The measure of the angle of descent should be 2.15° from the horizontal line of sight, if the altitude of the plane is 7.5 km above the ground.
The Altitude of the plane above the ground, h = 7.5 km
The straight line distance of the landing place from the airplane, d = 200 km
For the decent landing of the airplane, there should not be an steep angle of landing. We know tanθ = Height/base
tanθ = h/d
So the descent angle will be tan⁻¹(h/d)
So, tan⁻¹(7.5/200)
θ = 2.1475 ≈ 2.15°
So, θ = 2.15°
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A man is driving through his neighborhood
when a boy on a bike comes out of a driveway.
The driver skids to a stop in an attempt to avoid
hitting the biker, but ends up knocking the boy
off of his bike. The biker has minor injuries and
his parents file a lawsuit against the driver,
claiming that the car was going over the speed
limit at the time. The drag of the road is 0. 75
You might need to slow down because, generally speaking, a bicycle moves more slowly than other vehicles.
What sort of vehicle can a driver encounter on a slow-moving road? You might need to slow down because, generally speaking, a bicycle moves more slowly than other vehicles.Before overtaking a bicycle in a lane that is too small to share, wait until there is a clear section of the road.Before opening your automobile door into a traffic lane or a cycling lane, look out for passing bicycles.I'd like to outline three fundamental ideas that, in my opinion, form the basis of this skill set, despite the fact that defensive and professional driving entail many specific techniques:1) fault vs. avoidability; 2) following distance; and 3) detachment from other driversYour following distance should be extended.The interior and outside mirrors, as well as a head check, can be used to assess the mirror blind spots by the driver.
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nitrogen is compressed to a density of 4 kg/m3 under an absolute pressure of 400 kpa. determine the temperature in degrees fahrenheit.
The temperature in Fahrenheit is 146.799°F.
The equation of state for a fictitious ideal gas is known as the ideal gas law, sometimes known as the generic gas equation. Although it has some restrictions, it is a good approximation of the behavior of numerous gases under various circumstances. Benoît Paul Émile Clapeyron introduced it for the first time in 1834 as a synthesis of the empirical Boyle's law, Charles' law, Avogadro's law, and Gay's law. Lussac's. The empirical form of the ideal gas law is frequently used which is PV = nRT. The ideal gas constant is R.
Density = ρ = 4 kg/m3
Pressure = P = 400 kPa
As we know the ideal gas equation is PV = nRT
P = ρRT
400 = 4 x 0.2968 x T
T = 336.927 K
The temperature in Fahrenheit is 146.799°F.
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when the moon is waxing, what side of the moon do we see illuminated?
We see the right side of the moon illuminated when the moon is waxing.
What is waxing?The Moon is in the Waxing Crescent phase when its western edge is bright but the majority of the surface that can be seen from Earth is dark. Waxing refers to the fact that the amount of light visible during this phase increases day by day.
What are the phases of the moon?The Earth's moon cycle has four phases, to start. A new moon, first quarter, third quarter, and full moon are among them.
There are 29.5 days in a lunar cycle. The moon completes one orbit of the Earth in around 27.3 days. Given that the Earth has travelled around 45 million miles during the time it takes the moon to complete one full orbit around the Earth, the 2.2-day delay is effectively the moon "catching up" to the Earth.
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Metal ball A ha a charge of -9, and metal ball B ha a charge of 3. What will be the charge on the ball after they come in contact while remaining inulated from their urround?
Upon coming into contact with an uncharged metal sphere B, metal sphere A becomes positively charged, making both spheres positively charged.
How fully charged is sphere B at this point?A ultimate charge state of -1 will be present for each sphere. The spheres effectively combine to form one conductor when they come into contact.Upon coming into contact with an uncharged metal sphere B, metal sphere A becomes positively charged, making both spheres positively charged.Since there is no net electric field within a solid ball, the electric field created by charges on the metal ball's surface will be equal to and opposing to the electric field created by charges on a hollow plastic ball at the metal ball's center.To learn more about metal sphere refer to:
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A box is pushed across a room. What are the force pairs?
