This is the Answer: 7.3 m/s.
Explanation:
You can use the equation from the conservation of mechanical energy, potential energy to kinetic energy.
1/2 [tex]mv^{2}[/tex] = mgh ……… factoring out the mass m and multiplying both sides by 2
[tex]v^{2}[/tex] = 2gh …. v is its velocity, g = 9.8 [tex]m/s^{2}[/tex] and h = 2.7 m
[tex]v^{2}[/tex] = 2 * 9.8 [tex]m/s^{2}[/tex] * 2.7 m ….. the unit becomes [tex]m^{2}[/tex]/[tex]s^{2}[/tex]
[tex]v^{2}[/tex] = 52.92 [tex]m^{2}/s^{2}[/tex]
v = √(52.92) m/s
v = 7.3 m/s
When the rock hits the ground its velocity is 7.3 m/s.
WHAT DOES MGH MEAN? MEANING DOWN BELOW!!
“m” is the symbol for mass. This would be measures in kilograms (kg) in SI Units.
“g” is the symbol for the acceleration due to gravity. This value is the only one of these three symbols that is a constant. This constant will change depending on what planet, where you are in the universe, and how far from the surface of the planet you are. For Earth, the value used for SI is 9.81 m/s^2, and this is accurate within 15 kilometers of the Earth’s surface.
“h” is the symbol for the vertical height or position. What is interesting here is this value actually can change because in physics, we can design whatever parameters we want to. So, if I wanted to know the height of a ball that is over a table, you must ask what are we calling the point of vertical height equal to zero. Because this value can be either defined from ball to table surface or ball to ground below the table. This value is measured in meters (m) under SI.
Together the product of m, g, and h gives us what is called the gravitational potential energy. This is the amount of an energy that a certain object possesses because the force of gravity will pull it towards the ground in order to achieve a lower mechanical energy.
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What effect does increasing volume have on equilibrium?
As the volume rises, the equilibrium shifts to the left, favoring the reactants. As the volume is decreased, the equilibrium will shift toward the component of the reaction in which there are fewer moles.
What causes an unstable equilibrium?An object is considered to be operating in unstable equilibrium when ever a destructive force is applied if the center of mass is lowered and the object moves from its starting position.
Why is equilibrium such a priority?Equilibrium is important for understanding chemical processes since it tells us how the reaction will proceed. We can control the reaction's parameters to help the creation of desirable products while it is in equilibrium. It is also used to calculate the final reaction mixture's composition.
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a swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. what is the mass of water in the pool?
volume of the pool= area of trapezium × breadth , the mass of water in the pool is = 144000.
How many grams of water are there?One H2O molecule weighs 18.02 amu on average.The number of atoms and molecules is an exact number; neither of these factors affects the amount of significant figures.An average mole of water weighs 18.02 grams.It is reported that water has a molar mass of 18.02 g/mol.
How much water does one milliliter weigh?Answer and justification One gram of water makes up one milliliter.Since water has a density of 1 g/ml, 1 ml of volume of water corresponds to 1 g of mass.
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a continuous line of charge lies along the x axis, extending from x 0 to positive infinity. the line carries a uniform linear charge density ?0 . what are the magnitude and direction of the electric field at the origin?
At the origin, the electric field has a magnitude of [tex]\frac{k\lambda_0}{x_0}[/tex] and is oriented in a positive x-direction.
Coulomb's law may be used to determine the size of the electric field at the origin caused by a continuous line of charge:
[tex]E = \frac{kq}{r^2}[/tex]
Using the superposition principle, the electric field owing to a differential element of charge dq is:
[tex]dE = \frac{k dq} {r^2}[/tex]
Because the differential charge element is proportional to the linear charge density and the differential length, [tex]dq = \lambda_0 dx[/tex]. Because the distance r from the origin to the differential element equals [tex]r = x_0 + x[/tex],
[tex]dE = \frac{k\lambda_0 dx}{(x_0 + x)^2}[/tex]
Integrating this formula from x = 0 to x = infinity yields the total electric field at the origin:
[tex]E = k\lambda_0 \int_{0}^{\infty} \frac{dx}{(x_0 + x)^2}[/tex] from 0 to infinity
Using partial fractions, the integral may be calculated as follows:
[tex]E = \frac{k\lambda_0}{x_0}[/tex]
The linear charge density and the distance x0 from the closest point on the line of charge are both inversely correlated with the electric field at the origin.
