The spring constant can be calculated as: 12.51 N.
The formula for calculating the period of oscillation is written as the following:
[tex]T=2\pi \sqrt{\frac{m}{k} } \\[/tex]
m is the mass of the spring.
k is the spring constant.
Making the spring constant "k" the subject of the formula will give us the following expression;
[tex]k=4\pi ^{2} \frac{m}{T^{2} } \\[/tex]
Get the period of oscillation "T"
T= 1/f
frequency "f" can express the number of oscillations completed in one second.
If a student with a stopwatch finds that 12 oscillations take 15.0 s, the number of oscillations in one sec will be 9/14 = 0.64 osc.
Period T = 1/0.64 = 1.56sec
Get the required spring constant
[tex]K=4\pi ^{2} \frac{m}{T^{2} } \\k= 4(3.14)^{2}\frac{0.13}{0.64^{2} } \\[/tex]
K= 12.51 N
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A crate of mass m1 = 14.00 kg is pulled by a massless rope up a 36.9° ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m2 = 16.30 kg. The crates move 1.61 m, starting from rest.
Find the work done by gravity on the sliding crate.
The work done by gravity on the sliding crate is 176.6 J.
What is the work done by gravity on the sliding crate?
The work done by gravity on the sliding crate is calculated by applying the following formula.
W = Fd cosθ
W = mg x d cosθ
where;
m is the mass of the crateg is acceleration due to gravityd is the displacement of the crateθ is the angle of inclination of the ropeW = ( 14 kg x 9.8 m/s² ) x ( 1.61 m ) x cos ( 36.9 )
W = 176.6 J
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A pinball bounced around its machine before resting between two bumpers. Before the ball came to rest, its displacement was recorded as a series of vectors. All the angles are measured counterclockwise from the horizontal ‑axis.
⃗ 1:83.0 cm at 90.0∘
⃗ 2:57.0 cm at 159∘
⃗ 3:67.0 cm at 221∘
Find the magnitude and direction of the ball's total displacement.
The magnitude and direction of the ball's total displacement is 119.6 cm and 29.8⁰ respectively.
What is the magnitude of the ball's total displacement?
The magnitude of the ball's total displacement is calculated by applying the following formula.
The sum of the horizontal displacement is calculated as follows;
∑X = 83 cm x cos (90) + 57 cm x cos (159) + 67 cm x cos (221)
∑X = -103.78 cm
The sum of the vertical displacement is calculated as follows;
∑Y = 83 cm x sin (90) + 57 cm x sin (159) + 67 cm x sin (221)
∑Y = 59.47 cm
The magnitude of the displacement is calculated as follows;
d = √ [ ( -103.78 )² + ( 59.47)² ]
d = 119.6 cm
The direction of the displacement is calculated as follows;
θ = arc tan ( 59.47 / 103.78 )
θ = 29.8⁰
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Which of the following determines the earth's temperature?
Answers:
A. Carbon dioxide in the atmosphere
B. Energy output of the sun
C. All of these are correct.
D. Distance from the sun
The greatest option is C because all of them are correct. The planet's temperature is affected by the sun's energy output, the amount of carbon dioxide in the atmosphere, and its distance from the earth.
The atmosphere of Earth is the layer of gases with high speed, collectively known as air, that envelops the planet and gives it its planetary atmosphere. The Earth's atmosphere keeps life on the planet safe by maintaining the pressure necessary for liquid water to exist on the surface. The distance between any two places in space is equal to the length of the straight line connecting them, which is also the shortest path. This is the usual conception of distance in classical physics, especially in Newtonian mechanics.
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in the circuits shown, the brightness of the bulbs is observed to compare as follows: a is the brightest, and b and c are equally bright and dimmer than A (A>B=C)
Why is bulb A brighter than bulb B or C?
Because the voltage is greater across A than across B or C
Because the current is greater through A than through B or C
Because the circuit containing bulb A has less overall resistance
Because there is more curren from the battery in the circuit containing bulb A Because bulbs B and C only get half the current from the battery, while A gets all of it
The reason bulb A is brighter than bulbs B and C is because it has a higher voltage and a lower resistance than either of them.
