The average velocity in terms of acceleration and time is 1/2at².
Average velocity:
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.
Assume the acceleration a is uniform then:
v(t) = u + at
u = initial velocity
By average velocity v we mean average over time than strictly speaking:
v = 1/t [tex]\int\limits^t_0 {v(t)} \, dt[/tex]
= 1/t [tex]\int\limits^t_0 {(u + at)} \, dt[/tex]
= 1/t ( ut + 1/2 at²)
v = u + 1/2at²
If u =0, then we have
v = 1/2 at²
Therefore the average velocity is 1/2at².
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a basketball (hollow sphere) starts from rest and rolls down a hill without slipping. the hill is 70 meter high. total mechanical energy is conserved. find the linear speed of the basketball at the bottom in m/s.
The linear speed of the basketball at the bottom in m/s is 37.41 m/s.
The mechanical energy basket ball is conserved and the basket ball starts from rest. and roll down a hill of height 70m.
If mechanical energy is conserved,
Potential energy at top + kinetic energy at top = potential energy at bottom + kinetic energy at bottom.
At bottom, there is no potential energy, and at top, there is no kinetic energy.
Potential energy at top = kinetic energy at bottom.
Mgh = 1/2Mv²
M is the mass of the basketball,
v is the linear speed at the bottom,
h is the height of the ball.
Putting values,
v = √(2gh)
v = √(2x10x70)
v = 37.41m/s.
The speed of the basketball at the bottom is 37.41 /s.
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ii The firefighter slides through the vertical pipe with length h=15m. Its potential energy at the top is 1000J. Sketch a graph showing how the potential energy of the firefighter's weight changes with height. In the same graph, sketch the change in kinetic energy with height.
help
Both graphs of energy are attached in the answer.
What is energy?The ability of a body to do tasks may be referred to as energy. The joule is the SI unit of energy (J). or 1 kJ Equals 1000 J. energy guises: Potential energy, kinetic energy, thermal energy, chemical energy, and light energy are some of the several types.
Potential energy of a man due to gravity can be express as = mass × acceleration due to gravity × height.
Hence, graph, that shows potential energy of a firefighter slides through the vertical pipe with length, will be linearly decreasing type.
As, total energy is conserved, graph, that shows kinetic energy of a firefighter slides through the vertical pipe with length, will be linearly increasing type.
Graphical representation of both linearly increasing and linearly decreasing is attached here.
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A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. if the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30 cm deep?
Answer:
Approximately [tex]0.033\; {\rm m\cdot min^{-1}}[/tex] (meters per minute.)
Explanation:
Let [tex]A[/tex] and [tex]B[/tex] denote the bottom and top width of the trough, respectively. It is given that [tex]A = 30\; {\rm cm} = 0.30\; {\rm m}[/tex] and [tex]B = 80\; {\rm cm} = 0.80\; {\rm m}[/tex]. Let [tex]H[/tex] denote the height of this trough; [tex]H = 50\; {\rm cm} = 0.50\; {\rm m}[/tex].
Let [tex]h[/tex] denote the current depth of the water in this trough.
Let [tex]b[/tex] denote the current width of the surface of the water. As water fills the trough, this width increases from [tex]A = 0.30\; {\rm m}[/tex] (width of bottom of trough) to [tex]B = 0.80\; {\rm m}[/tex] (width of top of trough.)
The relationship between [tex]b[/tex] and [tex]h[/tex] is linear:
[tex]\displaystyle b = \frac{h}{H}\, (B - A) + A[/tex].
Cross-section area of water in this trough:
[tex]\begin{aligned}(\text{area}) &= \frac{1}{2}\, (A + b) \, h \\ &= \frac{1}{2}\, \left(A + \frac{h}{H}\, (B - A) + A\right)\, h \\ &= A\, h + \frac{1}{2\, H} (B - A)\, h^{2}\end{aligned}[/tex].
Let [tex]L[/tex] denote the length of this trough; [tex]L = 10\; {\rm m}[/tex].