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We fear too little those events that will claim lives. A) accidentally. *B) undramatically. C) in the near future. D) one person at a time.
We fear too little for all those events that will claim lives undramatically.
Fear is an extremely unpleasant feeling that occurs when one perceives or recognizes a threat or danger. Fear results in physiological alterations that might result in behavioral responses like mounting an aggressive defence or running away from the threat.
Our physical, emotional, or let us consider psychological health may be at risk. While most of us have particular things that make us fearful, we can learn to be scared of almost anything that are around us.
Cortisol and adrenaline, two stress hormones, are released. Your heart rate and blood pressure rise. Your respiration quickens. Even your blood supply alters; blood actually moves out from your heart and towards your limbs, facilitating the initiation of punches or other physical attacks.
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In a food chain, the flow of energy and matter are depicted with an _____
Answer:
flujo de energia
Explanation:
after a package is dropped from the plane, how long will it take for it to reach sea level from the time it is dropped? assume that the package, like the plane, has an initial velocity of 482 km/hour in the horizontal direction.
Therefore the speed at the ground is 185. 3 m/s.
horizontal speed = 485 km/hr
= 485 * (5/18)
= 134.72m/s
h = 875 m
g = 9.8 m/s^2
a) Using formula,
h = (1/2) gt^2
875 = (9.8/2) t^2
t = 13.36 seconds
b)
D = u * t
D = 131.11 * 13.36
D = 1751.64 m
D = 1.75 km
c) when it lands on the ground
Vx = 131.11 m/s
Vy = gt
= 9.8 * 13.36
= 130.9 m/s
Therefore the speed at ground = [ 131.11^2 + 130.9^2]^(1/2)
= 185. 3 m/s
The pace is the directional speed of an item in motion as a demonstration of its price of alternate in the role as observed from a specific body of reference and as measured via a particular widespread of time (e.g. 60 km/h northbound). speed is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of our bodies.
Velocity is a bodily vector amount; each significance and route are needed to define it. The scalar absolute value (significance) of speed is known as velocity, being a coherent derived unit whose quantity is measured inside the SI (metric device) as meters in step with second (m/s or m⋅s−1). as an example, "5 meters in step with 2d" is a scalar, whereas "5 meters consistent with 2nd east" is a vector. If there is a trade-in velocity, route, or each, then the object is stated to be present process an acceleration.
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A ball is thrown from a window 2.1m above the ground with a initial velocity of 18m/s (37 degrees above horizon). How far was the ball thrown? What is the maximum height of the ball?
The ball was thrown a total distance of 52.7 meters. The maximum height of the ball is 8.8 meters.
What is the distance ?The distance refers to the amount of space between two points. It is typically measured in units of length such as meters, kilometers, or miles. Distance can also be measured in terms of time, as in the distance between two points in terms of the amount of time it takes to travel between them. Distance is an important concept in mathematics and can be used to calculate the length of a line, the area of a shape, or the volume of an object.
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A 12.5 kg ball moving to the right at 4 m/s strikes a 10 kg ball at moving at 2m/s to the left. After the collision the 12.5 kg ball is moving with a velocity of 1.6 m/s to the left and the 10kg ball moving at 5 m/s to the right . Is momentum conserved? Show your calculations on a half sheet of paper, then explain your thinking here.
Momentum is conserved in this collision.
How The answer was obtainedMomentum is conserved in this collision. To show this, we can calculate the initial momentum of the system and compare it to the final momentum.
Initial momentum:
12.5 kg * 4 m/s + 10 kg * -2 m/s = 50 kg m/s
Final momentum:
12.5 kg * -1.6 m/s + 10 kg * 5 m/s = 50 kg m/s
As we can see, the initial momentum is equal to the final momentum, so momentum is conserved in this collision.
This is because momentum is a conserved quantity, which means that it can be neither created nor destroyed, only transferred from one body to another. In this case, the momentum of the 12.5 kg ball was transferred to the 10 kg ball, and the final result was that the momentum of the system remained unchanged.
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under what situation would the instantaneous velocity of an object differ from the average velocity?
The instantaneous velocity of an object can differ from its average velocity if the object is accelerating, that is, if its velocity is changing with time.
What is instantaneous velocity?
Instantaneous velocity is the speed of an object at a specific moment in time. It is the limit of the average velocity over an infinitesimal time interval as the interval approaches zero. In other words, it is the rate of change of an object's position with respect to time at a specific moment.
