(A) Units for derivative is d(t) = 16t^2, (B) height of the ledge is 0 feet, and stone is moving with a speed of 46.667 x s mph.
A. The units associated with the derivative of d(t) = 16t^2 are feet per second, and it measures the velocity of the object at a certain point in time.
B. To find the height of the ledge, we need to find the value of t when the stone reaches the ground. We can set d(t) = 0 and solve for t:
16t^2 = 0
t^2 = 0
t = 0
Since t = 0, the stone was dropped from rest, so the height of the ledge is d(0) = 16(0)^2 = 0 feet.
To find the velocity of the stone when it strikes the ground, we can find the derivative of d(t) = 16t^2 at t=s.
d'(t) = 32t
d'(s) = 32s
Since the stone was falling in feet per second. To convert to miles per hour we need to multiply the value by 1.46667 (conversion factor)
d'(s) x 1.46667 = 32s x 1.46667 = 46.667s mph
So the stone is moving at 46.667 x s mph when it strikes the ground.
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Why is it that the lower mass individual may appear to experience more force from the larger mass player in a collision?
Answer:
One possible reason is that change in velocity is greater for the individual with lower mass.
Explanation:
By Newton's Law of Mechanics, magnitude of the force on two players would be the same in the collision. Let [tex]F[/tex] denote this magnitude.
Assume that the duration of the collision is [tex]\Delta t[/tex]. In this collision, magnitude of the impulse [tex]J[/tex] on each player would be the same: [tex]J = F\, \Delta t[/tex].
At the same time, impulse is equal to the change in momentum. Specifically, if the mass of one player is [tex]m[/tex] and the change in their velocity is [tex]\Delta v[/tex], the change in their momentum would be [tex]m\, \Delta v[/tex]. Thus:
[tex]m\, \Delta v = J = F\, \Delta t[/tex].
Rearrange to obtain an expression for the change in velocity:
[tex]\begin{aligned}\Delta v &= \frac{J}{m} = \frac{F\, \Delta t}{m}\end{aligned}[/tex].
In other words, in this collision, change in velocity is inversely proportional to the mass of the participant. Hence, even though the two players experienced force of the same magnitude, the participant with a lower mass would experience a greater change in velocity.
question in a certain region of space, there is an electric potential difference of 120v between two points that are 0.25m apart. what is the magnitude of the average electric field in between the two points?
The magnitude of the average electric field in between the two points is 480V/m
What is electric field?Electric field is an important concept in physics that describes the force exerted by a charged particle or object on other particles or objects in its vicinity. It is a vector field, meaning it has both magnitude and direction. The electric field is created when an electric charge is placed in a region of space. The electric field will then act on any other charges in the region, producing a force on them.
Electric field (E) is defined as the electric potential difference (V) divided by the distance (d) between two points:
E = V / d
In this case, the electric potential difference is 120V and the distance between the two points is 0.25m. Therefore, the magnitude of the average electric field in between the two points is:
E = 120V / 0.25m = 480V/m
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An experiment is conducted to determine the thermal conductivity of a hot dog. First water is boiled in a large pan and measured to have a temperature of 94°c (at an elevation of 1650 m). The hot dog has dimensions of 12. 5 cm long and 2. 2 cm in diameter
Thermal conductivity may be measured with simple equipment.A slab of the material to be tested is clamped between an ice block and a steam chamber that both maintain constant temperatures of 0 °C and 100 °C.
How is thermal conductivity experiment measured? Thermal conductivity may be measured with simple equipment.A slab of the material to be tested is clamped between an ice block and a steam chamber that both maintain constant temperatures of 0 °C and 100 °C.Temperature variation and nonlinear heat flow specifically are the error sources.There are two ways that temperature can vary at contact surfaces: (a) gradually drifting over the board, and (b) momentarily varying throughout the platen surface.Using the Searle's bar method, calculate Copper's thermal conductivity.Steam is heated in this experiment.Don't touch the steam generator, tubing, or the Searle's bar equipment because they have hot surfaces.To learn more about Thermal conductivity refer
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a) Two tugboats are towing a tanker of mass 3.30 x 107 kg. If one tug is pulling at 2.40 X 104 N [E16°N] and the other is pulling at 2.40 x 104 N [E9°S], calculate the acceleration of the tanker, assuming no resistance. Use both vector methods to solve this part of the problem.
b) If the tanker has a resistive force on it of 5.60 x 10³ N, find its acceleration using the component method.
c) Calculate the speed reached in each of the two cases after 2.0 minutes. Convert it to km/h.
d) Calculate the distance required in each case to reach a speed of 5.0 km/h.
