According to the above statement, each charge has a magnitude of 2.23μC according to Coulomb's law.
What does Coulomb's law aim to achieve?When two items behave as point charges, the force between them may be accurately described by the Coulomb's law equation. When interacting with other charged objects, a spent conducting sphere behaves as though its whole charge were concentrated in its center. According to Coulomb's law, the force F between two triangular charges, Q1 and Q2, in a void is proportional to the inverse of their separation, r, and proportional to their product, Q1.
Coulomb's law states:
F = KQ²/r²
18 = (9*10⁹)*Q²/0.07²
Q = 2.23*10⁻⁶C or 2.23 μC
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let the samples of the noise voltage, v (nt) be jointly gaussian random variables. show that x(t) is a gaussian process.
Since x(t) is a linear function of v(nt) which is jointly Gaussian, and the mean of x(t) is a linear function of t, x(t) is also a Gaussian process.
What is Gaussian process?A Gaussian process is a stochastic process whose realizations are Gaussian random variables. To show that x(t) is a Gaussian process, we need to show that:The mean of x(t) is a linear function of t.The covariance function of x(t) is a valid covariance function.The mean of x(t) is defined as E[x(t)], where E[] denotes the expectation operator. Since the noise voltage v(nt) is jointly Gaussian, it follows that x(t) = v(nt) is also Gaussian, and thus its mean is a linear function of t.The covariance function of x(t) is defined as C(s,t) = E[(x(s) - E[x(s)]) (x(t) - E[x(t)])].Since v(nt) is jointly Gaussian, the covariance function of x(t) is also a valid covariance function.Therefore, x(t) is a Gaussian processx(t) = v(nt) is jointly GaussianSince x(t) is a linear function of v(nt) which is jointly Gaussian, and the mean of x(t) is a linear function of t, x(t) is also a Gaussian process.The covariance function of x(t) is a valid covariance function, as it is derived from jointly Gaussian variables.To learn more about Gaussian process refer:
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define, identify, describe and understand various heat sources capable of being a source of ignition.
When anything, a process, or an event may ignite or transport energy into a medium to cause combustion, it is said to be a source of ignition. This standard permits the use of open flames as a source of ignition.
Friction, hot surfaces, sparks, and static electricity. bursts of lava and friction-based electricity warmers. Sun Everyone who lives on Earth gets most of their heat from the sun. For plants to prepare their food, they require energy from the sun. The warmth of the sun makes it possible for humans to survive. Fuel ignition results in the release of energy. Heat is the energy that is transmitted when two objects with different surface temperatures touch. system of the sun.
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the chart shows different speeds at which theoretical spacecraft are traveling horizontally. the speeds are represented as percentages of the speed of light the spacecrafts are traveling, where 0.20c
The figure below displays various horizontal spaceship travel speed, with y being the farthest away from zero. Y is the solution
A spacecraft has never traveled faster than 163 km/s (586,800 km/h; 364,660 mph), which was accomplished by the Parker Solar Probe on November 20, 2021, at 21:25:24 UTC. The probe received a gravity boost from a fly-by of Venus on October 16 that tightened its orbit, allowing it to achieve this speed at perihelion (the closest point in its elliptical orbit around the Sun). It came within 5,307,594 miles (8,541,744 km) of the surface of the Sun. Until the Parker Solar Probe's 17th perihelion on September 27, 2023, this record will hold.
For instance, a spacecraft leaving the surface of the Earth has to be traveling at a speed of about 40,000 kilometers per hour (25,000 miles per hour), or approximately 11 kilometers per second (7 miles per second), in order to enter orbit.
The correct question is:
The chart shows different speeds at which theoretical spacecraft are traveling horizontally. The speeds are represented as percentages of the speed of light the spacecraft are traveling, where 0.20c = 6 × 107 m/s.
Which spacecraft appears the longest to an outside observer?