Answer:
Once static friction gives up, it allows the box to begin sliding across the floor, the frictional force acting on the box, is now the force of sliding friction exerted by the floor on the box
Explanation:
.
a nonconducting sphere with center c and radius a has a spherically symmetric electric charge density. the total charge of the object is q > 0. a. determine the magnitude and direction of the electric field at point p, which is a distance r > a to the right of the sphere's center. b. determine
the magnitude and the polarisation of the electric field at point p, with the polarisation of the electric field pointing away from charge B. (to the left). If the sphere has a nonconducting , the magnitude is force*q.
The magnitude of the electric field at point P is 3*10^5 N/C. The electric field strength at point P, which is along the straight line between point P and Q, is parallel to the direction of the charge Q. (since there is a negative charge). The equation E = F Q thus describes the electric field at point p that point charge Q produces. The electric field created by a point charge Q is shown in the accompanying graphic in its direction.
magnitude = force*q for q>0.
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Derive the equation for the buoyant force from these two ideas.
The expression for the buoyant force is F = ρghs²
What is buoyant force?Buoyant force is the force exerted on a object by a liquid.
How to derive the expression for the buoyant force?Given that the pressure from the fluid at a certain depth is given by P = P₀ + ρgh where
P₀ = atmospheric pressure, ρ = density of fluid, g = acceleration due to gravity and h = depth of object in fluidWe know that the buoyant for is due to the pressure difference frm the top and bottom of the fluid.
Since
P = P₀ + ρgh
P - P₀ = ρgh
ΔP = ρgh
Now, we know that pressure difference, ΔP = F/A where
F = buoyant force and A = areaSo, making F subject of the formula, we have that
F = ΔPA
Now since the object is a perfect cube of length, s, its area at its bottom surface perpendicular to F is A = s²
So, F = ΔPA
F = ΔPs²
So, substituting ΔP into the equation, we have that
F = ΔPs²
F = ρghs²
So, the buoyant force is F = ρghs²
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eating broccoli _________ chemical energy that your body converts to energy that your body needs, such as energy for movement , temperature control and other life processes. fill in the blank releases or absorbs
Eating broccoli absorbs chemical energy that your body converts to energy that your body needs, such as energy for movement , temperature control and other life processes.
What is broccoli?This refers to a green plant that is edible. It is in the cabbage famil. It has a large flowering head, stalk, and small associated leaves that are eaten as a vegetable. Broccoli is classified in the Italica cultivar group of the species Brassica oleracea.
Broccoli is a nutrient-rich vegetable that may enhance your health in a variety of ways, such as by reducing inflammation, improving blood sugar control, boosting immunity, and promoting heart health.
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we are experiencing a gravitational pull from the sun and from the laptop in front of us. true or false
Answer:
the answer it's flas
Explanation:
I wish I help you
a constant force acts upon an object moving along a straight line from point (9, -7, -10) to point (10, -5, 9). find the work done by the force if the distance is measured in meters, and the magnitude of the force is measured in newtons.
The work done by the force is √7 Newtons. The result is obtained by multiplying the distance by the force.
How to find the work done on an object?The work done on an object can be counted by the equation:
W = F × d
Where
W = Work (Joule or Nm)F = Force (Newton)Find the work done by the force!
We have:
(x₁, y₁, z₁) = (9, -7, -10)(x₂, y₂, z₂) = (10, -5, 9)The distance (straight line) is
[tex]d = \sqrt{(x_{1}- x_{2})^{2} + (y_{1}- y_{2})^{2} + (z_{1}- z_{2})^{2} }[/tex]
[tex]d = \sqrt{(9-19) + (-7 + 5) + ((-10) - (-9)) }[/tex]
[tex]d = \sqrt{(10) -2 + (-1 )[/tex]
d = √7 meters
The force is F.
Hence, the magnitude of the force on the object are √7 F.
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a ball loses 15% of its kinetic energy when it bounces back from a concrete floor. with what speed, must you throw it vertically downward from a height of 12.4 m to have it bounce back to the same height? ignore air resistance.
