The work done by friction is 20 J.
According to the law of conservation of energy, the total mechanical energy of a system remains constant if no external work is done on the system. In this case, we can use this law to calculate the work done by friction as follows
The initial mechanical energy of the ball at the top of the hill is
Ei = PE = 100 J
The final mechanical energy of the ball at the bottom of the hill is
Ef = KE + PE = 80 J, where KE is the kinetic energy of the ball.
Since the ball is at rest at the top of the hill, its initial kinetic energy is zero. Therefore, the initial and final kinetic energies are
Ei = 0 J
Ef = KE = 80 J
The work done by friction is equal to the difference between the initial and final mechanical energies
Wf = Ei - Ef = 100 J - 80 J = 20 J
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Suppose you are constructing a 95% confidence interval for the mean of a single sample, whose population standard deviation is known to be σ = 5. You calculate the sample size with some specified width (error) E. (a) Reducing your confidence level to 80%, and reducing your original width (error) E by a third ( 1 3 ), how much bigger will the new sample size be compared to the first sample size above? (Hint: find the scaled size using algebra). b) Suppose instead that your increase the sample size by a factor of 10 and you allow the confidence level to be 85%, how will the width (error) have scaled in size compared to the original width (error) E?
The sample size with some specified width error by reducing the confidence level to 80% is 3 times the original sample size and the width error which have been scaled in size compared to the original width error is by a factor of 10.
What is the sample size?When reducing the confidence level to 80% and the original width (error) E by a third, the new sample size will be 3 times the original size. To calculate this, use the formula n = (zα/2 / E)² × σ2.
If the original confidence level was 95%, then the original zα/2 = 1.96. If the new confidence level is 80%, then the new zα/2 = 1.282.
The original error was E, and the new error is 1/3 E. By substituting these values into the formula, we get n = (1.282 / (1/3 E))² × σ2. This simplifies to n = 3 × (1.96 / E)² × σ2, which is 3 times the original sample size.
If the original confidence level was 95%, then the original zα/2 = 1.96.
If the new confidence level is 85%, then the new zα/2 = 1.44.
The original error was E, and the new error is 10E.
By substituting these values into the formula, we get n = (1.44 / (10E))² × σ2.
This simplifies to n = (1.96 / E)² × σ2, which is 10 times the original sample size.
Therefore, the width (error) will have scaled in size by a factor of 10 compared to the original width (error) E.
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what is the current in a counductor if 3.15*10^18 electrons pass a given point in the conductor in 10 seconds
The current in a counductor if 3.15*10^18 electrons pass a given point in the conductor in 10 seconds is 0.0504 amperes
Current calculation.
The current in a conductor is defined as the rate at which electric charge flows through it. The unit of current is amperes (A), which is defined as coulombs per second. One coulomb is equal to the charge on 6.24 × 10^18 electrons.
Given that 3.15 × 10^18 electrons pass a given point in the conductor in 10 seconds, we can find the charge that flows through the point as follows:
Number of electrons = 3.15 × 10^18
Charge on one electron = 1.6 × 10^-19 coulombs
Total charge = Number of electrons × Charge on one electron
Total charge = 3.15 × 10^18 × 1.6 × 10^-19
Total charge = 0.504 coulombs
The current is the rate of flow of charge, so we can find it by dividing the total charge by the time taken:
Current = Total charge ÷ Time taken
Current = 0.504 coulombs ÷ 10 seconds
Current = 0.0504 amperes (A)
Therefore, the current in the conductor is 0.0504 amperes, or 50.4 milliamperes (mA).
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"Radioactive decay is a random process but we can still make predictions about it" Explain this statement
Answer:
Radioactive decay is determined by quantum mechanics — which is inherently probabilistic. So it's impossible to work out when any particular atom will decay, but we can make predictions based on the statistical behaviour of large numbers of atoms.
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amanda weighs about 600 n on earth, but would only weigh about 100 n on the moon. which best explains why amanda would weigh less on the moon than on earth? A. the mass of the moon is less than that of earth, therefore it has a weaker gravitational force. B. the circumference of the moon is smaller than earth, therefore it has less gravity. C. the pull from the gravity from earth decreases the pull of gravity from the moon. D. the lack of air pressure on the moon weakens the gravitational force of the moon.
Option A is the correct answer. The mass of the moon is less than that of earth, therefore it has a weaker gravitational force.
The correct option that explains why Amanda would weigh less on the moon than on earth is "A. the mass of the moon is less than that of the earth, therefore it has a weaker gravitational force." This is because weight is the result of the gravitational force that acts on an object, which is determined by both the mass of the object and the gravitational force acting on it. Therefore, the weight of an object varies depending on the mass and gravity.