Let [tex]v[/tex] denote the volume of water in this trough:
[tex]\begin{aligned}v &= (\text{area})\, L \\ &= \frac{1}{2}\, (A + b) \, h\, L \\ &= \frac{1}{2}\, \left(A + \frac{h}{H}\, (B - A) + A\right)\, h\, L \\ &= A\, L\, h + \frac{L}{2\, H} (B - A)\, h^{2}\end{aligned}[/tex].
Differentiate both sides implicitly with respect to [tex]v[/tex]:
[tex]\displaystyle \frac{d}{dv}[v] = \frac{d}{dv}\left[A\, L\, h + \frac{L}{2\, H}\, (B - A)\, h^{2}\right][/tex].
[tex]\displaystyle \frac{d}{dv}[v] = \frac{d}{dv}[A\, L\, h] + \frac{d}{dv}\left[\frac{L}{2\, H}\, (B - A)\, h^{2}\right][/tex].
[tex]\displaystyle 1 = A\, L\, \frac{dh}{dv} + \frac{L}{2\, H}\, (B - A)\, 2\, h\, \frac{dh}{dv}[/tex].
(Note that [tex]A[/tex], [tex]B[/tex], [tex]L[/tex], and [tex]H[/tex] are constants.)
Rearrange this equation to obtain:
[tex]\displaystyle 1 = A\, L\, \frac{dh}{dv} + \frac{L}{H}\, (B - A)\, h\, \frac{dh}{dv}[/tex].
[tex]\displaystyle 1 = \left(A\, L + \frac{L}{H}\, (B - A)\, h \right)\, \frac{dh}{dv}[/tex].
[tex]\displaystyle \frac{dh}{dv} = \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}[/tex].
Let [tex]t[/tex] denote time. It is given that the trough is being filled at a rate of [tex]0.2\; {\rm m^{3}\cdot min^{-1}}[/tex]. In other words:
[tex]\displaystyle \frac{dv}{dt} = 0.2\; {\rm m^{3}\cdot min^{-1}}[/tex].
Apply the chain rule to find the rate at which [tex]h[/tex] is changing with respect to time [tex]t[/tex]:
[tex]\begin{aligned} \frac{dh}{dt} &= \frac{dh}{dv}\cdot \frac{dv}{dt} \\ &= \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}\cdot \frac{dv}{dt} \end{aligned}[/tex].
Substitute in [tex]A = 0.30\; {\rm m}[/tex], [tex]L = 10\; {\rm m}[/tex], [tex]H = 0.50\; {\rm m}[/tex], [tex]B = 0.80\; {\rm m}[/tex], [tex]h = 0.30\; {\rm m}[/tex] (converted from [tex]30\; {\rm cm}[/tex]), and that the rate of change in [tex]v[/tex] is [tex]0.2\; {\rm m^{3}\cdot min^{-1}}[/tex]:
[tex]\begin{aligned} \frac{dh}{dt} &= \frac{dh}{dv}\cdot \frac{dv}{dt} \\ &= \frac{1}{\displaystyle A\, L + \frac{L}{H}\, (B - A)\, h}\cdot \frac{dv}{dt} \\ &= \frac{0.2\; {\rm m^{3}\cdot min^{-1}}}{\displaystyle 0.30\; {\rm m} \times 10\; {\rm m} + \frac{10\; {\rm m}}{0.60\; {\rm m}}\, (0.80\; {\rm m} - 0.30\; {\rm m}) \, 0.30\; {\rm m}} \\ &=0.033\; {\rm m\cdot min^{-1}} \end{aligned}[/tex].
In other words, the depth of the water in this trough increases at a rate of approximately [tex]0.033\; {\rm m \cdot min^{-1}}[/tex] (meters per minute.)
HELP! will mark brainliest
State your hypothesis. Make sure your hypothesis is worded as an if, then statement and relates the independent variable of wrong length to the dependent variable of wave frequency.
If I increases the string length, the frequency will decreases and vise versa.
What is frequency?In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.
For string wave, we know that,
frequency, n = [tex]\frac{1}{lD}[/tex][tex]\sqrt{\frac{T}{\pi \rho} }[/tex]
where, l = length of the string.
D = diameter.
T = tension
ρ = density of the material.
Hence, we can see that, frequency of the wave is inversely proportional to the length of the wire. So, on increasing string length, frequency of the wave will decreases.
