The displacement of the runner after four seconds is 78.4 m.
What is the displacement after 4 seconds?We know that in this case, we are dealing with a case of an object that has a motion under gravity. We are told that the road runner an fell straight down off a cliff. The fact that we have been told that the runner just fell down the cliff means that the initial velocity of the runner would have to be taken in this context as zero since the runner was dropped from a height as shown.
Acceleration of the runner (g) = 9.8 m/s^2
Initial velocity of the runner (u) = 0 m/s
Time take (t) = 4 seconds
We then have;
h = ut + 1/2gt^2
If we then know that the initial velocity of the person is zero, then we have;
h = 1/2gt^2
h = 0.5 * 9.8 * (4)^2
h = 78.4 m
The height is 78.4 m.
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charging a capacitor involves a voltage source redistributing some electrons from one side of the capacitor to the other. T/F
True. When a voltage source is connected to a capacitor, it causes a redistribution of electrons within the capacitor. The voltage source drives the flow of electrons from one plate of the capacitor to the other, causing a separation of charge between the plates. This separation of charge is what gives rise to the electrical potential energy stored in the capacitor.
When charging a capacitor, the voltage source drives the flow of electrons from the negative terminal to the positive terminal. This flow of electrons is opposed by the capacitor, which acts like a resistor to the flow of current. As a result, the capacitor begins to charge up and the voltage across the capacitor increases until it reaches the voltage of the voltage source. At this point, the capacitor is fully charged and the flow of current stops. The charge on the capacitor can then be used to power an electrical circuit or to store electrical energy for later use.
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The horn of a stationary car emits sounds at a frequency of 440 HZ.What frequency of note will you hear if gov drive toward this car at m/s (Vsound = 340m/s)?
Answer: The frequency of the sound that you will hear depends on the speed of the car relative to the speed of sound. If you are driving towards the stationary car, the speed of the car will be added to the speed of sound, so the frequency of the sound that you will hear will be higher than 440 Hz.
To calculate the frequency of the sound that you will hear, you can use the Doppler effect equation:
f' = f * (Vsound + Vcar) / (Vsound - Vcar)
where f' is the observed frequency, f is the source frequency, Vsound is the speed of sound, and Vcar is the speed of the car.
Plugging in the values given in the question, we get:
f' = 440 * (340 + Vcar) / (340 - Vcar)
This equation will give you the frequency of the sound that you will hear as you approach the stationary car at a speed of Vcar meters per second.
The wavelength of the yellow light from a sodium flame is 589 nm. This light originated from a sodium atom in the hot flame.
(a) In the sodium atom from which this light originated, what was the period of the simple harmonic motion which was the source of this electromagnetic wave? Give your answer in seconds per cycle.
(b) What is the frequency of this light wave? Give your answer in hertz.
From wave speed formula, period is 1.96 × 10^-15 seconds per cycle and the frequency is 5.1 × 10^14 Hertz
What is Frequency ?The frequency of a wave is the number of complete revolution per second made by a vibrating body.
Given that the wavelength of the yellow light from a sodium flame is 589 nm. This light originated from a sodium atom in the hot flame.
(a) In the sodium atom from which this light originated, the period of the simple harmonic motion which was the source of this electromagnetic wave will be found by using the formula
v = λ/T
Where
v = speed of light = 300,000,000 m/sλ = wavelength = 589 × 10^-9 mT = periodSubstitute all the parameters
300000000 = 589 × 10^-9/T
T = 589 × 10^-9/300000000
T = 1.96 × 10^-15 seconds per cycle.
(b) The frequency of this light wave is the reciprocal of its period. That is,
F = 1/T
F = 1/1.96 × 10^-15
F = 5.1 × 10^14 Hertz
Therefore, the period of the wave is 1.96 × 10^-15 seconds per cycle and its frequency is 5.1 × 10^14 Hertz
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You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope, produces a tension of 505 N in the rope
A. If Sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (Recall that the earth is rotating about an axis through its north and south poles.) Consult Appendix F in the textbook.
The Final tension in the rope is 473.4N.