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A car accelerates uniformly from rest and reaches a speed of 33.8 m/s in 4.7s the diameter of the tire is 64.6 cm find the number of revolutions the tire makes during this motion
The tire makes approximately 280.57 revolutions during this motion.
What are the revolutions?Generally, To find the number of revolutions the tire makes during this motion, we first need to find the distance traveled by the car.
Distance = Initial velocity x time + (1/2) x acceleration x time^2
Since the car starts at rest, the initial velocity is 0 m/s.
The acceleration is uniform, so we can use the formula:
Final velocity = Initial velocity + acceleration x time
In this case, the final velocity is 33.8 m/s, and the time is 4.7s.
So, acceleration = (33.8 m/s - 0 m/s) / 4.7s
= 7.19 m/s^2
Now we can use this value of acceleration to find the distance traveled:
Distance = 0 m/s x 4.7s + (1/2) x 7.19 m/s^2 x (4.7s)^2
= 570.98 m
To find the number of revolutions of the tire, we divide the distance traveled by the circumference of the tire.
The circumference of the tire is equal to the diameter x pi.
Circumference = 64.6 cm x 3.14
= 203.5 cm
Number of revolutions = Distance / Circumference
= 570.98m / (203.5 cm)
=280.57
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Regarding memory, conscious is to _____ as unconscious is to _____. Please choose the correct answer from the following choices, and then select the submit answer button. Answer choices explicit memory; implicit memory shallow processing; deep processing echoic memory; iconic memory recognition; recall
Regarding memory, conscious is to explicit memory as unconscious is to implicit memory.
A charged rod is brought near a negatively charged pith ball electroscope. What conclusion would you draw about the charge on the rod if pith ball moves away from the rod ?O PositiveO NegativeO No chargeO Cant say
The negatively charged rod attracts positive charges and repels negative charges when it is located closer to the electroscope.
What happens when a neutral pith ball is in close proximity to a negatively charged rod?The pith balls' charges polarize when ever an electrified rod is introduced in close proximity to them. They may pick up this very same sign charge if they come into contact the with charged rod. The pith balls act like siblings and avoid touching one another because like charges repel one another.
What is the electroscope's conclusion?We can infer from all of these statistics that charge induction, underlying atomic and molecular structure of something like the metal components, and the idea that an electroscope operates.
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When a right force is applied to a dresser to push it across a room, what force works in the opposite direction of the applied force? gravity normal friction tension
Friction force works in the opposite direction of the applied force. So, the correct option is (C).
What is Friction?Friction is defined as the force opposing the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are many types of friction such as dry friction which is a force that opposes the relative lateral motion of two solid surfaces in contact.
The force of friction is described as the resistance to motion that arises when two objects rub against each other, so this force always acts in the opposite direction to the motion of an object.
Thus, Friction force works in the opposite direction of the applied force. So, the correct option is (C).
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The scalar product of the vectors A=3i+4j-5k and B=-i+j-2k
The scalar product of the vectors A = 3i + 4j - 5k and B = -I + j - 2k is -9.
The scalar product (also known as the dot product) of two vectors is a scalar quantity that can be calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The formula to calculate the scalar product of two vectors A and B is:
A.B = |A| |B| cos(theta)
To find the scalar product of two vectors we can also use the following formula:
A.B = (A.i) (B.i) + (A.j) (B.j) + (A.k) (B.k)
where A.i, A.j, A.k, B.i, B.j, B.k are the projections of vectors A and B on the i, j, and k axis respectively.
So, in this case, we have:
following A = 3i + 4j - 5k and B = -i + j - 2k
A.B = (3)(-1) + (4)(1) + (-5)(-2) = -3 + 4 - 10 = -9
Therefore, the scalar product of the vectors A = 3i + 4j - 5k and B = -I + j - 2k is -9.