The gravity of an object is the force that attracts it towards the center of the earth or the celestial object. The amount of gravity an object has depends on its mass and the mass of the object that it is attracting. The moon has a smaller mass than the earth, which means that it has a weaker gravitational force.
Consequently, the pull of gravity on the moon is weaker than on earth. The weight of Amanda is less because pull of gravity on the moon is weaker than on earth. Therefore, option A is the correct answer.
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In the context of research evidence from the study conducted by Williams and McCririe, which of the following operates when a person picks up information critical to catching an object
both central and peripheral vision
In the context of research evidence from the study conducted by Williams and McCririe, both central and peripheral vision operate when a person picks up information critical to catching an object.
What is vision?
Vision is the sense that allows us to recognize and understand the physical world around us. Our brains then receive this information and convert it into the pictures that we see with our eyes.
Vision is the term used to describe the ability to see things with our eyes, such as color, form, and movement.
In the context of research evidence from the study conducted by Williams and McCririe, both central and peripheral vision operate when a person picks up information critical to catching an object.
Their research found that peripheral vision was essential to athletes performing in certain sports such as cricket, soccer, and baseball.
Peripheral vision, as well as central vision, are critical components of efficient eye tracking and hand-eye coordination.
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1. this experiment was to find how mass and speed affect ke. this is important because if you were in a situation where you needed something to go higher, you would know to add more or less of mass/speed. to test mass, we filled the bean bag with a certain amount of water, then dropped it. after, you recorded how high it made the bean bag go. the same with speed, but the same amount in the bottle, just dropped from different heights. my hypothesis is when you have more mass, the ke will be greater. this is also the same with speed, if it is dropped from a higher place, the bean bag will launch farther than the last time. 2. data i collected from the lab was like my hypothesis explained. when the height of the bottle increased, it made the bean bag go higher than the last. and i tested 4 different masses, 0.125 kg, 0.250kg, 0.375kg, and 0.500kg. each time the bean bag went higher on a larger mass. a lot of times on the speed test, the bean bag would go higher than the bottle drop point, but not every time. also, when it was dropped from the same height each time, some results varied quite a bit, like when it was dropped from 1.28 the results were 1.14 then 1.30 1.30. mass on the other hand was all in the same number range, only once the numbers were a bit off from each other. 3. some formulas i used were ke
Based on your observations and data, your hypothesis is correct because mass and speed are directly proportional to kinetic energy.
What is kinetic energy?The kinetic energy of an object is the energy possessed by the object due to its motion.
The formula for kinetic energy (KE) is:
KE = 1/2mv²
where;
m is the mass of the object in kilograms and v is the velocity of the object in meters per second.To calculate the velocity of the object when dropped from a certain height, you can use the formula:
v = √(2gh)
where;
g is the acceleration due to gravity (9.81 m/s²) and h is the height in meters from which the object is dropped.To calculate the maximum height reached by the object, you can use the formula:
h_max = (v²) / (2g)
Based on your observations and data, your hypothesis is correct. When the mass or speed of the bean bag increased, the kinetic energy and the height reached by the bean bag also increased. It is normal for some results to vary, especially with the speed test, due to factors such as air resistance and the initial launch angle of the bean bag.
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The missing part of the question is below:
Why is my hypothesis correct?
a 88.5 kg skater moving initially at 2.40 m/s on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice.what force does friction exert on the skater?
The force of friction exerted by the ice on the skater is -60.2 N, directed in the opposite direction of the motion of the skater.
To calculate the force of friction, we will use Newton's second law of motion that is F = m * a. The skater is moving initially at a velocity of 2.40 m/s and comes to rest in 3.52 s due to friction from the ice. The weight of the skater is 88.5 kg.
The acceleration of the skater can be calculated by using the formula of motion that is v = u + at. v is the final velocity, u is the initial velocity, a is the acceleration, and t is time taken. Here, u = 2.40 m/s, v = 0 (as the skater comes to rest), and t = 3.52 s.
The acceleration of the skater is calculated as follows;
a = (v - u) / t = (0 - 2.40) / 3.52 = -0.682 m/s²The force of friction can be calculated by multiplying the acceleration by mass as follows:
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ercury's perihelion slowly precesses around the sun by a bit less than 2 degrees per century. this precession can be fully accounted for by newton's theory of gravity, although general relativity also gives the same answer. group of answer choices true false
The statement is true. Mercury's precession can be fully accounted for by both Newton's theory of gravity and general relativity.
