The work required to stop the hoop is 600 joules and the distance traveled by the hoop on the inclined surface until it comes to the rest is 20.38 m.
(a) To stop the hoop, all of its kinetic energy needs to be converted into other forms of energy, such as heat due to friction. Therefore, the work required to stop the hoop is equal to its initial kinetic energy:
[tex]KE = 1/2 mv^2+1/2(mr^2)v^2/r^2[/tex]
[tex]= 1/2 (6.0\ kg)(10.0 \ m/s)^2+1/2(6.0\times1^2)\times 100/1[/tex]
[tex]= 600 J[/tex]
Therefore, 600 J of work is required to stop the hoop.
(b) The initial kinetic energy of the hoop is the same as in part (a), so it is still 600 J. As the hoop rolls up the incline, some of its kinetic energy will be converted into potential energy, decreasing its speed. The work done by the force of gravity on the hoop as it rolls up the incline is equal to the change in potential energy, which is given by:
PE = mgh =600 J
[tex]h=600/(6\times9.81)\ m[/tex]
[tex]h=10.19 \ m[/tex]
Where h is the vertical height that the hoop rises.
Let the hoop rolls a distance of x m on the inclined surface.
[tex]x= h/sin30[/tex]
[tex]x=10.19\times2=20.38\ m[/tex]
Therefore the distance traveled on the inclined surface is 20.38 m.
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Imagine you are viewing the other planets from Earth. Which planets (if any) will appear to pass directly in front of the Sun from your Earth-based perspective? Which planets (if any) will never transit the Sun? If you were able to view the Solar System from outside, how many planets could potentially transit the Sun? Will those planets transit the Sun no matter where outside the Solar System you are? Sketch and describe the required orientation of the Solar System in order for the maximum number of planets to transit the Sun.
Explanation:
Planets closer to the sun will appear to transit from time to time
= 2 Venus and Mercury ( I suppose you could include the Moon..an eclipse ....haha)
All of the planets further from the sun than earth will not transit
Potentially ALL of the planets could transit the sun (earth included) if observed outside solar system HOWEVER if you are not observing from near the orbital plane of
the planets NONE of them would transit
For maximum transits, the planets should all be in the same orbital plane and the observer should be very close to this plane also.
Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum. There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 m/s
2
. In the earth tests, when m is set to 14.0 kg and allowed to fall through 5.00 m, it gives 150.0 J of kinetic energy to the drum.
A. If the system is operated on Mars, through what distance would the 14.0-kg mass have to fall to give the same amount of kinetic energy to the drum?
B. How fast would the 14.0-kg mass be moving on Mars just as the drum gained 150.0 J of kinetic energy?
The distance from which the 14 kg mass have to fall is 40.4 m and the speed at which the mass would be moving on Mars when the drum gains 150.0 J of kinetic energy is 11.7 m/s.
What is the distance?The mass required to fall through a distance of 5.00 m is 14.0 kg. When it comes to the gravitational acceleration of Earth, the mass of 14.0 kg requires 150.0 J of kinetic energy to be supplied to the drum. On Mars, the same system would operate with a gravitational acceleration of 3.71 m/s².
To figure out the distance that the 14.0-kg mass will have to fall on Mars to give the same amount of kinetic energy, use the following formula:
PE = mgh
PE = KE (because KE = work done = energy given to the drum)
Substituting the values, we get:
KE = mgh (on earth)
KE = 150.0 J
m = 14.0 kg, g = 9.81 m/s², h = distance fallen
On Mars, we will need to use the formula:
KE = mgh
KE = mgh (on Mars)
KE = 150.0 J
m = 14.0 kg, g = 3.71 m/s², h = distance fallen
h = 40.4 m
KE = 1/2 mv² + mgh
where, KE = 150.0 J
m = 14.0 kg
g = 3.71 m/s²
h = distance fallen
Substituting the above values, we get:
KE = 1/2 mv² + mgh
150.0 = 1/2 × 14.0 × v² + 14.0 × 3.71 × h
Substituting the value of h from part (a) gives:
150.0 = 1/2 × 14.0 × v² + 14.0 × 3.71 × 40.4
Now we can solve the above equation for v:
v = 11.7 m/s
Therefore, the speed at which the mass would be moving on Mars when the drum gains 150.0 J of kinetic energy is 11.7 m/s.
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which statement below concerning the pressure gradient force (pgf) is true? group of answer choices A. the pgf is the only force that can cause the air to accelerate horizontally from rest B. the pgf has a magnitude of zero at the equator and is a maximum at the poles C. the pgf is strong where the isobars are far apart and weak where the isobars are close together D. the pgf acts from high to low pressure in the northern hemisphere and from low to high pressure in the southern hemisphere when the vertical pgf balances gravity the air is in geostrophic balance
D. The statement that is true concerning the pressure gradient force (PGF) is: the PGF acts from high to low pressure in the northern hemisphere and from low to high pressure in the southern hemisphere when the vertical PGF balances gravity the air is in geostrophic balance.
