Answer:
Stars are powered by nuclear fusion in their cores, mostly converting hydrogen into helium. The production of new elements via nuclear reactions is called nucleosynthesis. A star's mass determines what other type of nucleosynthesis occurs in its core (or during explosive changes in its life cycle).
a book weighing 1.0 newton is lifted 2m. how much work was done?
Answer:
Work done, W = 2 J
Explanation:
Given that,
Weight of a book, W = F = 1 N
It is lifted to a height of 2 m
We need to find the work done. It can be calculated using the formula as follows :
W = F d
Put all the values,
W = 1 N × 2 m
W = 2 J
So, 2J of work was done.
The lungs are large organs which contain smaller, expandable sacs.
These sacs greatly increase the surface area of the lungs.
Why is a large surface area important to the function of the lungs? A. Large amounts of liquid wastes and fatty tissue must be stored in the lungs. B. Oxygen in air taken in by the lungs must move quickly through the lung tissue and into the blood. C. The lungs must be very sturdy and rigid so they cannot move. D. The lungs must be able to filter oxygen from water while the organism is swimming.
Answer:
B. It is B because without this much space for oxygen and blood to flow and go through, we would not survive.
Explanation:
(a) Calculate the force (in N) the woman in the figure below exerts to do a push-up at constant speed, taking all data to be known to three digits. (You may need to use torque methods from a later chapter.) 401.15
(b)How much work (in J) does she do if her center of mass rises 0.260 m?
(c) What is her useful power output (in W) if she does 30 push-ups in 1 min? (Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.)
the force the woman exerts to do a push-up at constant speed is 333 N.
the work the woman does is 152 J.
her useful power output is 76 W.
(a) To calculate the force the woman exerts to do a push-up, we need to use torque methods. The woman is doing a push-up at constant speed, which means that the net torque on her body is zero. The only torque acting on her body is due to her weight W, which acts at the center of mass of her body. The distance between her center of mass and her hands is 0.76 m, and the angle between her body and the horizontal is 45 degrees.
The torque due to her weight about her hands is given by:
τ = r x W = (0.76 m) x (cos 45°)(W)
where r is the distance between her hands and her center of mass and cos 45° is the component of the distance perpendicular to the weight vector. Since the woman is at constant speed, the torque she exerts about her hands must be equal and opposite to the torque due to her weight. Therefore:
τ = (0.76 m)(cos 45°)(W) = (1/2)(W)(0.76 m)
Solving for W, we get:
W = 2(τ/0.76 m) = 2[(0.5)(mg)(0.76 m)/(0.76 m cos 45°)] = 333 N
Therefore, the force the woman exerts to do a push-up at constant speed is 333 N.
(b) The work the woman does is equal to the change in her potential energy as her center of mass rises. The woman's mass is not given, so we will assume a value of 60 kg. The gravitational potential energy of the woman is given by:
U = mgh
where m is the mass of the woman, g is the acceleration due to gravity (9.81 m/s^2), and h is the height her center of mass rises (0.26 m). Therefore:
U = (60 kg)(9.81 m/s^2)(0.26 m) = 152 J
Therefore, the work the woman does is 152 J.
(c) The useful power output of the woman is the work she does per unit time, taking into account the work done in lowering her body. Each push-up involves two phases: lifting her body and lowering her body. When she lowers her body, the work done is negative, as the force she exerts is in the opposite direction to the displacement. The work done in lowering her body is equal to the work done in lifting her body, so the total work done in one push-up is zero.
The woman does 30 push-ups in 1 minute, which means she does one push-up every 2 seconds. Therefore, the useful power output of the woman is:
P = (152 J)/(2 s) = 76 W
Therefore, her useful power output is 76 W.
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"Blue notes" are_____
the bending of pitches
high pitched notes
never played
Only need question number 3
The magnetic field at a point due to wires with distance r = C cm and carrying the current I is 2 mA is 0.29 T.
The magnetic field is produced over the magnet or current-carrying conductor. The Biot-Sarvat law is defined as the magnetic field produced due to the current-carrying conductor. The magnetic field is the vector quantity and the unit of the magnetic field is Tesla. It is the vector quantity.
Magnetic field, B = μ₀/2π (I/R), where μ₀ is the permeability of the magnetic field, I is current, and R is the distance between two points.
B₁= μ₀/2π (I/R)
= (1.26×10⁻⁶)×2×10⁻³/(2π×1.35m)
= 0.29T
B₂ = 0.29T
The net magnetic field is B=B₁+B₂=0.58T.
Thus, the magnetic field is 0.29T. The left wire carries the current outward direction and the right wire carried the current inward direction and hence the direction magnetic field given by the right-hand thumb rule is inside.
