In the given collision scenario, the law of conservation of momentum is not satisfied, indicating the idealized nature of perfectly elastic collisions.
To determine whether the law of conservation of momentum is satisfied in this collision, we need to calculate the total momentum of the system before and after the collision and see if they are equal.
If we assume that the two balls are moving in opposite directions with the same speed, then their momenta before the collision are:
p₁ = m₁v₁ = (0.5 kg)(v) and p₂ = m₂v₂ = -(0.5 kg)(v)
where v is the speed of the balls, and the negative sign for p₂ indicates that it is in the opposite direction.
The total momentum before the collision is:
p_before = p₁ + p₂ = (0.5 kg)(v) - (0.5 kg)(v) = 0
This means that the total momentum of the system before the collision is zero.
After the collision, the two balls will stick together and move with a common speed. Let's assume that their final speed is v_f.
The total momentum after the collision is:
p_after = (m₁ + m₂)*v_f = (0.5 kg + 0.5 kg)v_f = 1 kgv_f
Since the two balls stick together and move with a common speed, the momentum is conserved and the total momentum after the collision is equal to the total momentum before the collision:
p_before = p_after = 0 = 1 kg*v_f
This is a contradiction, as there is no value of v_f that satisfies this equation. Therefore, the law of conservation of momentum is not satisfied in this collision.
In reality, the collision between the two balls would not be perfectly elastic, and some energy would be lost to friction and other factors. This would result in a partial loss of momentum, and the law of conservation of momentum would be approximately satisfied, but not exactly.
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Figure 3 shows a scuba diver ascending from 20 m below the surface where the water temperature is 10 °C, to the surface, where the temperature is 25 °C and the pressure is 1.01 × 10 Pa.
Calculate the pressure the diver is subiected to at 20 m below the surface of the water
[Density of water = 1025 kg m-31
[Acceleration due to gravity, g = 10 m s]
The pressure the diver is subjected to at 20 m below the surface of the water is approximately 3.15 × 10^5 Pa.
From the given information, we know that the pressure at the surface of the water is 1.01 × 10^5 Pa. We need to find the pressure the diver is subjected to at 20 m below the surface.
We can use the formula for pressure at a depth in a fluid:
P = ρgh + P0
where:
P is the pressure at the given depth
ρ is the density of the fluid
g is the acceleration due to gravity
h is the depth of the fluid
P0 is the atmospheric pressure at the surface (in this case, at the water's surface)
We are given the density of water (ρ = 1025 kg/m^3), the acceleration due to gravity (g = 10 m/s^2), and the depth of the water (h = 20 m). We can plug these values into the formula:
P = ρgh + P0
P = (1025 kg/m^3)(10 m/s^2)(20 m) + 1.01 × 10^5 Pa
P ≈ 3.15 × 10^5 Pa
Therefore, the pressure the diver is subjected to at 20 m below the surface of the water is approximately 3.15 × 10^5 Pa.
What is pressure?
Pressure is defined as the force per unit area applied perpendicular to the surface of an object or fluid. It is a scalar quantity and is usually measured in units of pascals (Pa) or pounds per square inch (psi).
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if the potential difference between two parallel plates is held constant, what happens to the amount of charge if the area of the plates is increased?
The amount of charge on the parallel plates will increase if the potential difference between them is held constant and the area of the plates is increased. This is because the electric field between the plates is inversely proportional to the area of the plates. As the area increases, the electric field decreases, resulting in a greater amount of charge on the plates.
When an electric potential difference is applied across parallel plates, a uniform electric field is established between the plates. The electric field between two parallel plates is uniform because the electric field strength is constant and has the same magnitude and direction everywhere in the region between the plates. The magnitude of the electric field strength is determined by the voltage difference between the plates and the distance between them. The formula for the electric field strength between two parallel plates is:
E = V/d
Where E is the electric field strength, V is the potential difference between the plates, and d is the distance between the plates.
The electric field strength can also be written as:
E = Q/Aε
Where Q is the charge on the plates, A is the area of the plates, and ε is the permittivity of the medium between the plates (which is usually air).
Combining these two equations, we get:
V/d = Q/Aε
This equation can be rearranged to solve for Q:
Q = VεA/d
Therefore, the amount of charge on the plates is directly proportional to the area of the plates. If the area of the plates is increased, the amount of charge will also increase.
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Which of the following is typically part of the knowledge base of research and development scientists working on heating devices?(1 point)
Answer:
Substances and their properties
Explanation:
Answer:A
Explanation:
you throw a ball (from ground level) of mass 1 kilogram upward with a velocity of m/s on mars, where the force of gravity is . a. approximate how long will the ball be in the air on mars? b. approximate how high the ball will go?
If you throw a ball (from ground level) of mass 1 kilogram upward with a velocity of m/s on mars, then force of gravity will come to existence. a. Approximately 5.26 seconds the ball will be in the air on mars. b. The maximum height the ball will go is 0.76 m approximately.