So the net force acting on the tanker is: F_net = sqrt(Fx^2 + Fy^2) = 2.4 x 10^4 N And the acceleration of the tanker is: a = F_net / m = 2.4 x 10^4 N / 3.3 x 10^7 kg = 7.27 x 10^-4 m/s^2.
How to calculate net force and acceleration?
To find the acceleration of the tanker using vector methods, we can use the following equation:
F_net = ma
where F_net is the net force acting on the tanker, m is the mass of the tanker, and a is the acceleration of the tanker.
In this case, the two tugboats are pulling in opposite directions, so we need to find the vector sum of their forces to find the net force acting on the tanker.
Using the component method, we can find that the x-component of the net force is:
Fx = 2.4 x 10^4 N * cos(16) - 2.4 x 10^4 N * cos(9) = -2.4 x 10^4 N
and the y-component of the net force is:
Fy = 2.4 x 10^4 N * sin(16) + 2.4 x 10^4 N * sin(9) = 0 N
So the net force acting on the tanker is:
F_net = sqrt(Fx^2 + Fy^2) = 2.4 x 10^4 N
And the acceleration of the tanker is:
a = F_net / m = 2.4 x 10^4 N / 3.3 x 10^7 kg = 7.27 x 10^-4 m/s^2
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Decribe how an electric field and potential gradient affect the performance of inulation
Only in the presence of an electric potential difference does the electric field exist. There won't be any electric field if the charge is homogeneous throughout, regardless of how high the electric potential is.
What connection exists between the potential gradient and the electric field?Potential gradient is calculated by integrating the negative of the electric field's intensity with respect to distance. E = - d V d r describes the relationship between the magnitude of the electric field and the potential gradient.Of course, an insulator can let an electric field through. As it passes through an insulator or dielectric medium, the electric field polarises it.Only in the presence of an electric potential difference does the electric field exist. There won't be any electric field if the charge is homogeneous throughout, regardless of how high the electric potential is.To learn more about electric potential difference refer to:
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An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0. 0 degrees Celsius and rejects heat to a room at a temperature of 19. 2 degrees Celsius. Suppose that liquid water with a mass of 76. 3kg at 0. 0 degrees Celsius is converted to ice at the same temperature. Take the heat of fusion for water to be L_f = 3. 34*10^5 J/kg.
How much energy E must be supplied to the device?
Express your answer in joules
The energy E must be supplied to the device is 1.8x10^3kJ when an ice-making machine inside a refrigerator operates in a Carnot cycle.
Given the temperature initially (Tl) = 0degrees Celsius = 273K
The final temperature (Tc) = 19.2degrees Celsius = 273 + 19.2 = 292.2K
Mass of liquid water (m) = 76.3kg
The water is converted to ice at 0 degrees Celsius
The heat of fusion for water to be Lf = 3.34*10^5 J/kg.
Let heat released from ice = Qc
Heat absorbed by water = Ql
We know that Ql = mLf = 76.3 x 3.34*10^5 = 2.54*10^4kJ
Then Qc/Ql = -Tc/Tl
Qc = - 254.842*10^5 (292.2/273)
Qc = -2.72x10^4kJ
The heat being lost to the hot reservoir is the cause of the negative sign.
We know that Ql = Qc + W where W is the work done
W = Qc - Ql = 2.54*10^4kJ - 2.72x10^4kJ
W = 1.8x10^3kJ
Hence the energy E that must be supplied to the device is 1.8x10^3kJ
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A small car (1400 kg) moving 35 m/s gradually comes to a complete
stop when the brakes are applied. It comes to a complete stop over a
period of 15.2 seconds. What is the force in newtons that is exerted
on the car during this time? (Remember, the force is negative
because it is exerted opposite to the motion).
The force in newtons that is exerted on a car during the given time is 3,223.68N.