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A bicycle tire is spinning clockwise at 2.30 rad/s. During a time period =1.95 s, the tire is stopped and spun in the opposite direction, also at 2.30 rad/s. Calculate the change in the tire’s angular velocity and the tire’s average angular acceleration
If a bicycle tire is spinning clockwise at 2.30 rad/s. the change in the tire’s angular velocity and the tire’s average angular acceleration is: 2.63 rad/s².
How to find the average angular acceleration?Change in angular velocity
Δw = wf -wi
Δw = (2.30 rad/s) - (-2.30 rad/s)
= 4.60 rad/s
w_ is negative because it is in the clockwise direction.
Average angular acceleration:
Average angular acceleration = 4.60 rad/s/ 1.75s
Average angular acceleration = 2.63 rad/s²
Therefore the average angular acceleration is 2.63 rad/s².
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hardening parameter is assumed to be related to some measure of the plastic strains via the equation ___
Hardening parameter is assumed to be related to some measure of the plastic strains via the equation [tex]$\sigma_{y0} = K \varepsilon_p^m$[/tex].
What is parameter?Parameter is a special kind of variable used in a function or subroutine to refer to one of the pieces of data provided as input to the function. It is a value that controls the behaviour of a function. It can be used to provide a certain type of flexibility in the function, allowing it to act differently in different situations.
where [tex]$\sigma_{y0}$[/tex] is the hardening parameter, [tex]$K$[/tex] is a material constant, and [tex]$m$[/tex] is the hardening exponent. This equation is used to determine the relationship between the yield stress and the plastic strain, providing a useful tool for predicting the behavior of a material under cyclic loading.
The strain hardening increases the yield strength of the material.
and
Modulus of toughness = [tex]\dfrac{\text{Yieldstress}^2}{2(\text{{Youngs Modulus)}}}[/tex]
Hence, if the yield stress increases, the modulus of toughness increases too.
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A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward with a speed of 10m/s, with respect to the train at an angle of 60 derajat to the horizontal. The boy has to move forward by 1.15m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^2 , is:
The acceleration of the train is 5 [tex]m/[/tex] [tex]s^{2}[/tex] .
We can clearly see that the ball will follow a parabolic path so we break it into vertical and horizontal axis
The boy throws the ball and gives it a vertical velocity on which constant acceleration 'g' acts
For the vertical movement
[tex]S = ut - \frac{1}{2} g t^{2}[/tex]
[tex]0 = 10 sin 60[/tex]° - [tex]\frac{1}{2} 10 t^{2}[/tex]
[tex]t = \sqrt{3} s[/tex]
We know that the ball already has a horizontal velocity equal to the moving train's velocity.
For the vertical movement
[tex]S = ut + \frac{1}{2} a t^{2}[/tex]
[tex]1.15 = 10 cos 60[/tex]° [tex]\sqrt{3} \ \frac{1}{2} \ a \ 3[/tex]
[tex]a = 5 m/ s^{2}[/tex]
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A horizontal string tied at both ends is vibrating in its fundamental mode. The traveling waves have speed v, frequency f, amplitude A, and wavelength λ.
A) Calculate the maximum transverse velocity of the point located at x=λ/2.
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. vmax =
B) Calculate the maximum transverse acceleration of the point located at x=λ/2.
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. amax =
C) What is the amplitude of the motion at the point located at x=λ/2?
Express your answer in terms of the variables v, f, A, λ, and appropriate constants.
ASW = D) How much time does it take the string to go from its largest upward displacement to its largest downward displacement at the point located at x=λ/2?
Express your answer in terms of the variables v, f, A, λ, and appropriate constants. t =
What happens
to the energy
level of particles
when melting
occurs?
A. it decreases
B. it increases and
decreases rapidly
C. it increases
D. it stays the same
It decreases happens to the energy level of particles when melting occurs. So, option (a) is correct.
What is energy level?
The fixed distances between the atom's nucleus and the location of electrons are known as energy levels, sometimes known as electron shells. A tiny, positively charged nucleus at the center of an atom is surrounded by electrons, which are tiny, negatively charged particles. A staircase's steps can be compared to energy levels.