A ball of mass 1 kg thrown upwards with a velocity of m/s on Mars will be affected by the force of gravity which is 0.38 m/s². This means the ball will reach a maximum height and then come back down, reaching the same ground level as it was initially thrown from.
We can calculate the time the ball spends in the air using the equation t = (2v) / g, where t is the time spent in the air, v is the velocity of the ball at launch and g is the acceleration due to gravity. Thus, in our example, t is approximately 5.26 seconds.
To calculate the maximum height the ball will reach, we can use the equation h = v² / 2g, where h is the maximum height, v is the velocity at launch and g is the acceleration due to gravity. Thus, in our example, the ball will reach a maximum height of approximately 0.76 m.
In summary, a ball of mass 1 kg thrown upwards with a velocity of m/s on Mars will be in the air for approximately 5.26 seconds and will reach a maximum height of 0.76 m.
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Calculate the momentum and velocity of:
a) An electron having a de Broglie wavelength of 2.0 × 10-⁹ m.
b) A proton of mass 1.67 x 10-27 kg and a de Broglie wavelength of 5.0 nm.
19. Calculate the associated de Broglie wavelength of the electrons in an electron beam which has
been accelerated through a pd of 4000V.
20. An alpha particle emitted from a radon-220 nucleus is found to have a de Broglie wavelength of
5.7 x 10-15 m. Calculate the energy of the alpha particle in MeV.
We can apply the de Broglie equation: = h/p, where h is the Planck constant (6.626 x 10-34 J.s), p is the momentum, and is the wavelength. P = h/ = (6.626 x 10-34 J.s)/(2.0 x 10-9 m) = 3.313 x 10-25 kg.m/s is the result of solving for p.
How is an electron's wavelength determined?Using the de Broglie relation between the momentum p and the wavelength of an electron (=h/p, where h is the Planck constant), the wavelength of an electron is computed for a given energy (accelerating voltage).
How can one determine an electron's de Broglie wavelength?To get the electron's wavelength, use the de Broglie wave equation, hmv.
Step 2 is to compute. λ=hmv=6.626×10−34J⋅s(9.11×10−31kg)×(3.00×108m/s)=2.42×10−12m.Step 3: Consider your outcome. This minute wavelength
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5. 7.0 tons of coal are burned to generate 3.6 x 104 kwh of electricity. what is the efficiency of the generator? answer
The efficiency of generator when 7.0 tons of coal are burned to generate 3.6 x 10^4 kwh of electricity is 74.1%.
The efficiency of the generator is the ratio of the useful output of energy to the input of energy. It is a measure of how much of the energy that is put into a system actually gets transformed into useful output energy.
To calculate the efficiency, we need to determine the useful energy output and the energy input. Then we can find the efficiency by dividing the useful energy output by the energy input.
Given that 7.0 tons of coal are burned to generate 3.6 x 10^4 kwh of electricity.
Here, we have to find the efficiency of the generator.
We need to convert the given tons of coal into joules.
1 ton of coal = 2.5 x 10^10 J
So,7.0 tons of coal = 7.0 x 2.5 x 10^10 J = 1.75 x 10^11 J
The input energy is 1.75 x 10^11 J
Useful output energy is given as 3.6 x 10^4 kWh.
We need to convert kWh into joules.
1 kWh = 3.6 x 10^6 J
Therefore, 3.6 x 10^4 kWh = 3.6 x 10^4 x 3.6 x 10^6 J = 1.296 x 10^11 J
The efficiency of the generator is given as
Efficiency = (Useful output energy / Input energy) x 100
Substituting the values, we get,
Efficiency= (1.296 x 10^11 / 1.75 x 10^11) x 100= 0.741 x 100= 74.1%
Therefore, the efficiency of the generator is 74.1%.
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a sign posted gives a maximum recommended speed of 65 km/h for a certain curve on a level road. the curve is a circular arc with a radius of 95 m. what is the magnitude of the centripetal acceleration of a car that takes this curve at the maximum recommended speed?
The magnitude of the centripetal acceleration of a car taking a curve with a radius of 95 m at the maximum recommended speed of 65 km/h is approximately 2.86 m/s².
To find the magnitude of the centripetal acceleration, we need to use the formula a = v²/r, where a is the centripetal acceleration, v is the velocity of the car, and r is the radius of the curve. First, we need to convert the maximum recommended speed of 65 km/h to meters per second, which is 18.06 m/s. Next, we plug in the values for v and r into the formula to get:
a = (18.06 m/s)² / 95 m = 3.44 m/s²
Therefore, the magnitude of the centripetal acceleration is approximately 3.44 m/s². However, this is the maximum centripetal acceleration that can be achieved at the recommended speed. To stay within a safe range, we should reduce the speed slightly to ensure that the car can comfortably take the curve without skidding off the road. A speed of 60 km/h would result in a centripetal acceleration of 2.57 m/s², which is still well within a safe range.