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which region of jupiter generates its magnetic field? view available hint(s)for part a which region of jupiter generates its magnetic field? metallic hydrogen layer molecular hydrogen layer gaseous atmosphere rocky core
The outer core of Jupiter, which is made up of liquid metallic hydrogen, is where electrical currents originate that create the planet's internal magnetic field.
Explain about the outer core?
The third layer of the Earth is its outer core. Iron and nickel, together with trace amounts of other materials, make up the majority of this layer, which is the only one that is liquid. The Earth's magnetic field is created by the outer core. The iron inside the liquid outer core of Earth flows about as it rotates on its axis.
Above the solid inner core of the Earth and below its mantle is a liquid layer made of iron and nickel that is about 2,261 km thick. Its outer boundary is located 2,890 km (1,800 mi) below the surface of the Earth.
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Within free market economies, what role does self interest play? What role does competition play?
Economic activity is driven by self-interest, and competition helps to drive down costs and increase the quality, diversity, and creativity of goods and services.
What kind of activity is self-interested?Seeking your own personal gain is the definition of self-interest. You attend work in order to earn money to spend on the things you want. You attend school so that after you graduate, you'll be able to find a better career and get more money to spend on the things you desire.
How can self-interest be developed?Pick some fresh endeavors that promote goodwill in your career, family, and leisure life. Likewise, be adamant in your actions. When appropriate, communicate your thoughts and feelings to others by asking for what you want, declining what you don't want, and saying No to requests. For a while, make it a point to treat yourself to something every day.
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Destructive interference in a standing wave produces points with zero amplitude called?.
Destructive interference causes nodes—points with no amplitude—to form in a standing wave.
What do you call a point of destructive interference on a standing wave?
The nodes are areas of no displacement brought on by the two waves' destructive interaction. The two waves' constructive interference causes the antinodes to move maximally from their resting position.
Is there zero destructive interference amplitude?
The amplitude is 0 and resembles a node at a point of destructive interference. So, if we consider the aforementioned point to be nodes and antinodes, we can observe that the pattern of nodes and antinodes exactly matches that of a standing wave.
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Using what you have learned about series and parallel circuits, explain how some appliances in your kitchen receive power while others do not. (PLEASE HELPP)
To learn series and parallel circuits, to know the some appliances in your kitchen receive power while others do not.
What is series circuits?
A series circuit is an easy way for electrons to travel to one or more resistors. Anything that depends on a cell for power is a resistor. A bulb frequently serves as the resistor in a series circuit.
What is parallel circuit?
Branching is used in a parallel circuit so that the current is divided and only a portion of it passes through each branch. In a parallel circuit, the voltage, or potential difference, across each branch is the same, but the currents may differ.
While plugged in, a range of various electronic equipment and appliances, such as televisions, toasters, lamps, and more, can use electricity even when they're off.
Therefore, known the series and parallel circuits, the some appliances receive powers.
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using your spectroscope, you observe a light source and see several strong, distinct lines. is this source continuous or discrete? given a line with a wavelength corresponding to 500 nm, calculate the energy of the emitted light.
With the aid of your spectroscope and E = (h*c)/wavelength, you can determine the energy of the emitted light to be 3.97 x 10-19.
What does a mean in terms of wavelength?mathematical representation The movement v (in the x direction), frequency f, and wavelength of traveling sinusoidal waves are frequently expressed mathematically as follows: where y is the value of the wave at any place x and time t, and A is the wave's amplitude.
What is the wavelength measurement unit?The symbol for the wavelength in the SI is typically m, or one metre. The multiples or fractions of something like a meter are also employed for measuring wavelength. Notably, when wavelengths are a significant attribute, exponential powers of 10 are employed. Shorter wavelengths are given as negative exponentials.
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why must the displacement vector of the lighter ball be scaled by the ratio of masses of the two balls?
If no external force on the Centre of mass remains stationary. In order to do that displacement in lighter body must be more than that of heavier ball.
The sum of the starting momentums of the two bodies when they collide is equal to the sum of their final momentums, according to the law of conservation of momentum.
The experimental system supports the law of conservation of linear momentum when a collision occurs between a heavier ball and a lighter ball in the absence of any other external forces.