To find the speed at which the ball must be thrown, we need to use the conservation of energy. The final potential energy is v = 8.14 m/s .
The initial potential energy of the ball is given by mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which the ball is thrown. The final kinetic energy of the ball is given by 1/2mv^2, where v is the speed at which the ball bounces back.Since the ball bounces back to the same height, the final potential energy is also mgh. Since kinetic energy is lost when the ball bounces, we know that the final kinetic energy is 85% of the initial kinetic energy.
So we can set up the following equation:
mgh = 0.85 * (1/2mv^2)
Solving for v, we get:
v = sqrt(2gh/0.85)
v = sqrt(2 * 9.8 * 12.4 / 0.85)
v = 8.14 m/s
So the speed at which the ball must be thrown is 8.14 m/s vertically downward from a height of 12.4 m to have it bounce back to the same height.
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A student connects a resistor to a cell for 60 seconds.
The current through the resistor is 0. 97 A
Calculate the charge flow.
Use the equation:
charge flow = current × time
Give your answer to 2 significant figures
A student connects a resistor to a cell for 60 seconds and resistor is 0. 97. So the charge flow is 58.2 coulombs.
What is meant by resistor ?
A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device.A specified voltage can be supplied via resistors to an active device like a transistor.Modern resistors are often constructed from a carbon, metal, or metal-oxide layer.In these resistors, an insulating material is wrapped in a helix around a thin film of conductive (but still resistant) material.A passive electrical component called a resistor prevents the flow of electric current by introducing resistance. They are present in practically all electrical networks and electronic circuits. Ohms are used to measure resistance.To learn more about resistor refer to
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Copper wire with a diameter of 0. 5 cm is covered with a 0. 65-cm layer of insulating material having a thermal conductivity of 0. 242W/m⋅K. The air adjacent to the insulation is at 290 K. If the wire carries a current of 400 A, determinea. The convective heat-transfer coefficient between the insulation surface and the surrounding airb. The temperatures at the insulation-copper interface and at the outside surface of the insulation
The convective heat-transfer coefficient between the insulation surface and the surrounding air is approximately 19.59 W/m²K; b.
The required details for insulation surface in given paragraph
The temperatures at the insulation-copper interface is approximately 324.96 K, and at the outside surface of the insulation is approximately 305.57 K.
What is the temperature of the air surrounding the insulated copper wire?
The temperature of the air surrounding the insulated copper wire is 290 K (or 17°C or 62.6°F). This is specified in the problem statement as being the temperature of the air adjacent to the insulation. This information is important for determining the heat transfer between the insulation and the surrounding air, which will affect the temperature at the insulation-copper interface and at the outside surface of the insulation.
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Little kids at Newton's preschool are always dropping their lunch boxes on the floor,
causing the boxes to either break or pop open and spill lunches everywhere. Mrs.
Suki wants to get a new mat to put on the floor under the preschooler's cubbies that
will keep the lunch boxes from breaking when the kids drop them.
Mrs. Suki tested 2 different materials and this is what she found:
.
• The bare floor causes the lunch box momentum to decrease to 0 in 3 seconds.
• Material #1 causes the lunch box momentum to decrease to 0 in 1 second.
• Material #2 causes the lunch box momentum to decrease to 0 in 2 seconds.
Mrs. Suki is looking for a material to place on the floor under the preschooler's cubbies that will reduce the momentum of a dropped lunch box and prevent it from breaking.
What is preschooler's cubbies?A preschooler's cubby is a small, personal storage space designed for children to store their belongings at school, daycare, or a similar educational setting. It is typically an open shelf or cabinet with multiple compartments for each child to store their items.
Based on her testing, she found that Material #1 is the best option because it causes the lunch box momentum to decrease to 0 in the shortest amount of time, 1 second. Material #2 is a good option too, but it takes 2 seconds for the momentum to decrease to 0, which is slightly longer than Material #1. Therefore, Material #1 is the best choice for reducing the momentum of a dropped lunch box and keeping it from breaking.