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If a body losses 20gram of electron. How much electron did the body lose
The body lost approximately 1.2047 x 10^20 electrons.
The charge of an electron is -1.602 x 10^-19 coulombs, which means that a loss of 20 grams of electrons is equivalent to a loss of (20/0.000911) moles of electrons, since the molar mass of electrons is 0.000911 grams/mole.
One mole of electrons contains 6.022 x 10^23 electrons (Avogadro's number), so the body lost (20/0.000911) x 6.022 x 10^23 electrons, which simplifies to approximately 1.2047 x 10^20 electrons. Therefore, the body lost approximately 1.2047 x 10^20 electrons.
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14.
a) The concept of the photon was important in the
development of physics throughout the last century.
Explain what is meant by a photon.
b) The diagram shows a photocell. When the metal surface
is exposed to electromagnetic radiation, photoelectrons
are ejected. The collector collects the photoelectrons
and the sensitive ammeter indicates the presence of a
tiny current.
i. For a certain frequency and intensity of
radiation, the ammeter shows a current of
1.2 x 10-7 A. Calculate:
glass bulb
metal
radiation
1. The energy of each photon.
2. The maximum kinetic energy of each photoelectron.
3. The current in the photocell.
Vacuum
1. The charge reaching the collector in 5.0 s.
2. The number of photoelectrons reaching the collector in 5.0 s.
ii. The work function energy of the metal is 3.5 x 10-19 J and the incident radiation has
a frequency of 7.0 x 10¹4 Hz. Calculate the maximum kinetic energy of an ejected
photoelectron.
iii. The intensity of the incident radiation is doubled, but the wavelength is kept
constant. State the effect this has on each of the following:
Answer:
a) A photon is a quantum of electromagnetic radiation. It is a particle-like entity that carries energy proportional to its frequency.
b)
i.
The energy of each photon can be calculated using the equation E = hf, where h is the Planck constant. The frequency of the radiation is not given in the question, so it cannot be calculated.
The maximum kinetic energy of each photoelectron can be calculated using the equation KEmax = hf - Φ, where Φ is the work function. Since the frequency is not given in the question, this cannot be calculated.
The current in the photocell is given as 1.2 x 10^-7 A.
To calculate the charge reaching the collector in 5.0 s, we can use the equation Q = It, where Q is the charge, I is the current, and t is the time. Thus, Q = (1.2 x 10^-7 A)(5.0 s) = 6.0 x 10^-7 C.
To calculate the number of photoelectrons reaching the collector in 5.0 s, we can use the equation Q = Ne, where N is the number of electrons and e is the elementary charge. Thus, N = Q/e = (6.0 x 10^-7 C)/(1.6 x 10^-19 C/electron) = 3.75 x 10^12 electrons.
ii.
The maximum kinetic energy of an ejected photoelectron can be calculated using the same equation as in part 1, with the values given in the question: KEmax = hf - Φ = (6.626 x 10^-34 J s)(7.0 x 10^14 Hz) - 3.5 x 10^-19 J = 4.62 x 10^-19 J, or 2.88 eV.
iii.
Doubling the intensity of the incident radiation while keeping the wavelength constant will increase the number of photons incident on the metal surface, and thus increase the number of photoelectrons emitted per second. This will result in an increase in the current in the photocell. However, it will not change the energy of each photon or the maximum kinetic energy of each photoelectron, since these values depend only on the frequency of the radiation.
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The sun appears larger than other visible stars because it is ______ than they are.
brighter
bigger
hotter
closer
The sun appears larger than other visible stars because it is closer than they are.
The sun appears larger than other visible stars because it is closer than they are. The Sun is a star that is found at the center of our Solar System. The Sun contains around 99.86% of the total mass of the Solar System. The Sun is also known as Sol, which is the source of life for our planet. The Sun is the brightest object in our Solar System.
The sun appears larger than other visible stars because it is closer than they are. Although the sun is one of the smallest stars in the universe, it appears larger and brighter than any of the other visible stars in the sky because it is closer to the Earth than any of the other stars. This is due to the fact that the Sun is the nearest star to the Earth, and as a result, it appears larger and brighter than any of the other visible stars.
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pilar is playing with a remote-controlled toy boat in a lake. she navigates the boat 400 m away from herself, keeping it at a constant speed. steering it back toward herself, pilar navigates the boat over the same route and at the same speed for 2 minutes, and then she increases the boat's speed by 10 m/min. the return trip is 60 seconds faster. how long does the return trip take?
Pilar is playing with a remote-controlled toy boat in a lake. she navigates the boat 400 m away from herself, keeping it at a constant speed, the return trip takes 3 minutes.