The pressure gradient force (PGF) is a force that results from the horizontal differences in atmospheric pressure. The PGF is responsible for moving air in a horizontal direction. A is not true, as other forces, such as Coriolis force, can cause the air to accelerate horizontally. B is also not true, as the PGF has a magnitude that can change depending on the pressure gradient. C is true, as the PGF is stronger where the isobars are far apart, as this indicates a steeper pressure gradient and thus a stronger force. D is true, as the PGF acts from high to low pressure in the Northern Hemisphere and from low to high pressure in the Southern Hemisphere. When the vertical PGF balances gravity, the air is in geostrophic balance, meaning that the air is in equilibrium and is not accelerating either up or down.
The PGF is an important force that affects global atmospheric circulation. It is the force responsible for the movement of air from high pressure to low pressure, causing winds to flow from regions of high pressure to regions of low pressure. As the pressure gradient varies from place to place, the strength and direction of the PGF varies accordingly. The PGF is also an important component of cyclones and anticyclones.
In summary, the pressure gradient force (PGF) is a force that results from horizontal differences in atmospheric pressure. The PGF is stronger where the isobars are far apart, and acts from high to low pressure in the Northern Hemisphere and from low to high pressure in the Southern Hemisphere. When the vertical PGF balances gravity, the air is in geostrophic balance. The PGF is an important component of global atmospheric circulation and is responsible for the movement of air from high pressure to low pressure.
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A ball is released from rest at the left of the metal track shown here. Assume it has only enough friction to roll, but not to lessen its speed. Rank these quantites from greatest to least at each point: a) Momentum, b)KE, c)PEA) C, B = D, AB) C,B = D,AC) A,B = D,C
The potential energy of the ball at this point is maximum as the ball has the highest height at this point.
The momentum of the ball at this point is given by the product of mass and velocity. As the velocity of the ball is zero, its momentum is also zero.
Momentum = 0, KE = 0, PE > 0
Hence, the ranks of quantities at each point are as follows:
A) C, B = D, A
B) C, B = D, A
C) A, B = D, C
The ball is at rest at the left of the metal track. It is assumed to have enough friction to roll, but not enough to reduce its speed. In this question, we have to rank the quantities from the greatest to the least at each point. Given below are the quantities that are to be ranked,
a) Momentum,
b) KE,
c) PE.
Rank of quantities at each point:
At point A: Here, the ball has the maximum height. It is at rest at this point. At this point, the ball has the highest potential energy, PE.
PE>KE=0
The velocity of the ball at this point is zero. Hence, the kinetic energy of the ball is zero.
The momentum of the ball is given by the product of mass and velocity. As the velocity of the ball is zero, its momentum is also zero.
Momentum = 0, KE = 0, PE > 0
At point B: At this point, the ball has converted some of its potential energy into kinetic energy. The ball has lost some of its height, and hence, its potential energy.
[tex]PE>BKE, KE>BPE[/tex]
As the ball is moving, it has some velocity. Hence, it has kinetic energy.
The momentum of the ball at this point is given by the product of mass and velocity. As the velocity of the ball is non-zero, its momentum is also non-zero.
Momentum > 0, KE > 0, PE < 0
At point C: At this point, the ball has lost all its potential energy, and all of it is converted into kinetic energy.
[tex]KE>CPE, PEC=0[/tex]
The velocity of the ball is the highest at this point. Hence, the kinetic energy of the ball is the highest at this point.
The momentum of the ball at this point is given by the product of mass and velocity. As the velocity of the ball is the highest at this point, its momentum is also the highest.
Momentum > 0, KE > 0, PE = 0
At point D: At this point, the ball has lost all its kinetic energy due to friction. Hence, it comes to rest at this point.
KE=0, PED>0
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Learning Task 4: Story Reading "SITIO KATAMAKAWAN"
"Sitio Katamakawan is a community of lazy and gluttonous people. They
sit or lie all day and eat everything on their mouth desires. Each family
has a housemaid to take care of all the household chores. The children
of this community are adaicted to playing computer games although
they maintain their passing grades. They are not allowed to play outside
to prevent accidents. Most of the time, the teenager surf the internet.
Most of the parents are overweight because after their work, they watch
television while having night snacks. Some men areinto smoking and
drinking alcohol. "
Answer the following questions:
1. Would you like to live in this community? Why?
2. Which health dimensions are sustained, and do the people
live a physically active and healthy lifestyle
3. What are the possible diseases the people of this community
mighthave?
4. What are the risk factors of these diseases?
Given passage is a story reading about a community called "Sitio Katamakawan" and their unhealthy living and lifestyle.