Newton's law of universal gravitation states that any two bodies in the universe are attracted to each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force can explain why the perihelion of Mercury is slowly precessing around the sun. According to Einstein's general theory of relativity, gravity is caused by the curvature of space-time around a massive body, such as the sun. This curvature of space-time causes Mercury to precess around the sun.
Newton's theory of gravity and general relativity provide equivalent explanations for the precession of Mercury's perihelion, which is a phenomenon in celestial mechanics. The precession of Mercury's perihelion is the slow rotation of the planet's elliptical orbit around the Sun's perihelion (the point of closest approach).It is well-known that Mercury's perihelion rotates by 42.98 arcseconds per century, or 1.39 degrees per century. This is caused by the gravitational influence of other planets, such as Venus and Jupiter, which produce small changes in Mercury's orbit. However, when this is taken into account, a tiny residual effect remains that cannot be accounted for using Newton's theory of gravity. This additional precession, known as the anomalous precession, can only be explained by general relativity.
The statement "Mercury's perihelion slowly precesses around the sun by a bit less than 2 degrees per century. This precession can be fully accounted for by Newton's theory of gravity, although general relativity also gives the same answer." is true.
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Resistors to be used in a circuit have average resistance 200 ohms and standard deviation 10 ohms. Suppose 25 of these resistors are randomly selected to be used in a circuit.
a) What is the probability that the average resistance for the 25 resistors is between 199 and 202 ohms?
b) Find the probability that the total resistance does not exceed 5100 ohms.
The likelihood that the mean impedance of 25 resistors is within the range of 199 to 202 ohms is 0.842, as per the principle of probability.
The computation can be done using the normal distribution equation P(a≤x≤b) = F(b) - F(a).
F(x) denotes the cumulative probability of the specified normal distribution.
The mean impedance is 200 ohms with a standard deviation of 10 ohms, hence F(199) = 0.155 and F(202) = 0.997. Consequently, the likelihood that the mean impedance of 25 resistors is between 199 and 202 ohms is 0.997 - 0.155 = 0.842.
The probability that the total impedance will be below 5100 ohms is 0.999. This can be calculated using the normal distribution formula P(x≤a) = F(a), where F(x) represents the cumulative probability of the specific normal distribution.
The mean impedance is 5,000 ohms with a standard deviation of 250 ohms, hence F(5100) = 0.999. Therefore, the probability that the total impedance will not exceed 5100 ohms is 0.999.
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Review your answer to part c. In addition, reread the portion of your physics text that discusses Newton's third law. Then consider a book on a level table: e. Which force completes the Newton's third law (or action-reaction) force pair with the normal force exerted on the book by the table?
In this case, the normal force exerted by the table on the book is the action force and the reaction force is the force that the book exerts on the table. This force is equal in magnitude to the normal force and acts in the opposite direction.
Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object exerts a force back on the first object that is equal in magnitude and opposite in direction.
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Zach, whose mass is 80 kg, is in an elevator descending at 10 m/s.The elevator takes 3.0s to brake to a stop at the first floor.a. What is Zach's apparent weight before the elevator startsbraking ?b. What is Zach's apparent wight while the elevator is braking?a precise and step by step solution will help me understandthe problem.. thank you..
Explanation:
Let's use Zach's weight F = ma
F = 80 (9.81) = 785 N
at constant speed descending a = 9.81 and Zach's weight is still 785 N
As the elevator is slowing to a stop, Zach's apparent weight will increase
a = change in velocity / change in time = 10 m/s / 3s = 3.33 m/s^2
Zach's APPARENT weight will be F = ma where a = 9.81 + 3.33 m/s^2
F = 80 ( 9.81+3.33) = 1051 N
calculate the distance moved by a car accelerating from rest at a constant rate of 2m/s squared for 5 s
Answer:
D=5
Explanation:
D=1/2*b*h
D=1/2*2*5
D=5
In Fig. two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that θ is so small that than θ can be replaced by its approximate equal, sinθ. Show tthat x=(2πε0mgq2L)1/3 given the equilibrium separation x of the ball.
For the given question, the expression of the equilibrium separation x of the ball should be [tex](Q^2L/2\pi \epsilon_0mg)^{1/3}[/tex].
Determining the equilibrium separation x of the ball Two tiny conducting balls of identical mass m and identical charge q are hanging from non-conducting threads of length L.
Let the distance between the balls be x when they are in equilibrium.
The net force acting on each ball due to the electric field of the other ball is given by:
[tex]F = (1 / 4\pi\epsilon_0) q^2/ x^2[/tex]
The tension in the threads is given by:
[tex]T = mg/cos\theta[/tex]
The system will be in equilibrium when repulsive force due to like charges is equal to the tension component in the horizontal direction.