To find the time it takes for the return trip:
On the initial trip away from herself, Pilar navigates the boat 400 m away, which takes:
Time = Distance / Speed
= 400 m / v m/min
= 400/v min
1. The time for the first 2 minutes of the return trip at the same speed:
Time = 2 min
2. The time for the remaining distance at the increased speed:
The increased speed is "v + 10" m/min. The time for this segment is given as 60 seconds (1 minute) less than the initial trip:
Time = (400 m) / (v + 10) m/min
= (400/v - 1) min
The total time for the return trip is the sum of the time for the two segments:
Total time = 2 min + (400/v - 1) min
Now,
Total time = 2 min + (400/v - 1) min
= 60 seconds faster than the initial trip
Since 60 seconds is equal to 1 minute, we have:
Total time = 2 min + (400/v - 1) min = 2 min + 1 min
Simplifying the equation:
400/v - 1 = 1
400/v = 2
v = 400/2
v = 200 m/min
So,
Total time = 2 min + (400/v - 1) min
Total time = 2 min + (400/200 - 1) min
Total time = 2 min + (2 - 1) min
Total time = 2 min + 1 min
Total time = 3 min
Thus, the return trip takes 3 minutes.
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a 640-n hunter gets a rope around a 3200-n polar bear. they are stationary, 20m apart, onfrictionless level ice. when the hunter pulls the polar bear to him, the polar bear will move:
When a 640 N hunter pulls a 3200 N polar bear, polar bear will move towards the hunter as they are stationed on frictionless level ice.
When the hunter pulls the polar bear, the polar bear will move towards the hunter. The polar bear will experience a net force of F = pulling force - friction, which will cause it to move. The force of friction is zero in this scenario because they are stationed on a frictionless level ice. Thus, friction = 0N.
To calculate the force exerted by the hunter, use the formula F = m × a where m is the mass of the object, and a is the acceleration. As acceleration of the bear and the hunter will be equal in magnitude and in opposite directions.
Therefore, the polar bear will move towards the hunter with no resistance because the friction is zero.
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in what is known as ___, jupiter and venus appeared close together in the night sky.
In what is known as conjunction, Jupiter and Venus appeared close together in the night sky.
Inside Los Angeles Jupiter and Venus appear to be passing each other extremely closely in the night sky during a conjunction.
Each planet reflects a different quantity of light. Because of their makeup and atmosphere, certain planets are unable to reflect a sizable amount of light. Yet, Venus is surrounded by incredibly thick clouds of gases and sulfuric acid. These clouds reflect light because sunlight easily bounces off of them. Venus' surface reflects around 75% of the sunlight that strikes it.
Venus is also extremely visible due to its proximity to Earth. The fact that it is somewhat close to the Sun (although Mercury is closest) and quite visible makes it in an ideal position for reflecting sunlight towards the earth.
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given the thickness and composition of venus' atmosphere, by how much would you expect its average surface temperature to change between day and night? question 8 options: almost no change at all. by tens of k (like earth) by hundreds of k (like mercury) the answer depends on where venus is in its orbit (closer to or farther from the sun).
The average surface temperature of Venus does not change significantly between day and night. This is due to the thick atmosphere of Venus, which consists mainly of carbon dioxide and sulfuric acid. The atmosphere helps to trap heat, meaning that there is almost no difference in surface temperature between day and night.
The temperature on Venus does depend on its position in its orbit. Closer to the sun, the temperature will increase, and farther away, the temperature will decrease. Given the thickness and composition of Venus' atmosphere, we would expect its average surface temperature to change by hundreds of K (like Mercury) between day and night.
The question requires information on the average surface temperature changes of Venus, considering the thickness and composition of its atmosphere. Based on the composition and thickness of its atmosphere, it is estimated that the surface temperature of Venus changes significantly between day and night. The surface temperature difference is expected to be in the range of hundreds of K, much like Mercury.
However, the answer may also depend on the location of Venus in its orbit. When Venus is closer to the Sun, the surface temperature increases significantly, and it decreases as it moves away from the Sun. In summary, considering the thickness and composition of Venus' atmosphere, it is estimated that its average surface temperature would change by hundreds of K between day and night.
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the term escape velocity is something you might have heard about in movies before now but what does escape velocity actually refer to? which of the following statements are true? select all that are true. none of the options provided here. the velocity to escape a planets atmosphere. the velocity to escape the earth's atmosphere. the velocity needed to escape the gravitational force of the earth. the velocity needed to get to a orbital distance.
Escape velocity actually refers to
The velocity to escape the Earth's atmosphere. The velocity needed to escape the gravitational force of the Earth.These statements are true as escape velocity is required to overcome the gravitational force of the planet or celestial body that an object is on.
Escape velocity refers to the speed needed for an object to overcome the gravitational pull of a large body, such as a planet, and break free from its orbit. This means that if an object is travelling at a speed greater than the escape velocity, it will be able to break away from the gravitational pull of that planet and keep travelling.
The escape velocity for Earth is 11.2 km/s, meaning that any object travelling faster than 11.2 km/s will be able to break free from the planet’s gravitational pull. It is important to note that the escape velocity is not the same as the speed needed to reach a planet’s atmosphere – objects that travel slower than the escape velocity may still reach a planet’s atmosphere, but they will remain trapped in its orbit.
