is equal to zero at the points where the gradient is equal to zero. So, each component of the gradient has to be set equal to zero and solve [tex]x[/tex]and[tex]y[/tex]:
[tex]2y - 2x = 0 = > y = x[/tex]
[tex]2x - 1 = 0 = > x = 1/2[/tex]
Therefore, the electric field is equal to zero at the point[tex](x, y) = (1/2, 1/2)[/tex].
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Please help me out!
Match potential answers to the relating images
1. All elastic potential
2. Elastic + gravitational potential
3. All kinetic potential
If we consider the rank of image from left to right:
image 1: all kinetic energy.
image 2: Elastic + gravitational potential
image 3: All elastic potential
What is potential energy?The energy that an item retains due to its position in relation to other objects, internal tensions, electric charge, or other reasons is known as potential energy in physics.
Potential energy can take many different forms. Some examples are an object's gravitational potential energy, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field.
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a certain radar uses microwave radiation with a wavelength of 2.33 mm. what is the frequency of this electromagnetic radiation (s-1 )?
The frequency (in s⁻¹) of the electromagnetic radiation having a wavelength of 2.33 mm is 1.29×10¹¹ s⁻¹
How do I determine the frequency of the electromagnetic radiation?When the wavelength of a radiation is given, we can obtain the frequency using the following formula:
Velocity (v) = wavelength (λ) × frequency (f)
The following data were obtained from the question
Wavelength (λ) = 2.33 mm = 2.33 / 1000 = 2.33×10⁻³ m Speed of electromagnetic wave (v) = 3×10⁸ m/sFrequency of electromagnetic radiation (f) =?Thus, the frequency of the electromagnetic radiation can be obtained as follow:
Velocity (v) = wavelength (λ) × frequency (f)
3×10⁸ = 2.33×10⁻³ × frequency
Divide both sides by 2.33×10⁻³
Frequency = 3×10⁸ / 2.33×10⁻³
Frequency = 1.29×10¹¹ s⁻¹
Thus, we can conclude, the frequency is 1.29×10¹¹ s⁻¹
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sequence the events that occur when an electroscope is used to detect a charge on an object. write numbers from 1 to 4 to the left of the events to show the correct sequence.
Electrons are moved into or out from the leaves by an electroscope in response to the existence of a charge. The charged object's positive or negative charge cannot be determined by the electroscope.
What takes place during the electroscope experiment?Electrons went back through copper to your palm when you contacted the electroscope, then through you body to the earth. The metals inside the electroscope lost its charge as a result of the ground dispersing the energy away from you. They hang lifeless in the jar without any charge and no longer repel.
How is an electroscope tested?Create some electrical currents by rubbing the Polystyrene on a piece of wool to test your electroscope. With the wool, repeatedly rub the Styrofoam. Hold your electrically charged Styrofoam quickly in close proximity to the metal wire's coiled portion on your electroscope. Don't touch the wire, please!
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a car backfires as it drives along the highway between two mountains. the echo from one side of mountain is heard 1.5 s after the car backfire was fired. the echo from the other mountain is heard 1.0 s after the first echo. how far apart are the mountains? assume the speed of sound in air is 343 m/s. (use guess method)
The echo from the other mountain is heard 1.0 s after the first echo. So, the two mountains are approximately 600.25 meters apart.
The time for the sound to travel to the first mountain and back is 1.5 seconds, so we can use that time to calculate the distance traveled.
The distance traveled is equal to the speed of sound multiplied by the time it takes for the sound to travel that distance.
d = v * t
d = 343 m/s * 1.5 s = 514.5 m
This distance is the total distance traveled by the sound to reach the first mountain and back to the listener. Since this is a round trip, the distance to the first mountain is half of this value:
d1 = 514.5 m / 2 = 257.25 m
Next, we can use the time it took for the second echo to arrive (1.0 s) to find the distance to the second mountain:
d2 = 343 m/s * 1.0 s = 343 m
Finally, to find the distance between the two mountains, we simply add the distances to the two mountains:
d = d1 + d2 = 257.25 m + 343 m = 600.25 m
Echo is a technology that allows sound to be reflected and repeated back to its source. It is commonly used in a variety of applications including sonar, radar, and audio systems. In sonar and radar, echo is used to determine the distance, speed, and direction of objects. In audio systems, echo is used to create a sense of space and depth in sound recordings. Echo can also be used to reinforce sound in concert halls and other large spaces.