What is lower resistance?Lower resistance is the measure of how easily an electrical current can flow through an object or circuit. It refers to how much opposition a material presents to the flow of an electric current. The lower the resistance of a material, the easier it is for an electric current to flow through it, and the higher its conductivity.
This is because the circuit containing bulb A has the least overall resistance, meaning more current is able to flow through it and it is able to operate at a higher voltage. This means that the current is able to provide more energy to the bulb, causing it to be brighter than bulbs B and C.
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A⃗ = 22x^ + (-14)y^, and B⃗ = 2.5x^ + 13y^. Express A⃗ −B⃗ in unit vector notation.
The unit vector notation in the given direction is [tex]0.58 \hat x + 0.81 \hat y[/tex].
What is vector quantity?A physical quantity that has both directions and magnitude is referred to as a vector quantity.
A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.
In terms of subtracting a vector, it works the same as adding the vector's opposite.
Given that:
[tex]\vec A = 22 \hat x + (-14)\hat y,\\\vec B = 2.5\hat x + 13\hat y.[/tex]
( two given vectors are written here.)
Therefore: the subtraction of these two vectors will be:
[tex]\vec A - \vec B = (= 22 \hat x + (-14)\hat y) - (2.5\hat x + 13\hat y)\\= 19.5\hat x - 27 \hat y[/tex]
Unit vector in that direction of vectors is =
[tex]= \frac{19.5\hat x - 27 \hat y}{\sqrt{19.5^2 + (-27)^2} } \\= 0.58 \hat x + 0.81 \hat y[/tex]
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evaluate the numerical value of the final momentum of the t-shirt using the results from parts a and b. view available hint(s)
The final momentum of the t-shirt can be evaluated by multiplying the mass of the t-shirt (from part a) by its final velocity (from part b). Final momentum = (1.0 kg) x (20.0 m/s) = 20 kg m/s.
What is final momentum?Final momentum is the momentum of an object after it has been acted upon by an external force. It is calculated by taking the initial momentum of an object and adding or subtracting the force of the external force to determine the final momentum. The final momentum is equal to the initial momentum plus the change in momentum caused by the external force. Final momentum can be calculated using the equation pfinal = pinitial + FΔt, where pfinal is the final momentum, pinitial is the initial momentum, F is the force of the external force, and Δt is the change in time caused by the force.
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Using an ohmmeter, a student measures the resistance between various points on his body. He finds that the resistance between two points on the same finger is about the same as the resistance between two points on opposite hands—both are several hundred thousand ohms. Furthermore, the resistance decreases when more skin is brought into contact with the probes of the ohmmeter. Finally, there is a dramatic drop in resistance (to a few thousand ohms) when the skin is wet. Explain these observations and their implications regarding skin and internal resistance of the human bo
The resistance between two points on the same finger is likely due to the resistance of the skin and the small amount of muscle and fat that is present in the finger.
What is the cause of resistance between two points on opposite hands?The resistance between two points on opposite hands is likely due to the resistance of the skin and the larger amount of muscle and fat that is present in the hand. The resistance decreases when more skin is brought into contact with the probes of the ohmmeter because more skin in contact means more surface area for the current to flow through, thus reducing the resistance. The dramatic drop in resistance when the skin is wet is likely due to the fact that water is a better conductor than dry skin. This observation suggests that the resistance of the human body is largely due to the resistance of the skin, and that the internal resistance of the body (i.e., the resistance of muscles, bones, etc.) is relatively low in comparison.
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According to the TARGET acronym, which of the following is not a measure to use to foster a mastery-oriented environment
According to the acronym TARGET, affiliation is not a strategy to support a mastery oriented environment.
Creating a mastery oriented environment is where students are actively engaged in the learning process, setting and achieving meaningful goals, and feeling a sense of accomplishment. TARGET is a useful acronym for that goal.
TARGET stands for:
Trust: Building trust between teacher and students is essential so that it increases the likelihood for taking risks and giving feedback.
Authenticity: Teachers must be authentic in their interactions with students. This means being genuinely interested and honest in teaching and assessment.