How to calculate force?Force refers to a physical quantity that denotes ability to push, pull, twist or accelerate a body.
The force exerted on an object can be calculated by multiplying the mass of the body by the acceleration as follows:
Force = mass × acceleration
Force = mass × speed/time
According to this question, a small car (1400 kg) moving 35 m/s gradually comes to a complete stop when the brakes are applied. It comes to a complete stop over a period of 15.2 seconds.
Force = 1400 × 35/15.2
Force = 3,223.68N
Therefore, 3,223.68N is the force acting on the small car.
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what are tiny solid and liquid particles of matter suspended in the atmosphere?
Answer:
I think the answer you're looking for is particulate matter.
Explanation:
An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 1450 kg. When that occupant drops a coin, the tension in the cable is 12. 0 kN. What is the acceleration of the coin relative to the cab
The cable will be under 12.0 KN of tension when that person drops a coin. Then the acceleration of the coin relative to the cab is 0.00828 m/s^2.
To find the acceleration of the coin relative to the cab, we can use the equation for tension force:
Tension force = mass x acceleration
We are given the tension force (12.0 kN) and the combined mass of the cab and its occupant (1450 kg). Therefore, we can solve for acceleration:
12.0 kN = (1450 kg) x acceleration
acceleration = 12.0 kN / (1450 kg)
acceleration = 0.00828 m/s^2
So the acceleration of the coin relative to the cab is 0.00828 m/s^2
It is worth noting that the coin will fall with respect to the elevator with an acceleration of 9.8 m/s^2 (upwards) but relative to the elevator, the coin is accelerating downwards with 9.8 m/s^2 + 0.00828 m/s^2 = 9.80828 m/s^2.
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what is the magnitude and direction of the electric force on an electron ina uniform electric field of strenght 2360n/c that points due east
The magnitude of the electric force on the electron is 2360 N and it points due east.
What is electric force?Electric force is an attractive or repulsive force between two particles that have an electric charge. This force is generated when two charged particles interact due to their charges. The strength of the electric force depends on how much charge each particle has, as well as their distance from each other. Electric forces are responsible for phenomena such as static electricity and lightning, and they can also be used to power electric motors and other devices.
This is because an electric field exerts a force on a charged particle in the direction that is opposite to the direction of the field. Since the electric field points due east, then the force on the electron will point due west.
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a quartz crystal vibrates with a frequency of 77,621 hz. what is the period of the crystal's motion?
Formula for period:
[tex]T=\dfrac{1}{f}[/tex]
period(measured in seconds) = 1 / frequency(measured in hertz)
__________________________________________________________
Given:
[tex]f=77,621Hz[/tex]
[tex]T=?[/tex]
__________________________________________________________
Finding period:
[tex]T=\dfrac{1}{f}[/tex]
[tex]T=\dfrac{1}{77,621}[/tex]
__________________________________________________________
Answer:
[tex]\fbox{T = 0.0000129}[/tex]
A skydiver is falling through the air because his:____. question 7 options: a. weight is over 100 n b. weight force down is greater than the air drag c. drag force needs to be at least 50 n because nothing can stop gravity from making an object fall
The correct option is B. weight force down is greater than the air drag.
What is weight force?Weight force is the force of gravity acting on a body or object. It is the magnitude of the force of gravity acting on an object or body and is determined by the object or body's mass multiplied by the acceleration due to gravity. Weight force is a type of force, and is a vector quantity which has both magnitude and direction. Weight force acts in the downward direction of the Earth's gravitational field and its direction is always towards the center of the Earth. Weight force is important in determining the motion of objects and bodies, and is one of the most important fundamental forces in physics.
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study the editorial cartoon total eclipse 2017 by nate beeler. what is the purpose of this editorial cartoon? to show that today's kids are interested in learning about astronomical events to show that technology prevents people from directly experiencing major events to show how small computers have become with advances in technology to show that children often do not realize what is going on around them
To illustrate how technology keeps people from experiencing significant events firsthand, consider Nate Beeler's editorial comic Total Eclipse 2017.
The editorial cartoon's goal is unclear?Cartoon editorials share this educational goal with prose editorials. They are created with the intention of getting readers to reflect on contemporary political concerns. A reader-friendly visual and linguistic language is required for editorial cartoons.