Sneezy doesn't move in circles at the north pole, so there is no acceleration. The earth's rotation, however, causes him to accelerate toward the earth's center at the equator.Set up: Use coordinates with the y direction pointing toward the center of the earth because the earth has mass and a rotational period of T = 24 hr = 8.64 104 sdot. Sneezy's circular motion at the equator's radial acceleration.Sneezy has a= 0 and T = w = 475.0 N (the earth's gravitational pull) at the north pole. Sneezy weighs 48.47 point-47 kilograms. Sneezy is moving in a circle and experiencing radial acceleration as it approaches the equator.The outward tension is less than the true weight at the equator because there is a net inward force, and Sneezy is moving inward at an acceleration.a=0.0337m/s²
T=mg-ma=m[g-a]
=473.4N
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1. How can you make thoughtful spending decision?
2. Why do people pay more for Name Brand products?
EACH questions MUST be answered with a MINIMUM of 2 paragraphs (minimum 5 sentences in a paragraph)
Answer:
How can you make thoughtful spending decision?
To make thoughtful spending decisions, it's important to consider your financial goals and priorities. Start by creating a budget that reflects your income and expenses, and consider what you can afford to spend on non-essential items.
One effective way to make spending decisions is to use the 50/30/20 budgeting rule. This rule suggests that you should allocate 50% of your budget to necessities like housing and groceries, 30% to discretionary spending like entertainment and dining out, and 20% to saving or paying off debt. By following this rule, you can ensure that you're meeting your basic needs while still allowing yourself some flexibility for fun and leisure activities.
It's also a good idea to consider the long-term value of a purchase. For example, investing in a high-quality item that will last for many years may be more cost-effective in the long run than buying a cheaper item that needs to be replaced frequently. Additionally, think about whether a purchase aligns with your values and goals. If it doesn't, it may not be worth the money, even if it seems like a good deal at the time.
Why do people pay more for Name Brand products?
People often pay more for name-brand products for a variety of reasons. One reason is that these products are often perceived as being of higher quality than generic or store-brand products. This perception may be based on the brand's reputation for producing high-quality products, or it may be the result of marketing efforts that position the brand as a luxury or premium option.
Another reason people may be willing to pay more for name-brand products is that they believe these products will bring them status or social recognition. Some people may view certain brands as symbols of success or status, and may be willing to pay a premium to be associated with these brands.
Additionally, some people simply prefer the look, feel, or other aspects of name-brand products, and are willing to pay more for the product they feel best meets their needs or preferences. In some cases, people may be willing to pay more for name-brand products simply because they are more convenient or easier to find than generic alternatives.
An astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.850c. Which of the following effects would she experience?
(Select all that apply.)
A She would feel heavier.
B She would find it harder to breathe.
C Her heart rate would change.
D Some of the dimensions of her spacecraft would be shorter.
E None of those answers is correct
Due to traveling in a spacecraft in outer space in a straight line at a constant speed of 0.850c, an astronaut experiences: she would feel heavier, her heart rate would change, some of the dimensions of her spacecraft would be shorter.
What is special relativity?The theory of special relativity explains how speed affects space, time, and mass. Small amounts of mass (m) can be interchangeable with large amounts of energy (E), as defined by the classic equation E = mc^2, according to the theory, which offers a means for the speed of light to define the link between energy and matter.
When talking about extremely high energy, incredibly fast speeds, and astronomical distances without the difficulties of gravity, special relativity is typically employed.
The mass of an object and the energy needed to move it both grow unlimited as it gets closer to the speed of light. This implies that no substance can move more quickly than light does.
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What kind of machines do astronautical engineers work with?
The astronautical engineers work with machine that fly outside the Earth's atmosphere.
What is aerospace engineering?
The design, development, testing, and production of aircraft, spacecraft, and associated systems and equipment fall within the purview of aerospace engineering. The two main and overlapping sections of the field—aeronautical engineering and astronautical engineering—have historically concentrated on issues relating to air and space flight.
The theory, technique, and application of flight within the earth's atmosphere are the main topics of aeronautical engineering.The science and technology of spacecraft and launch vehicles are the main areas of interest in astronautical engineering.Learn more about aerospace and aeronautical engineering here:
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Specify the SI unit for the penetration coefficient of ultrasonic waves:
m-1
m/s
non-dimensional quantity
The SI unit for the penetration coefficient of ultrasonic waves is m⁻¹.
option A is the correct answer.
What is penetration coefficient?Penetration coefficient describes the amount of particles reduced from the infiltration of outdoor particles due to the filtering effect of the building envelope.