B) By using the equation, F=q(v×B), where q is the charge, v is the velocity and B is the magnetic field. Path b is followed by a neutron as it is not deflected by a Magnetic field. The path a is the upward path followed by a negatively charged particle(electron) and Path C is the downward path followed by a positively charged particle(proton).
C) The circular conductor undergoes thermal expansion while it is a uniform magnetic field the direction of the current is a clockwise direction given by the Right-hand thumb rule.
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Use the following free body diagram to answer questions 8 and 9:
8. Calculate the net force acting on the cart.
A 0N
B. +60N
C -60N
D. +240 N
9. Calculate the cart's rate of acceleration
A +60 m/s
B. +8 m/s
C.-2m/s
D. +2 m/s
Answer:
8 is c and 9 is b it is shown though the practice as god lol
Question 8
The net force acting on the cart is:
F = 150 N - 90 N
F = 60 N
Question 9
By the Newtons second law:
F = ma
Solving for a:
a = F/m
a = 60 N / 30 kg
a = 2 m/s²
An object of mass 3.00 kg, moving with an initial velocity of 5.05 m/s, collides with and sticks to an object of mass 2.76 kg with an initial velocity of -3.66 m/s. Find the final velocity of the composite object.
Answer:
0.752 m/s
Explanation:
m1 = 3.00kg
u1 = 5.05m/s
m2 = 2.76kg
u2 = -3.66m/s
According to the law of conservation of momentum,
m1u1 + m2u2 = (m1+m2)v
3(5.05) + 2.76(-3.66) = (5.05+2.76)v
15.15 - 9.2736 = 7.81v
5.8764 = 7.81v
v = 5.8764/7.81
v = 0.752m/s
Calculate the moment of force F=8i-4j+3k about point 0(2i +0j+k).if the force is applied at the point p(6i+2j+3k)
Answer:
Moment of the force = (-10i-28j+32k)Nm
Explanation:
Moment of a force is expressed mathematically as force(F) multipled by its distance(d) and its unit is in newton metre (Nm).
F×d
(8i-4j+3k)×[(6i+2j+3k)-(2i+0j+k)]
-10i-28j+32k
A 4.0 kilogram projectile is fired horizontally from a 500 kilogram cannon initially at rest. The momentum of the projectile after being fired is 600 kilogram-meters per second to the north
(neglecting friction).
What is the speed of the cannon after firing?
0.83 m/s
1.2 m/s
o
3.3 m/s
150 m/s
The speed of the cannon after firing is 1.2 m/s
This can be solved using the law of conservation of momentum.
From the law of conservation of momentum,
⇒ The momentum of the projectile is equal to the momentum of the cannon.
MV = P................ Equation 1⇒ Where :
M = mass of the cannon,V = velocity of the cannonP = momentum of the projectile.⇒ make V the subject of the equation
V = P/M.................. Equation 2From the question,
⇒ Given:
P = 600 kgm/sM = 500 kg⇒ Substitute these values into equation 2
V = 600/500V = 1.2 m/sHence, The speed of the cannon after firing is 1.2 m/s
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Question 16 of 17
Figure (a) shows a wire that forms a rectangle (W = 23.0cm, H = 31.0cm) and has a resistance of 4.00 mOhm. Its interior is split into three equal areas, with magnetic fields B₁, B₂, and B. The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components B, of the three fields with time t; the vertical axis scale is set by B, = 3.00 μT
and B-2.50B, What are the
(a) the magnitude and
(b) direction of the current induced in the wire?
For the magnetic fields:
(a) 53.8 A(b) The induced current will flow counterclockwise.How to determine magnitude and direction?From Faraday's law of electromagnetic induction, the emf induced in the wire is given by:
emf = -dΦ/dt
where Φ is the magnetic flux through the wire. The negative sign indicates that the induced emf opposes the change in magnetic flux.
The magnetic flux through each of the three regions can be calculated as follows:
Φ₁ = B₁WH/3
Φ₂ = B₂WH/3
Φ₃ = BWH/3
The total magnetic flux through the wire is:
Φ = Φ₁ + Φ₂ + Φ₃ = (B₁ + B₂ + B)WH/3
Taking the time derivative of the magnetic flux:
dΦ/dt = (B₁ + B₂ + B)(WH/3)(dB/dt)
Substituting the given values:
dΦ/dt = (3.00 μT + 2.50(3.00 μT))(0.23 m)(0.31 m)(1.00 m)/(3)(0.010 s) = 0.215 V
The induced emf is equal to the product of the current and the resistance of the wire:
emf = IR
Solving for I:
I = emf/R = 0.215 V / 4.00 mΩ = 53.8 A
The direction of the induced current can be determined using Lenz's law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. In this case, the induced current will produce a magnetic field that opposes the change in the magnetic field through the wire.