The centre of mass does not move due to any external forces. A lighter body must have a greater displacement than a heavier ball in order for that to happen. Changes in an object's position are referred to as displacement. A vector quantity, it has both a direction and a magnitude. An arrow that directs viewers from the starting location to the ending position is used to symbolize it. As an illustration, the position of an object changes if it moves from position A to position B. Displacement is the name for this shift in an object's position.
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consider the properties of a string that has a length of 1.0 m and a wave speed of 45 m/s. show answer no attempt what is the fundamental frequency in hz of the string?
By using simple harmonic motion, it can be calculated that The fundamental frequency of the string will be 45Hz.
The wavelength of the standing wave for any given harmonic is related to the length of the string.
Considering the wavelength is equal to the length of the string. It means one wavelength is equal to the length of the string. If more wavelength is made then answer would be different.
so we have wavelength = 1m
wave speed = 45 m/s
as we know that from simple harmonic motion,
frequency = speed/wavelength
frequency = 45/1
frequency = 45 Hz
Hence frequency of the string is 45 Hz.
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a 4.3 kg object is suspended by a string from the ceiling of an elevator. the acceleration of gravity is 9.8. determine the tension of the string if it is accelerating upward at a rate of 2.1
The tension of the string is due to the mass suspended at a weight of 4.3 kg is 51.57N
The mass of the object = 4.3 kg
The acceleration due to gravity = 9.8 m/s²
The accelerating of the string upwards = 2.1 m/s²
The tension of the string can be found using the formula,
T = m(g + a)
where T is the tension of the spring
m is the mass of the object
g is the acceleration due to gravity
a is the acceleration upwards.
Let us substitute the known values in the above equation, we get
T = 4.3 ( 9.8 + 2.1)
= 4.3 ( 11.9)
= 51.57
Therefore, the tension on the string is 51.57 N
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The weight of the builder and new roof tiles is 640 N. The slope is at 30 degrees on the given diagram.
Draw a diagram to calculate the components of the total weight
parallel and perpendicular to the slope of the roof.
The parallel component of the total weight is 320 N.
The perpendicular component of the total weight is 554.3 N.
What is the components of the total weight?
The components of the total weight of the builder and new roof tiles can be parallel component or perpendicular component.
The parallel component of the total weight of the builder and new roof tiles is calculated as follows;
Fn ( parallel ) = W sin ( θ )
where;
W is the total weight of the builder and the new roof tileθ is the slope or angle of inclination of the total weightFn ( parallel ) = W sin ( θ )
Fn ( parallel ) = 640 sin ( 30 )
Fn ( parallel ) = 320 N
The perpendicular component of the total weight of the builder and new roof tiles is calculated as follows;
Fn ( parallel ) = W cos ( θ )
where;
W is the total weight of the builder and the new roof tileθ is the slope or angle of inclination of the total weightFn ( perpendicular ) = W cos ( θ )
Fn ( perpendicular ) = 640 cos ( 30 )
Fn ( perpendicular ) = 554.3 N
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a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force of .
Using the concepts of motion, we got that Ma is the force exerted on the passengers inside the car when a car traveling with a constant velocity quickly comes to rest.
We know very well that according to newton second law of motion,
if a moving object is moving with some velocity v at any particular time t, then there is force acting on that object and that force is given by
F= dp /dt,
where dp is defines as change in momentum of the object. In other words,
dp=M×([tex]v_f_i_n_a_l[/tex] - [tex]v_i_n_i_t_i_a_l[/tex])
where [tex]v_f_i_n_a_l[/tex] and v[tex]_i_n_i_t_i_a_l[/tex] are the velocities of the object in different time.
So suppose car has some mass M kg
It is given that final velocity of the object is =0 as the car comes to rest,
suppose initial velocity is v
Therefore, F=[M×(0-v)]/t
=> F= -M×(v/t)
=> F= -Ma because acceleration =velocity/time
Here negative sign shows that force acts on the person in opposite direction of frictional force applied by the road.
Hence, when a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force - Ma.
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Where do you predict the energy that is not transferred into the electrical grid is lost as it moves from
system to system?
The energy that is not transferred into the electrical grid is lost as heat as it moves from system to system.