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a ringing alarm clock is put under a glass jar. the air is slowly removed from the space around it. what will happen as the air is removed? (1 point)
As the air is removed from space around a ringing alarm clock that is placed under glass jar, sound of the alarm will become progressively quieter, and the clock's mechanical parts will move more smoothly.
What will happen as the air is removed?As the air is slowly removed from space around a ringing alarm clock that is placed under a glass jar, the sound of alarm will become progressively quieter. This is because sound is a mechanical wave that travels through a medium.
The air particles in jar vibrate as the sound waves pass through them, which allows us to hear the sound. As the air is removed, number of air particles available to vibrate and carry the sound waves decreases, which reduces the intensity of sound. As the air is almost completely removed, there will be very few air particles left to vibrate, then the sound will be almost inaudible.
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tell me a reasonable number of significant figures to use when measuring: a) thickness of measurements book b) outdoor air temperature with bulb thermometer c) wind speed with vane anemometer d) weight of platinum bar that is approximately 50 lbs
Significant figures are a number of digits used to describe a particular measurement. While considering the significant figures, it must be noted that to define a measurement, it is necessary to define its unit too. So unit consideration is also a factor before defining the number of reasonably significant figures.
a ) Considering the thickness unit to be ( mm ). So the thickness of the measurement book will satisfy two nondecimal digits. So its significant figure is 2.
b ) Considering air temperature unit to be ( °C ). So the outdoor temperature with bulb thermometer will satisfy with three decimal digits. Because it is a fluid measuring device it is difficult to get the measurement without decimal digits. So its significant figure is 3.
c ) Considering wind speed unit to be (m/s ). So the wind speed with a vane anemometer will satisfy with three decimal digits as a vane anemometer is also a device. So its significant figure is 3.
d ) As the weight of the platinum bar unit is defined as ( lb ). So significant figure with three decimal digits must satisfy the weight of approximately 50 lb. So its significant figure is 3.
Dimension is the quantification of attributes of an item or occasion, which may be used to compare with different items or activities. In different words, size is a technique of figuring out how massive or small a bodily amount is compared to a basic reference amount of the equal type. The scope and application of measurement are depending on the context and field.
In herbal sciences and engineering, measurements do now not observe nominal residences of items or events, that's constant with the recommendations of the worldwide vocabulary of metrology posted through the International Bureau of Weights and Measures. but, in different fields including facts as well as the social and behavioral sciences, measurements can have multiple tiers, which could consist of nominal, ordinal, c language, and ratio scales.
Dimension is a cornerstone of change, technological know-how, era, and quantitative studies in many disciplines. traditionally, many dimension systems existed for the various fields of human life to facilitate comparisons in those fields. frequently those have been achieved by means of local agreements among trading companions or collaborators.
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A lawn mower that weighs 196 N is pushed along the ground at a constant speed with a force of
240 N applied to the handle, which makes an angle of 40 degrees with the ground. With what force does the ground push upward on the mower?
Answer:(i) The magnitude of the force that is pressing the lawn-mower directly into the ground is 25 N
(ii) The magnitude of the effective force that moves the mower forward is approximately 43.3 N
(iii) Because there are no net downward force acting on the lawn-mower
Explanation:
which measurement has the fewest number of significant figures? a. 0.001280 m b. 12.8 m c. 12.80 m d. 12.08 e. 0.1280 m
In the followings set of the numbers given, 12.8 m have the fewest number of significant figures.
Significant figures can be described as the number of digits that is present in a in a value, and made up of the degree of accuracy of the value.
The rules for calculations using significant figures are:
1. All non-zero numbers are included.
2. Leading zeros are not significant.
3. Zeros that is found in between two non-zero digits are included.
4. All trailing zeros to the right of the decimal are significant.
5. Trailing zeros in a whole number with no decimal shown are significant.
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Need this ASAP please because it's for a homework!
Make a time line where you organize the events since the Big Bang in sequence.
After the universe's 13.7 billion year old Big Bang, it has gone through numerous phases or epochs.
What is Big bang theory?It may have experienced more activity and change in the first second than in all the billions of years since because of the harsh environment and violence of its very early beginnings.