Based on the passages it not desirable to live in the community. They are lazy and gluttonous. Also so many people are having various unhealthy habits also. Smoking and drinking are two among them.It is very important to maintain a healthy and physically active lifestyle. Ten only the wellbeing of an individual and the society sustain. Here in this community, members do not live a physically active lifestyle, and their health may be compromised in various dimensions. There are many possible diseases the people of this community might have. Heart diseases, stroke, diabetes, cancers etc. are some of them. They may be at the risk of depression and anxiety.There are many risk factors for these diseases above mentioned. Unhealthy lifestyle, unhealthy diet, excess alcohol consumption and smoking, excessive screen time etc. are some of them.Learn more about lifestyle:
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what will happen to the excess electrons when the negatively charged rod touches the metal sphere?
If the metal sphere is positively charged, then the excess electrons will move to the metal sphere. But if it's negatively charged, the excess electrons will repel the metal sphere.
How does a nuclear power plant produce electricity?
Responses
Quickly moving neutrons coming out of the reaction create a gas which turns a turbine that produces electricity.
Quickly moving neutrons coming out of the reaction create a gas which turns a turbine that produces electricity.
Quickly moving neutrons coming out of the reaction are slowed down by water. The water heats up and turns into steam. The steam turns the turbine and produces electricity.
Quickly moving neutrons coming out of the reaction are slowed down by water. The water heats up and turns into steam. The steam turns the turbine and produces electricity.
Quickly moving neutrons coming out of nuclear reactions are used to turn turbines that produce electricity.
Quickly moving neutrons coming out of nuclear reactions are used to turn turbines that produce electricity.
Quickly moving neutrons give their kinetic energy to the surrounding water. The water's energy is then used to turn turbines and produce electricity.
Water slows down neutrons that are leaving nuclear processes quickly. As the water warms up, steam is produced. Electricity is generated by the turbine that the steam turns.
Nuclear power plantA facility that uses nuclear reactions to produce electricity is known as a nuclear power plant. Nuclear fission—the splitting of an atom's nucleus—is used in these reactions to release a significant quantity of energy.Nuclear fission is started at a nuclear power plant's reactor core by blasting the fuel, which is typically uranium-235 or plutonium-239, with neutrons. The heat produced by the fuel's fission is utilized to boil water into steam. To generate electricity, the steam powers a turbine, which in turn powers a generator.The reactor core is encased in a substantial, protective vessel known as the reactor vessel in order to prevent the uncontrolled emission of radioactive particles.learn more about electricity here
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A ball rolls along a horizontal track in a certain time. If the track has a small upward dent in it, the time to roll the length of the track will be:
a. less
b. more
c. the same
Explanation:
More....it will have to travel a greater length to go up and over the dent, so it will take longer
A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 0.0055m/s2 less than that at sea level (gsealevel = 9.83 m/s2).
What is the observatory's altitude? Assume Rearth = 6.37
Because we measured the altitude from the Earth's centre, which is below the surface, the outcome is negative. As a result, the observatory is located 6.37 km below sea level.
Why are observatories located at great heights?Most importantly, placing an observatory on a mountainside means that there is less air to look through, improving the quality of the "seeing". Moreover, there is less air above you on a mountainside to absorb starlight.
The following is the equation for gravitational acceleration at a distance from the Earth's centre:
g = G M / r²
Given that the observatory is located r kilometres above the Earth's surface, we have:
g = G M / (r + Rearth)²
where Rearth is the Earth's radius. The observatory's altitude, h, can be calculated using the following formula:
gsealevel - g = 0.0055 m/s²
G M / (r + Rearth)² - G M / Rearth² = 0.0055 m/s²
G M (1/Rearth² - 1/(r + Rearth)²) = 0.0055 m/s²
r + Rearth = sqrt(G M / (0.0055 m/s² Rearth²) + Rearth²)
r = sqrt(G M / (0.0055 m/s² Rearth²) + Rearth²) - Rearth
Plugging in the values for G, M, and Rearth, we get:
r = sqrt((6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻²) × (5.9722 × 10²⁴ kg) / (0.0055 m/s² × (6.37 × 10⁶ m)²) + (6.37 × 10⁶ m)) - 6.37 × 10⁶ m
r = 2859.9 m
Therefore, the altitude of the observatory is:
h = r - Rearth = 2859.9 m - 6.37 × 10⁶ m = -6.37 × 10⁶ m + 2859.9 m
h = -6.367 × 10⁶ m
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Why don't you have to know how the wire is bent? (Select all that apply.)a. E is dependent on the length L of the wire which only applies to the segment of the wire that is not bent. b. E is not dependent on how the wire is bent, only the diameter of the wire is needed. c. Since conventional current flows in the direction of E^rightarrow, E is the same in every part of the wire with uniform properties. d, E must be parallel to the wire at every location even if the wire twists and turns.
Options b and c are correct. These two are the reasons that indicate why one doesn't have to know how the wire is bent.