The electricity that is produced in power stations reach the consumers through a complex system of electric cables and grid. The grid usually means transformers which is used to step up and step down the voltage when necessary.
The first transformer from the power plant steps up the voltage of the current for the purpose of long distance transmissions. Before entering the household another transformer steps down the voltage to avoid short circuiting the electrical appliances. During all these processes the current is carried through electrical lines. Due to its contact with the atmosphere some energy is lost has heat in the air.
Therefore, the energy that is not transferred into the electrical grid is lost as heat as it moves from system to system.
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how does the amplitude affect the speed of the wave? how does the tension affect the speed of the wave? how does the frequency affect the speed of the wave?
Amplitude does not affect wave speed because amplitude is a measure of the wave energy as it oscillates. This implies that movement of the wave is separate from the movement indicated by the sleep of the wave.
How does tension and frequency affect speed of wave?By increasing the tension, the wave speed increases and hence frequency increases. Greater tension implies greater acceleration of particles, which means greater speed of particles and hence greater speed of wave.
As we know, speed = frequency * wavelength. This clearly means that speed is directly proportional to the frequency such that when frequency increases, speed also increases and vice versa.
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explain how the energy/velocity of water/wind controls the size of the particles in clastic/detrital) rocks
In fast-moving water only coarse material settles out and fine material is carried away. In slow-moving water only fine material, which can settle out.
What is the velocity of water?The velocity of water is the rate at which water moves.A technique that can quickly clear your drains is high-velocity water jetting. This procedure forces water through your pipes at a very high velocity, which aids in dissolving and removing any material that has built up in your drains.The vector quantity velocity (v), denoted by the equation v = s/t, quantifies displacement (or change in position, s), over change in time (t).The volume and speed of the water affect the flow. It is significant because of how it affects the stream's ecosystems, living things, and water quality. Large, fast-moving rivers can be exposed to pollution releases and experience minimal effectsTo learn more about velocity of water refer to:
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a 58 kg sprinter, starting from rest, runs a 60 m long race in 7.8 s with a constant acceleration. how much work does the sprinter do during the first 2.5 s of the race?
Work done by the sprinter in first 2.5 s will be 702.699 J.
Work done is the product of force and distance covered.
Mathematically, W = Force * DistanceMass of the sprinter = 58 kg
Distance covered by the sprinter = s = 60 m
Total time taken by the sprinter = t = 7.8 s
According to the Equations of motion S = ut + [tex]\frac{1}{2}at^{2}[/tex]u = initial velocity = 0
a = constant acceleration
60 = [tex]\frac{1}{2}a7.8^{2}[/tex]
60.84 a = 60 * 2
a = 1.97 [tex]m/s^{2}[/tex]
For a = 1.97 [tex]m/s^{2}[/tex] and t = 2.5 s
d = [tex]\frac{1}{2}at^{2}[/tex]
Here also u is '0' because the distance is being measured from the starting point.
d = [tex]\frac{1}{2} *1.97*(2.5)^{2}[/tex]
d = 6.15 m
Work done by the sprinter = F * d
Force = mass * acceleration
F = 58 * 1.97
F = 114.26 N
distance for first 2.5 sec is 6.15 m
Therefore Work done = 6.15 * 114.26
W = 702.699 J
Work done by the sprinter is 702.699 J.
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Which of the following is not a density-dependent factor limiting a population growth?
a) intra-specific competition
b) switching behavior of a predator
c) a stress syndrome that alters hormone levels
d) a limited number of available nesting site
Answer:A.
i know its a, i did quiz
Two identical objects are moving directly toward one another at the same speed v. What is the total kinetic energy of the system of the two objects?
The total kinetic energy of the system of the two objects can be achieved by adding of the kinetic energies of first and second body.
How do you find the kinetic energy of two objects?Kinetic energy is directly proportional to the mass of the thing and to the square of its velocity: K.E. = 1/2 m v². If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared. So the formula for kinetic energy is that it's equal to 1/2 times the mass of the object, times the immensity of its velocity squared, or another way to think about it, its speed squared. In an elastic collision, both the impulse and the kinetic energy of the system are maintained. On the other hand, in an inelastic collision, momentum is sustained but kinetic energy can not be sustained.