Average velocity is calculated as the total displacement divided by the time interval, but it does not take into account changes in velocity that occur during that time interval. In contrast, instantaneous velocity is the velocity of an object at a particular moment in time, and it can be different from the average velocity if the object's velocity changes over time.
Therefore, The instantaneous velocity of an object can differ from its average velocity if the object is accelerating, that is, if its velocity is changing with time.
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A company is looking for a new child-safe liquid to use for filling a thermometer. Scientists on the team argue that water with food coloring added would be a great substitute, but that the scale on the thermometer could not go below 4 °C (about 39 °F). What was their reasoning?
Group of answer choices
The color would change as the temperature dropped to low.
The water would solidify at 4°C, making it not work anymore.
The water that had been contracting as it cooled would start to expand.
The density of the water would become too great to support the column.
The water that had been contracting as it cooled would start to expand. Option C
What is the thermometric liquid?
We have to note that the liquid that we have inside the thermometer is what we call the thermometric liquid. This is the kind of liquid that would increase in volume or decrease in volume so that the temperature can be measured.
We must note that water has an anomalous behavior and this is one of the reasons that stops water from being used as a thermometric liquid. This is the fact that water would begin to expand at about 4 degrees centigrade.
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Two aluminum balls are 5 cm apart. One is
negatively charged, and the other is
positively charged. A small magnet is placed
between the two balls but is not touching
either of them. The aluminum balls remain
stationary. Which statement describes the
electric and magnetic fields?
Each ball has an electric field surrounding it, and the magnet creates a magnetic field as well.
What is an example of an electric field?The area of space surrounding an electrical charges particle or object within which the charged body perceives force is known as the electric field .Examples: -Electric fields are created by charges and their configurations, such as capacitor and battery cells.
In basic terms, what is an electric field?Each location in space at which a charge exists in any form can be regarded to have an electric field attached to it. The electrostatic force per mass unit is another name for an electric field. The electric field's equation is stated as E = F / Q.
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an earth satellite moves in a circular orbit at a speed of 5500 m/s . part a what is its orbital period?
According to the solving using gravitational law the earths its orbital period = 5.6 hours.
What does the gravity principle mean?Every particle in the universe is drawn to every other component with a force that is directly related to the product between their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation. As a result, the general gravitation equation takes shape. F ∝ m 1 m 2 r 2.
What precisely is the first law of gravitation?Newton's first law asserts that an object at rest will stay at rest and also an object in motion will keep moving at a fixed pace unless they are both subject to a net external force.
According to the given information:The strength of attraction between two particles can be expressed as follows, according to Newton's gravitational law:
F = [tex]G\frac{M_1M_2}{R^2}[/tex]
speed of satellite = v = 5000 m/s
mass of earth = M = 6 × 10²⁴ kg
orbital period = T = ?
∑F = ma
[tex]G\frac{mm_2}{R^2}[/tex] = M[tex]\frac{v^2}{r}[/tex]
Substituting the value we get:
T = 2πG[tex]\frac{M}{v^3}[/tex]
T = 2π × 6.67 × 10⁻¹¹ [tex]\frac{ 6 * 10^2^4}{5000^3}[/tex]
T = 20116s
T = 5.6 hours.
According to the solving the earths its orbital period = 5.6 hours.
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according to stefan's law, if you have stars which are identical, except that one is 4 times hotter than the other, how much more light is emitted by the hotter star?
The radiation radiated from an area A on a black body at actual temperature T is directly in proportion to the fourth power of a temperature, according to Stefan Boltzmann's law.
What significance do ratio and proportion have?
The ratio and ratio are important building blocks for understanding the numerous ideas in science and mathematics. Several challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship among two or more numbers and aids in comparing them.
What would a proportional statement look like in practice?
For instance, the proportion statement for the ratio 45 is 20/25 = 45. This proportional statement can be solved to yield: The relationship between two quantities, such as a:b, when b is not equal to 0, is thus defined by the ratio. Example: 2:4 = 1:2 is used to show the proportion of 2 to 4. Here, it is claimed that the statement is in proportion.
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the temperature of an object is raised by 120° Celsius the resulting increase in its absolute temperature is
The absolute temperature is 393 K
How do you obtain the absolute temperature?Absolute temperature is a temperature scale that starts at absolute zero, which is the temperature at which all matter has zero thermal energy. The most commonly used absolute temperature scale is the Kelvin scale. The conversion from Celsius or Fahrenheit to Kelvin can be done using the following formulas:
Kelvin = Celsius + 273
Here we would have that;
T = 120° Celsius + 273 = 393 K
This is the absolute temperature that we seek.