Ultrasonic waves describes sound waves with frequencies higher than the upper audible limit of human hearing.
The SI unit of penetration coefficient of ultrasonic waves is expressed in either decibels per meter ( dB/mv ), or nepers per meter ( Np/m ) or equivalent to per meter ( m⁻¹ ).
Thus, the SI unit for the penetration coefficient of ultrasonic waves is per meter ( m⁻¹ ).
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The elevation of city A is 80 feet below sea level; the elevation of city C is 16 feet below sea level. The elevation of city D is 1 over 2 of the elevation of city C.
Part A: Write an expression to represent the elevation, in feet, of city D. (5 points)
Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
The expression of elevation and solution of the expression is as below -
[tex][X-80x] + [X-16c] +2d/c=0\\x=2c-d[/tex]
All elevations are measured from sea level, which is defined as a height of 0 feet. Positive elevations are found in locations on Earth that are higher than sea level, and negative elevations are found in locations that are lower. As a result, Death Valley is situated below sea level at a height of -282 feet.Distance above sea level is known as elevation. In most cases, elevations are expressed in meters or feet. On maps, they can be represented by contour lines that link points of the same elevation, by color bands, or by numbers that indicate the precise elevations of specific points on the surface of the Earth.On Earth, sea level serves as the reference point for determining elevation and depth. The ocean is a single, unbroken body of water, so its surface tends to seek uniformity everywhere it is. In relation to the nearby land, the sea level is determined. Land elevation can fluctuate over time, just like that of the ocean.To learn more about Land elevation -
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in the context of the roles of nmda receptors and ampa receptors in long-term potentiation (ltp), which of the following occurs during weak electrical stimulation of the presynaptic neuron?
That which occurs during weak electrical stimulation of the presynaptic neuron is;
Weak activity of the presynaptic neuron leads to modest depolarization and calcium influx through NMDA receptors.
what are NMDA receptors?
The N-methyl-D-aspartate receptor, is described as a glutamate receptor and ion channel found in neurons.
The NMDA receptor is one of three types of ionotropic glutamate receptors, the other two being AMPA receptors and kainate receptors.
In the context of the roles of nmda receptors and ampa receptors in long-term potentiation (ltp), weak activity of the presynaptic neuron leads to modest depolarization and calcium influx through NMDA receptors.
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Suppose you observe a star orbiting the galactic center at a speed of 1100 km/s in a circular orbit with a radius of 22 light-days. Part A What would your estimate be for the mass of the object that the star is orbiting? Express your answer using two significant figures.
According to the given statement M = 18.67 x 10⁶ Solar masses of the object that the star is orbiting.
How speed does physics move?The rate at which the position of an object shifts in any direction. Speed is defined as the ratio of the distance traveled to the time required to cover that distance. Speed is a numerical number since it just has a path and no magnitude.
Briefing:
M = Mass of Object = ?
v = orbital speed of star = 1100 km/s = 1100000 m/s
G= 6.67 x 1011 N.m2/kg is the universal gravitational constant,
r = distance between star and object = (22 light-days)(2.59 x 10¹³ m/1 light-day) = 5.698 x 10¹⁴ m
Therefore,
[tex]M=\frac{(1100000 \mathrm{~m} / \mathrm{s})^2\left(5.698 \times 10^{14} \mathrm{~m}\right)}{6.67 \times 10^{-11} N . \mathrm{m}^2 / \mathrm{kg}^2}[/tex]
M = (9.39 x 10³⁷ kg)(1 solar mass/ 1.989 x 10³⁰ kg)
M = 18.67 x 10⁶ Solar masses
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a square conductor moves through a uniform magnetic field. which of the figures shows the correct charge distribution on the conductor?.
The figure D shows the correct charge distribution on the conductor. The magnetic field is out of the page and velocity is upwards.
A substance as well as material that permits the flow of electricity is known as an electrical conductor. When voltage was provided, electric charges carriers, often electrons as well as ions, travel effortlessly between atom to atom inside a conductor.
Insulators were substances that prevent electricity from passing through them. Insulators are employed as a defense against the potential dangers of electricity because they oppose electric currents. Glass, air, wood, plastic, as well as rubber are just a few characteristics of insulators.