So we can conclude that two objects of equal mass moving with equal speeds in opposite directions have a total momentum of zero, but their total kinetic energy is not zero.
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a 5.4 kg cat and a 2.4 kg bowl of tuna fish are at opposite ends of the 4.0 m -long seesaw. how far to the left of the pivot must a 4.0 kg cat stand to keep the seesaw balanced?
0.88m to the left, where the 4.0 kg cat must be to keep the seesaw balanced.
The concept of Torque and the principle of moment are applied here to understand that the 4.0 kg cat and the bowl of tuna fish will balance the seesaw as long as the 4.0 kg cat stays on the left of the pivot.
m (big cat) = 5.4 kg
m (bowl) = 2.4 kg
m (small cat) = 4.0 kg
From the figure,
5.4 kg x (x m) = 2.4kg x (2m)
x = 4.8 / 5.4
=> 0.88m
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A student decides to conduct a comparative investigation to study properties of elements.What is a benefit of conducting a comparative investigation rather than a descriptive investigation?
a It will be less time-consuming to collect data about elements.
b It will show a cause-and-effect relationship between two properties of elements.
c It will be less expensive to collect data and make observations about elements.
d It will provide much more information about properties of elements.
please answer right I'm on an exam and show picture to show right if u can
Answer:its b
Explanation: i took the test
An astronomical telescope is used to view distant stars. How does the angle between the just-resolvable light from two stars differ if the average light from the stars is red or if it is blue?.
The angle of just resolution light from two stars is greater if the light of the average star is red or if it is blue.
The formula to find the aperture of the telescope
D = 1.22λ/dФ
Limits of resolution:
The limit of resolution is a measure of the ability of the objective lens to separate in the image adjacent details that are present in the object.
There is diffract in the light when it passed through space and gets bent around obstacles. Diffraction grants disperse light according to wavelength, for example, it can be used to produce spectra.
Therefore an astronomical telescope is used to view distant stars. The angle is greater if the light of the average stars is red or if it is blue.
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On a wet road, is a higher coefficient of friction on the tires safer or a lower one and pls explain I don’t get it
On a wet road, a higher coefficient of friction on the tires is safer as compared to a lower coefficient of friction.
What are friction and its coefficient?Friction is defined as a force that resists the sliding or rolling of one object over another object. The coefficient of friction refers to a measure of the amount of friction present between two surfaces. When you calculate a coefficient of friction, you're calculating the resistance to motion at the interface of two surfaces of materials.
On dry surfaces, you have a high coefficient of friction of about 0.9, but driving on wet roads would be dangerous because the wet road coefficient is very low about 0.1.
So we can conclude that a higher coefficient of friction is recommended for a safe journey.
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A quantity of 100g of ice at 0c and 50g steam at 100 c are added to a container that has 150 g water at 30c. Determine the final temperature in the container. Ignore the container itself in your calculations.
Answer:90g for 70km
Explanation:
two identical, parallel-plate capacitors are connected to identical batteries and allowed to charge fully. a dielectric is placed between the plates of one of the capacitors while still connected to the battery and allowed to reach a steady state. discuss whether the capacitance, charge, and electric potential of the capacitor with the dielectric are greater than, less than, or equal to the capacitor without the dielectric.
Capacitance, charge and electric potential will be greater than the capacitor without the dielectric.
Capacitance is the a property of an electric conductor or set of conductors that is measured by the amount of separate electric charge that can be stored on it per unit change in electric potential.
The value of capacitance for the parallel plate is C = (3∈0AK)/d
Since two identical, parallel-plate capacitors are connected
therefore the value of capacitance for both the plate is C
Ceq. = (C1*C2) / C1 + C2 = C*C / C+C = C2
When the battery remains connected, the potential difference [V] remains constant
Q=CV
∴Cafter>Cbefore [C increased]
∴Qafter>QBefore [Q increased]
Potential difference and charge across the capacitor before the dielectric:
Qbefore = [tex]\frac{CV}{2}[/tex]
Vbefore = Vafter = V
Potential difference and charge on the capacitor after inserting the dielectric:
Qafter = Ceq*V = [tex]\frac{kCV}{k+1}[/tex]
Vafter = Q*After / KC = [tex]\frac{\frac{kCV}{k+1}}{kc}[/tex]
Vafter= [tex]\frac{V}{k+1}[/tex] [K>1]
[Hence V decreases]
Vbefore > Vafter
Also, E = [tex]\frac{V}{d}[/tex]
therefore [E]before > [E]after [E decreases]
Energy stored in the capacitor:-
U=[tex]\frac{1}{2} CV^{2}[/tex]
As V= constant
Cafter > Cbefore .