Echo is created by reflecting sound waves off of a surface, such as a wall or a solid object. The time it takes for the echo to return to its source is called the echo delay time, and it can be used to determine the distance of the reflecting surface. In audio systems, echo can be added artificially by using echo chambers, digital signal processors, or other electronic devices.
Echo can also cause problems in audio systems, particularly in communication systems, where echoes can interfere with the clarity of speech. To reduce unwanted echoes, many audio systems use echo cancellers, which are algorithms that identify and subtract echoes from the audio signal.
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a stone is projected at a cliff of height h with an initial speed of 42.0m/s directed at angle theta0=60.0 above the horizontal. The stone strikes at A, 5.50s after launching. Find (a) the height h of the cliff, (b) the speed of the stone just before impact at A, and (c) the maximum height H reached above the ground.
Answer:
Height of the cliff: approximately [tex]51.7\; {\rm m}[/tex].
Speed right before landing: approximately [tex]27.4\; {\rm m\cdot s^{-1}}[/tex].
Maximum height reached: approximately [tex]67.4\; {\rm m}[/tex] above the ground (relative to the base of cliff.)
(Assumption: air resistance is negligible, and that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
Let [tex]u[/tex] denote the velocity of the projectile at launch.
Initial horizontal velocity: [tex]u_{x} = u\, \cos(\theta) = 42.0\; {\rm m\cdot s^{-1}}\, \cos(60.0^{\circ}) = 21.0\; {\rm m\cdot s^{-1}}[/tex].Initial vertical velocity: [tex]u_{x} = u\, \sin(\theta) = (21.0\, \sqrt{3})\; {\rm m\cdot s^{-1}}[/tex].(a)Under the assumptions, velocity in the vertical direction changes at a constant [tex]a_{y} = (-9.81)\; {\rm m\cdot s^{-2}}[/tex]. Velocity in the horizontal direction would be constant.
Apply the SUVAT equation [tex]x = (1/2)\, a\, t^{2} + u\, t[/tex] to find the vertical displacement after the [tex]t = 5.50\; {\rm s}[/tex] flight:
[tex]\begin{aligned}x_{y} &= \frac{1}{2}\, a_{y}\, t^{2} + u_{y}\, t \\ &= \frac{1}{2}\, (-9.81)\, (5.50)^{2} + (21.0\, \sqrt{3})\, (5.50) \\ &\approx 51.7\; {\rm m}\end{aligned}[/tex].
Thus, the cliff is approximately [tex]51.7\; {\rm m}[/tex] above the ground.
(b)It is given that the flight took [tex]t = 5.50\; {\rm s}[/tex]. At a rate of [tex]a_{y} = (-9.81)\; {\rm m\cdot s^{-2}}[/tex], vertical velocity would have changed by [tex]a_{y}\, t[/tex] during the flight. Hence, the vertical velocity right before landing would be:
[tex]\begin{aligned}v_{y} &= u_{y} + a_{y}\, t \\ &= 21.0 \sqrt{3} + (-9.81)\, (5.50) \\ &\approx 17.582\; {\rm m\cdot s^{-1}} \end{aligned}[/tex].
Under the assumptions, horizontal velocity would stay constant: [tex]v_{x} = u_{x} = 21.0\; {\rm m\cdot s^{-1}}[/tex].
Apply the Pythagorean Theorem to find the overall velocity right before landing:
[tex]\begin{aligned}v &= \sqrt{{v_{x}}^{2} + {v_{y}}^{2}} \\ &\approx \sqrt{21.0^{2} + (17.582)^{2}} \\ &\approx 27.4\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
(c)When height is maximized, vertical velocity would be [tex]0[/tex]. Apply the SUVAT equation [tex]x = (v^{2} - u^{2}) / (2\, a)[/tex] to find the vertical displacement when vertical velocity is exactly [tex]0\; {\rm m\cdot s^{-1}}[/tex]:
[tex]\begin{aligned}x_{y} &= \frac{{v_{y}}^{2} - {u_{y}}^{2}}{2\, a_{y}} \\ &= \frac{0^{2} - (21.0 \sqrt{3})^{2}}{2\, (-9.81)} \\ &\approx 67.4\; {\rm m} \end{aligned}[/tex].
a thin lens of focal length 42 cm forms a real image 5.2 times as high as the object. how far apart are the object and image?