What viewpoint possesses the cartoonist?someone's opinion or point of view on something. How might a political cartoonist's point of view be impacted. The point of view of a cartoonist will direct their work. The opinions of others may be taken into consideration by cartoonists, or they may solely express their own opinions.
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A box has a mass of 45,620 grams. How much force would you need to push the box to accelerate it 5 m/s2?
Taking into account the Newton's second law, the force needed to push the box to accelerate it 5 m/s² is 228.1 N.
Definition of Newton's second lawAcceleration in a body occurs when a force acts on a body. There are two factors that influence the acceleration of an object: the net force acting on it and the mass of the body.
Newton's second law defines the relationship between force and acceleration. This law says that the acceleration of an object is directly proportional to the sum of all the forces acting on it and inversely proportional to the mass of the object.
Mathematically, Newton's second law states that force is the multiplication of mass and acceleration:
F= m×a
where:
F = Force [N]m = Mass [kg]a = Acceleration [m/s²]Force needed in this caseIn this case, you know:
F= ?m= 45620 grams= 45.62 kg (being 1000 g= 1 kg)a= 5 m/s²Replacing in the definition of Newton's second law:
F= 45.62 kg× 5 m/s²
Solving:
F= 228.1 N
Finally, the force needed is 228.1 N.
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Within 4. 0 s of liftoff, a spacecraft that is uniformly
accelerating straight upward from rest reaches an altitude
of 4. 50 X 102 m [up).
(a) What is the spacecraft's acceleration?
The spacecraft's acceleration can be found using the equation: a = (v-u)/t = 4.50 x 10^2 m / 4.0 s = 11.25 m/s^2.
Can you explain the concept of uniformly accelerating motion?Uniformly accelerating motion refers to an object that is moving at a constant rate of acceleration. This means that the velocity of the object is changing at a constant rate, but the acceleration remains the same throughout the motion. An example of this type of motion is an object that is accelerating from rest at a constant rate. The motion of the object can be described mathematically by the equations of motion, such as distance = initial velocity * time + 1/2 * acceleration * time^2. The graph of uniformly accelerating motion is a parabola, with velocity on the y-axis and time on the x-axis. This type of motion is different from non-uniform acceleration, where the acceleration changes during the motion.
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A spacecraft that is uniformly accelerating straight upward from rest reaches an altitude of 4. 50 X 102 m [up) with acceleration of 11.25 m/s².
Evaluating :The spacecraft's acceleration can be found using the equation:
a = (v-u)/t
= 4.50 x 10² m / 4.0 s
= 11.25 m/s².
Uniformly accelerating motion :Uniformly accelerating motion refers to an object that is moving at a constant rate of acceleration. This means that the velocity of the object is changing at a constant rate, but the acceleration remains the same throughout the motion. An example of this type of motion is an object that is accelerating from rest at a constant rate.
The motion of the object can be described mathematically by the equations of motion, such as distance = initial velocity × time + 1/2 * acceleration × time². The graph of uniformly accelerating motion is a parabola, with velocity on the y-axis and time on the x-axis. This type of motion is different from non-uniform acceleration, where the acceleration changes during the motion.
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Jack and Jill ran up the hill at 3.0 m/s . The horizontal component of Jill's velocity vector was 2.3 m/s .
what was the angle of the hill
What was the vertical of Jill's velocity
(a) The angle of the hill is 40⁰
(b) The vertical of Jill's velocity is 1.93 m/s.
What is the angle of the hill?
The angle of the hill is calculated by applying the following kinematic equation as shown below.
Vₓ = V cosθ
where;
V is the velocity of JilVₓ is the horizontal component velocityθ is the angle of the hillcosθ = Vₓ / V
θ = arc cos (Vₓ / V)
θ = arc cos (2.3 / 3)
θ = 40⁰
The vertical component of the velocity is calculated as follows;
Vy = 3 m/s x sin (40)
Vy = 1.93 m/s
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Two people push on a shopping cart from opposite sides. In which situation
will the motion of the shopping cart stay the same?
A. The two people push with different amounts of force.
B. One of the people stops applying a force.
C. One of the people applies twice as much force.
D. The two people push with a balanced
face
Two people push on a shopping cart from opposite sides. Situation will the motion of the shopping cart stay the same, the correct option is (D) The two people push with a balanced face.