What is melting?
Melting is the transformation of a solid into a liquid under the influence of heat. When a solid is impure, it often melts over a wide range of temperatures below the melting point of the main component. In a pure crystalline solid, this process takes place at a specific temperature known as the melting point.
Therefore, decreases happens to the energy level of particles when melting occurs. So, option (a) is correct.
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PART ONE
A square plate is produced by welding together four smaller square plates, each of side a. The weight of each of the four plates is shown in the figure.
Find the x-coordinate of the center of gravity (as a multiple of a).
Answer in units of a.
PART TWO
Find the y-coordinate of the center of gravity (as a multiple of a).
Answer in units of a.
(a) The x coordinate of the center of the gravity is 1.48 a
(b) The y coordinate of the center of the gravity is 1.33 a.
What is the direction of the center of the gravity?
The direction of the weights of the four square plates is calculated as follows;
θ = arc tan ( dy / dx )
where;
dy is the displacement in vertical directiondx is the displacement in the horizontal directiondy = 2a
dx = 2a
θ = arc tan ( dy / dx )
θ = arc tan ( 2a / 2a )
θ = arc tan ( 1 )
θ = 45⁰
The x coordinate of the center of the gravity is calculated as follows;
x = ( m₁x₁ + m₂x₂ ) / ( m₁ + m₂ )
x = ( (90 + 50)a + (40 + 90)2a ) / ( 90+50 + 40 + 90 )
x = (140a + 130(2a) ) / ( 140 + 130 )
x = (140a + 260a ) / (270)
x = 1.48 a
The y coordinate of the center of the gravity is calculated as follows;
y = ( m₁y₁ + m₂y₂ ) / ( m₁ + m₂ )
y = ((90 + 90)a + (50 + 40)2a ) / (90+90 + 50+40 )
y = (180a + 90(2a) ) / (180 + 90)
y = (180a + 180a) / (270)
y = (360a) / ( 270)
y = 1.33 a
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figure 21-42 shows a long, nonconducting, massless rod of length l, pivoted at its center and balanced with a block of weight w at a distance x from the left end. at the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. a distance h directly beneath each of these spheres is a fixed sphere with positive charge q. (a) find the distance x when the rod is horizontal and balanced
Let the distance of weight W from the bearing is x3,
Then as we can see weight W is trying to give a clockwise rotation around the bearing similarly the charge +q is also applying the same clockwise torque because of the repulsion from the charged sphere beneath it.
But +2q charge torque is in a counter-clockwise direction. thus to make the rod balanced torque from weight W and +q charge must be balanced by the torque by +2q charge.
Let F and F1 be the force on +q and +2q respectively because of the fixed +Q charge.
as, F= kq[tex]\frac{Q}{h^2}[/tex] and F1= 2kq[tex]\frac{Q}{h^2}[/tex] =2F
as for the balance of the rod
FL/2+ Wx3 = 2FL/2
Wx3= FL/2
x3 = kqQ[tex]\frac{L}{2Wh^2}[/tex]
x= [tex]\frac{L}{3} +x3[/tex]
x= [tex]\frac{L}{2} * (kq\frac{Q}{Wh^2} +1)[/tex]
so put the weight above x to balance the rod.
Maximum such notions of distance, both physical and metaphorical, are formalized in arithmetic the use of the perception of a metric place.inside the social sciences, distance can test with a qualitative size of separation, along with social distance or psychological distance.
Distance is a numerical or every so often qualitative dimension of how a long way aside gadgets or points are. In physics or regular utilization, the space may seek advice from a physical period or an estimation primarily based on different criteria (e.g. " counties over"). due to the fact spatial cognition is a wealthy source of conceptual metaphors in human thought, the time period is also often used metaphorically to mean a measurement of the quantity of distinction between similar objects (which includes statistical distance between possibility distributions or edit distance among strings of text) or a degree of separation (as exemplified by using the gap between human beings in a social community).