The relationship between the object distance (d_o), the image distance (d_i), and the focal length (f) of a thin lens is given by the lens equation:
1/d_o + 1/d_i = 1/f
We know that the focal length of the lens is 42 cm, so the lens equation becomes:
1/d_o + 1/d_i = 1/42
Let's call the height of the object "h_o".
We also know that the image is 5.2 times as high as the object,
so the height of the image (h_i) is given by:
h_i = 5.2 * h_o
Since the image is real,
we also know that the image distance is positive, so d_i is positive.
We can now use the magnification equation to find the ratio of the image height to the object height:
magnification (m) = h_i/h_o
= 5.2
Since the magnification is equal to the ratio of the image height to the object height,
we can write:
h_i/h_o = d_i/d_o
Now we can substitute the expression for h_i/h_o into the lens equation:
1/d_o + 1/d_i = 1/42
d_i/d_o = 5.2
1/d_o + 1/5.2d_o = 1/42
Solving for d_o, we find:
d_o = 21.6 cm
And since d_i/d_o = 5.2, we can find d_i:
d_i = 5.2 * d_o = 5.2 * 21.6
= 112.32 cm
So the object is 21.6 cm away from the lens, and
the image is 112.32 cm away from the lens.
The distance between the object and the image is
112.32 cm - 21.6 cm
= 90.72 cm.
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Water is liquid at room temperature due to weak hydrogen bonds.
ATrue
BFalse
It is accurate to say that water is a liquid at room temperatures because of the weak hydrogen bonds.
What is hydrogen used for?Fuel cells may create power, power, and heat using hydrogen. The industries where hydrogen is currently most widely employed are fertilizer manufacturing and petroleum refining, with growing markets of utilities and transportation.
Can hydrogen be used as fuel?The fuel for combustion engines can also be hydrogen. These, however, are less effective than FCEVs and emit tailpipe pollution. Try reading up on fuel cells. A gallon of gasoline has about the same amount of energy as 2.2 gbp (1 kilogram) in hydrogen gas.
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a measure of compactness is the extent to which the district is spread out from its center. A. True B. False
It is true that the measure of compactness is the extent to which the district is spread out from its center.
The measure of compactness is defined as the the spread of the area of the space, the term compactness here do not have its regular meaning of the less area. It signifies that how much an area is spread in the space so do not get confused with the terms.
There are various compactness measure and one of them is the spread of the area from the center of the body. It means if we are measuring a square than we should measure its compactness by taking the center of the square as the point of origin.
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figure shows the motions of stars a and b in the sky. what direction would you face (look) to see star a when it is highest in the sky?
The northern celestial pole as well as the stars that surround it will look higher up in the sky as you travel further north, whereas all the stars in the south will appear lower as you travel farther south.
What is the sky's star motion like?The daily movement of stars as well as other celestial objects across the sky is known as diurnal motion. Celestial bodies appear to move from east because of the Earth's west to east rotation, which creates this motion.
Where do stars start to rise from?The rotation of the Earth is what causes this motion. Stars can be seen rising in the eastern, flying overhead, and set in the west as the Earth spins us eastward at a speed of about a thousand miles per hour.
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a baseball is thrown vertically into the air. the magnitude of the acceleration of the ball at its highest point is
The magnitude of the acceleration of a baseball thrown vertically into the air at its highest point is 9.8 m/s^2.
This is due to the fact that gravity is the only force acting on the baseball at its highest position. The amount of this force, which has a downward direction, is equal to the baseball's mass times the gravitational acceleration (g = 9.8 m/s2). The magnitude of the net force exerted on the baseball is equal to its weight, which is determined by multiplying its mass by the gravitational acceleration. As a result, the acceleration at the highest point is 9.8 m/s2, which is the same as the acceleration caused by gravity.
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picture wind blowing steadily at 7 m/s. determine the mechanical energy of air per unit mass and power generation potential of a wind turbine with 80 m diameter blades. also, if the overall efficiency of the turbine is 30%, find the actual electric power generated. take air density as 1.25 kg/m3.
Actual electric power generated of turbine is [tex]306.25 kW \times 0.3 = 91.875 kW[/tex]
How does a Turbine work?A turbine is a mechanical device that converts energy from a fluid (such as air or water) into rotational energy, which can be used to generate electricity. It works on a basic principle that the energy of a moving fluid is used to turn a rotor.
What are different types of Turbine?There are various types of turbines, including steam turbines, gas turbines, and wind turbines. For example, if we talk about wind turbine, the blades of the rotor are shaped like airfoils and are oriented so that they face the wind.