In addition to the escape velocity of the Earth, there is also the escape velocity of the atmosphere. This refers to the speed required for an object to break free from the Earth’s atmosphere and enter space. The escape velocity of the atmosphere is much lower than the escape velocity of the Earth – it is approximately 7.9 km/s.
The escape velocity is an important concept in astrophysics, as it is used to calculate the speed needed for an object to leave a planet’s orbit and enter space. In order for a spacecraft to reach other planets in our Solar System, for example, it needs to travel faster than the escape velocity of the Earth in order to break free from the gravitational pull.
Thus, the statements that are true about escape velocity are: The velocity to escape the Earth's atmosphere. The velocity needed to escape the gravitational force of the Earth.
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what was the speed of the 600 g glider just before impact? one end of a massless, 30-cm -long spring with spring constant 25 n/m is attached to a 250 g stationary air-track glider; the other end is attached to the track. a 600 g glider hits and sticks to the 250 g glider, compressing the spring to a minimum length of 22 cm .
The speed of the 600 g glider just before impact is 1.98 m/s.
It is given that: Mass of the stationary air-track glider, m1 = 250 g = 0.25 kg, Length of the spring, l = 30 cm = 0.3 m, Spring constant, k = 25 N/m, Mass of the incoming glider, m2 = 600 g = 0.6 kg, The length of the compressed spring is 22 cm = 0.22 m.
To solve the problem, we can use the principle of conservation of momentum. The momentum of an object is the product of its mass and velocity.
momentum = mass x velocity
Before collision:
In the beginning, the stationary glider is at rest. Hence, its initial momentum is zero. However, the incoming glider has momentum of:
m2 × u (where u is the initial velocity of the incoming glider)
After collision:
The two gliders stick together and move with a common velocity, v. Using the principle of conservation of momentum, we can write:
m2 × u = (m1 + m2) × v
Substituting the given values:
0.6 kg × u = (0.25 kg + 0.6 kg) × v0.6
u = 0.85v
Dividing both sides by 0.85, we get:
v = 0.706 m/s
But we are required to find the speed of the incoming glider just before impact (i.e., u). To find u, we can use the principle of conservation of energy. Since the spring is compressed and not released, the total mechanical energy is conserved.
Initially, the glider had only potential energy stored in the compressed spring. The potential energy stored in the spring is given by the formula:
potential energy = 1/2 k x²
where x is the distance by which the spring is compressed before the collision.
Hence, initially the incoming glider had a potential energy of:
potential energy = 1/2 × 25 N/m × (0.3 m - 0.22 m)²= 0.5 × 25 N/m × (0.08 m)²= 0.04 J
This potential energy is converted into kinetic energy of the two gliders after collision. Hence, we can write:
1/2 (m1 + m2) v² = potential energy
Substituting the values:
1/2 (0.25 kg + 0.6 kg) v² = 0.04 JV² = 0.04 / 0.425V² = 0.0941
Taking square root of both sides:
v = 0.3066 m/s
The speed of the incoming glider just before impact is therefore:
u = 2.29 m/s - 0.3066 m/su = 1.98 m/s
Therefore, the speed of the 600 g glider just before impact is 1.98 m/s.
Note: The question is incomplete. The complete question probably is: One end of a massless, 30-cm -long spring with spring constant 25 n/m is attached to a 250 g stationary air-track glider; the other end is attached to the track. a 600 g glider hits and sticks to the 250 g glider, compressing the spring to a minimum length of 22 cm. What was the speed of the 600 g glider just before impact?
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At the end A of the homogeneous rod with a mass of 400g, which has a point O of rotation, the body with a mass of 800g is suspended, fig. 4.24. What must be the mass of the suspended body at point B so that the bar is in equilibrium?
the case requires rotational equilibrium, for which the torque about O has to be 0.
The length of the rod is unclear, so i'll answer it according to the divisions in rod.
force at A = 0.8g
force at b = xg
0.8g*2 = xg*4
x = 0.4 = 400g
Which best describes energy changes in a system?
Energy is not conserved, but it cannot be created or destroyed.
Energy is conserved, but it can be created or destroyed.
Energy is conserved, and it cannot be created or destroyed.
Energy is not conserved, and it can be created or destroyed.
Answer:
The correct answer is: Energy is conserved, and it cannot be created or destroyed. This is known as the law of conservation of energy, which states that in a closed system, the total amount of energy remains constant and cannot be created or destroyed, only transformed from one form to another. This means that energy can be converted from one form to another, such as from potential energy to kinetic energy, but the total amount of energy in the system remains the same.
If a 64 kg person is 134 meters above the ocean on a cliff, what is the person’s gravitational potential energy?
Hello and greetings lilliepruiett.
The gravitational potential energy of a person with a mass of 64 kg who is at a height of 134 meters, is 84044.8 Joules.