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Two balls are dropped on the floor from the same height. The balls are made up of different types of rubber so that one bounces back at nearly the same height while the other does not bounce at all. Assuming both balls have the same mass, which ball experiences the greater impusle in colliding with the floor? Why?
The balloon will bounce a highest when two balls of equal weight are placed from the same location as a result of its greatest elasticity. The rubber ball is squashed or squeezed when it strikes the ground.
Explain what elasticity is.Elasticity is the capacity of a material body to regain its original dimensions and shape after being deformed by external forces. This capability is referred to as elastic behavior (or response) in a body. Hoare's rule.
What are some examples of elasticity?When anything is stretched or squeezed, it can regain its original shape thanks to its elastic properties. A rubber, for instance, can quickly restore its shape after being stretched out significantly.
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You are handed an apple that has a mass of 102g. To get a better idea of what different pressures feel like, you rig up several systems where the force of the apple is distributed over objects of different size. a) What is the weight of this apple? (in units of N and lbf) b) You stick a square-ended toothpick into the apple and balance it on your finger. What is the pressure of the apple (in units of Pa, psi, and atm) that you feel on your finger? c) You cut the apple up into slices and place them on your hand. What is the pressure of the apple on your hand (in units of Pa, psi, and atm)? d) You smash the apple into applesauce and spread it over a table. What is the pressure of the applesauce on the table (in units of Pa, psi, and atm)?
a) 9.80 N b) 0.0059 atm c) P = (9.80 N) / (total area of slices) d) P = (9.80 N) / (total area of applesauce)
What is pressure of applesauce?a) The weight of an object is equal to its mass multiplied by the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.81 m/s^2. So the weight of the apple is:Weight = (102 g) * (9.81 m/s^2) = 1004.82 g * 9.81 m/s^2 = 9.80 Nb) To find the pressure on your finger when the apple is balanced on a toothpick, we can use the formula P = F/A, where P is pressure, F is force, and A is area. The force of the apple is its weight (9.80 N) and the area of contact on your finger is the cross-sectional area of the toothpick. So, the pressure on your finger is:P = (9.80 N) / (pi * (0.00625 cm/2)^2) = 9.80 N/ 2.44 x 10^-5 cm^2 = 4.01 x 10^5 Pa or 4.01 x 10^5 N/m^2 = 4.01 x 10^5 Pa = 4.01 x 10^5 N/m^2 = 4.01 x 10^5 Pa = 59 psi = 0.0059 atmc) To find the pressure on your hand when the apple is cut into slices, we can use the same formula P = F/A, where P is pressure, F is force, and A is area. The force of the apple is still its weight (9.80 N) and the area of contact on your hand is the total area of the slices. So, the pressure on your hand is:P = (9.80 N) / (total area of slices)d) To find the pressure of the applesauce on the table, we can use the formula P = F/A, where P is pressure, F is force, and A is area. The force of the applesauce is still its weight (9.80 N) and the area of contact on the table is the area of the applesauce. So, the pressure on the table is:P = (9.80 N) / (total area of applesauce)It should be noted that the above calculations are based on the assumption that the apple is a homogeneous object and that the cross sectional area of toothpick is constant. In reality, the pressure will vary depending on the apple's density and the toothpick's shape and size.To learn more abut pressure refer:
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transitions between solid, liquid, and gaseous states of a substance occur when conditions of temperature or pressure favor the associated changes in phase. when the temperature of a gas is
A substance will switch between its solid, liquid, and gaseous forms when temperature, pressure circumstances encourage corresponding transitions. When a gas's temperature increases, pressure falls.
A state of matter that is gaseous has a distinct mass but no distinguishable shape or volume. Pressure, volume, temperature, material quantity, specific heat, and other quantifiable characteristics of gases include these. The most important characteristics are the four independent variables quantity, volume, pressure, and temperature, which describe the gas's state. When describing how hot or cold something is, the idea of temperature is used. One can measure temperature by using a thermometer. The calibration of thermometers involves the use of various temperature scales.