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astronomers split up the ancient constellation of argo navis because it was too large to be useful as a celestial landmark. group of answer choices true false
True, astronomers split up the ancient constellation of argo navis because it was too large to be useful as a celestial landmark.
Why was Argo Navis a constellation but is no longer?
The only star design that was abandoned due to strictly practical considerations is Argo Navis; it was simply too large. So Nicolas Louis de Lacaille, a French astronomer, separated it into the constellations Carina, Puppis, and Vela in the year 1750.
Sir John Herschel suggested the complete dissolution and elimination of Argo Navis in 1841 and 1844. Despite this, the constellation and its component pieces continued to be used well into the 20th century. It was given the three-letter abbreviation Arg in 1922, along with the other constellations. In 1930, when the IAU established the 88 contemporary constellations, Carina, Puppis, and Vela were split up and demoted to a previous constellation.
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a student's calculation was found to have a 35.5 % error, and his experimental measurement was 15.6 cm. what are the two true/actual measurements?
A student's calculation was found to have a 35.5 % error, and his experimental measurement was 15.6 cm. The two true/actual measurements are 24.19 and 11.53.
Let x and y be the two possible real measurements, with x being less than 15.6 and y being more than 15.6.
x + 35.5% of x = 15.6
y-35.5% of y
35.5% as decimal is 0.355
x + 0.355x = 15.6 , and
y - 0.355y = 15.6
Solving
x + 0.355x = 15.6
1.355x = 15.6
x = [tex]\frac{15.6}{1.355}[/tex] = 11.53
Solving
y - 0.355x = 15.6
0.645y=15.6
0.645y = 15.6
y = 24.19
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suppose that an astronomical object that emits light with a rest wavelength of 500 nm is observed to have a wavelength of 400 nm, what is the speed of the object and in what direction is it moving?
The speed of the astronomical object is moving away from the observer at 261,922,999 m/s or approximately 87.37% of the speed of light and its direction is away from the observer.
The speed of the object can be calculated using the formula for the Doppler shift, which states that the observed wavelength (λ') of an object moving away from an observer is longer than the rest wavelength (λ) by a factor of (c+v)/(c-v), where c is the speed of light and v is the speed of the object.
The formula for the Doppler shift is:
λ' = (c+v)/(c-v) × λ
Where c is the speed of light, v is the speed of the object and λ and λ' are the rest wavelength and observed wavelength, respectively.
Given the rest wavelength of 500 nm and the observed wavelength of 400 nm, we can rearrange the formula to solve for v (speed of the object):
v = c × (λ/λ' - 1)/(λ/λ' + 1)
v = c × (500 nm/400 nm - 1)/(500 nm/400 nm + 1)
Using the value of the speed of light, c = 299792458 m/s, we can calculate the speed of the object as follows:
v = 299792458 m/s × (500 nm/400 nm - 1)/(500 nm/400 nm + 1)
v = 0.87 × 299792458 m/s = 261922999 m/s
Converting the speed in percentage:
261922999 / 299792458 × 100% = 87.37%
So, the speed of the object is 261,922,999 m/s or approximately 87.37% of the speed of light and is moving away from the observer.
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find the boyant force acting on when submerged in mercey given the density of the density of the mercery is 13,600 kg/m^3
The buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.
What is Buoyant force?
The buoyant force is caused by the pressure difference that exists between the top and the bottom of an object immersed in a fluid. The pressure at the bottom of the object is greater than the pressure at the top, due to the weight of the fluid above it. This difference in pressure creates an upward force, which is called the The buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.
Buoyant force = weight of displaced fluid
The weight of the displaced fluid is equal to the density of the fluid times the volume of the displaced fluid times the acceleration due to gravity (9.81 m/s^2).
Let's assume that the object has a volume of V and a weight of W.
Since the object is submerged in mercury, the weight of the displaced mercury is equal to the weight of the object (W), so we can write:
Weight of displaced fluid = W
Density of mercury = 13,600 kg/m^3
Volume of displaced fluid = V
Acceleration due to gravity = 9.81 m/s^2
Therefore, the buoyant force acting on the object is:
Buoyant force = Weight of displaced fluid
= Density of fluid x Volume of displaced fluid x Acceleration due to gravity
= 13,600 kg/m^3 x V x 9.81 m/s^2
= 133,176 V N/m^3
So, the buoyant force acting on the object submerged in mercury is 133,176 V N/m^3.