As the magnetic field increases in the downward direction, the induced current will produce a magnetic field in the upward direction to oppose the increase. As the magnetic field decreases in the downward direction, the induced current will produce a magnetic field in the downward direction to oppose the decrease.
Therefore, the direction of the induced current will be counterclockwise.
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Before a collision, a 25 kg object is moving at 12 m/s to the right. After a collision with stationary box, the 25 kg object moves at 8 m/s to the right. What is the resulting momentum of the box?
The initial momentum of the 25 kg object is 25 kg * 12 m/s = 300 kgm/s. After the collision, the momentum of the 25 kg object is 25 kg * 8 m/s = 200 kgm/s. According to the conservation of momentum, the momentum lost by the 25 kg object is equal to the momentum gained by the box. Therefore, the resulting momentum of the box is 300 kgm/s - 200 kgm/s = 100 kg*m/s.
2. An archer shoots an arrow. The action force is the bowstring against the arrow, The reaction force is...
a. Air resistance against the bow
b. Arrow's push against the bowstring
c. Grip of the archer's hand on the bow
Answer:b the arrows push against the bow string
Explanation:
The reaction force will be Arrow's push against the bowstring.
Option b is correct.
From Newton's Third Law of Action & Reaction, It states that for every action in nature there is an equal and opposite reaction.
It means that If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.Therefore, If an archer shoots an arrow. The action force is the bowstring against the arrow, The reaction force will be Arrow's push against the bowstring
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A concept is the general idea of objects, events, animals, or people based on common features, traits, or characteristics.
Please select the best answer from the choices provided
ОТ
OF
Answer:
True.
Explanation:
Science can be defined as a branch of intellectual and practical study which systematically observe a body of fact in relation to the structure and behavior of non-living and living organisms (animals, plants and humans) in the natural world through experiments.
A concept is the general idea of objects, events, animals, or people based on common features, traits, or characteristics. It is typically considered to be an abstract idea or general notion that is formed by the mental combination of all the characteristics pertaining to the idea.
Generally, concepts are used in the problem-solving process as it serves as a benchmark or yardstick for the solutions. Some examples of concepts in physics are conservation of energy and momentum, electromagnetic waves, heat, motion and forces, electricity and magnetism, gravity, etc.
Answer:
TRUE
Explanation:
edge
Why would you want to slow down the movement of heat?
Answer: heat is transferred to and from objects -- such as you and your home -- via three processes: conduction, radiation, and convection.
Explanation:
Hopes this helps!
14. Neglecting air resistance, what maximum height will be reached by a stone thrown straight up with an initial speed of 35 m/s?
(a) 98 m
(b) 18 m
(c) 160 m
(d) 63 m
Answer:
D
Explanation:
The maximum height reached by a stone thrown straight up with an initial speed of 35 m/s can be found using the kinematic equation:
v^2f = v^2i - 2gh
where vf is the final velocity (0 m/s at the maximum height), vi is the initial velocity (35 m/s, the magnitude of the velocity with which the stone is thrown upwards), g is the acceleration due to gravity (-9.8 m/s^2), and h is the maximum height reached by the stone.
Rearranging the equation, we get:
h = (vi^2)/(2g)
Substituting the given values, we have:
h = (35 m/s)^2 / (2 * 9.8 m/s^2)
= 62.6 m
Therefore, the maximum height reached by the stone is approximately 63 m.
The answer is (d).
Samir is waiting for a slow reaction to finish. What is the best way to make the reaction go faster?
Question 12 options:
Put it in the fridge where it is cold
Cover it with a blanket so it's dark
Warm it up on the stove
There is nothing you can do to change the speed of the reaction
In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.
Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct
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HURRY
Water boils at 100°C and freezes at 0°C. What best describes the molecules of water at 25°C?
A.
The particles are spread very far apart.
B.
The particles are close together and do not move.
C.
The particles are free to move easily past each other.
D.
The particles are in fixed positions.
Answer:
In be either B or C ! :))
Explanation:
Ik its not much but hope it helped for now :D
The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds
3)Is there any time interval in which no force acts on object.Justify
1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.
2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.
3) There is no time interval in which no force acts on the object.
(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.
In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.
Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2
Acceleration, a = slope= 20/3 m/s^2
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.
Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.
(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.
The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:
Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.
Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.
(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.
Therefore, there is no time interval in which no force acts on the object.