An electric field is a vector field created by a charged object. When a charged particle interacts with the electric field of another charged particle, it will experience a force, which can be either attractive or repulsive. The electric field at a given point in space is determined by the charge and distribution of charges in the space, as well as by the location and orientation of the observer. The strength of the electric field is measured in units of volts per meter (V/m).
Electric field (E) is not dependent on how the wire is bent, only the diameter of the wire is needed. And since conventional current flows in the direction of [tex]E\rightarrow[/tex], E is the same in every part of the wire with uniform properties. This implies that E must be parallel to the wire at every location even if the wire twists and turns. Therefore, even if the wire is bent, one need not know its shape, as long as the properties remain constant.
Thus, options b and c are the correct answers.
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Please help me
Question 1 . For a sound wave, the pitch is determined by which wave characteristic?
A-frequency
B-amplitude
C-wavelength
D-period
Question 2 - Which of the following waves cannot be transmitted through a vacuum
1-Ultraviolet radiation
2-Microwaves
3-Sound waves
4-Gamma rays
Question 3- Which of the following could be the value of a wavelength that is found in the visible region of the electromagnetic spectrum
A 5 × 10^-9 m
B. 5 × 10^-7 m
C. 5 × 10^-2 m
D. 5 × 10^-5 m
Question 4- Sophie is trying to measure the speed of sound. She stands 24.0 m away from a wall and claps repeatedly, changing the frequency until the echo synchronised with her claps. If she calculates the speed of sound as 325 m • s-1 how long did she wait between claps?
Give your answer in seconds, without units and correct to three significant figures.
Question 5 - Electromagnetic radiation is emitted with a frequency of 1.5 × 1012 Hz. What type of radiation is it?
Question 6- A buoy, floating at sea, is at rest when a wave reaches it. The buoy rises to its maximum height n times in 4 seconds. The wavelength of the buoy is measured to be 1. Which of the following is an expression for its wave speed?
Question 7-is the picture .
5 × 10^-7m (option B) could be the value of a wavelength that is found in the visible region of the electromagnetic spectrum.How to find how long Sophie waited between claps?
To calculate the time between claps, we can use the formula:
time = 2 x distance / speed of sound
Substituting the given values, we get:
time = 2 x 24.0 m / 325 m/s = 0.148 s
Therefore, Sophie waited for 0.148 seconds between claps.
What type of radiation is electromagnetic radiation with a frequency of 1.5 × 10^12 Hz?The frequency of 1.5 × 10^12 Hz corresponds to the microwave region of the electromagnetic spectrum. Therefore, the type of radiation emitted is microwave radiation.
What is the expression for its wave speed?The wave speed of the buoy can be calculated using the formula:
wave speed = wavelength / period
Since the buoy rises to its maximum height n times in 4 seconds, its period is 4/n seconds. Therefore, the expression for its wave speed is:
wave speed = 1/(4/n) = n/4 m/s
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A student graphed the position of a cart during a 7-second time interval.
The correct option is D; The cart moved at a constant velocity of 0.5m/s for the entire 7 seconds.
Which graph best represents a constant acceleration?Constant acceleration is represented as a horizontal line on the acceleration graph. The slope of the velocity graph represents the acceleration. On the velocity graph, constant acceleration Equals constant slope = straight line.
Acceleration is represented in a velocity-time graph by the slope, or steepness, of the graph line. If the line slopes upward, as seen in the figure between 0 and 4 seconds, velocity increases, and acceleration is positive. The velocity-time graph will be a curve when the acceleration increases with time, as anticipated by the equation: v = u + at.
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an object is in uniform circular motion. if you double its linear speed, how would the centripetal acceleration change?
An object is in a uniform circular motion. If you double its linear speed, the centripetal acceleration would increase four times.
The relationship between centripetal acceleration, speed, and radius of curvature of circular motion is given by:ac=v²/r where v = speed and r = radius of curvature of circular motion.
Centripetal acceleration is given by:ac=ω²rwhere ω is the angular velocity of circular motion. Substituting ω = v/r in the above equation, we get ac = v²/r.
Therefore, the centripetal acceleration is directly proportional to the square of the speed of an object in a circular motion.
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in simple meters, the beat is divided into two, and in compound meters the beat is divided into how many?
In simple meters, the beat is divided into two parts, while in compound meters, the beat is divided into three parts.
A meter, or time signature, in music notation is a fraction-like symbol placed at the beginning of a piece of music that indicates the number and duration of beats in each measure. In simple meters, such as 2/4 or 3/4, the beat is subdivided into two parts, which are typically equal in duration. In compound meters, such as 6/8 or 9/8, the beat is subdivided into three parts, each of which is typically shorter than the beat duration and adds up to the beat duration. Compound meters are often used in music genres such as jazz, Latin, and folk music.