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Calculate the Tangential Velocity of a ball with mass 0. 50 kg rolling in a circle with a radius of
0. 75m, if it makes a complete circle in 12s
The required tangential velocity of the ball with a mass of 0.50 kg rolling in a circle with a radius of 0.75 m and completing a circle in 12 secs is 0.4 m/s.
Any object moving along a circular path has a linear component to its speed called tangential velocity. When an object moves in a circular path at a distance r from the centre, then the body’s velocity is directed tangentially at any instant. This is termed tangential velocity.
The ball weighs m = 0.50 kg
r = 0.75 m is the radius of the circle
The time is taken by the ball to complete the circle, t = 12 secs
The tangential velocity is given as, v = 2πr/t,
v = 2π × 0.75/12 = 0.4 m/s
Thus, the required tangential velocity of the ball is calculated to be 0.4 m/s.
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Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 22 m/s ?
The radius of the turn for the falcon flying at 22 m/s is approximately equal to: radius ≈ 5.18 m.
The centripetal acceleration required for a tight circular turn can be calculated using the formula:
centripetal acceleration = velocity² / radius
where velocity is the speed of the falcon and radius is the radius of the turn.
Given that the centripetal acceleration is 1.5 times the free-fall acceleration (g), we can write:
centripetal acceleration = 1.5 × g = 1.5 × 9.8 m/s²
Substituting this value into the above equation and solving for the radius, we get:
radius = velocity² / centripetal acceleration = (22 m/s)² / (1.5 × 9.8 m/s²) = (22²) / (1.5 × 9.8) m.
So the radius of the turn for the falcon flying at 22 m/s is approximately equal to: radius ≈ 5.18 m.
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a hammer (500 grams), a small parachute (21 grams), and a baseball (145 grams) are all dropped from a height of 25 meters. the hammer and baseball take about the same amount of time to fall. which statement describes the time it takes for the parachute to fall?
The parachute takes longer to fall because of greater air resistance describes the time it takes for the parachute to fall.
How does air resistance slow the fall rate of a parachute?
The drag force resists the downward movement of gravity, pushing the parachute back up. As the parachute falls, the drag increases until it just balances out the pull of gravity. At that point, the parachute stops speeding up and begins to fall at a steady speed.
Why does a parachute increase air resistance?
An open parachute increases the cross-sectional area of the falling skydiver and thus increases the amount of air resistance that he encounters (as observed in the animation below). Once the parachute is opened, the air resistance overwhelms the downward force of gravity.
How does air resistance affect fall time?
With air resistance, acceleration throughout a fall gets less than gravity (g) because air resistance affects the movement of the falling object by slowing it down.
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a stone is dropped from a height of 4.9 m . find the time taken to cover this distance
Answer:
Explanation:
Initital velocity = 0
s=1/2*g*[tex]t^{2}[/tex]
4/9 = 1/2*9.8 * [tex]t^{2}[/tex]
[tex]t^{2} =1\\t=1 sec[/tex]
correct application of fermats theorem to fluid dynamics
Fermat's Theorem states that the path taken by a wave traveling from one point to another in a medium is the path that takes the least time, which is applicable in fluid dynamics to explain why fluids tend to follow the path of least resistance.
Fermat's theorem, also known as the "principle of least time," states that the path taken by a wave traveling from one point to another in a medium is the path that takes the least time.
In fluid dynamics, this principle is used to explain why fluids tend to follow the path of least resistance, as they seek to minimize the time it takes to move from one point to another. This results in the fluid flowing along the path of least energy, which is also known as the path of least resistance. The principle of least time is used to predict the behavior of fluids under different conditions, and it is an important concept in the field of fluid dynamics.
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The process of boiling actually cools the water.
Is this true or false? Can someone explain what this actually means or why it does that? Makes no sense to me.
Answer:
Boiling is the process where liquid (water) changes to gas (vapor) directly by no cooling process. As it's boiling, heat is being continuously give continuously so how can cooling happen?
But in the another way this statement can be correct too as evaporation too changes liquid to gas but does cools the liquid as high energetic liquid particles are escaping while leaving down the low energetic particles causing cooling.
To sum it up, boiling doesn't make any cooling.
a solid uniform ball of mass m and radius r rolls without slipping down a ramp from height h. how fast is the ball going at the bottom of the ramp?
The ball will be moving at a velocity of 14.0 meters per second when it reaches the bottom of the ramp.