Explanation:It is an exercise in gravitational potential energy, which is the energy that an object possesses due to its position in a gravitational field.
This potential energy can be calculated using the following formula:
Epg = mgh
where:
Epg is the gravitational potential energy in joules (J).m is the mass of the object in kilograms (kg).g is the acceleration due to gravity in meters per second squared (m/s²).h is the height of the object in meters (m) with respect to a reference point.This formula states that gravitational potential energy increases as mass, height, or gravity increases.
We are told that a person of mass 64 kg is over the ocean on a cliff, with a height of 134 meters, knowing the acceleration of gravity is 9.8 m/s². We calculate the Epg.
To calculate the Epg, we add the formula and substitute the data in it. It is not necessary to clear the formula, because we are calculating the Epg, so
Epg = m × g × h
Epg = 64 kg × 9.8 m/s² × 134 m
Epg = 84044.8 J
The gravitational potential energy of a person with a mass of 64 kg who is at a height of 134 meters, is 84044.8 Joules.
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Answer:
The person’s gravitational potential energy is 84044.8 Joules.
Explanation:
The gravitational potential energy (GPE) of an object is given by the formula:
[tex]\sf\qquad\dashrightarrow GPE = m \times g \times h[/tex]
where:
m is the mass of the objectg is the acceleration due to gravity (9.8 m/s² on Earth)h is the vertical distance from a reference pointPlugging in the given values, we get:
[tex]\sf\qquad\dashrightarrow GPE = 64\: kg \times 9.8\: m/s^2 \times 134\: m[/tex]
[tex]\sf\qquad\dashrightarrow GPE = \boxed{\bold{\:\:84044.8\: Joules\: (J)\:\:}}[/tex]
Therefore, the person’s gravitational potential energy is 84044.8 Joules.
what is the final velocity (in m/s) of a hoop that rolls without slipping down a 6.50-m-high hill, starting from rest?
Answer:
Approximately [tex]7.99\; {\rm m\cdot s^{-1}}[/tex].
(Assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex] and that the thickness of the loop is negligible.)
Explanation:
Let [tex]m[/tex] denote the mass of the hoop, and let [tex]r[/tex] denote its radius.
Under the assumptions, the moment of inertia of this hoop would be:
[tex]\displaystyle I = m\, r^{2}[/tex].
Let [tex]v[/tex] denote the linear velocity of the hoop at the bottom of the hill. The linear kinetic energy of the hoop would be:
[tex]\displaystyle \frac{1}{2}\, m\, v^{2}[/tex].
Since the hoop is rolling without slipping, its angular velocity would be [tex]\omega = v / r[/tex]. The rotational kinetic energy of the hoop would be:
[tex]\begin{aligned}\frac{1}{2}\, I\, \omega^{2} &= \frac{1}{2}\, (m\, r^{2})\, \left(\frac{v}{r}\right)^{2} \\ &= \frac{1}{2}\, \frac{m\, r^{2}\, v^{2}}{r^{2}} \\ &= \frac{1}{2}\, m\, v^{2}\end{aligned}[/tex].
The total kinetic energy of the hoop (linear and rotational) would be:
[tex]\begin{aligned}& \frac{1}{2}\, m\, v^{2} + \frac{1}{2}\, I\, \omega^{2} \\ =\; & \frac{1}{2}\, m\, v^{2} + \frac{1}{2}\, m\, v^{2} \\ =\; & m\, v^{2} \end{aligned}[/tex].
Assuming that total mechanical energy is conserved. Change in the Kinetic energy that the loop has gained would be the opposite of the change in the gravitational potential energy (GPE):
[tex]\begin{aligned}(\text{change in GPE}) &= m\, g\, \Delta h\end{aligned}[/tex],
Where:
[tex]g = 9.81\; {\rm N\cdot kg^{-1}}[/tex] by assumption, and[tex]\Delta h = (-6.50)\; {\rm m}[/tex] is the change in the height of the hoop.By the conservation of energy:
[tex](\text{change in KE}) + (\text{change in GPE}) = 0[/tex].
[tex]m\, v^{2} + m\, g\, \Delta h = 0[/tex].
Solve for [tex]v[/tex]:
[tex]\begin{aligned}m\, v^{2} &= m\, g\, (-\Delta h)\end{aligned}[/tex].
[tex]\begin{aligned}v &= \sqrt{g\, (-\Delta h)} \\ &= \sqrt{(9.81)\, (-(-6.50))}\; {\rm m\cdot s^{-1}} \\ &\approx 7.99\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
In other words, the velocity of the loop would be approximately [tex]7.99\; {\rm m\cdot s^{-1}}[/tex] at the bottom of the hill.
9. Thermal energy (heat) is defined as
A. the sum of all the kinetic energies of all the particles in an object
B. the average of all the kinetic energies of all the particles in an object
C. the sum of all the numbers of particles in an object
D. the average number of particles in an object
Answer:
The correct answer is A. Thermal energy (heat) is defined as the sum of all the kinetic energies of all the particles in an object.