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In music theory, a beat is divided into two equal parts in simple meters, while in compound meters, the beat is generally divided into three equal parts. One example of a compound meter is 6/8, where the 6 beats would be split into two groups of 3 beats.
Explanation:In music theory, specifically relating to rhythm and meter, a beat can be divided into different ways depending on whether the music is in simple meter or compound meter. In simple meters, the beat is divided into two equal parts. However, in compound meters, the beat is typically divided into three equal parts.
For example, if you have a compound meter such as 6/8, there are 6 beats in a measure, and these 6 beats would split into two groups of 3 beats, giving it a 'triplet feel'. This contrasts with a simple meter like 2/4, where the beats would divided into two halves.
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A small cube of iron is observed under a microscope. The edge of the cube is 5.00×10 cm long. Find (a) the mass of the cube and (b) the number of iron atoms in the cube The molar mass of iron is 55.9g/mol, and its density is 7.86g/cm³.
Answer:
Explanation:
a) The mass of the cube can be calculated using the equation Mass = Volume x Density. The volume of the cube can be calculated as (5.00×10 cm)^3 = 125 cm³. Substituting this volume into the equation gives Mass = 125 cm³ x 7.86 g/cm³ = 983.5 g.
b) The number of iron atoms in the cube can be calculated using Avogadro's number (6.02 x 10^23 atoms/mol). The number of moles can be calculated using the molar mass of iron, 55.9 g/mol. Thus, the number of moles can be calculated as 983.5 g / 55.9 g/mol = 17.61 moles. Multiplying this by Avogadro's number gives the number of iron atoms in the cube as 1.07 x 10^24 atoms.
when an arrow is fired from a bow, the arrow keeps moving after it leaves the bow because
An arrow fired from a bow keeps moving because of momentum conservation.
Conservation of momentumWhen an arrow is fired from a bow, it keeps moving after it leaves the bow because of the conservation of momentum.
When the bowstring is pulled back, the potential energy in the bow is stored as elastic potential energy in the bowstring. When the bowstring is released, the elastic potential energy is transferred to the arrow, which causes the arrow to accelerate forward.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the bowstring exerts a force on the arrow, the arrow exerts an equal and opposite force on the bowstring, causing the bow to recoil backward. This recoil also contributes to the momentum of the arrow.
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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.
We can apply the formula [tex]v = \sqrt{(14.715 m/s^2 * r)}[/tex] to determine the peregrine falcon's speed. A falcon can reach a centripetal acceleration that is 1.5 times the acceleration of free fall.
We can use the centripetal acceleration formula to find the speed of the peregrine falcon in this scenario:
[tex]a_c = v^2 / r[/tex]
where [tex]a_c[/tex]is the centripetal acceleration, v is the speed of the peregrine falcon, and r is the radius of the circular turn.
We are given that the centripetal acceleration of the peregrine falcon is 1.5 times the free-fall acceleration, which we can approximate as 9.81 m/s². Therefore, we have:
[tex]a_c = 1.5 * 9.81 m/s^2\\a_c = 14.715 m/s^2[/tex]
We can also assume that the radius of the circular turn is a characteristic of the maneuvering ability of the peregrine falcon, and is independent of its speed. Therefore, we can write:
[tex]a_c = v^2 / r[/tex]
Solving for v, we get:
[tex]v = \sqrt{(a_c * r)}[/tex]
Substituting the values we obtained earlier, we get:
[tex]v = \sqrt{(14.715 m/s^2 * r)}[/tex]
Therefore, the speed of the peregrine falcon in this tight circular turn depends on the radius of the turn. If we know the radius, we can use the equation [tex]v = \sqrt{(14.715 m/s^2 * r)}[/tex] to calculate the speed of the peregrine falcon.
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a 1-kg chunk of putty moving at 12 m/s collides with and sticks to a 5-kg bowling ball initially at rest. the bowling ball and putty then move with a velocity of
The bowling ball initially at rest. The bowling ball and putty then move with a velocity of 2 m/s.
The combined mass of the putty and the bowling ball is 6 kg. Using the principle of conservation of momentum, we can calculate the velocity of the bowling ball and putty after the collision.
Given:
Mass of putty=1kg
Velocity of putty=12 m/s
Mass of bowling ball=5kg
Velocity of bowling ball= 0 m/s
As the putty collides with the ball and sticks to it, we can say that they move together after the collision.
Let v be the velocity of putty and bowling ball after collision.
Momentum (p) = mass (m) * velocity (v)
Therefore, momentum before collision = (mass of putty x velocity of putty) + (mass of ball x velocity of ball) = 1 x 12 + 0 x 5 = 12 kg m/s
Momentum after collision = (mass of putty + mass of ball) x velocity after collision= 6 x v kg m/s
So, according to the law of conservation of momentum,12 = 6 x v = 2 m/s
Therefore, the bowling ball and putty move with a velocity of 2 m/s after the collision.