We can construct a rough timeline as follows using our current understanding of how the Big Bang might have developed, taking into account notions about inflation, the Grand Unification, etc.
The Planck Epoch (or Planck Era), which spans from 0 to around 10-43 seconds (1 Planck Time), is the closest that modern physics can come to the beginning of time itself.
Therefore, After the universe's 13.7 billion year old Big Bang, it has gone through numerous phases or epochs.
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despite emitting the same power as a 100 w incandescent bulb, humans don't shine as brightly. we'll learn in week 4 why that is, but for now, let's compute the first step of the difference: the temperature. a human has a surface area of roughly 1.6 m2, but the filament a surface area of 6e-5 m2, so to emit the same power, it needs a much higher power density, and so needs to be at a higher temperature. what temperature is the lightbulb at (in kelvin)?
According to the problem the temperature of the light bulb is 1 Kelvin.
What is temperature?Temperature is a measure of how hot or cold something is. It is measured using a thermometer or thermocouple and is usually expressed as a number on a scale, such as Celsius or Fahrenheit.
The temperature of a light bulb can be calculated using the Stefan-Boltzmann law. This law states that the power emitted by a blackbody is proportional to the fourth power of its temperature. Therefore, the temperature of the light bulb can be calculated by taking the fourth root of the ratio of the power emitted by the human to the power emitted by the light bulb.
The power emitted by a human is around 100 watts and the power emitted by a 100 watt incandescent bulb is also 100 watts. Therefore, the temperature of the light bulb is the fourth root of 100/100, which is 1.
Therefore, the temperature of the light bulb is 1 Kelvin.
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where m 0 is the mass of the particle at rest and c is the speed of light. what happens as v goes to c?
As velocity, v of the object approach the speed of light c, the energy of the particles will increase.
From the famous equation of Einstein of mass-energy relationship, that is
E = m₀c²/√(1-v²/c²)
Where E denotes the energy, c is the speed of light, v is the speed of the object.
If mass of the object at rest is m₀, we can see from the above relationship that as we approaches c, the denominator terms goes closer to 0. And when v becomes speed of light c, then the denominator becomes zero. Thus making the Energy infinite. So the energy becomes infinite.
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a point charge is placed at the center of an uncharged, spherical, conducting shell of radius r. the electric fields inside and outside the sphere are measured. the point charge is then moved off center a distance r/2 and the fields are measured again. what is the effect on the electric fields? (a) changed neither inside nor outside (b) changed inside but not changed outside (c) not changed inside but changed outside (d) changed inside a
As the charge is relocated because of that charge, the configuration of the field lines inside will alter. The induced surface charge outside the sphere is uniformly dispersed throughout the exterior surface.
Two point charges: what are they?Two point charges A and B are set at a specific distance apart with force F acting between them. They have charges of +Q and -Q, respectively. It is accurate to say that only stationary electric charges are subject to Coulomb's law. This is because, in the case of moving charges, a current exists, which produces a magnetic field, which in turn exerts force on moving charges; as a result, Coulomb's Force is no longer the only force to be taken into account. A charge distribution that has a value solely at one specific place is known as a point charge. A test charge is a point charge that is so little that it has no impact on the charge distribution you are testing.
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Objects with masses of 111 kg and 290 kg are separated by 0.396 m. A 23.9 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the two larger masses on the 23.9 kg mass. The value of the universal gravitational constant is 6.672 × 10^-11 N • m^2 /kg^2.
Answer in units of N.
part 2 of 2
Leaving the distance between the 111 kg and the 290 kg masses fixed, at what distance from the 290 kg mass (other than infinitely remote ones) does the 23.9 kg mass experience a net force of zero?
Answer in units of m.
F_net = 6.672 × 10^-11 * ((111 * 23.9) / (0.396 / 2)^2 + (290 * 23.9) / (0.396 / 2)^2) N part 2) x = sqrt((111 * 23.9) / (290 * 23.9)) * (0.396/2) m
What is gravitational force?According to Newton's universal law of gravitation, force of attraction between any two bodies is directly proportional to product of their masses and is inversely proportional to square of the distance between them.