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What is the repulsive force between two pith balls that are 18.5 cm apart and have equal charges of −30.5 nC?
The repulsive force is 2.4435 X 10 ^ -4 N between the two pith balls with charge equale to -30.5 nC and distance of 18.5 cm.
What is Coulomb's Law?
According to this law, charges repel one another and attract one another with a force that is inversely proportional to the square of the distance between them and proportional to the product of the charges.
According to Coulomb's law, the force of attraction or repulsion between two charged bodies should be directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The image shows the calculation of force between the two pith balls using Coulomb's law.
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A cello string 0.75 m long plays a fundamental frequency of 220hz . The wavelength and speed of a wave on the string is
the wavelength was found to be1.5m and the speed was found to be 330m/s
define wavelength ?
The distance over which a periodic wave's form repeats is known as the wavelength in physics. It is a property of both travelling waves and standing waves as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings. The spatial frequency is the reciprocal of wavelength. The Greek letter lambda is frequently used to represent wavelength. The term wavelength is also occasionally used to refer to modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids.
A string's length must be half its wavelength for the fundamental frequency to be present. This is,
L is the string's length, and y is its wavelength, therefore 1/2y = L.
y = 2L = 2x0.75 = 1.5 m as a result.
and y=v/f
v=y*f
=15x220
=330 m/s
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Using the technique of main-sequence fitting to determine the distance to a star cluster requires that _____.
we have telescopes powerful enough to allow us to identify the spectral types of main-sequence stars of many masses in the cluster
To calculate the distance to a star cluster using the main-sequence fitting method, we must first be able to build the cluster's main sequence in order to "fit" it to the standard main sequence.
The vast collections of stars known as stellar clusters. There are two primary categories of star clusters: globular clusters, which are gravitationally coupled tight groups of stars between 10,000 and 500,000 years old, and open clusters, which are more loosely bound groups of stars, typically with fewer than a few hundred members and frequently extremely young. While open clusters are being disrupted over time by the gravitational pull of massive molecular clouds as they move through the galaxy, cluster members will still move through space largely in the same direction even though they are no longer gravitationally bound; at this point, they are known as a stellar association, also known as a moving group.
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A train travels with a constant speed of 20.0m/s for 8.00s. Determine all unknowns and answer the following question(s).
Answer: Since the train travels with a constant speed, it does not experience any acceleration. The magnitude of the train's acceleration is 0 m/s^2.
The distance the train travels during this time can be calculated using the formula d = vt, where d is the distance, v is the velocity, and t is the time. Plugging in the values given, we have:
d = 20.0 m/s * 8.00 s = <<20*8=160>>160 m
Therefore, the train traveled a distance of 160 meters during this time.
A 1.0 kg block is pushed 20 m at a con-
stant velocity up a vertical wall by a constant
force applied at an angle of 26.0° with the
horizontal, as shown in the figure.
The acceleration of gravity is 9.81 m/s².
1 kg
Drawing not to scale.
If the coefficient of kinetic friction between
the block and the wall is 0.20, find
a) the work done by the force on the block.
Answer in units of J.
Answer in units of J
part 2 of 3
b) the work done by gravity on the block.
Answer in units of J.
c) the magnitude of the normal force between the block and the wall.
A 1.0 kg block is pushed 20 m at a constant velocity up a vertical wall by a constant force applied at an angle of 26.0° with the horizontal.The acceleration of gravity is 9.81 m/s². Thus, calculated values are:
a) the work done by the force on the block: 19.62 J
b) the work done by gravity on the block: -19.62 J
c) the magnitude of the normal force between the block and the wall: 17.7 N
What is acceleration?Anything that causes a change in velocity is referred to as an acceleration. You can only accelerate by changing the speed, direction, or both as velocity is a function of both speed and direction.
let m = 1.0 kg
d = 2.0 m
θ = 29°
let, F is the applied force.
let, Fx and Fy are components of F.
As the block is moving upward with constant velocity, net force acting on the block must be zero.