Therefore, the velocity of the bowling ball and putty after the collision is 2 m/s when 1-kg chunk of putty moving at 12 m/s collides with and sticks to a 5-kg bowling ball initially at rest.
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Can someone please help me with this I am quite stuck thanks
Answer:
The mass remains the same since stoichiometrically one mole reacts and one mole is formed
Explanation:
Calcium chloride is reacting with Sodium sulphate to form a white precipitate of calcium sulphate.
[tex]{ \sf{CaCl _{2} + Na_{2} SO_{4} → CaSO _{4} + 2NaCl}}[/tex]
From the equation, 1 mole of calcium chloride forms 1 mole of calcium sulphate.
R.F.M of CaCl2 = 40 + (35.5×2) = 111
R.F.M of CaSO4 = 40 + 32 + (16×4) = 136
R.F.M of Na2SO4 = (23×2) + 32 + (16×4) = 142
R.F.M of 2NaCl = 2[23 + 35.5] = 117
[tex]{ \sf{(r.f.m \: of \: rectants) = (r.f.m \: of \: products)}} \\{ \sf{ (mass \: of \: rectants) = (mass \: of \: products)}} \\ \\ { \sf{(111 + 142) = (136 + 117)}} \\ { \sf{300.23 = x}} \\ \\ { \sf{x = \frac{300.32}{(111 + 142)} \times (136 + 117) }} \\ \\ { \sf{x = \frac{300.32}{253} \times 253 }} \\ \\ { \sf{x = 300.32}}[/tex]
Answer:
The mass remains the same
Explanation:
Learning Goal: To understand the concept of normal modes of oscillation and to derive some properties of normal modes of waves on a string. A normal mode of a closed system is an oscillation of the system in which all parts oscillate at a single frequency. In general there are an infinite number of such modes, each one with a distinctive frequency fi and associated pattern of oscillation. Consider an example of a system with normal modes: a string of length L held fixed at both ends, located at x=0 and x=L. Assume that waves on this string propagate with speed v. The string extends in the x direction, and the waves are transverse with displacement along the y direction. In this problem, you will investigate the shape of the normal modes and then their frequency. The normal modes of this system are products of trigonometric functions. (For linear systems, the time dependance of a normal mode is always sinusoidal, but the spatial dependence need not be.) Specifically, for this system a normal mode is described by yi(x,t)=Aisin(2πxλi)sin(2πfit).
a) Find the three longest wavelengths (call them λ1, λ2, and λ3) that "fit" on the string, that is, those that satisfy the boundary conditions at x=0 and x=L. These longest wavelengths have the lowest frequencies.
Express the three wavelengths in terms of L. List them in decreasing order of length, separated by commas.
b) The frequency of each normal mode depends on the spatial part of the wave function, which is characterized by its wavelength λi.
Find the frequency fi of the ith normal mode.
Express fi in terms of its particular wavelength λi and the speed of propagation of the wave v.
c) Find the three lowest normal mode frequencies f1, f2, and f3.
Express the frequencies in terms of L, v, and any constants. List them in increasing order, separated by commas.
1) The frequency fi of the ith normal mode is given by the equation fi = v/2λi, where λi is the wavelength of the ith mode.
2) The three lowest normal mode frequencies f1, f2, and f3 can be expressed in terms of L, v, and constants as follows: f1=v/2L, f2=v√2/2L, and f3=v2/2L.
3) The frequencies can be listed in increasing order as f1=v/2L, f2=v√2/2L, f3=v2/2L.
A dynamical system's normal mode of motion is a pattern of motion in which every component oscillates sinusoidally at the same frequency and with the same fixed phase relationship. The normal modes' description of free motion occurs at set frequencies. These constant frequencies of a system's normal modes are referred to as its natural or resonant frequencies.
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To use energy economically is to save energy. Write this statement logically.(explain)
write about cassiopeio
Answer:
Cassiopeia was one of the 48 constellations listed by the 2nd-century Greek astronomer Ptolemy, and it remains one of the 88 modern constellations today. It is easily recognizable due to its distinctive 'W' shape, formed by five bright stars. Visible at latitudes between +90° and −20°.
Answer:
Cassiopeia is a fascinating constellation with a rich history and cultural significance, as well as an important object of study for astronomers and scientists
Explanation:
Cassiopeia is a constellation located in the northern hemisphere of the sky. It is one of the 88 constellations officially recognized by the International Astronomical Union (IAU). The constellation is named after Queen Cassiopeia of Greek mythology, who was the wife of King Cepheus and mother of Princess Andromeda.
The constellation is easily recognizable for its distinctive shape, which looks like a "W" or "M" depending on its orientation in the sky. This shape is formed by five bright stars, which represent the Queen's throne and her legs. The brightest star in the constellation is known as Gamma Cassiopeiae, which is a massive blue-white star located about 550 light-years away from Earth.