Respect: It is important to create an atmosphere of respect in the classroom. Respect should be shown to all students.
Growth Mindset: A growth mindset is essential and it means emphasizing effort and progress over ability and success.
Expectations: Teachers should set clear expectations for students, but be flexible in how these expectations are met.
Affiliation is not a measure for fostering a mastery-oriented environment.
It refers to the quality of being intimately connected to or allied with a certain individual, organization, party, business, etc.
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if the cart moves along the track at a constant speed, what are the cart's velocity and acceleration vectors at points a, b, and c? start your vectors at the corresponding black dots. the orientation of your vectors will be graded. the exact length of your vectors will not be graded.
Since the cart moves along the track at a constant speed, its velocity vector at points a, b, and c will have the same magnitude and direction.
The velocity vector can be represented as an arrow pointing in the direction of motion with the magnitude being the speed of the cart.
The acceleration vector at points a, b, and c will be zero since the cart is moving at a constant speed. The acceleration vector can be represented as a zero vector or a vector of length 0 with no direction.
So, the velocity and acceleration vectors at points a, b, and c can be represented as:
Point a:
Velocity vector: constant magnitude and directionAcceleration vector: zero vectorPoint b:
Velocity vector: constant magnitude and directionAcceleration vector: zero vectorPoint c:
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21. A 110-V household circuit that contains an
1800-W microwave, a 1000-W toaster, and an
800-W coffeemaker is connected to a 20-A fuse.
Determine the current. Will the fuse melt if the
microwave and the coffeemaker are both on?
The final current will be 32.7 A and Yes, the fuse will melt if the microwave and the coffeemaker are both on at the same time.
How to determine current and whether or not a fuse has melted?
To determine the current, we can use Ohm's Law, which states that current (I) is equal to power (P) divided by voltage (V).
I = P/V
The total power of the three appliances is 1800 W + 1000 W + 800 W = 3600 W.
Therefore, the current is:
I = 3600 W / 110 V = 32.7 A
The fuse is rated at 20 A, so it will melt if the current exceeds 20 A. Since the current is 32.7 A, the fuse will melt if the microwave and the coffeemaker are both on at the same time.
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As CJ k ad l ad my G My h KD h KD h my SJ KD zhh MD
Cause: According to this law, the skateboard requires an external source of force to move, which the skateboarder indirectly provides.
Effect: On the pavement, the skateboarder reverses forward (that is he applies a force on the road in a direction opposite the direction of intended motion).
What connection exists between a cart's mass and its acceleration after the spring is let go?
The acceleration of the cart is inversely proportional to its mass. As a result, the acceleration of the cart will decrease as its mass increases.
The mass and acceleration are inversely correlated: the acceleration decreases as mass increases.
Newton's second law states that force and acceleration are directly proportional to one another, so if a cart's mass is held constant while the force acting on it increases, the cart will accelerate. When an object moves, it has kinetic energy, which it then expends.
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A machine of efficiency 80% does 3000j of work. caculate the energy used in over function?
The machine does 3000 J of work.
This is 80% of the energy that was put into the machine.
3000 J = 0.80 x (Input energy)
Divide both sides of the equation by 0.80 .
Input energy = 3000 J / 0.8
Input energy = 3750 J
In the video, the loaded car accelerated less than the unloaded car when the same force was applied. This was noticeable because the loaded car
Choose one or more:
A. was traveling faster after a little time had passed.
B. reached the end of the track more slowly.
C. reached the end of the track faster.
D. was traveling less quickly after a little time had passed.
When the same force was supplied to the loaded and unloaded cars, the loaded car accelerated less, which was visible since the laden car arrived at the track's finish more slowly. and after a little while, she started moving less swiftly. so Option B and option Dare correct
The rate at which an object's velocity with respect to time changes is referred to as the mechanics of acceleration. Acceleration is a vector quantity (in that they have magnitude and direction). The direction of an object's acceleration is determined by the direction of the net force acting on it.According to Newton's Second Law, an object's acceleration is determined by a combination of two factors: its mass, which depends on the materials it is made of, and the net balance of all external forces acting on it. The magnitude of an object's acceleration is inversely proportional to the mass of the object.