F×nety = 0
or, Fy - m×g = 0
or, Fy = m×g
or, Fy = 1×9.81 N
or, Fy = 9.81 N
a) The work done by the force on the block, WF = Fy×d×cos(0°)
= (9.81×2) J
= 19.62 J
b) The work done by gravity, Wg = Fg×d×cos(180°)
= 1 ×9.81×2×(-1)
= -19.62 J
c) we know, Fy = F×sin(29°)
Fx = F×cos(29°)
Fy/Fx = tan(29°)
Fx = Fy/tan(29°)
Fx = 9.81/tan(29)
Fx = 17.7 N
now use, Fnetx = 0
or, Fx - N = 0
or, N = Fx
or, N = 17.7 N
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Find the Thevenin equivalent of the circuit with respect to Z - Express the answer in terms of the Thevenin voltage (Vr), short-circuit current (ise), and Thevenin impedance (ZT).
The Thevenin Voltage (Vr) of the circuit with respect to Z is 6V.
Thevenin Voltage (Vr) is the equivalent voltage source in a Thevenin equivalent circuit. It is the open circuit voltage that exists between the two terminals of a circuit when all other elements are removed.
The Thevenin equivalent of the above circuit with respect to Z is Vr
= 6V, ise = 0.5A, and ZT = 4Ω.
Calculate the Thevenin Voltage (Vr)
Step 1a: Calculate the total resistance in the circuit
Rtotal = (2Ω + 3Ω) || (4Ω + 5Ω)
= (2Ω*5Ω)/(2Ω + 5Ω) + 4Ω
= 7 Ω
Step 1b: Calculate Thevenin Voltage (Vr):
Vr = (Rtotal/(Rtotal + 4Ω))*6V
= (7Ω/(7Ω + 4Ω))*6V = 6V
Calculate the Thevenin Impedance (ZT)
ZT = Total = 7Ω
Calculate the short-circuit current (ise)
ise = Vr/ZT = 6V
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Which of the models predict that galaxies should be getting farther apart now? (Keep in mind that now is located at at time=0years on the graph.)acceleratingcoastingcriticalrecollapsing
Galaxies should be getting farther apart right now, according to the accelerating coasting critical re collapse model, which is positioned on the graph at time=0 years.
In mechanics, acceleration is the rate at which an object's velocity with respect to time changes. The vector quantity of accelerations (in that they have magnitude and direction). The direction of the net force imposed on an object determines its acceleration in relation to that force. The rate of change in an object's position relative to a frame of reference is called velocity, and it depends on time. An object's speed and direction of motion are specified by its velocity.
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In the space below, draw and label a circuit diagram that has a 24.0 V power supply and two 10.0 Ω resistors connected in parallel
Thank you!
Here is the diagram,
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If a roadway is banked at the proper angle, a car can round a corner without any assistance from friction between the tires and the road. Find the appropriate banking angle for a 900-kg car traveling at 20.5 m/s in a turn of radius 85.0 m.
Answer:
N cos θ = m g where N is the normal force
N sin θ = m v^2 / R
tan θ = v^2 / (R g) dividing equations
tan θ = 20.5^2 / (85 * 9.80) = .505
θ = 26.8 deg banking angle required
the width of a rectangle is 5 feet longer than four times its length, and its area is 26 . if you use l to represent the length of the rectangle, then an expression representing the width is w = ___ The length of the rectangle is feet. feet and the width is ___
The expression representing width is w = 3l +5, where l = length. When area is 26, the equation for length is 4[tex]l^{2}[/tex]+5l -26=0.
Rectangle is a parallelogram with its opposite sides equal. We can find area of rectangle using the formula,
Area is defined as the extent occupied by an object in 2D plane. The plane may be flat or curved region. The S.I. unit of area is square meter.
Area = length × width
So, we have length = l,
as per the given information in the question,
width = w = 4l+5
So, area, a = (4l+5) ×l= 26
4[tex]l^{2}[/tex] +5l = 26
4[tex]l^{2}[/tex] +5l-26 = 0
Solving this equation, we can find the value of l and then width.
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1) In the nuclear reaction shown, one deuterium (hydrogen- 2 ) and one tritium (hydrogen-3) fuse to form one helium-4 and one neutron.
Data: Hydrogen-2 mass: 3.34450 10⁻²⁷ kg
Hydrogen-3 mass: 5.00827 10⁻²⁷ kg
Helium-4 mass: 6.64648 10⁻²⁷ kg
Neutron mass: 1.67493 10⁻²⁷ kg
a) What is the total mass of the pieces going into the reaction?
b) What is the total mass of the pieces coming out of the reaction?
c) How much energy is converted from rest energy to other forms of energy if one mole of deuterium (about 2.0 g ) and one mole of tritium (about 3.0 g ) are converted?