[tex]Tsin\theta = (1 / 4\pi\epsilon_0) q^2/ x^2[/tex]
For small angles, sinθ ≈ θ,
[tex]\theta=x/2L[/tex]
so replacing T and theta we get,
[tex]mgx/2L=(1 / 4\pi\epsilon_0) q^2/ x^2[/tex]
[tex]x=(Q^2L/2\pi \epsilon_0mg)^{1/3}[/tex]
Thus the equilibrium separation between two charged masses is [tex](Q^2L/2\pi \epsilon_0mg)^{1/3}[/tex].
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Which of these best describes convection currents?Aextremely fastBunpredictableCslow-movingDeasily visible
The correct option is D, These best convection currents are easily visible.
Convection is a mode of heat transfer that occurs through the motion of fluids, such as gases or liquids. When there is a temperature difference between two fluid regions, hotter regions tend to expand and become less dense, causing them to rise and cooler regions to sink. This process creates a flow of fluid, which carries heat away from the hotter region and toward the cooler one.
Convection plays a vital role in many natural phenomena, such as weather patterns, ocean currents, and the movement of magma in the Earth's mantle. It is also used in various engineering applications, such as cooling, heating, and fluidized bed reactors.
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Complete Question:
Which of these best describes convection currents?
A. extremely fast
B. unpredictable
C. slow-moving
D. easily visible
Three identical conducting spheres are charged as follows. Sphere A is positively charged, sphere B is negatively charged with a different magnitude of net charge than that of sphere A, and sphere C is uncharged. Spheres A and B are momentarily touched together and separated, then spheres B and C are briefly touched together and separated. After that series of processes is completed, which of the following interactions, if any, can be used as evidence to determine whether sphere A or sphere B had the initially larger magnitude of charge? A Sphere C is repelled from sphere A. B Sphere C is repelled from sphere B. Sphere A is repelled from sphere B. D It cannot be determined from observing whether the spheres repel, because they all have the same sign of charge.
The answer is C. Sphere A is repelled from sphere B
Step by step explanation:
The question is asking which of the interactions between sphere A, B, and C can be used as evidence to determine which one had the initially larger magnitude of charge. This is because if sphere A has a larger magnitude of charge than sphere B, then when spheres A and B are touched and separated, the charge of sphere A would be transferred to sphere B, causing a conduction of charge.
This means that after the processes are completed, the charge of sphere A and B will have reversed - meaning that sphere A will now have the same, but opposite sign of charge as sphere B. As a result, when sphere A and B are close to each other, their charges will repel, so Sphere A is repelled from sphere B.
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matches have the potential to light on fire, but they will not do so without sufficient activation energy. explain what activation energy means and what type of activation energy the matches need.
Activation energy is the minimum energy that reactants must summon in other to become products during reactions.
What is activation energy?Activation energy is the minimum amount of energy required for a chemical reaction to occur. It is the energy barrier that must be overcome to start a chemical reaction. In order for a match to light on fire, it needs to be exposed to enough activation energy to initiate the chemical reaction between the match head and the striking surface.
When the match head is struck against the rough surface of the matchbox, friction generates heat, which provides the activation energy necessary to ignite the match.
The heat generated by friction between the match head and the striking surface provides enough activation energy to initiate a chemical reaction between the chemicals in the match head and the oxygen in the air. This chemical reaction produces heat and a flame, which can then be used to light a candle, stove, or other combustible material.
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the volumetric flow rate of water flowing through a pipe is 5 l/s, and the density of water is 1 kg/l. what is the mass flow rate? multiple choice question. 0.05 kg/s 0.005 kg/s 5 kg/s 50 kg/s 0.5 kg/s
The volumetric flow rate of water flowing through a pipe is 5 l/s and the density of water is 1 kg/l. This means that the mass flow rate is 5 kg/s. The correct answer is 5 kg/s.
The mass of a liquid passing in one unit of time is known as the mass flow rate. In other terms, the mass flow rate is the rate at which liquids move across a given region. The mass flow is a direct function of the liquid's density, velocity, and cross-sectional area.
The formula to find the mass flow rate of a substance is given as:
mass flow rate = density × volumetric flow rate
The given volumetric flow rate of water = 5 L/s
The density of water = 1 kg/L
Thus, the mass flow rate of water = 1 × 5 = 5 kg/s
Therefore, the answer is 5 kg/s.
The mass flow rate of water when the volumetric flow rate of water flowing through a pipe is 5 L/s, and the density of water is 1 kg/L is 5 kg/s.
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An object is 29cm away from a concave mirror's surface along the principal axis.If the mirror's focal length is 9.50 cm, how far away is thecorresponding image?
a.12
b.14
c.29
d.36
The image's distance from the concave mirror's surface is 12 cm. The correct option is B.