We know, F = G * (m1 * m2) / r^2
Given m1 = 23.9 kg and m2 = 290 kg
m1 and m2 are the masses of the two objects, r is separation distance between them, and G is universal gravitational constant.
F1 = G * (111 * 23.9) / (0.396 / 2)^2
F2 = G * (290 * 23.9) / (0.396 / 2)^2
As, F_net = F1 + F2
F_net = 6.672 × 10^-11 * ((111 * 23.9) / (0.396 / 2)^2 + (290 * 23.9) / (0.396 / 2)^2) N
part 2) As, F = G * (m1 * m2) / r^2
G is the universal gravitational constant and r is distance between the two masses.
Let x be the distance of the 23.9 kg mass from 290 kg mass. Then the distance between 111 kg mass and 23.9 kg mass is x - 0.396/2.
So, F1 = G * (111 * 23.9) / (x - 0.396/2)^2
and F2 = G * (290 * 23.9) / x^2
Setting F1 = -F2, :
G * (111 * 23.9) / (x - 0.396/2)^2 = G * (290 * 23.9) / x^2
So, x = sqrt((111 * 23.9) / (290 * 23.9)) * (0.396/2) m
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A certain vector A, of magnitude 4.68 units, points in a direction 30.7° to the left of the negative y-axis. Find Ax and Ay.
The x-component of A vector is - 2.39 unit.
The y-component of A vector is - 4.02 unit.
What is vector?Vector is a colloquial term that refers to some quantities that cannot be expressed by a single number (a scalar) or to elements of some vector spaces.
The magnitude of A vector is 4.68 unit.
The direction of A vector is 30.7° to the left of the negative y-axis.
So, A vector is in 3rd co-ordinate.
Hence, the x-component of A vector is = - Asin30.7°
= - 4.68 × sin30.7°
= - 2.39 unit.
Hence, the y-component of A vector is = - Acos30.7°
= - 4.68 × cos30.7°
= - 4.02 unit.
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A 45 kg boy is riding a 15 kg bicycle with a speed of 8. 0 m/s. What is the combined kinetic energy of the boy and the
bicycle?
The combined kinetic energy of the boy and the bicycle is 1920 J.
Kinetic energy is the measure of the work that an object does by virtue of its motion. Simple activities like walking, jumping, throwing, and falling involve kinetic energy.To accelerate an object, we have to apply force. To apply force, we need to do work. When work is done on an object, energy is transferred, and the object moves with a new constant speed. We call the energy that is transferred kinetic energy, and it depends on the mass and speed achieved.The SI unit of kinetic energy is Joule.Kinetic energy is transferred between objects and can be transformed into other forms of energy. Yo-Yo is a great example to describe the transformation of kinetic energy.We know that kinetic energy of a body is given by K.E. : [tex]\frac{1}{2} mv^{2}[/tex]
Here m = combined mass = 45+15 kg = 60 kg
Given speed = v = 8 m/s
Putting these values in above equation we get K.E. = 1920 J
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what is the strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc ?
The strength of the electric field 4.0 cm from a small glass bead that has been charged to 5.0 nc will be 7.912 x 106 N/C.
The strength of an electric field 4.0 cm from a small glass bead that has been charged to 5.0 nC can be calculated using Coulomb's law.
According to this law, the electric field, E, is equal to the charge, Q, divided by the permittivity of free space, ε, multiplied by the distance between the charge and the point in space, r, squared.
Therefore, the electric field at a distance of 4.0 cm from the bead is equal to:
E = (5.0 nC) / (8.854 x 10-12 [tex]C^{2}/ nm^{2}[/tex]) x (0.04 m)
E = 7.912 x 106 N/C
This means that the electric field at a distance of 4.0 cm from the glass bead charged to 5.0 nC is 7.912 x 106 N/C.
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on the left side of the simulation, click on to turn on an animated energy bar chart. pause the simulation, and drag your skater up and down. what do you notice is happening to the amount of potential energy as you do this? describe the cause and effect relationship you see.