When helium-3 and deuterium combine in this nuclear process, regular helium and a proton are produced, wasting less energy and making the reaction easier to contain.
What energy forms of energy if one mole of deuterium?The fusion of deuterium and tritium is the most promising of the hydrogen fusion processes that make up the deuterium cycle.
The reaction produces 17.6 MeV of energy, but in order to induce fusion, one must tunnel through the coulomb barrier, which requires extremely high temperatures.
Therefore, 8.4 1020 joules of energy would be released if one ton of deuterium were to undergo the fusion reaction with tritium. This is comparable to the 2.9 1010 joules of energy found in a ton of coal.
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A student runs a simulation of a skateboarder going back and forth on a U-shaped ramp. The skateboarder begins with 1,560 joules of potential energy. The bar graph shows the energy of the skateboarder system at the end of the simulation. What are the potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation?
PE = 520 J; KE = 520 J.
PE = 0 J; KE = 1,560 J.
PE = 0 J; KE = 0 J.
PE = 780 J; KE = 0 J.
The potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation is PE = 0 J; KE = 1,560 J. Hence option 2 is correct.
What is potential energy?Potential energy is defined as the energy stored that an object can hold due to its position in relation to other objects, internal tensions, electric charge, or other circumstances. One of the two types of energy is potential energy, which is the latent energy in an object at rest.
The skateboarder's potential energy is transformed into kinetic energy, also known as the energy of motion, as her position along the track and speed vary. The system's total potential energy determines the maximum amount of kinetic energy the skateboarder can possess.
Thus, the potential energy (PE) and kinetic energy (KE) of the skateboarder at the end of the simulation is PE = 0 J; KE = 1,560 J. Hence option 2 is correct.
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According to Newtonian mechanics, the momentum of an interplanetary express bus is p=mv. According to relativity, it is p=γmv.A.) How does the actual momentum of the bus moving at 0.98 c compare with the momentum it would have if classical mechanics were valid? Express your answer using two significant figures.prel/pNewt=____B) How does the momentum of an electron traveling at 0.98 c compare with its classical momentum? Express your answer using two significant figures.prel/pNewt=____
Part A: Y is 7.1 when v = 0.98c.
Part B: When compared to what would be predicted if classical mechanics was accurate, the bus's momentum is much more than seven times greater.
Explain the term Newtonian mechanics?The foundation of Newtonian mechanics is the application of Newton's Laws of Motion, which make the assumption that space, time, and mass are absolute concepts and that motion occurs in an inertial frame.Part A: Actual momentum of the bus moving at 0.98 c.
velocity of interplanetary express bus v = 0.98 c.
Thus,
Y = 1/√(1 - v²/c²)
Y = 1/√(1 - (0.98c)²/c²)
Y = 7.07
Thus, Y = 7.1 for v = 0.98c.
Part B: Momentum of an electron traveling at 0.98 c
As Y = 7.1 for v = 0.98c.
Thus, when compared to calculations made using classical physics, the bus's momentum is more than seven times greater.
The same holds true for electrons and other fast moving objects.
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A bowler rolls a 4.5 kg ball down the lane. The ball hits a 0.25kg bowling pin and accelerates the pin away from it at 6.6 m/s2. What is the acceleration felt by the ball (in m/s2)
Answer: 0.37 m/s2
Explanation:
This is a Newton's 3rd Law of Motion problem. The force exerted on the pin by the ball is equal and opposite to the force exerted by the pin on the ball. F = ma
let x = acceleration of the ball after it hits the pin
(4.5 kg)(x) = (0.25 kg)(6.6 m/s2)
x = ((0.25 kg)(6.6 m/s2)) / (4.5 kg) = 1.65 / 4.5 = 0.37 m/s2
Retrograde motion, which confused astronomers and mathematicians for centuries, is actually caused by a planet that is?
Retrograde motion, which confused astronomers and mathematicians for centuries, is actually caused by a planet that is on the same side of the Sun as the Earth, the planet catches up with, and passes the Earth ( planets revolving counterclockwise around the Sun).
What is retrograde motion?This refers to the movement of a planet in a direction opposite to that of other bodies within its system, as can be seen from a particular viewing point.
