The mass of the asteroid Swift is approximately 377.55 kg.
What is mass?Mass can be best described as the amount of matter present in any object or body.
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2.
To calculate the mass of the asteroid Swift, we will convert its weight from newtons to kilograms (kg), which is the unit of mass in the International System of Units (SI):
Weight = 3700 N
Acceleration due to gravity on Earth (g) = 9.8 m/s^2
Weight = Mass x Acceleration due to gravity
Mass = Weight / Acceleration due to gravity
Mass = 3700 N / 9.8 m/s^2
Mass = 377.55 kg
In conclusion, The mass of the asteroid Swift is approximately 377.55 kg.
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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 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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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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(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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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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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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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 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 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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"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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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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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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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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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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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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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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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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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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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
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
You kind of answered my question, I was wondering an object accelerates in the direction of the net force always but what is the opposite and equal reaction, since it is accelerating it is an unbalanced force so what is the equal and opposite reaction?
Answer:
According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. When an object experiences an unbalanced force in a certain direction, it will accelerate in that direction. The equal and opposite reaction to this force is the force that the object exerts on the other object causing the original force. For example, if you push on a box with a force of 10 Newtons to the right, the box will experience an unbalanced force in the right direction and accelerate to the right. The equal and opposite reaction to your push is the box pushing back on you with a force of 10 Newtons in the left direction. The force you exerted on the box and the force the box exerted back on you are equal in magnitude and opposite in direction.
Does this help?
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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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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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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After You Read
1. Give an example in which the distance you travel is different from your
displacement.
The example in which the distance you travel is different from your
displacement will be "Suppose a person starts at point A and walks 5 meters to point B, and then turns around and walks back to point A, covering another 5 meters. The distance traveled by the person is the total length of the path traveled, which is 10 meters (5 meters + 5 meters).
However, the displacement of the person is the change in position from the starting point to the ending point, which is zero. So the distance traveled is different from the displacement, as the person ends up at the same position where they started, despite covering a total distance of 10 meters.
What is displacement?Displacement is a verb that denotes movement or displacement of an object. The definition of displacement is the modification of an object's position.
The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.
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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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which phenomenon causes precipitation to reach earth?
"Precipitation occurs due to condensation of water molecules in the air into droplets and they fall to the ground due to gravity."
One of the stages of the water cycle is precipitation. Clouds are areas of the sky with enough water content for drops to condense, and they are where precipitation originates. Therefore, precipitation follows mist. Although clouds are the source of all precipitation, not all clouds generate precipitation.
When cloud droplets or crystals become too dense to continue floating in the atmosphere, precipitation starts to descend from the clouds. If droplets do not become sufficiently dense, precipitation will not occur, and if the cloud is sufficiently heated by the Sun, it may even disperse. But for there to be a place for precipitation to come from, clouds do need to develop.
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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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suppose that you drop a solid iron ball and a hollow iron ball, both the exact same diameter, from the same height at the same time. aristotle would predict that
If you drop a solid iron ball and a hollow iron ball of the same diameter from the same height at the same time, Aristotle's prediction would be that the solid iron ball will fall faster than the hollow iron ball.
Aristotle and gravity lawAristotle, who lived in ancient Greece, believed that heavier objects would fall faster than lighter ones. This was a commonly held belief at the time, but it has since been proven incorrect through scientific experiments.
In reality, when dropped from the same height at the same time, both the solid iron ball and the hollow iron ball of the same diameter would fall at the same rate, neglecting air resistance. This is because the rate at which an object falls is determined by its mass and the force of gravity acting on it, which are the same for both balls.
This was first demonstrated by Galileo Galilei in the late 16th century through his famous experiment involving dropping objects from the Leaning Tower of Pisa. He showed that objects of different masses would fall at the same rate in a vacuum and that air resistance was the primary factor that caused objects to fall at different rates in the real world.
In summary, Aristotle would have predicted that the solid iron ball would fall faster than the hollow iron ball, but this prediction has been shown to be incorrect by scientific experiments.
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A 4.00 g bullet is fired horizontally into a 1.20 kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet remains embedded in the block, which is observed to slide 0.390 m along the surface before stopping.
What was the initial speed of the bullet? Express your answer with the appropriate units.
The initial speed of the bullet is 0.390 m/s.
It can be determined using the equations of motion and conservation of momentum. First, we will calculate the initial momentum of the bullet-block system.
Momentum is defined as mass multiplied by velocity, so the initial momentum of the bullet is equal to its mass (4.00 g) multiplied by its initial velocity (v). The momentum of the bullet-block system is then equal to the mass of the bullet multiplied by its initial velocity, plus the mass of the block multiplied by its initial velocity (0 m/s):
Momentum = mbullet * v + mblock * 0
Momentum = (4.00 g) * v + (1.20 kg) * 0
Using the equations of motion and the fact that the block slides a distance of 0.390 m before stopping, we can calculate the final momentum of the system. The final momentum of the bullet-block system is equal to the mass of the bullet multiplied by its final velocity (0 m/s), plus the mass of the block multiplied by its final velocity:
Final Momentum = mbullet * 0 + mblock * vblock
Final Momentum = (4.00 g) * 0 + (1.20 kg) * (0.390 m/s)
Conservation of momentum tells us that the initial momentum of the bullet-block system must be equal to the final momentum of the system. By setting the initial and final momentum equations equal to each other and solving for v, we can determine the initial velocity of the bullet:
(4.00 g) * v + (1.20 kg) * 0 = (4.00 g) * 0 + (1.20 kg) * (0.390 m/s)
v = 0.390 m/s
Therefore, the initial speed of the bullet is 0.390 m/s.
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