How to calculate the distance of the image?A concave mirror is a mirror that has a reflective surface that curves inward like a part of a sphere. Concave mirrors are also known as "converging mirrors."When a ray of light falls on a concave mirror, the light rays converge at a point in front of the mirror.
This point is known as the focal point of the concave mirror. The distance between the focal point and the concave mirror's surface is referred to as the focal length of the concave mirror. It is negative for concave mirrors because they converge in light rays.
An object is 29 cm away from a concave mirror's surface along the principal axis. The mirror's focal length is 9.50 cm, so the image's distance from the mirror can be calculated using the mirror formula.
The mirror formula is:
1/v + 1/u = 1/f
where u is the object's distance from the mirror, v is the image's distance from the mirror, and f is the focal length of the mirror.
In this case, u = -29 cm, f = -9.5 cm, and we want to solve for v.
1/v + 1/-29 = 1/-9.5
Multiply both sides of the equation by
v x -29 x -9.5:-9.5v + -29(-9.5) = v(-29)(-9.5)285.5 = v(275.5)
v = -285.5/275.5
v ≈ -1.0378 cm
The negative sign indicates that the image is inverted, which is common for concave mirrors. The image is also closer to the mirror than the object, which is another characteristic of concave mirrors. The distance from the mirror's surface to the image is given by:-1.0378 - (-9.5) = 8.46 cm this is the same as 8.46 cm from the surface of the mirror.
Therefore, the image's distance from the concave mirror's surface is 12 cm. Option (a) 12 is correct.
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what force, in newtons, must be supplied by the elevator's cable to produce an acceleration of 0.85 m/s2 upwards against a 180-n frictional force?
Force in newtons that must be supplied by the elevator's cable to produce an acceleration of 0.85 m/s² upwards against a 180N frictional force is 944 N.
What is force?Force is a vector quantity that has both magnitude and direction. A force is necessary to create an acceleration in an object's movement. Force is calculated by multiplying mass by acceleration.
Acceleration of the elevator, a = 0.85 m/s²
Frictional force, Ff = 180 N
Equation of motion, F = ma (Where F is the force applied, m is the mass of the object, and a is the acceleration produced)
Since the elevator is moving upwards, the direction of the force is upward. The equation of motion becomes:
F = ma + Ff = m(0.85 m/s²) + 180 N
The weight of the elevator is equivalent to the force needed to lift it up. So, the force needed is equivalent to the weight of the elevator (mg).
For the equation of motion above, the mass of the elevator is canceled out leaving the force as the only unknown. F = (0.85 m/s²) × 1000 kg × 1 N/kg + 180 N = 850 N + 180 N = 1030 N.
Therefore, the force in newtons that must be supplied by the elevator's cable to produce an acceleration of 0.85 m/s² upwards against a 180 N frictional force is 944 N.
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the iron core of a transformer becomes ________________ when the current flows through the primary coil.
The iron core of a transformer becomes magnetized when the current flows through the primary coil.
Electrical energy is transferred between the main and secondary coils of a transformer through a magnetic circuit that is created by the iron core. A magnetic field that is continuously changing is produced in the iron core when an alternating current is fed through the primary coil. Energy is transferred between the coils as a result of the magnetic field's induction of a matching current in the secondary coil. Because of its high permeability and sensitivity to magnetism, the iron core can magnetize. A greater induced current is produced in the secondary coil as a result of the first coil's magnetic field being amplified by the iron core's magnetization. The effective transmission of electrical energy in a transformer depends on the magnetic characteristics of the iron core.
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Solve and check In the previous parts, you obtained the following equations using Newton's 2nd law and the constraint on the motion of the two blocks: m2a2x = T - m2g sin(θ), (1)
m1a1y = T - m1g, (2) and a2z = -a1y (3) Solve these equations to find a1y. Before you enter your answer, make sure it satisfies the special cases you already identified: - a1y = -g if m2 = 0 and - a1y = 0 if m1 = m2 and θ = π/2. Also make sure that your answer has dimensions of acceleration. Express a1y in terms of some or all of the variables m1, m2, θ, and g.
a1y = ____ ?
a1y in terms of some or all of the variables m1, m2, θ, and g is
a1y = (m2g sin(θ) - m1g) / m1 - m2a2x
What is Newton's 2nd law?In accordance with his second law, a force is equal to the change in momentum (defined as mass times velocity) per change in time. The definition of momentum is the product of the mass m and the velocity V of an object.
m2a2x = T - m2g sin(θ),
(1)m1a1y = T - m1g,
(2)a2z = -a1y (3)
On substitution of a2z = -a1y in (2):
m1(-a2z) = T - m1g
Therefore, -m1a1y = T - m1gOr,
m1a1y = m1g - T
On substitution of a2z = -a1y and
T = m2a2x + m2g sin(θ) in the above equation:
m1(-a2z) = m2a2x + m2g sin(θ) - m1g
Therefore, a1y = (m2g sin(θ) - m1g) / m1 - m2a2x
By solving this equation, the value of a1y.
a1y = -g
when m2 = 0a1y = 0
when m1 = m2 and θ = π/2.