When viewed from a position in space north of the solar system all the major planets revolve counterclockwise around the Sun. But Venus and Uranus rotate counterclockwise on their own axes; these two, therefore, have retrograde rotation.
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you take a running leap, leaving the ground with a speed 6.00 m/s at an anglle 40.0 degrees above horizontal.
The maximum height reached while running is calculated to be 0.75m.
The formula for the maximum height of the projectile motion is given by
H = u² (sin θ)²/2g
where, θ is the angle made with the horizontal
H is the maximum height reached
g is the acceleration due to gravity
u is the initial velocity
Given that, u = 6 m/s
g = 10 m/s²
θ = 40°
Substituting the above values, we have,
H = u² (sin θ)²/2g = 6² * (sin 40°)² / 2 * 10 = 36* 0.414/20 = 0.75 m
Thus, the maximum height reached while running is 0.75m.
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A gold sphere of radius R=100 μm and density 19g/cm^3 falls through water. Given the viscosity of water is about 10^-3 Pa s and the density of water is 1.0g/cm^3, calculate the terminal velocity of the sphere. The viscous drag coefficient for a sphere is α=6π.
Don't forget to consider the buoyant force on the sphere when calculating net force!
The terminal velocity of gold sphere is 39.2 cm/s
What is terminal velocity?Terminal velocity is the maximum velocity attainable for an object as it falls through a fluid.
How to calculate the terminal velocity of the gold sphere?The terminal velocity of the gold sphere is given by v = 2gr²(ρ - σ)/9η where
g = acceleration due to gravity = 9.8 m/s², r = radius of sphere = 100 μm = 100 × 10⁻⁶ m = 10⁻⁴ m = 10⁻² cm, ρ = density of sphere = 19 g/cm³, σ = density of water = 1.0 g/cm³ and η = viscosity of water = 10⁻³ Pa-sSo, susbtituting the values of the variables into the equation, we have that
v = 2gr²(ρ - σ)/9η
v = 2 × 9.8m/s²× (10⁻² cm)²(19 g/cm³ - 1.0 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 9.8 m/s² × 10⁻⁴ cm² × (18 g/cm³)/(9 × 10⁻³ Pa-s)
v = 2 × 980 cm/s² × 10⁻⁴ cm² × 2 g/cm³/(1 × 10⁻³ Pa-s)
v = 3920 g/s² × 10⁻⁴/(1 × 10⁻³ Pa-s)
v = 392 cm/s × 10³ × 10⁻⁴
v = 392 × 10⁻¹ cm/s
v = 39.2 cm/s
So, the terminal velocity is 39.2 cm/s
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a system consists of three particles, each of mass 7.50 g, located at the corners of an equilateral triangle with sides of 35.0 cm.
The magnitude of net force exerted on each one of the three masses is 0.53 * 10⁻¹³ N.
Given, m₁ = m₂ = m₃ = 7.5 g = 7.5 * 10⁻³ kg
Sides of the triangle = 35 cm = 35 * 10⁻² m
As the masses are the same and are at the corners of an equilateral triangle, two equal forces will act on each of the masses.
The forces on mass 1 due to mass 2 and due to mass 3 will be
| F₁₂| = Gm²/r²
⇒ 6.67* 10⁻¹¹* (7.5 * 10⁻³)²/(35 * 10⁻²)² = 375.19* 10⁻¹⁷/(35²* 10⁻⁴)
⇒ 0.306 * 10⁻¹³ N
| F₁₂| = | F₁₃| = 0.306 * 10⁻¹³ N
The magnitude of the net force on mass 1 can be found by the parallelogram law formula giving the magnitude of the resultant of two forces, given their magnitudes and the angle in between:
F₁ = | F₁₂ + F₁₃|
F₁ = √(| F₁₂| ² + | F₁₃|² + 2* | F₁₂|* | F₁₃| cos 60°) = √3 (F)
⇒ √3 * 0.306 * 10⁻¹³ = 0.53 * 10⁻¹³ N
The magnitude of force on each of the mass will be same.
Thus, the magnitude of force on each mass on the corners of the triangle will be 0.53 * 10⁻¹³ N.
The question is incomplete. The continuation to the above question is 'Find the magnitude of net force exerted on each of the three masses.'
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