In this situation, the net force on the shopping cart will be zero, since the two forces are equal in magnitude and opposite in direction. If the forces are balanced, the shopping cart will not accelerate and will stay in the same state of motion (at rest or moving at a constant velocity). In scenario A and C, the forces are not balanced and therefore will cause acceleration. In scenario B, the net force will be non-zero and the acceleration will cause the shopping cart to change its velocity and direction.
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while in horizontal flight at a speed of 20 m/s, a baseball of mass 0.11 kg is struck by a bat. after leaving the bat, the baseball has a speed of 29 m/s in a direction opposite to its original direction. the magnitude of the impulse given the ball is
The baseball's change in momentum is equal to the impulse applied to it. An object's momentum is determined by multiplying its mass by its velocity. The baseball received an impulse with a magnitude of -5.39 kg*m/s.
The baseball's change in momentum is equal to the impulse applied to it. An object's momentum is determined by multiplying its mass by its velocity.
The baseball's initial momentum is equal to 0.11 kg times 20 m/s, or 2.2 kg/s.
The baseball's ultimate velocity is calculated as (0.11 kilogramme) * (-29 m/s) = -3.19 kgm/s.
The difference between the baseball's final and starting velocities, or its change in momentum, is equal to 5.39 kg*m/s (final momentum - beginning velocities = -3.19 kgm/s - 2.2 kgm/s).
As a result, the baseball received an impulse with a magnitude of -5.39 kg*m/s.
Due to the ultimate velocity being in the opposite direction of the original vector, the impulse is negative.
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if dust deosnt have an intitial charge , then how can a charged object(such as a piece of paper) attract bits of dust, since coulombs law states tgat two different charges are needed for an attractive force?
Dust particles can acquire a charge through a process called triboelectrification, which occurs when two materials rub against each other, transferring electrons from one material to the other.
What is triboelectrification?Triboelectrification is the phenomenon in which a charge is generated through the contact and separation of two materials. It is also known as "friction electrification" or "contact electrification".
When dust particles rub against a piece of paper, transferring electrons from the dust particles to the paper and giving the dust particles a negative charge. Once the dust particles have acquired a charge, they can be attracted to a charged object, such as a piece of paper, through Coulomb's law, which states that objects with opposite charges will experience an attractive force.
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Suppose that Ben Pumpiniron elevates his 80-kg body up the 2.0-meter stairwell in 1.8
seconds. Calculate Ben's power.
Ben's power is 871W
What is the short definition of power?
Power can be defined as the amount of work completed in a given amount of time. Watt (W), which is derived from joules per second (J/s), is the SI unit of power. Horsepower, or roughly 745.7 watts, is a unit of measurement used to describe the power of machinery and motor vehicles.
We could determine Ben's power rating if this were the case. Ben must presumably push down on the stairs with an 800-Newton force in order to raise his body. Ben's body would be pushed upward by the stairs in this way with just enough force to raise him up the stairs. Ben's power rating might be calculated using these two estimations, as illustrated below.
Power = work done / time
Power = 784*2/ 1.8
P= 871W
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a 2.0-mm-diameter glass bead is positively charged. the potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 v. what is the charge on the bead?
The glass bead has a 0.001 m radius. The distance between the first and second points from the bead's center is 0.003 and 0.005 meters, respectively.
How big is a circle's radius?The radius of a circular is the distance a circle's center from any point along its perimeter. Usually, "R" or "r" is used to indicate it.
In geometry, what is a radius?A radius is indeed a line segment that has one endpoint in the circle's center and the other terminus on the circumference of the circle. Circle's diameter equals the radius The diameter of a circle is a line segment that has its ends on the circle and passes through its center. Radius x 2 equals the diameter.
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A 60 kilogram person jumps off a platform, landing while moving at 2. 0 meters per second. Determine the force exerted on the persons feet when he lands if he stops in 0. 25 seconds
The force exerted on the person's feet when he lands if he stops in 0. 25 seconds is found to be 480 N.
What is Force?Force may be characterized as a type of circumstance that significantly deals with the pushing or pulling of an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects.
According to the context of this question,
The mass of a person, m = 60 Kg.