As you drag the skater up higher, the potential energy increases. As you drag the skater down lower, the potential energy decreases.
This is because potential energy is determined by the skater’s height, so as the skater’s height changes, the amount of potential energy changes accordingly.
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. The potential energy of a steel ball is greater when it is raised above the earth than when it is brought to Earth.
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a car slows down uniformly from a speed of 25.0 m/sm/s to rest in 9.00 ss . part a how far did it travel in that time?
The distance car travel at 9.00 s is 112.8 m.
What is the distance car travelled?Displacement is the measurement of a change in position of an object or person in meters. And acceleration is the rate of change in velocity, measured in meters per second per second (or meters per second squared).The rate of change of velocity is defined as acceleration. Acceleration usually indicates that the speed is changing, but this is not always the case. When an object moves in a circular path at a constant speed, it is still accelerating because its velocity direction changes.Acceleration of car = (v - u)/t
Here given,
v = 0 m/s
u = 25 m/s
t = 9.00 s
By substituting values,
a = (0 m/s - 25.0 m/s) / 9.00 s
a = -2.77 ms⁻²
S = V² - u² / 2a
= ((0 ms⁻¹)² - (25.0 ms⁻¹)²) / 2 x -2.77 ms⁻²
= 112.8 m
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A sail boat is in a 1000 m race, and it crosses the starting line when it is already at full speed. It reaches the finish line in exactly 1 minute and 20 seconds (= 80.0 s). What is the velocity of the sail boat?
The velocity of the sailboat is 12.5 meters per second.
What is velocity and how is it calculated?Velocity is a measure of how fast an object is moving in a specific direction. It is calculated by dividing the distance traveled by the time it took to travel that distance. The unit of velocity is meters per second (m/s) or kilometers per hour (km/h).
To understand how the velocity of the sailboat was calculated, it is important to understand the concept of velocity and how it is measured. Velocity is a vector quantity, meaning it has both magnitude (size) and direction. The magnitude of velocity is measured in units of distance per unit of time, such as meters per second (m/s) or kilometers per hour (km/h). The direction of velocity is the direction in which an object is moving.
In this scenario, the sailboat was in a 1000-meter race and reached the finish line in exactly 1 minute and 20 seconds, or 80 seconds. To calculate the velocity of the sailboat, we used the formula: Velocity = distance / time. Substituting in the given values, we have: Velocity = 1000 meters / 80 seconds = 12.5 meters per second. This means that the sailboat was moving at a speed of 12.5 meters per second.
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The distance an object falls (when released from rest, under the influence of Earth's gravity, and with no air resistance) is given by d(t)16t, where d is measured in feet and t is measured in seconds. A rock climber sits on a ledge on a vertical wall and carefully observes the time it takes for a small stone to fall from the ledge to the ground. A. Compute. What units are associated with the derivative, and what does it measure? b. If it takes s for a stone to fall to the ground, how high is the ledge? How fast is the stone moving when it strikes the ground (in miles per hour)?
(A) Units for derivative is d(t) = 16t^2, (B) height of the ledge is 0 feet, and stone is moving with a speed of 46.667 x s mph.
A. The units associated with the derivative of d(t) = 16t^2 are feet per second, and it measures the velocity of the object at a certain point in time.
B. To find the height of the ledge, we need to find the value of t when the stone reaches the ground. We can set d(t) = 0 and solve for t:
16t^2 = 0
t^2 = 0
t = 0
Since t = 0, the stone was dropped from rest, so the height of the ledge is d(0) = 16(0)^2 = 0 feet.
To find the velocity of the stone when it strikes the ground, we can find the derivative of d(t) = 16t^2 at t=s.
d'(t) = 32t
d'(s) = 32s
Since the stone was falling in feet per second. To convert to miles per hour we need to multiply the value by 1.46667 (conversion factor)
d'(s) x 1.46667 = 32s x 1.46667 = 46.667s mph
So the stone is moving at 46.667 x s mph when it strikes the ground.
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