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Small spheres of diameter 1.05 mm fall through 20.0°C water with a terminal speed of 2.34 cm/s. Use 1.00 x 10-3 §a for the viscosity of water. Calculate the density of the spheres.
The density of the spheres is 1.004 gm/cm³.
What is terminal velocity?The maximum velocity attained by an object as it falls through a fluid is known as terminal velocity.
It occurs when the sum of the drag and buoyancy forces acting on the object equals the downward force of gravity. Because the object's net force is zero, it has no acceleration.
The terminal speed = 2.34 cm/s.
The viscosity of water = 1.00 × 10⁻³ CGS unit.
Terminal velocity: v = (2/9)(σ − ρ)gr²/η.
σ = 9vη/{2gr²} + ρ
= (9 × 2.34 × 1.00 × 10⁻³)/(2×980×(0.105/2)²) + 1
= 1.004 gm/cm³
Hence, The density of the spheres is 1.004 gm/cm³.
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A cheetah is running at 40 m/s and catches his prey at 12 m/s. The chase took 30s. What is the
acceleration?
Formula for acceleration:
[tex]a=\dfrac{Vf-Vi}{t}[/tex]
acceleration(measured in m/s^2) = Final velocity(measured in m/s) - Initial velocity(measured in m/s) / time(measured in seconds)
__________________________________________________________
Given:
[tex]Vi=40m/s[/tex]
[tex]Vf=12m/s[/tex]
[tex]t=30s[/tex]
[tex]a=?[/tex]
__________________________________________________________
Finding acceleration:
[tex]a=\dfrac{Vf-Vi}{t}[/tex]
[tex]a=\dfrac{12-40}{30}[/tex]
__________________________________________________________
Answer:
[tex]\fbox{a = -0.93 m/s squared}[/tex]
in the collision theory of kinetics, which of the following is required to have a successful collision? select all that apply. i. three or more species must collide simultaneously. ii. a collision of the appropriate orientation must occur. iii. transfer of energy must occur in a collision such that the molecule has energy equal to or greater than the activation energy. iv. the temperature of the sample must be greater than 298k. v. formation of products.
The following is required to have a successful collision: ii. A collision of the appropriate orientation must occur, iii. Transfer of energy must occur in a collision such that the molecule has energy equal to or greater than the activation energy, v. Formation of products.
What is collision?Collision is when two objects come in contact with one another and experience a force as a result. This force can be a direct result of the objects hitting each other, or it can be the result of the objects exerting a force on one another in order to move away. In either case, the objects experience a momentary change in their respective velocities.
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Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and
points***
The battery has an internal resistance of 2.50
4.1 Show that the resistance of the 6.2 V, 4.5 W lamp at its working potential difference
(pd) is about 9.
Look at photo for more info
4.2 The terminal pd across the battery is 6.2 V.
Calculate the emf of the battery.
rope
Pulleys P and M are frictionless so that the tension in the rope attached to A is equal to the weight of A
A weighs 35 N and the weight of moveable pulley M is negligible.
Calculate the tension in the horizontal cable C when the gate is closed.
tension
3.3 Pulley M is pulled to the left as the gate is opened.
10/36
Explain why this increases the tension in the horizontal cable C.
The resistance of working potential difference of the 6.2 V, 4.5 W lamp is 8.54 ohm. When terminal pd across the battery is 6.2 V, the emf of the battery is 8.01 V.
What is resistance?The opposition that a substance provides to the flow of electric current is referred to as resistance. The uppercase letter R represents it. The ohm is the standard unit of resistance, which is sometimes written as a word and sometimes represented by the uppercase Greek letter omega. Resistance is a measure of an electrical circuit's resistance to current flow. Resistance is measured in ohms, which is represented by the Greek letter omega ().
Here,
r=2.5 ohm
V= 6.2 volts
P=4.5 watt
P=V²/R
R=V²/P
R=6.2*6.2/4.5
R=8.54 ohm that is about 9 ohm.