Firstly, we will find Mechanical energy = [tex]0.5 \times velocity^{2}[/tex]
= [tex]0.5 \times (7 m/s)^{2} = 24.5 J/kg[/tex]
To determine the power generation potential of the wind turbine:
[tex]A = \pi \times (diameter / 2)^2[/tex]
[tex]= \pi * (80 m / 2)^2 = 10,000 m^2[/tex]
Power generation potential = Mechanical energy × air density × swept
area = [tex]24.5 J/kg \times 1.25 kg/m^3 \times 10,000 m^2[/tex]
= 306,250 W or 306.25 kW
Now, Actual power = Power generation potential × efficiency
=[tex]306.25 kW \times 0.3 = 91.875 kW[/tex]
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a solid cylinder with center-of-mass inertia 1 2 m r2 rolls without slipping on a horizontal surface at constant center-of-mass velocity. vcm what is the ratio between its rotational and center-of-mass kinetic energies?
The ratio of rotational and kinetic energy of center-of-mass is, 1/2.
If a solid cylinder is placed at top of inclined plane due to mgsinθ linear velocity increases and friction apply torque so angular velocity increases.
If cylinder is performing rolling without friction then displacement of point of contact is zero so work done by friction is zero so mechanical energy is conserved here.
So it's kinetic energy = (1/2) m v²
And rotational energy is, (1/2) I ω²
The moment of inertia is, I = (1/2) m r², and the angular velocity, ω = v/r.
Using these values, rotational energy is,
[tex]\dfrac{1}{2} \times \dfrac{1}{2} \times m r^2 ({\dfrac{v}{r}})^2\\= \dfrac{1}{4} \times m v^2[/tex]
Now, the ratio of rotational and kinetic energy is, 1/2.
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a girl whose weight is 200 n hangs from a bar supported by two strands of rope. what is the tension in each strand?
The tension in the rope is 490 N.
The force balancing principle can be used to determine each strand's tension. The girl must be subject to zero forces overall because she is hanging vertically and not moving at all. This indicates that the tension in the ropes acting upward balances the force of gravity acting downward.
Let's refer to each rope's tension as T. In that case, the force balance equation would look like this:
T + T = m * g
where g is the acceleration caused by gravity (9.8 m/s2) and m is the girl's mass (200 N).
2T = m * g 2T = 200 N * 9.8 m/s2 2T = 980 N / 2T = 490 N 2T = m * g
Thus, there is 490 N of strain in each strand.
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What can you infer about the Maastrichtian Age from its name?
The first research on these rocks took location near to Maastricht, Netherlands.
Whats is a rock?A rock is a dense mass of granules that have grown or been cemented together over time. There are big rocks and little rocks. Pebbles are little rocks. One or more metals can be found in every rock. According to how they were formed, rocks are categorized by geologists (those who study minerals and minerals).
What are the 3 types of rocks?When molten, heated material cools and solidifies, extrusive, and volcanic, igneous rocks are created. Sedimentary, igneous, or metamorphic rocks are the three main categories of rocks. Each of these rocks is the result of physical processes that are a part of the rock cycle, including such melting, cooling, erosion, compacting, or deforming.
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a rock is thrown downward from a cliff with an initial speed of 6.50 m/s. the rock takes 2.65 seconds to hit the ground. how high is the cliff, in meters?
The height of the cliff is 30.2 m.
What is the height of the cliff?We have to note that in this case we would have to use the equations of motion so as to obtain the height of the cliff as we know.
We can now write that we have that;
h = ut + 1/2gt^2
h = height of the cliff
u = initial speed
g = acceleration due to gravity
t = time taken
We would then have that;
h = 6.5 * 2.65 + (0.5 * 9.8 * 2.65)
h = 30.2 m
The cliff is found that it would have a height of 30.2 m as we can see above
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calculate the magnitude (in m/s2) of the centripetal acceleration at the tip of a 3.20 m long helicopter blade that rotates at 205 rev/min
The magnitude of the centripetal acceleration at the tip of a 3.20 m long helicopter blade that rotates at 205 rev/min can be calculated using the formula a = (2πr)²/T, where r is the radius of the blade (in this case 3.20 m), and T is the period of rotation (in this case 1/205 seconds).
This gives a value for an of 37.22 m/s2.
It is important to note that the centripetal acceleration of an object can be affected by various external forces, such as friction and air resistance. These forces can cause the magnitude of the centripetal acceleration to be different from the value calculated using the above formula.
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