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indicate whether the following statements are true or false. In each case give a reason for your answer. If W ⊂ Rn is a subspace and v ∈ Rn, then prW (v) is the least-squares approximation to v by a vector in W except when prW (v) = 0..
A. True
B. False
The level of magnification that produces the best images using an electron microscope is _____.
A. 2,500 times
B. 100,000 times
C. 250,000 times
D. 1,000,000 times
The level of magnification that produces the best images using an electron microscope is 250,000 times.
What is electron microscope?In order to "image" the specimen and learn more about its structure and composition, electron microscopes (EMs) work similarly to their optical equivalents but employ a focussed beam of electrons rather than photons. There are several kinds of electron microscopes, such as the scanning electron microscope (SEM), the transmission electron microscope (TEM), and the reflection electron microscope (REM.)
Universities, research facilities, and institutes for nanotechnology frequently employ electronic microscopes. These facilities allow for a close examination of the specimen's structure, which can reveal details about its intended use.
correct option: C
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a block of known mass mm is on a disk that rotates about its center, as shown above. the block does not slip on the disk, and travels at a constant tangential speed vv when at a distance rr from the center with a centripetal force of magnitude ff exerted on it. which of the following statements about other quantities that might be determined is correct?
When the block's radius and tangential speed are known, the centripetal acceleration of the block may be determined because ac=v2rac=v2r.
What exactly is a force in science?
Physics appears to have a clear definition for the word "force." A force of this magnitude can be described as either a push or a pull. A force does not "be in it" or "be inside it." A force from another object can affect something else.
What do the terms force and motion mean?
Basically, a push or pull that impacts anything or energy as a property of physical motion or movement is referred to as force. It happens when two things come together. A body is also considered to be in motion when it is moving.
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Liquid Distilled water Isopropanol Mineral oil Salt water Density (kg/m3) 1000 786 850 1025 Sinks or Floats? Sinks Sinks Sinks Floats In an experiment, a student releases an object from rest in four different liquids and observes whether it floats. The results are listed in the table. Which of the following is true about the density of the object?
The object has a density less than 1000 kg/m³ because it floats in mineral oil which has a density of 1025 kg/m³.
The density of a substance is a measure of its mass per unit volume. In the table provided, the densities of four different liquids are given, along with whether an object floats or sinks in each liquid.
Since the object floats in mineral oil, which has a density of 1025 kg/m³, it means that the density of the object must be less than that of mineral oil, or less than 1025 kg/m³.
This is because objects with a density greater than the liquid they are placed in will sink, while those with a lower density will float. Therefore, the object has a density less than 1000 kg/m³.
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conservation of momentum: a small car meshes with a large truck in a head-on collision. which of the following statements concerning the magnitude of the momentum change during the collision is correct? (there could be more than one correct choice.)
The truck and the tiny car both experience the same amount of momentum difference.
What is the definition of momentum in physics?
whenever a person is struck in the face by a ball that was thrown at him. It demonstrates how challenging it might be to change the course of events. A baseball is swooping in the air. A large truck is moving. This kind of firearm discharged a bullet.
In what situations does momentum actually matter?
Momentum is a property of almost all motion-related activities. It is a cornerstone of physics. In sports, the word "momentum" is frequently used. A side that has momentum is therefore moving and will require effort to stop.
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a fly enters through an open window and zooms around the room. in a cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point (4.00 m, 1.50 m, 2.50 m) to (1.57 m, 2.7 m, 0.55 m).
In a cartesian coordinate system with three axes along three edges of room, fly changes its position from point (4.00 m, 1.50 m, 2.50 m) to (1.57 m, 2.7 m, 0.55 m), then Displacement vector = -2.43 i + 1.2 j - 1.95 m
What is meant by displacement vector?A geometric object which encodes both displacement and direction is called displacement vector. Displacement vector from one point to another is an arrow with its tail at first point and its tip at second.