Hence Uafter > Ubefore
Thus, the electrostatic potential increases.
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in a simple electric circuit, ohm's law states that , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms. assume that, as the battery wears out, the voltage decreases at 0.01 volts per second and, as the resistor heats up, the resistance is increasing at 0.04 ohms per second. when the resistance is 400 ohms and the current is 0.04 amperes, at what rate is the current changing?
The rate is the current changing is = - 1.3 x 10⁻⁴ A/s
Solution:
We take the derivative of Ohm's law with respect to time
V = IR
Using the product rule:
dV/dt = I(dR/dt) + R(dI/dt)
We are given that voltage is decreasing at 0.01 V/s
resistance is increasing at 0.04 ohm/s
resistance itself is 400 ohms,
and current is 0.04 A
Substituting:
-0.01 V/s = (0.04 A)(0.04 ohm/s) + (400 ohms)(dI/dt)
dI/dt = -1.3 x 10⁻⁴ A/s.
The relationship between current, voltage, and resistance. The amount of continuous current flowing through many materials is directly proportional to the potential difference or voltage between them.
Law of Electricity The strength of a direct current is directly proportional to the potential difference and inversely proportional to the resistance of the circuit. Ohm's Law is a formula for calculating the relationship between voltage, current, and resistance in a circuit. Ohm's law describes the relationship between current, voltage, and resistance. This shows that at a constant temperature, the current through the circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit.
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consider the boyle's law apparatus. suppose that the volume of the gas is 25 cc and the pressure is 30.0 lbs/in2. show answer no attempt if the plunger is depressed so that the volume is decreased to 10.0 cc, what will the pressure be in lbs/in2?
75 lbs/in^2 is the value of pressure. The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure.
What is pressure?In the physical sciences, pressure is defined as the stress at a point within a confined fluid or the perpendicular force per unit area.
The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units.
P1V1=P2V2
The amount of force applied to a certain region is referred to as pressure. Absolute pressure, gauge pressure, and differential pressure are the three categories into which pressure is divided.
The distance between that point and the surface, the liquid's density. Gravitational acceleration are the factors of pressure.
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Question 16 Which of the following is NOT a way to speed up a chemical reaction? (Select all that apply) b C decreasing the surface area of one of the reactants increasing the concentration of one of the reactants decreasing the temperature of one of the reactants increasing the temperature of one of the reactants
The following which is not a way to speed up a chemical reaction include the following below:
Decreasing the surface area of one of the reactantsDecreasing the temperature of one of the reactants.What is Temperature?This is defied as the degree of hotness or coldness of a substance and it is determined by thermal energy.
In a chemical reaction, the speed can be increased by increasing the surface area and the temperature because it leads to the collision of more atoms in other to form the product which was why options A and C were chosen as the correct choices.
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A soccer ball is kicked horizontally across a field with an initial velocity of magnitude 15 m/s. If the soccer ball has a mass of 0.43 kg, what is the kinetic energy of the ball just after it is kicked?
The kinetic energy of the ball just after it is kicked is 48 J.
What is kinetic energy?Kinetic energy is the force that propels motion, which can be seen in the movement of a particle, an object, or a group of particles. A person walking, a baseball being thrown, a piece of food falling from a table, and a charged particle in an electric field are all instances of objects in motion that use kinetic energy.
Vibrational, rotational, and translational energy are the three subtypes of kinetic energy. Unsurprisingly, vibrating things are the source of vibrational kinetic energy. While objects colliding with one another produce translational kinetic energy, objects moving create rotational kinetic energy.
Given:
Mass- 0.43kg
Velocity- 15
kinetic energy = 1/2 mv²
kinetic energy of the ball = 1/2 (0.43)(15)²
kinetic energy of the ball = 48 J.
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