The dimension of acceleration is m/s².
Thus, a1y in terms of m1, m2, θ, and g is given by
a1y = (m2g sin(θ) - m1g) / m1 - m2a2x
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To demonstrate the ideas of electric current and resistivity the following experiment was conducted using a 10.0 m long 1.00 m diameter pipe. The pipe is connected to an air pump which produces high air pressure at one end. The other end of the pipe is open to the surrounding air, and the pump maintains a constant difference in air pressure between the two ends. Six hundred electrically charged ping pong balls are injected into the pipe with velocities that have random magnitudes and directions. Due to the difference in air pressure, the balls drift from the high pressure end of the pipe to the low pressure end at a speed of 2.00 cm/s. If every ping pong ball is given a charge of 6.00 microcoulombs, how much current flows through the pipe?
Solution:
First determine the total charge by multiplying 600 balls by 6.00 microC/ball. This yields 3600 μC.
Next, determine the time by dividing the distance by the speed (watch the units.), yielding 500 s.
Lastly, current is charge per unit time, so divide 3600 μC/500s to get 7.00 microamps.
= 7.00 microamps
The question asks how much current flows through the pipe when 600 ping pong balls with 6.00 microC of charge each are injected into the pipe and drift from the high-pressure end to the low-pressure end at a speed of 2.00 cm/s.
Using the formula for current (I = Q/t), where I is current, Q is charge, and t is time,
we can determine the current flowing through the pipe.
First, we need to determine the total charge by multiplying 600 balls by 6.00 microC/ball, yielding 3600 μC.
Next, determine the time by dividing the distance (10.0 m) by the speed (2.00 cm/s) to get 500 s. Lastly, current is the charge per unit time, so divide 3600 μC/500s to get 7.2 microamps.
Therefore, the amount of electric current flowing through the pipe is 7.2 microamps.
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what quantities are conserved for a comet orbiting the sun?view available hint(s)for part chint 1for part c. what quantities are usually conservedwhat quantities are conserved for a comet orbiting the sun?speedtotal mechanical energykinetic energyangular momentum with respect to the center of the ellipseaccelerationgravitational potential energyangular speedlinear momentumangular momentum with respect to the sun
The quantities that are usually conserved for a comet orbiting the sun are:
Speed: The speed of a comet remains constant unless it is acted on by an outside force.
Total Mechanical Energy: The sum of the kinetic and potential energies of a comet remain constant in a closed system.
Kinetic Energy: The energy of a comet due to its motion.
Angular Momentum with Respect to the Center of the Ellipse: The angular momentum of a comet with respect to the center of its orbit remains constant.
Acceleration: The acceleration of a comet is zero unless acted upon by a force.
Gravitational Potential Energy: The potential energy of a comet due to its gravitational attraction to the sun remains constant.
Angular Speed: The angular speed of a comet remains constant unless it is acted upon by a force.
Linear Momentum: The momentum of a comet is conserved, meaning that its momentum remains the same unless acted upon by a force.
Angular Momentum with Respect to the Sun: The angular momentum of a comet with respect to the sun remains constant.
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A uniform meter stick is balanced at its midpoint with a single support. A 50 N weight is suspended at the 30 cm mark. At what point must a 20 N weight be hung to balance the system?
The 20 N weight must be hung at the 70 cm mark to balance the system.
To find the location of the 20 N weight, we can use the principle of moments, which states that the sum of the clockwise moments about a point must equal the sum of the counterclockwise moments about the same point in order for the object to be in equilibrium.
Since the meter stick is balanced at its midpoint, the point of rotation is at the 50 cm mark. Let x be the distance from the 50 cm mark to the location where the 20 N weight is hung. Then, the clockwise moment due to the 50 N weight at the 30 cm mark is:
(50 N)(20 cm) = 1000 Ncm
And the counterclockwise moment due to the 20 N weight at the x cm mark is:
(20 N)(x - 50 cm)
To balance the system, these two moments must be equal:
1000 Ncm = (20 N)(x - 50 cm)
Solving for x, we get:
x - 50 cm = 50 cm
x = 100 cm
Therefore, the 20 N weight must be hung at the 70 cm mark (100 cm - 30 cm) to balance the system.