The velocity of a person, v = 2.0 meters/sec.
The time is taken, t = 025 seconds.
The formula for calculating force is as follows:
F = mv/t.= 60 × 2 ÷ 0.25 = 480 N.
Therefore, the force exerted on the person's feet when he lands if he stops in 0. 25 seconds is found to be 480 N.
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your friend, who is in a field 70 meters away from you, kicks a ball towards you with an initial velocity of 18 m/s. assuming the grass causes the ball to decelerate at a constant rate of 1.0 m/s2, how long does it take for the ball to reach you?
With the use of formula, the time taken for the ball to reach you is 31.6 s
What is Acceleration ?Acceleration can be defined as velocity change per time taken. It is a vector quantity.
Given that your friend, who is in a field 70 meters away from you, kicks a ball towards you with an initial velocity of 18 m/s. assuming the grass causes the ball to decelerate at a constant rate of 1.0 m/s2, to know how long it takes for the ball to reach you, we will use the formula
s = ut - 1/2at² where
v = 0
u = 18 m/s
a = 1 m/s²
s = 70 m
t = ?
70 = 18t - 1/2 × 1 × t²
70 = 18t - 0.5t²
Multiply all by 2
140 = 36t - t²
t² - 36t + 140 = 0
Using completing the square method
t² - 36t + 18² = 18² - 140
( t - 18 )² = 324 - 140
( t - 18 )² = 184
t - 18 = √184
t = 18 + 13.6 or 18 - 13.6
t = 31.6 s or 3.4 s
Therefore, the ball will reach you in the next 31.6 s
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a 1,200 kg car is traveling at 10 m/s. what is the minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object? (note: the braking system can decelerate the car at 2 m/s2.) a. 2.5 m b. 5.0 m c. 25 m d. 50 m
The minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object is 2.5 meter. The correct answer is a.
To calculate this, we can use the equation:
distance = initial velocity² / (2 × deceleration).
In this case, the initial velocity is 10 m/s and the deceleration is 2 m/s². Plugging these values into the equation gives us:
distance = 10² / (2 × 2)
distance = 25 meter
Since the car's speed is slowing down at a rate of 2m/s², the car will need 25 meter distance to come to a complete stop. However, the question asked for the minimum distance at which the automatic braking system needs to activate, therefore the minimum distance at which the automatic braking system needs to activate is 10% of the stopping distance which is:
10/100 × 25 = 2.5 meter
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When a charged balloon sticks to a wall the downward gravitational force is balanced by an upward static friction force. The normal force is provided by the electrical attraction between the charged balloon and the equal but opposite charged polarization induced in the walls molecules. If the mass of the balloon is 1. 4g it's coefficient of static friction with the wall is. 73 and the average distance between the opposite charges is. 75mm what minimum amount of charge must be placed on the balloon in order for it to stick to the wall
The balloon needs to be charged with a minimum of 1.3 x 10-10 Coulombs for it to adhere to the wall.
To find the minimum amount of charge required on the balloon for it to stick to the wall, we can use the following equation:
Friction force = friction coefficient x normal force
The electrical attraction between the charged balloon and the molecules of the wall, which cause an equal but opposing charged polarization, produces the normal force and may be computed as follows:
Normal force = k x q1 x q2 / r^2
where k is Coulomb's constant, q1 and q2 are the charges on the balloon and the wall's molecules, respectively, and r is the average distance between the opposite charges.
The gravitational force acting on the balloon is given by:
Fg = m x g
Since the downward gravitational force is balanced by the upward static friction force, we can set the gravitational force equal to the friction force:
m x g = friction coefficient x k x q1 x q2 / r^2
Solving for q1, the charge on the balloon, we have:
q1 = (m x g x r^2) / (friction coefficient x k x q2)
Given that the mass of the balloon is 1.4 g, coefficient of static friction with the wall is 0.73, the average distance between the opposite charges is 0.75mm, and Coulomb's constant is 910^9 Nm^2/C^2.
q1 = (1.4 x 9.8 x (0.75 x 10^-3)^2) / (0.73 x 9 x 10^9)
The minimum amount of charge required on the balloon in order for it to stick to the wall is 1.3*10^-10 Coulombs
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note that in this arrangement, the net charge is zero (so we expect no monopolar field far away). the two visible dipoles also cancel, so we expect no dipolar field far away. what might we call the first surviving term in the distant field?