I=V/R
I=0.726 A
EMF=V+Ir
=6.2+0.726*2.5
=6.20+1.81
=8.01 volts
The resistance of the 6.2 V, 4.5 W lamp at its working potential difference is 8.54 ohm. The emf of the battery when terminal pd across the battery is 6.2 V is 8.01 V.
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Methane and oxygen combine in a synthesis reaction. true or false
Answer:
True.
Explanation:
A synthesis reaction is a type of chemical reaction in which two or more substances combine to form a new compound. Methane (CH4) and oxygen (O2) can combine in a synthesis reaction to form carbon dioxide (CO2) and water (H2O). This reaction is exothermic and is the basis of combustion reactions.
The balanced equation for this reaction is:
CH4 + 2O2 -> CO2 + 2H2O
In this reaction, one methane molecule and two oxygen molecules combine to form one carbon dioxide molecule and two water molecules.
It's worth mentioning that methane is considered a greenhouse gas, and the combustion of methane releases carbon dioxide and water vapor into the air, which contribute to global warming and climate change.
two identical springs are attached to two different masses, ma and mb , where ma is greater than mb . the masses lie on a frictionless surface. both springs are compressed the same distance, d , as shown in the figure. which of the following statements descibes the energy required to compress spring a and spring b?
The amount of energy required to compress spring A and spring B would be the same.
What is energy?Energy is the capacity to do work. It is the ability to cause change and is found in many forms, including chemical, electrical, mechanical, nuclear, radiant, and thermal energy. It is often referred to as the "lifeblood" of our modern society, as it is necessary for everything from powering homes and businesses, to providing energy for transportation and communication.
This is because the springs are identical and the amount of compression (d) is the same. The masses of the objects don't affect the energy required to compress the springs since the objects are lying on a frictionless surface and will not resist the springs being compressed.
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An object moves from location D to location F on a trajectory (dotted line) in the direction indicated; arrows representing the momentum at locations D, E, and F. ' EP 9 zero magnitude 10 more info needed (a 15pts) Using the numbered direction arrows shown, indicate (by number) which direction arrow best represents the direction of the quantities listed below. If the quantity has zero magnitude or cannot be determined, indicate using the corresponding number listed below. • The position vector at location D • The change in position the displacement) between location D and location F • The change in velocity between location D and location F_ • The change in momentum between location D and location F • The average net force between location D and location F
• The position vector at location D: 1
• The change in position (the displacement) between location D and location F: 3
• The change in velocity between location D and location F: 2
• The change in momentum between location D and location F: 4
• The average net force between location D and location F: EP (zero magnitude)
The position vector at location D is represented by arrow 1, as it indicates the location of the object at that point. The change in position, or displacement, between location D and location F is represented by arrow 3, as it shows the overall change in position of the object from one location to the other. The change in velocity between location D and location F is represented by arrow 2, as it shows the overall change in the object's velocity during that time.
The change in momentum between location D and location F is represented by arrow 4, as it shows the overall change in the object's momentum during that time. The average net force between location D and location F cannot be determined with the information given.
The complete question is given below in the image.
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which substances could be present in earths spectrum, but it is difficult to say that they are definitely present? why?
Traces gases and heavy elements are the examples of the substances that could be in the earths spectrum. They cannot be detected because the technology to do this is not available.
Which substances could be present in earths spectrum?There are several substances that could be present in Earth's spectrum, but it is difficult to say that they are definitely present due to the limitations of current technology and methods for detecting and analyzing these substances. Some examples include:
Trace gases: Gases such as methane, nitrous oxide, and carbon monoxide can be present in small concentrations in the Earth's atmosphere, but it is difficult to detect them with high accuracy due to the limitations of current sensing technology.
Heavy elements: Elements such as gold, platinum, and mercury are present in trace amounts in the Earth's crust, but it is difficult to detect them using current analytical methods.
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Dependent, immature children who frequently misbehave were most likely raised by _____ parents.
(a) authoritarian
(b) authoritative
(c) generative
(d) overly permissive.
Answer: d
Btw if you get it wrong, sry.. :(
I think its d because overly permissive means that you give people freedom and if a parent gives their kid freedom they would be very dependent and immature. (freedom as in the parent dosen't care what the kid does and gives into the kid.)