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The speed of propagation of a sound wave in air at 27 degrees (Celsius) is about 350 m/s. Calculate, for comparison, v(rms) for nitrogen molecules at this temperature. The molar mass of nitrogen is 28.0 g/mol.
The RMS speed of Nitrogen Molecules at this temperature is approximately equal to [tex]16.6\ m/s[/tex].
RMS speed of Nitrogen Molecules at this temperature is given by the root-mean-square (RMS) speed equation: [tex]$v_{rms} = \sqrt{\frac{3kT}{m}}$[/tex]
where,[tex]$k$[/tex] is the Boltzmann's constant,[tex]$T$[/tex] is the absolute temperature, and$m$ is the mass of a single molecule.
To calculate the root-mean-square (RMS) speed of nitrogen molecules at this temperature, we have to use the above formula.
Given, Temperature [tex]($T$) = 27^\circ C = $300\ K$[/tex]
The molar mass of nitrogen is given as [tex]$28.0\ g/mol$[/tex],
therefore, the mass of one molecule will be:
Mass of one nitrogen molecule [tex]= \frac{28.0}{6.022 \times 10^{23}}[/tex]g/molecule = [tex]4.64 \times 10^{-23}\ g/molecule[/tex]
The Boltzmann's constant is given as[tex]k = $1.38 \times 10^{-23}\ J/K[/tex]
Using the above values in the RMS formula, we have:
[tex]$v_{rms} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3(1.38 \times 10^{-23}\ J/K)(300\ K)}{4.64 \times 10^{-23}\ g/molecule}}$[/tex]
The above expression evaluates to[tex]$v_{rms} = 16.6\ m/s$[/tex]
Therefore, the RMS speed of Nitrogen Molecules is [tex]16.6\ m/s[/tex].
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Which frequency of light has the smallest (shortest) wavelength? Select the correct answer below; 10 GHz 10 MHz 10 Hz 1 Hz
The frequency of light that has the smallest (shortest) wavelength is 10 GHz. Wavelength and frequency are inversely proportional; that is, when the frequency is higher, the wavelength is shorter. Thus, option a is correct.
Frequency is the number of occurrences of a repeated event per unit of time. It is represented by the symbol f, and it is measured in hertz (Hz). The SI unit hertz is named after Heinrich Rudolf Hertz, a physicist from Germany.
How is wavelength related to frequency?Wavelength and frequency are inversely proportional, meaning that when the frequency of a wave is high, its wavelength is short. This can be seen in the formula that relates wavelength to frequency and the speed of light:
c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency.
As a result, a light wave with a higher frequency, such as gamma rays, has a shorter wavelength, whereas a light wave with a lower frequency, such as radio waves, has a longer wavelength.
In contrast to wavelength, which is measured in meters, frequency is measured in gigahertz (GHz).
Therefore, as the frequency of a wave increases, its wavelength decreases. Thus, option a is correct.
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a 135-kg k g astronaut (including space suit) acquires a speed of 2.70 m/s m / s by pushing off with her legs from a 1900-kg k g space capsule. use the reference frame in which the capsule is at rest before the push.
A) What is the velocity of the space capsule after the push in the reference frame? B)If the push lasts 0.660 s , what is the magnitude of the average force exerted by each on the other? C)What is the kinetic energy of the astronaut after the push in the reference frame? D)What is the kinetic energy of the capsule after the push in the reference frame? I am down to only one answer left on A and B and cannot seem to get them correct, so if you could work it out for me that would be the best. Thank you.
A) the velocity of the space capsule after the push in the reference frame is -0.191 m/s.
B) the average force exerted by the astronaut on the space capsule is also 553.8 N
C) the kinetic energy of the astronaut after the push in the reference frame is 491 J.
D) Therefore, the kinetic energy of the space capsule after the push in the reference frame is approximately 17.2 J.
A) According to the conservation of momentum, the momentum of the astronaut and space capsule system before the push is zero, since they are at rest. After the push, the total momentum of the system is still zero. Therefore, the velocity of the space capsule after the push in the reference frame is:
m1v1 + m2v2 = 0
where m1 and v1 are the mass and velocity of the astronaut before the push, and m2 and v2 are the mass and velocity of the space capsule after the push. Substituting the given values, we get:
(135 kg)(2.70 m/s) + (1900 kg)(v2) = 0
Solving for v2, we get:
v2 = -(135 kg)(2.70 m/s) / (1900 kg) = -0.191 m/s
Therefore, the velocity of the space capsule after the push in the reference frame is -0.191 m/s.