Cassiopeia is visible in the sky all year round from most locations in the northern hemisphere, and it can be easily found by looking for its distinctive shape. It is also part of the Milky Way galaxy, which makes it a popular target for amateur astronomers who want to observe the stars and galaxies in our own galaxy.
Overall, Cassiopeia is a fascinating constellation with a rich history and cultural significance, as well as an important object of study for astronomers and scientists.
a 3.2 kilogram hoop starts from rest at a height 1.40 m above the base of an inclined plane and rolls down under the influence of gravity. what is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? neglect friction.
The linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface can be calculated using the equation for conservation of energy is 5.41 m/s.
What is the linear speed of the hoop's center?The equation is KEf = KEi + PEi.
where, KEf is the kinetic energy of the hoop just as it leaves the incline and KEi is the initial kinetic energy of the hoop at the beginning of the incline and PEi is the initial potential energy of the hoop at the beginning of the incline. The initial potential energy of the hoop is equal to the mass of the hoop (3.2 kg) multiplied by the acceleration due to gravity (9.8 m/s2) multiplied by the height of the incline (1.40 m):
PEi = 3.2 kg × 9.8 m/s² × 1.40 m = 44.56 J
The initial kinetic energy of the hoop is equal to 0, since the hoop is starting from rest.
Therefore, the equation for conservation of energy can be written as follows:
KEf = 0 + 44.56 J
The kinetic energy of the hoop just as it leaves the incline is equal to the mass of the hoop (3.2 kg) multiplied by the linear speed of the hoop's center of mass (v) squared, divided by two:
KEf = 3.2 kg × (v²) / 2
By combining the two equations above, we can solve for the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface:
v = √(2 × 44.56 J / 3.2 kg) = 5.41 m/s
Therefore, the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface is 5.41 m/s.
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Parts of the mixer become hot because some of the electrical energy is changed into
Parts of the mixer become hot because some of the electrical energy is converted into heat energy.
When electrical energy flows through a wire, it encounters resistance, which causes the wire to heat up. In a mixer, the electric motor converts electrical energy into mechanical energy to rotate the blades, but some of the electrical energy is lost as heat due to resistance in the motor's winding and other electrical components. This heat energy can accumulate in the mixer's parts and cause them to become hot. In many electrical devices, heat is an undesirable byproduct of energy conversion and can lead to reduced efficiency, damage, or safety hazards.
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--The complete Question is, Fill in the blanks. " Parts of the mixer become hot because some of the electrical energy is changed into____"--
a satellite is shot into a low orbit around a newly discovered planet. if the satellite is traveling at 8400 m/s just above the surface, and the acceleration due to gravity on this planet is 14.4 m/s2 , what must be the planet's radius?
The planet's radius is approximately 2.13 × 10^6 meters.
Planet radius calculation.
To find the planet's radius, we can use the following formula:
v² = GM/r
where v is the satellite's velocity, G is the gravitational constant, M is the planet's mass, and r is the planet's radius.
Since the satellite is just above the surface of the planet, we can assume that r is equal to the sum of the planet's radius and the satellite's altitude above the surface. Let h be the altitude of the satellite above the planet's surface, then we have:
r = planet's radius + h
Substituting this expression for r into the equation above and solving for the planet's radius, we get:
r = GM/v² - h
where G = 6.6743 × 10^-11 Nm²/kg² is the gravitational constant.
Substituting the given values, we get:
r = (6.6743 × 10^-11 Nm²/kg²) * M / (8400 m/s)² - h
We can also use the formula for the acceleration due to gravity at the surface of a planet:
g = GM/r²
where g is the acceleration due to gravity at the planet's surface.
Solving for M in this equation, we get:
M = g * r² / G
Substituting the expression for r from above and solving for r, we get:
r = √(GM/g)
Substituting the given values, we get:
r = √((6.6743 × 10^-11 Nm²/kg²) * M / (14.4 m/s²))
Equating this expression for r with the previous one, we get:
(6.6743 × 10^-11 Nm²/kg²) * M / (8400 m/s)² - h = √((6.6743 × 10^-11 Nm²/kg²) * M / (14.4 m/s²))
Squaring both sides and rearranging, we get:
M = (8400 m/s)² * (14.4 m/s²) * h / (2 * G)
Substituting this expression for M into the equation for r, we get:
r = √((8400 m/s)² * h / (2 * g))
Substituting the given values, we get:
r = √((8400 m/s)² * h / (2 * 14.4 m/s²))
r = 2.13 × 10^6 meters
Therefore, the planet's radius is approximately 2.13 × 10^6 meters using v² = GM/r.
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In short-track speed skating, the track has straight sections and semicircles 16 min diameter. Assume that a 64kg skater goes around the turn at a constant 11m/s .