The drawing shows two situations in which charges are placed on a and y axes. They are located at the same distance if 6.80cm from the origin O. For each of the situations in the drawing, determine the magnitude of the net electric field at the origin
The electric field strength from the origin is 1.95 x 10¹² q ( N/C ).
What is electric field?
The electric field of a charged particle is the region of space where the influence of electric force is felt.
Mathematically, the formula for electric field strength is given as;
E = kq / r²
where;
k is the Coulomb's constantq is the magnitude of the charger is the position of the chargeThe electric field strength from the origin is calculated as follows;
E = ( 9 x 10⁹ x q ) / ( 0.068 m )²
E = 1.95 x 10¹² q ( N/C )
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In our warmup today we're looking closer at our aquariums. We need to get them clean so we can start a new aquarium setup , but there's something on the inside of the glass, the outside of the hood, and the outside of the filter.
1. What is that white residue on our aquariums?
2. How does it form?
3. Where does it come from?
4. How do we get rid of it?
The white residue on aquariums could be mineral , such as hard water stains, and it formed as a result of the hard substance remaining after water evaporation. It is from the water, and to remove it, a white vinegar and water mixture should be used.
What is the significance of the aquarium?Its significance includes that an aquarium can be a place for people to learn about aquatic animals, for the conservation of some animals, for entertainment, and also for use in research proposals, etc.
Hence, the white residue on aquariums could be mineral , such as hard water stains, and it formed as a result of the hard substance remaining after water evaporation. It is from the water, and to remove it, a white vinegar and water mixture should be used.
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T/F deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
Inferential statistics is used to determine whether a process that fills bottles with soda is working properly by weighing a sample of bottles, so the given statement is true.
What is Inferential statistics?Inferential statistics is a branch of statistics that employs analytical tools to draw conclusions about a population by analyzing random samples. Inferential statistics seek to make broad generalizations about a population.Descriptive statistics are statistics that summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or determine whether your data can be generalized to a larger population.Inferential statistics, or hypothesis testing, allows us to draw conclusions about an entire population based on a representative sample.Inferential statistics most common methodologies are hypothesis tests, confidence intervals, and regression analysis. Surprisingly, these inferential methods can produce summary values that are similar to descriptive statistics like the mean and standard deviation.To learn more about Inferential statistics refer to :
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if the vessel has a pinhole-sized leak, which of the following will be true regarding the relative values of the partial pressures of the gases remaining in the vessel after some of the gas mixture has effused?
The option that will be true regarding the relative values of the partial pressures of the gases remaining in the vessel after some of the gas mixture has effused is;
A) Pressure He < Pressure Ne < Pressure Ar
What is pressure?Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is dispersed. Gauge pressure is the pressure in relation to the surrounding atmosphere. Pressure is expressed using a variety of units. Pressure is the force acting on a unit area of a surface. It works perpendicular to the surface under pressure. Pressure = force multiplied by the area on which it operates. Pressure is defined as the amount of force exerted perpendicular to an object's surface per unit area, and the symbol for it is p. (or P). The pascal is the SI unit of pressure (Pa).
Here,
The option that will be true in terms of the relative partial pressures of the gases remaining in the vessel after some of the gas mixture has been effused is;
A) Pressure He < Pressure Ne < Pressure Ar
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a cylinder weighing 120 n rests between two frictionless walls as shown. the wall reaction in newton at point a is most nearly
The wall reaction at point A in newton is most nearly calculated to be equal to 60 N.
What is wall reaction?Wall reaction means that when you push on a wall, the wall pushes back on you with force equal in strength to the force you exerted.
Cylinder is in a state of static equilibrium, which means that net force and net torque acting on it are both zero. Force exerted by the wall at point A is equal in magnitude but opposite in direction to force exerted by the cylinder on wall at point A. Since the cylinder is not accelerating, net force acting on it is zero.
Since the force exerted by the wall at point A is equal in magnitude but opposite in direction to the weight of the cylinder, we say that the wall reaction at point A = 1/2 * weight of cylinder = 1/2 * 120 N = 60 N.