The velocity of the ball at the bottom of the ramp can be determined using the principle of conservation of energy. The potential energy of the ball at the top of the ramp will be converted into kinetic energy as it rolls down the ramp.
Potential energy = mgh
Kinetic energy = (1/2)mv²
At the bottom of the ramp, all of the potential energy has been converted into kinetic energy, so the equation can be written as:
mgh = (1/2)mv²
Solving for v, we have:
v = √(2gh)
where g is the acceleration due to gravity (9.8 m/s²). So, given the height h, we can calculate the velocity of the ball at the bottom of the ramp.
Let's assume the height of the ramp is h = 10 meters. Then, the velocity of the ball at the bottom of the ramp can be calculated as:
v = √(2gh) = √(2 × 9.8 m/s² × 10 m) = √(196 m²/s²) = 14.0 m/s
So, the ball will be moving at 14.0 meters per second when it reaches the bottom of the ramp.
It's important to note that the ball is rolling without slipping, meaning that its velocity is due to both its rotational motion and its translation. The velocity of the center of mass of the ball at the bottom of the ramp will be equal to the calculated velocity.
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Light of wavelength 575 nm falls on a double-slit and the third order bright fringe is seen at an angle of 6.5o. What is the separation between the double slits?
The separation between the double slits is 0.0506 mm.
What is interference?Interference in physics is a phenomena when two waves merge by adding their displacements at each and every point in space and time to produce a new wave that has a higher, lower, or identical amplitude.
The angular separation is = 6.5° = 6.5 × π/180
Wavelength of light is = 575 nm = 575 × 10⁻⁹ m
Let the separation between the double slits = d m.
Then;
6.5 × π/180 = 575 × 10⁻⁹/d
d = 5.06 × 10⁻⁶ meter
= 0.0506 mm.
Hence, the separation between the double slits is 0.0506 mm.
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Two forces of magnitude 10N each . Their resultant is equal to 20N . Then angle between them is
Answer:
0°
Explanation:
refer to the attachment
hope this helps!
Radar waves of wavelength 50 mm are emitted from two aerials and create a fringe pattern 1 kilometer from the aerials. Calculate the distance between the aerials if the fringe spacing is 80 cm.
If the fringe spacing is 80 cm, the distance between the aerials is 6.25 meter.
What is interference?In physics, interference refers to the combined result of two or more wave trains travelling along intersecting or converging trajectories. The result is the result of adding the individual wave amplitudes at each place that is influenced by multiple waves.
Given: wavelength = 50 mm = 50 × 10⁻⁴ m
the fringe spacing is = 80 cm = 0.80 m.
x = λD/d
d = λD/x
= 50 × 10⁻⁴ × 1000/0.80 m
= 6.25 meter.
Hence, the distance between the aerials is 6.25 meter.
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3-h) a mass m of 4.7 lbm is attached to a light spring of k lbf /ft elongates it by 1.3 in. determine the spring stiffness k (in lbf /ft) and the natural frequency f (in hz) of the system.
The spring constant k (in lbf /ft) is 248.62 lbf/ft and the natural frequency f (in hz) of the system is 10.54 Hz.
Given the mass of object (m) = 4.7lbm
The elongation in spring (L) = 1.3inches
The spring constant of spring = k
We know that the force exerted on the spring is = F
We determine Fs = kL
The force on object (F) = mg
Fs = F then,
mg = kL such that:
k = (4.7 lbm * 32.2 ft/s^2) / (1.3 in) where 1 lbm * 32.2 ft/s2 = 1 lbf
k = 248.62 lbf/ft
The frequency of spring = f
f = 1 / (2π * √(m/k))
f = 1 / (2π * √(4.7 lbm / 248.62 lbf/ft))
f = 10.54 Hz
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a hollow metal sphere of radius r is positively charged. of the following distances from the center of the sphere, which location will have the greatest electric field strength?
The location that will have the greatest electric field strength is the surface of the sphere, which is a distance of r away from the center.
This is because the electric field strength is inversely proportional to the square of the distance from the source, so the closer you get to the source, the stronger the electric field will be.
An electric field is an area of influence created by an electric charge, in which electric force is exerted on other charged objects. This electric force is described mathematically by the electric field vector, which specifies the direction and magnitude of the force. Electric fields can be created by stationary charges, or by time-varying magnetic fields. Electric fields can be used to control the motion of charged objects, and are also responsible for many of the phenomena associated with electricity, such as electric potential, capacitance, and electric current.
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