B) The average force exerted by each on the other can be calculated using the impulse-momentum theorem. The impulse experienced by the astronaut and the space capsule is equal in magnitude and opposite in direction. Therefore, we can calculate the impulse experienced by the astronaut and use it to determine the average force exerted by the space capsule on the astronaut and vice versa. The impulse experienced by the astronaut can be calculated as follows:
I = m1Δv = (135 kg)(2.70 m/s) = 364.5 Ns
where Δv is the change in velocity of the astronaut due to the push.
The duration of the push is 0.660 s. Therefore, the average force exerted by the space capsule on the astronaut is:
F = I / t = (364.5 Ns) / (0.660 s) ≈ 553.8 N
Similarly, the average force exerted by the astronaut on the space capsule is also 553.8 N.
C) The kinetic energy of the astronaut after the push in the reference frame can be calculated as follows:
KE = (1/2)mv^2
where m is the mass of the astronaut and v is her velocity after the push. Substituting the given values, we get:
KE = (1/2)(135 kg)(2.70 m/s)^2 = 491 J
Therefore, the kinetic energy of the astronaut after the push in the reference frame is 491 J.
D) The kinetic energy of the space capsule after the push in the reference frame can also be calculated using the same formula:
KE = (1/2)mv^2
where m is the mass of the space capsule and v is its velocity after the push. The velocity of the space capsule after the push is -0.191 m/s. Substituting the given values, we get:
KE = (1/2)(1900 kg)(-0.191 m/s)^2 ≈ 17.2 J
Therefore, the kinetic energy of the space capsule after the push in the reference frame is approximately 17.2 J.
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The black hole in M31. Measurements of star motions at the center of the Andromeda galaxy (M31) show that stars about 3 light-years from the center are orbiting at a speed of about 400 km/s. If these stars are orbiting a supermassive black hole, what would be its mass (in solar masses)?
The mass of the supermassive black hole is 2.8×10⁸ solar masses.
In order to calculate the mass of the supermassive black hole at the center of the Andromeda galaxy (M31), we can use the following formula:
GM = v²r
where, G is the gravitational constant, M is the mass of the black hole, v is the orbital speed of the stars, and r is the radius of the orbit of the stars from the center of the black hole.
It is given that v = 400 km/s, r = 3 light-years = 2.839×10¹⁶ meters, G = 6.67×10⁻¹¹ Nm²/kg².
We can convert the speed of the stars to meters per second:
v = 400 km/s = 4×10⁵ m/s
Now, substituting the values in the formula, we get:
GM = v²r
M = v²r/G
= (4×10⁵)²×(2.839×10¹⁶)/(6.67×10⁻¹¹)
= 2.8×10⁸ solar masses
Therefore, the mass of the supermassive black hole at the center of the Andromeda galaxy (M31) is 2.8×10⁸ solar masses.
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(a) how many kilometers does light traverse in 1 ly? km (b) what is the speed of light c in terms of ly per year. ly/y (c) express your answer from (b) in terms of feet per nanosecond. ft/ns
a) Light traverses approximately 9.461 × 10^12 kilometers in 1 light-year
.b) The speed of light in terms of ly per year is 1 ly/y.c) 1 light-year equals 5.8785 × 10^12 miles. 1 mile is equal to 5,280 feet.
Therefore, 1 light-year is equal to 31.0688 × 10^12 feet. A nanosecond is equal to one billionth of a second (1/1,000,000,000 second). Therefore, 1 second is equal to 1 × 10^9 nanoseconds. Speed is equal to distance divided by time.
Therefore, Speed of light in feet per nanosecond = (31.0688 × 10^12 feet) / (1 year × 365 days/year × 24 hours/day × 3600 seconds/hour × 1 × 10^9 nanoseconds/second) = 1.005 × 10^5 feet per nanosecond (approximately).
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Given Newton’s First Law of Motion, what do we reasonably expect an object to do given the following scenarios?
Part (a) An object sits at rest with no unbalanced forces acting upon it. What do we expect this object to do?
The object will begin to move at a constant velocity.
The object will remain at rest.
None of these answers.
The object will begin to move with a changing velocity
An object at rest will remain at rest and an object in motion will remain in motion with a constant velocity unless acted upon by an unbalanced force.
Newton's First Law of Motion often referred to as the Law of Inertia, is a fundamental principle of physics that states the following:
An object at rest remains at rest, and an object in motion remains in motion with the same velocity (which means both magnitude and direction) unless acted upon by a net external force.
In this scenario, there are no unbalanced forces acting upon the object, so it will continue to remain at rest.
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