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When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, e = -1.60 × 10-19 C, 1 eV = 1.60 × 10-19 J, mel = 9.11 × 10-31 kg)
(a) What is the work function of the metal, in eV?
(b) What is the maximum speed of the ejected electrons?
(a) Work function of the metal is 2.74 eV. (b) maximum speed of the ejected electrons is 1.15 x 10^6 m/s (1.15 million m/s)
What is work function?The work function is the minimum energy required to remove an electron from the surface of a metal.
AS, Work function (Φ) = hν - eV0
(V0) is stopping potential and (ν) is the frequency of the incident light
Given, wavelength of the incident light is 437 nm,
ν = c / λ = 3.00 x 108 m/s / 437 x 10-9 m = 6.87 x 1014 Hz
Hence, Φ = hν - eV0 = 6.626 x 10-34 J ∙ s * 6.87 x 1014 Hz - 1.60 x 10-19 C * 1.67 V = 4.36 x 10-19 J = 2.74 eV
So the work function of the metal is 2.74 eV.
(b) Maximum speed of the ejected electrons can be calculated using the formula: Vmax = √(2eV0/mel)
Vmax is the maximum speed of the ejected electrons, e is charge of an electron, V0 is stopping potential and mel is mass of the electron.
Vmax = √(2 * -1.60 x 10^-19 C * 1.67 V / 9.11 x 10^-31 kg) = 1.15 x 10^6 m/s
So, the maximum speed of the ejected electrons is 1.15 x 10^6 m/s (1.15 million m/s)
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find the magnitude of the electric field, in newtons per coulomb, at the center of the triangular configuration of charges, given that qa
4.33×103 N/C, 35.0∘ below the positive x-axis if qa=+2.50 nC, qb=−8.00 nC, and qc=+1.50 nC are the charges on all the three vertexes of an equilateral Triangle.
As we know the electric field at a point due to a charged particle is E = F/q where f is the force and q is the charge. If the orientation of charges is the same as shown in the image attached then
E = KQq/[tex]r^{2}[/tex]q where k = 8.99 × 10 9 N ⋅ m 2 /C 2.
where Q is charged particle and q is another charge so
E = 8.99 × 10 9*2.50*8.00 /3/4r*2.5
which results in
4.33*10^3 N/C
that is the net electric field at the center of the Triangle with charges on all the vertexes.
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An electron is launched at a 45∘ angle and a speed of 5.0×106m/s from the positive plate of the parallel-plate capacitor shown in the figure (Figure 1). The electron lands 4.0 cm away.
Part a) What is the electric field strength inside the capacitor?
Part b) What is the smallest possible spacing between the plates?
(a) The electric field strength inside the capacitor is 2,519.35 N/C.
(b) The smallest possible spacing between the plates is 2 cm.
What is the time of motion of the electron?The time of motion of the electron is calculated as follows;
X = Vₓt
t = X / Vₓ
where;
Vₓ is the horizontal component of the velocityX is the horizontal displacementt is the time of motiont = ( 0.04 m ) / ( 5 x 10⁶ x cos 45 )
t = 1.13 x 10⁻⁸ s
The force of the electron is calculated as follows;
F = mv / t
where;
m is the mass of the electronv is speedt is the timeF = ( 9.11 x 10⁻³¹ x 5 x 10⁶ ) / ( 1.13 x 10⁻⁸ )
F = 4.03 x 10⁻¹⁶ N
The electric field strength inside the capacitor is calculated as follows;
E = F / q
E = ( 4.03 x 10⁻¹⁶ ) / ( 1.6 x 10⁻¹⁹ )
E = 2,519.35 N/C
The smallest possible spacing between the plates is calculated as follows;
vertical acceleration of electron;
a = ( Vy ) / t
a = ( 5 x 10⁶ x sin45 ) / ( 1.13 x 10⁻⁸ )
a = 3.13 x 10¹⁴ m/s²
The vertical displacement of the electron;
0 = Vy² - 2ay
y = Vy² / 2a
y = ( 5 x 10⁶ x sin 45 )² / ( 2 x 3.13 x 10¹⁴ )
y = 0.02 m
y = 2 cm
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