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A positive test charge q is released from rest at distance r away from a charge of +Q and a distance 2r away from a charge of +2Q. 1)How will the test charge move immediately after being released?
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is the second option
Explanation:
Generally the electric force exerted by the charge Q on the charge (q) is mathematically represented as
\(F_Q = \frac{kqQ}{r^2}\)
Generally the electric force exerted by the charge 2Q on the charge (q) is mathematically represented as
\(F_{2Q} = \frac{kq2Q}{2r^2}\)
Now the net force exerted on q is
\(F_{net} = \frac{kqQ}{r^2} - \frac{2k q Q}{4r^2}\)
\(F_{net} = \frac{4kqQ- 2kqQ}{4r^2}\)
\(F_{net} = \frac{kqQ}{2r^2}\)
Looking at the resulting equation we see that \(F_{net} > 0\)
This implies that the charge q would move to the right
explain why our sweat is salty?
Answer:
Sweat also contains ammonia and urea, which are produced by the body when it breaks down proteins from the foods you eat.
Hope this helps..
What type of tv uses a VfL for backlighting
A VfL (Vertical Field LED) backlighting system is commonly used in LCD (Liquid Crystal Display) televisions.
LCD TVs rely on a backlight to illuminate the liquid crystal layer, which controls the passage of light to create the visual image. The VfL technology is a specific type of LED backlighting arrangement used in certain LCD TV models. In a VfL backlighting system, the LEDs (Light-Emitting Diodes) are positioned vertically along the edges of the LCD panel.
The light emitted by these LEDs is directed across the panel using light guides or optical films, illuminating the liquid crystal layer uniformly. One advantage of VfL backlighting is its ability to provide consistent illumination across the LCD panel, reducing any potential inconsistencies in brightness or color uniformity. The vertical orientation of the LEDs allows for more precise control over light distribution, improving overall image quality.
Additionally, VfL backlighting offers potential advantages in terms of power efficiency. By selectively dimming or turning off specific zones of LEDs, local dimming techniques can be employed to enhance contrast and black levels, resulting in improved picture quality while conserving energy. It's important to note that VfL backlighting is just one of several backlighting technologies available for LCD TVs.
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What is the wavelength of this wave
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the Waves.
Wavelength is the distance between two consecutive crest or trough.
hence, here the distance is 10cm
So the wavelength is 10cm
===> 10 cm
acceleration of 14 m/s/s mass of object is decreased by a factor of 2.2 then the new accelration woul dbe
When the mass of the object is decreased by a factor of 2.2, the acceleration is increased by a factor of 2.2, new acceleration would be of 30.8 m/s/s.
The effect of reducing the mass of an object by a factor of 2.2 on its acceleration is determined by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
In terms of calculations, the new acceleration can be calculated by multiplying the initial acceleration by the factor by which the mass is decreased. Therefore, the new acceleration of the object with a reduced mass of 2.2 times its original mass would be 2.2 times its initial acceleration of 14 m/s/s. This would result in a new acceleration of 30.8 m/s/s (14 x 2.2 = 30.8).
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Running at 2.0 m/s, Burce, the 45.0 kg quarterback, collides with Max, the 90.0 kg tackle, who is traveling at 7.0 m/s in the other direction. Upon collision, Max continues to travel forward at 1.0 m/s. Draw or describe simply the diagram before and after collision including objects, mass, velocity, and velocity vectors.
Answer:
max
Explanation:
because its right 90/7
What is the radius of a hemisphere with a volume of 61326 ft^3
, to the nearest tenth of a foot?
The radius of a hemisphere with a volume of 61326 ft^3 , to the nearest tenth of a foot is 30.827 f.
The volume of a sphere with radius R is known to be:
V = (4/3)*pi*R^3
in where pi = 3.14
A hemisphere is half a sphere, its volume is half that of a sphere, and its volume is as follows for a hemisphere of radius R:
V' = (1/2)*(4/3)*pi*R^3
Now that we are aware of the volume of our hemisphere:
V' = 61326 ft^3
The equation is then easy to solve:
61326 ft^3 = (1/2)*(4/3)*pi*R^3
For R.
(We need the diameter, but knowing the radius is a good place to start because the diameter is equal to two times the radius.)
61326 ft^3 = (1/2)*(4/3)*pi*R^3
61326 ft^3 = (4/6)
*3.14*R^3
61326 ft^3*(6/4*3.14) = R^3
∛( 61326 ft^3*(6/4*3.14) ) = R = 30.827 f
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Find the vector whose magnitude is 36 and inclination is 60°.
The vector whose magnitude is 36 and inclination is 60° is v = <18, 18√(3)>.