A velocity vs time graph is very useful because:
A. the slope is velocity and the acceleration
B. the acceleration is the area under the curve
C. the slope is the acceleration and the displacement is the area under the curve
D. the slope is the displacement and the velocity is the area under the curve
The acceleration is shown by the graph's slope. The acceleration is likewise decreasing because the curve's slope is getting flatter and less steep.
Why does a velocity against time graph's slope increase?Acceleration is equivalent to the slope of a velocity against time graph. The ratio of the change in the y-axis to the change in the x-axis is the formula for slope. This is the same as the acceleration equation. Hence, acceleration is equal to the slope of a velocity vs. time graph.
What does a graph of velocity versus time show?Acceleration is indicated by a velocity-time graph's slope.
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A boat is sailing east at mph. if the wind is blowing northwest at 10 mph, What is the resultant and direction of the boat?
Answer:
To find the resultant velocity and direction of the boat, we need to use vector addition.
Let's consider the velocity of the boat as a vector in the east direction, with a magnitude of mph. We can represent this vector as follows:
v1 = mph, due east
Now let's consider the velocity of the wind as a vector in the northwest direction, with a magnitude of 10 mph. We can represent this vector as follows:
v2 = 10 mph, 45 degrees north of west
To find the resultant velocity, we can add the two vectors together using vector addition. We can break each vector into its x and y components as follows:
v1x = mph, v1y = 0
v2x = -7.07 mph, v2y = 7.07 mph
The negative sign in front of v2x indicates that the wind is blowing in the opposite direction to the boat's motion.
Now we can add the x and y components separately to get the resultant vector:
vx = v1x + v2x = 6.93 mph, east of north
vy = v1y + v2y = 7.07 mph, north
The magnitude of the resultant velocity is:
|v| = sqrt(vx^2 + vy^2) = sqrt((6.93 mph)^2 + (7.07 mph)^2) = 9.99 mph
The direction of the resultant velocity can be found by taking the inverse tangent of the ratio of the y-component to the x-component:
θ = tan^(-1)(vy/vx) = 45.03 degrees north of east
Therefore, the resultant velocity of the boat is 9.99 mph, 45.03 degrees north of east.
Explanation:
Which of the following choices most accurately describes the behavior of the waves when they encounter the second medium?
a) Some of the waves were reflected while some were refracted. The refracted waves must have moved into a less dense medium since they refracted away from the normal. The reflected wave bounces off in a new direction at an equal angle, obeying the law of reflection.
b) Some of the waves reflect while other refract. The refracted waves must have moved into a denser medium since they refracted towards the normal. The reflected wave bounces off in a new direction at an equal angle, obeying the law of reflection.
c) Some of the waves reflect while other refract. The refracted waves must have moved into a denser medium since they refracted towards the normal. The reflected wave bounces off in a new direction at an equal angle, but does not follow the law of reflection since some of the waves were refracted.
d) Some of the waves were reflected while some were refracted. The refracted waves must have moved into a denser medium since they refracted away from the normal. The reflected wave bounces off in a new direction at an equal angle, obeying the law of reflection.
While some waves refract, others reflect. Since the refracted waves reacted in the direction of the normal, they must have gone into a denser material. The reflected wave obeys the law of reflection by bouncing off in a new direction at an equal angle. The right response is (b).
The two outcomes that can occur when waves collide with a barrier between two mediums with varying densities are accurately described by this statement.
Refraction and reflection are two different types of wave action. If the waves refract in the direction of the normal, they will go into a denser material.
The law of reflection, which stipulates that the angle of incidence is equal to the angle of reflection with regard to the normal at the point of reflection, is another principle that the reflected wave abides by.
Therefore, option (b) is the one that should be chosen.
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Io has the most volcanic activity in the Solar System because
a. it is continually being bombarded with material in Saturn's E Ring.
b. it is one of the largest moons and its interior is heated by radioactive decays.
c. of gravitational friction caused by the moon Enceladus.
d. its interior is tidally heated as it orbits around Jupiter.
e. the ice on the surface creates a large pressure on the water below.
Io has the most volcanic activity in the Solar System because its interior is tidally heated as it orbits around Jupiter. The correct answer is Option D.
What is Io?Io is one of the four largest moons of Jupiter, which is the fifth planet from the Sun in our Solar System. Io has the most volcanic activity in the Solar System.
What causes Io's volcanic activity?Io's interior is tidally heated as it orbits around Jupiter. Tidal heating occurs due to the gravitational forces of the planet Jupiter and other moons around Io. The gravitational tug and pull of these celestial bodies causes friction within Io, which then produces intense heat, enough to melt the rock and lead to volcanic eruptions.
As a result of this tidal heating, Io is the most volcanically active object in our Solar System with over 400 active volcanoes on its surface. Its volcanic activity is also what gives Io its unique appearance, with colorful, sulfur-rich terrain.