Given (4.00 m, 1.50 m, 2.50 m) to (1.57 m, 2.7 m, 0.55 m).
Displacement vector along x axes is 1.57 - 4.00= -2.43 m
Displacement vector along y axes is 2.7 - 1.50 = 1.2 m
Displacement vector along z axis is 0.55- 2.50 = - 1.95 m
Displacement vector is -2.43 i + 1.2 j - 1.95 m.
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Note: The given question on the portal is not incomplete. Here is the complete question.
Question: a fly enters through an open window and zooms around the room. in a cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point (4.00 m, 1.50 m, 2.50 m) to (1.57 m, 2.7 m, 0.55 m). Find the scalar components of the flies displacement vector (in m).
a car changes its velocity from 45 km/h to 65 km/h in 3 s. Find the magnitude of its acceleration
The magnitude of the acceleration of the car when its velocity changes from 45km/h to 65km/h in 3 s is 1.9 m/s^2
Let u be the initial velocity of the car.
u=45 km/h (given)
By converting it into m/s , we get:
u=12.5 m/s
Let v be the final velocity of the car, then :
v=65 km/h
v=18.1 m/s ( By converting them into m/s)
Now, let the acceleration of the car while moving to be a, then :
Using the formula, we get:
⇒v = u + at
⇒ 18.1 = 12.5 + a×3 ( Putting all the values)
⇒3a = 18.1 - 12.5
⇒a = 5.6/3
⇒ a = 1.9 m/s^2
Therefore, The magnitude of the acceleration of the car when its velocity changes from 45km/h to 65km/h in 3 s is 1.9 m/s^2
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The electric potential in a region of space as a function of position x is given by the equation V(x) = αx2 + βx - γ, where α = 2V/m2, β = 7V/m, and γ = 15V. All nonelectrical forces are negligible.An electron starts at rest at x = 0 and travels to x = 20 m.Calculate the magnitude of the work done on the electron by the electric field during this process.Calculate the speed of the electron at x = 20 m.
The magnitude of the work done on the electron by the electric field is given by W = qV, hence the speed of the electron at x = 20m is v = 42 m/s.
Calculate the speed of the electron at x = 20 m?The electric potential energy at x = 0 is V(0) = 15V and the electric potential energy at x = 20 m is V(20) = 715V. Therefore, the magnitude of the work done on the electron is [tex]W = q(715-15) = q700 V.[/tex]
The speed of the electron at x = 20 m can be calculated using the equation[tex]v = √2(V(20) - V(0))/m[/tex], where m is the mass of the electron. Substituting in the values, we get[tex]v = √2(715-15)/m = √1400/m[/tex]. Therefore, the speed of the electron at [tex]x = 20 m is v = √1400/m.[/tex]
The work done on the electron by the electric field during the process is equal to the change in electric potential energy. The electric potential energy at the starting point is equal to V(0) = -15V and the electric potential energy at x = 20 m is equal to V(20) = 215V. The magnitude of the work done can then be calculated as
[tex]W = 215V - (-15V) = 230V[/tex]
The speed of the electron at x = 20 m can be calculated using the equation of motion:
[tex]v^2 = 2a(x-x_0)[/tex]
where a is the acceleration. This can be calculated from the equation of electric potential as:
[tex]a = dV/dx = 2αx + β[/tex]
Plugging in the values for x and the constants, we get a = 44V/m. Substituting this in the equation of motion, we get
[tex]v^2 = 2(44V/m)(20m-0m) = 1760V[/tex]
Therefore, the speed of the electron at[tex]x = 20m is v = 42 m/s.[/tex]
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PART ONE
The figure shows a claw hammer as it pulls a
nail out of a horizontal board.
If a force of magnitude 99.9 N is exerted horizontally as shown, find the force exerted by the hammer claws on the nail. (Assume that the force the hammer exerts on the nail is parallel to the nail).
Answer in units of N.