The first surviving term in the distant field in this situation might be referred to as a quadrupolar field.
The Distant Field SituationThe determination that the first surviving term in the distant field is a quadrupolar field is based on the fact that the net charge and the visible dipoles in the arrangement cancel out, leaving no monopolar or dipolar fields.
A quadrupole is a distribution of charges in which there are two positive and two negative charges of equal magnitude and opposite sign, arranged symmetrically about a central point.
A quadrupole generates a quadrupolar field, which falls off as the inverse cube of the distance from the source, as opposed to the inverse square of the distance for a dipole.
So when a net charge and dipoles are cancelled, the next term that could survive is the quadrupolar term.
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7. Inferring Suppose you plot the distance
traveled by an object at various times and
you discover that the graph is not a straight
line. What does this indicate about the
object's acceleration?
When the graph of distance travelled with time is not straight, it implies that the acceleration is constant.
What is the acceleration of an object?The acceleration of an object is the rate of change of velocity with time.
Mathematically, the formula for the acceleration of an object is given as;
a = Δv / Δt
where;
Δv is the change in velocity of the objectΔt is the change in time of motionThe slope of velocity time graph is acceleration. This implies that acceleration increases with increase in velocity of an object.
However, if the graph of the distance travelled by an object with time is straight, it implies that the velocity is not uniform.
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medical x-rays have a wavelength of 0.052 nm. calculate the frequency of light, in hz (1/s), that this wavelength corresponds to?
The frequency of the light is 5.77 × 10¹⁸ Hz, if the wavelength of the x-rays is 0.052 nm.
Wavelength of the x-ray, λ = 0.052 nm = 5.2 × 10⁻¹¹ m.
Speed of x-rays, v = 3 × 10⁸ m/s
Let the frequency of the x-ray, = n
We know the relationship between speed of the wave, wavelength and the frequency of the wave is as follows:
speed = wavelength × frequency
3 × 10⁸ = 5.2 × 10⁻¹¹ × n
n = (3 × 10⁸)/(5.2 × 10⁻¹¹)
n = 5.77 × 10¹⁸ Hz
Alternate unit of frequency is 1/sec.
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A simple pendulum and a mass hanging on a spring both have a period of 1$ when set into small oscillatory
motion on Earth. They are taken to Planet X, which has a larger acceleration due to gravity. Which of the
following statements is true about the periods of the two objects on Planet X compared to their periods on Earth
a. Both are shorter
b. Both are the same
e. Both are longer
d. The period pf the mass on the spring is shorter, that of the pendulum is the same
e. The period of the pendulum is shorter, that of the mass on the spring is the same,
The pendulum's period is shorter, but the mass on the spring's is unchanged. A planet with twice the mass of Earth and the same size will accelerate through space twice as fast.
Given that the time period of a simple pendulum is = T
T = 2π√l/g where l is the pendulum length and g is the gravitational acceleration of the planet.
The time period of a mass-spring system is written as: T = 2π√m/k where m is the mass of system and k is spring constant.
The gravitational acceleration is defined as: g = GM/r^2
AS the acceleration due to gravity on planet X is greater than that of on earth we know that the time period is inversely proportional to g.
So, on planet X the time period is shorter and the mass-spring will remain same because the attached mass and spring constant are the same, the mass spring system is unaffected.
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at a stoplight, a truck traveling at 15 m/s passes a car as it starts from rest. the truck travels at constant velocity and the car accelerates at 3 m/s2. how much time does the car take to catch up to the truck?
The time taken by the car to overtake the the truck is found to be 10 seconds.
The car starts from rest and accelerate at the rate of 3m/s². The truck passes the car on the spotlight and it is travelling at a speed of 15m/s.
We know,
S = ut + 1/2at²
Where,
u is initial speed,
tis the time,
a is acceleration.
Also,
constant speed = dstance/time.
To overtake,
Distance covered by car = distance covered by the truck
So,
1/2at² = 15t
1/2at = 15
Putting a =3m/s²
1/2(3)t = 15
t = 10 seconds.
So, the time taken by the car to overtake is 10 seconds.
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