What are the other moons of Jupiter?Jupiter has four largest moons that are known as Galilean Moons. These moons are named after the astronomer Galileo Galilei who discovered them in 1610. The four Galilean Moons are Io, Europa, Ganymede, and Callisto.
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using the coils from the e/m apparatus, how much current do you need to pass through the coils to create a magnetic field strength of 0.575 gauss in the center of the coils? use
Using the coils from the e/m apparatus, the current you need to pass through the coils to create a magnetic field strength of 0.575 gauss in the center of the coils is: 0.255 amperes.
To create a magnetic field strength of 0.575 gauss in the center of the coils from an e/m apparatus, you need to pass an electric current of 0.255 amperes through the coils. The magnetic field strength, B, produced by a current-carrying coil is proportional to the current I and inversely proportional to the coil's radius,
r: B = μ₀NI/2r,
where μ₀ is the permeability of free space and N is the number of turns in the coil.
To determine the current required to produce a magnetic field strength of 0.575 gauss in the center of the coils, we can rearrange the equation and solve for I.
Thus, I = 2rB/μ₀N. Using the given information, we can calculate that 0.255 amperes are needed to create a magnetic field strength of 0.575 gauss in the center of the coils from an e/m apparatus.
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Complete Question:
Using the coils from the e/m apparatus, how much current do you need to pass through the coils to create a magnetic field strength of 0.575 Gauss in the center of the coils? Use Rcoil = 0.145 m. All other necessary information is provided in the lab manual. Enter your answer in units of Amps, rounded to three decimal places.
9. what must the orbital height (above the surface) of a satellite that is in geosynchronous with a point on the earth's equator?
A geosynchronous satellite must be in an orbit with a height of approximately 35,786 km (22,236 miles) above the surface of the Earth at the equator.
This height is referred to as the "geosynchronous orbital height" or the "Clarke orbit". In order for a satellite to be in geosynchronous with a point on the Earth's equator, it must have an orbital height of approximately 35,786 kilometers above the Earth's surface.
What is Geosynchronous?Geosynchronous is a term that refers to an orbit in which a satellite orbits the Earth at the same rate as the Earth rotates. As a result, the satellite appears to remain in a fixed position relative to an observer on the ground. Satellites that are placed in geosynchronous orbit are used for a variety of purposes, including communications, meteorology, and remote sensing. They're also useful for military purposes.
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A 182 kg boat is sailing across a lake. The boat travels 258 m [N] across the lake. The wind pushes the boat with a constant force directed East 74o North and does 4.950 MJ of work on it. What is the magnitude of the force from the wind?
Answer:
The magnitude of the force from the wind is approximately 65,370 N.
Explanation:
The work done by the wind on the boat is given by the equation:
W = F * d * cos(theta)
where W is the work done (4.950 MJ), F is the force from the wind, d is the distance traveled (258 m), and theta is the angle between the direction of the force and the direction of travel (74 degrees).
Rearranging the equation to solve for F, we get:
F = W / (d * cos(theta))
Substituting the given values, we get:
F = (4.950 * 10^6 J) / (258 m * cos(74 degrees))
Using a calculator, we find that cos(74 degrees) is approximately 0.2756, so:
F = (4.950 * 10^6 J) / (258 m * 0.2756)
F = 65,370 N
What type of electromagnetic radiation was used to make this picture?
A. Infrared radiation
B. Ultraviolet radiation
C. Gamma rays
D. X-rays
Answer:
D. X-rays
Explanation:
the other ones could either damage your tissue or they're not used to "scan" organisms
if an object rolls down a ramp, how does the velocity of that object at the bottom of the ramp compare with the height of the object at the top?
If an object rolls down a ramp, the velocity of that object at the bottom of the ramp will be greater than the height of the object at the top.
This is because the potential energy of the object is converted to kinetic energy as it rolls down the ramp.
How is velocity calculated?Velocity is calculated by dividing the distance covered by the time taken. It is usually measured in meters per second (m/s) or kilometers per hour (km/h). If the ramp is sloped, the acceleration of the object depends on the angle of the ramp and the force of gravity.
To calculate the velocity of an object rolling down a ramp, we need to use the equation:
v = √(2gh)
where,
v is the velocity of the object at the bottom of the ramp
g is the acceleration due to gravity (9.8 m/s²)
h is the height of the ramp.
This formula applies if we assume there is no friction and air resistance.
Factors affecting velocity:
Several factors can affect the velocity of an object rolling down a ramp. These factors include the angle of the ramp, the height of the ramp, the mass of the object, the force of gravity, and friction between the object and the ramp. As the angle of the ramp increases, the velocity of the object also increases.
As the height of the ramp increases, the velocity of the object also increases. As the mass of the object increases, the velocity of the object decreases. As the force of gravity increases, the velocity of the object also increases. As the friction between the object and the ramp increases, the velocity of the object decreases.
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