The inclination of a vector is the angle between the vector and a reference line. In this case, the reference line is the horizontal axis. Let the components be x and y. We know that the magnitude of the vector is 36, so,
magnitude = √(x² + y²) = 36
Squaring both sides of this equation, we get,
x² + y² = 1296
We also know that the inclination is 60°. The tangent of 60° is √(3), which is equal to the ratio of the vertical component to the horizontal component of the vector,
tan(60°) = y/x
y/x= √(3)
Multiplying both sides by x, we get,
y = √(3)x
Now we can substitute y in terms of x in the equation x² + y² = 1296,
x² + (√(3)x)² = 1296
Simplifying this equation, we get,
4x² = 1296
x² = 324
Taking the square root of both sides, we get,
x = +/- 18
Since the vector is making an angle of 60° with the horizontal, it must be in the first or fourth quadrant, where x is positive. Therefore, we take x = 18. Using y = √(3)x, we get,
y = sqrt(3)18
y = 18√(3)
So the vector is,
v = <18, 18√(3)>
Therefore, the vector whose magnitude is 36 and inclination is 60° is v = <18, 18√(3)>.
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Which one of the following statements is not true.
A. Soil is the second layer of Earth's crust.
B. Metals can be extracted from minerals.
C. Oil is made from dead plants and animals.
D. Chemical weathering can break down rocks into fragments.
Describe nuclear fission and how the chain reaction in a nuclear reactor is controlled.
Answer:
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The moderator helps slow down the neutrons produced by fission to sustain a chain of reaction. The chains are controlled by Boron control rods when Boron absorbs the neutrons then the chain reaction will slow down due to the lack of neutrons producing reactions due to the absorbent of Boron. Their reaction initiates its own repetition.
Nuclear fission is the splitting of nucleus into two smaller nuclei and high amount of energy.
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei as well as very high amount of energy. The nuclear fission process produces gamma photons, and releases a very large amount of energy.
Most reactors are controlled with the help of control rods that are made of a strongly neutron-absorbent material such as boron or cadmium so we can conclude that nuclear fission is the splitting of nucleus into two smaller nuclei and high amount of energy.
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An average force of magnitude 300 N exerted to compress a spring by 20 cm compute the work done by the force
Answer: 60 Joules (J)
Explanation:
To compute the work done by a force, you can use the formula:
Work = Force × Distance × cosθ
In this case, the force applied is 300 N, and the distance is 20 cm (which can be converted to meters by dividing by 100, giving us 0.20 m).
The angle θ represents the angle between the direction of the force and the direction of displacement. Since the force is used to compress the spring, the displacement is in the same direction as the force, and the angle θ is 0 degrees. The cosine of 0 degrees is 1, so we can omit the cosine term.
Now we can calculate the work done:
Work = 300 N × 0.20 m
Work = 60 Joules (J)
Therefore, the work done by the force in compressing the spring is 60 Joules (J).
A Typical operating voltage of an electron microscope is 50 kV. A Typical experimental operating voltage range of a Scanning electron microscope is 1kV to 30kV. Higher voltages can penetrate and causes deformation on the sample. Lets assume it operates at 10kV. (i)What is the smallest distance that it could possibly resolve
Answer:
y =\(\frac{1.22L}{D}\) \(\sqrt{\frac{h^2 m}{2eV} }\)
Explanation:
Let's solve this exercise in parts. Let's start by finding the wavelength of the electrons accelerated to v = 10 103 V, let's use the DeBroglie relation
λ= \(\frac{h}{p} = \frac{h}{mv}\)
Let's use conservation of energy for speed
starting point
Em₀ = U = e V
final point
Em_f = K = ½ m v²
Em₀ = Em_f
eV = ½ m v²
v =\(\sqrt{\frac{2eV}{m} }\)
we substitute
λ= \(\sqrt{ \frac{h^2 m}{2eV}}\)
the diffraction phenomenon determines the minimum resolution, for this we find the first zero of the spectrum
a sin θ = m λ
first zero occurs at m = 1, also these experiments are performed at very small angles
sin θ = θ
θ = λ / a
This expression is valid for linear slits, in the microscope the slits are circular, when solving the polar coordinates we obtain
θ = 1.22 λ / D
where D is the diameter of the opening
we substitute
θ = \(\frac{1.22}{D}\) \sqrt{ \frac{h^2 m}{2eV}}
this is the minimum angle that can be seen, if the distance is desired suppose that the distance of the microscope is L, as the angles are measured in radians
θ = y / L
when substituting
where y is the minimum distance that can be resolved for this acceleration voltage
y =\(\frac{1.22L}{D}\) \(\sqrt{\frac{h^2 m}{2eV} }\)