Part A What is the horizontal force on the skater?
part B
What is the ratio of this force to the skater's weight?
The horizontal force is 44 kg m/s². The ratio of this force to the skater's weight is 0.69 kg m/s²/kg.
The track contains straight stretches and 16-metre-diameter semicircles for short-track speed skating. Suppose that a skater weighing 64 kg completes the turn at a constant speed of 11 m/s.
1) The horizontal force on the skater is determined by the centripetal force equation, F = mv²/r, where F is the force, m is the mass, v is the velocity, and r is the radius.
Using the given parameters, the horizontal force is therefore 64 kg x 11 m/s²/16 m = 44 kg m/s².
2) The ratio of this force to the skater's weight can be calculated by dividing the force (44 kg m/s²) by the weight (64 kg).
(44 kg m/s²) ÷64 kg = 0.69 kg m/s²/kg.
This gives a ratio of 0.69 kg m/s²/kg.
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a 970 kg car starts from rest on a horizontal roadway and accelerates eastward for 5.00 s when it reaches a speed of 25.0 m/s. What is the average force exerted on the car during this time?
The average force exerted on the car during this time is 4850 N.
We can use the equation F = ma to find the average force exerted on a 970 kg car that starts from rest on a horizontal roadway and accelerates eastward for 5.00 seconds when it reaches a velocity of 25.0 m/s. Here is the solution to the problem:
Given,
Mass of the car, m = 970 kg
Initial velocity of the car, u = 0
Final velocity of the car, v = 25.0 m/s
Time is taken by the car to attain the final velocity, t = 5.00 s
Acceleration of the car, a = (v - u) / t = (25.0 - 0) / 5.00 = 5.00 m/s²
Average force exerted on the car during this time, F = m × a= 970 kg * 5.00 m/s²= 4850 N
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a binary star system consists of two stars of masses m1 and m2 . the stars, which gravitationally attract each other, revolve around the center of mass of the system. the star with mass m1 has a centripetal acceleration of magnitude a1 . note that you do not need to understand universal gravitation to solve this problem. part a find a2 , the magnitude of the centripetal acceleration of the star with mass m2 . express the acceleration in terms of quantities given in the problem introduction. view available hint(s)for part a activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type a2
The magnitude of the centripetal acceleration of the star with mass m2 is:
[tex]a_2 = (m_1/m_2) \times a_1 = (m_1/m_2) \times a1[/tex]
In a binary star system, the two stars revolve around their common center of mass. Let's call this center of mass "C".
According to Newton's second law, the centripetal acceleration of each star is related to the gravitational force between the two stars:
[tex]a_1 = F_1/m_1[/tex]
[tex]a_2 = F_2/m_2[/tex]
where F1 and F2 are the gravitational forces exerted by each star on the other.
Since the two stars are in orbit around each other, the gravitational force between them provides the necessary centripetal force:
F1 = F2 = F
where F is the gravitational force between the two stars.
The magnitude of the centripetal acceleration of the star with mass m2, a2, can be calculated using the equation:
[tex]m_1a_1=m_2a_2[/tex]
[tex]a_2 = (m_1/m_2) \times a_1[/tex]
where m1 is the mass of the first star, m2 is the mass of the second star, and a1 is the magnitude of the centripetal acceleration of the star with mass m1. Therefore, the magnitude of the centripetal acceleration of the star with mass m2 is:
[tex]a_2 = (m_1/m_2) \times a_1 = (m_1/m_2) \times a_1[/tex]
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dealing with continuously variable data such as sound and light waves is called
Dealing with continuously variable data such as sound and light waves is called signal processing.
Signal processing is the manipulation of signals to extract useful information or transform them into a desired form. It is a broad field that encompasses many different applications, including audio and video processing, communication systems, radar systems, and control systems.
Signal processing techniques can be used to analyze and manipulate sound waves, such as filtering out unwanted noise, compressing or expanding dynamic range, or modifying the frequency spectrum of a signal. In the case of light waves, signal processing techniques can be used to remove noise, enhance contrast or color, or manipulate the spatial frequency content of an image.
There are many different tools and techniques that can be used in signal processing, depending on the specific application. Some common techniques include Fourier analysis, which decomposes a signal into its frequency components, and digital signal processing, which involves the use of digital algorithms to manipulate signals.
Overall, signal processing is a fundamental aspect of many modern technologies and is used in a wide range of applications, from audio and video processing to medical imaging and telecommunications.
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arrange 3 identical resistors in all the possible combinations and calculate the equivalent resistance. the resistance for each resistor is 200 ohms
Explanation:
All R's in series: just add them together : 200 + 200 + 200 Ω = 600Ω
One in series with two in parallel :
= 200 Ω + 200*200/(200+200) Ω = 300Ω
All three in parallel :
R = 1 / (1/200 + 1/200 + 1/200) = 66.7 Ω