PART TWO
Find the force exerted by the surface on the point of contact with the hammer head. Assume that the force the hammer exerts on the nail is parallel to the nail.
Answer in units of N.
(1) The force exerted by the hammer claws on the nail is 57.3 N.
(2) The force exerted by the surface on the point of contact with the hammer head is 81.83 N.
What is the force exerted by the hammer claws on the nail?The force exerted by the hammer claws on the nail is calculated as follows;
Fy = Fn sinθ
where;
θ is the angle of inclination of the hammerFy = 99.9 N x sin (35)
Fy = 57.3 N
The force exerted by the surface on the point of contact with the hammer head is calculated as follows;
Fx = Fn x cosθ
Fx = 99.9 N x cos (35)
Fx = 81.83 N
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In Fig. 22−35 the four particles form a square of edge length a=5.00 cm and have charges q 1 =+10.0 nC,q 2 =−20.0 nC,q 3 =+20.0 nC, and q 4 =−10.0 nC, In unit vector notation, what net electric field do not particles produce at the square's center?
Net electric field produced by the four particles at the square's center is zero.
What is electric field?The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them is called an electric field.
Electric field produced by each particle at the center of the square can be calculated as:
E1 = k * q1 / (5/sqrt(2))^2 = 810^9 N/C * (1010^-9 C) / (5/sqrt(2))^2 = 410^9 N/C
E2 = k * q2 / (5/sqrt(2))^2 = 810^9 N/C * (-2010^-9 C) / (5/sqrt(2))^2 = -810^9 N/C
E3 = k * q3 / (5/sqrt(2))^2 = 810^9 N/C * (2010^-9 C) / (5/sqrt(2))^2 = 810^9 N/C
E4 = k * q4 / (5/sqrt(2))^2 = 810^9 N/C * (-1010^-9 C) / (5/sqrt(2))^2 = -410^9 N/C
So, E net = E1 + E2 + E3 + E4 = 410^9 N/C + (-810^9 N/C) + 810^9 N/C + (-410^9 N/C) = 0 N/C
Therefore, net electric field produced by the four particles at the square's center is zero.
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find the mass of a bullet moving at 45m/s and has kinetic energy of 51 j
The mass of a bullet moving at 45m/s and has kinetic energy of 51 j is 0.050 gram.
What is kinetic energy ?The term kinetic energy is defined as the energy of motion, observable as the movement of an object or subatomic particle.
There are five different types of kinetic energy: radiant, thermal, sound, electrical, and mechanical.
It is represented by formula
K.E = 1/2 mv²
Kinetic energy = 51 j
Mass = ?
Velocity = 45m/s
Then,
Mass = 2 K.E / v²
= 2 × 51 / 45²
= 102 / 2025
= 0.050 gram
Thus, The mass of a bullet moving at 45m/s and has kinetic energy of 51 j is 0.050 gram.
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Macmillan Learning
A black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. Suppose a mongoose and a black mamba find
themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 8.37 m/s² from rest.
How much time ftop does it take the snake to reach its top
speed?
How far dsnake does the snake travel in that time?
How much time freact does the mongoose have to react before
the black mamba's tail passes the mongoose's nose?
ftop
dsnake =
freact=
S
m
S
The black mamba travels a distance of 2.0828 m, which is less than its length of 4.50 m.
How far dsnake does the snake travel in that time?The first equation of motion states:
vf = at + vi
A top speed is _f.
Initial or lowest speed is v i, and acceleration is a.
2.60 = 4.50 t
t +0 = 1.28571sec
The snake needs 1.28571 seconds to attain its peak speed.
Part B:
The second equation of motion states:
S=0.5(4.50) S=vit+at2 w i=0 (1.28571)
2 S = 2.0828m
In that period, the snake moves 2.0828 metres.
Part C:
The black mamba travels a distance of 2.0828 m, which is less than its length of 3.12 m.
2.0828 m<3.12 m
A potential exists for monkeys to capture a black mamba.
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