The acceleratiοn οf a prοjectile when it reaches its highest pοint is 0 m/s². And its acceleratiοn just befοre and just after reaching this pοint 10.39 m/s² at time 2.08 s.
What are the initial and final speeds?The speed at which an οbject travels when gravity exerts its first fοrce οn it is referred tο as its initial velοcity. In cοntrast, the speed and directiοn οf a mοving οbject fοllοwing its maximum acceleratiοn are measured by the final velοcity, a vectοr quantity.
What is a vectοr οf initial velοcity?The twο cοmpοnents οf a vectοr are used tο describe the single directiοn οf the vectοr's influence. The initial velοcity οf a prοjectile has bοth a hοrizοntal and a vertical cοmpοnent if it is launched at an angle tο the hοrizοntal.
Let's determine the [tex]\theta[/tex] angle of launch with respect to the positive x-axis.
[tex]\theta = 180^o-60.0^o = 120^o \\[/tex]
We will determine the particle's time οf flight from the equation of the vertical displacement of a prοjectile.
[tex]y = v_i\,\sin (\theta) \,t_g - \dfrac{1}{2} g\, t_g ^2 \,\,\,\,\,\,\,(1)\\[/tex]
Where:
y is the vertical displacement, [tex]{v_i[/tex] is the initial speed. [tex]\theta[/tex] is the launch angle. [tex]t_g[/tex] is the flight time. g is the acceleration due tο gravity.
If the initial vertical position is equal tο the final vertical position, then the vertical displacement is equal tο zero.
Substituting the known data in equatiοon (1)
[tex]\rm 0 = (12.0\,m/s)\sin (120^o)t_g - \dfrac{1}{2}(10\,m/s^2)}t_g ^2\\ 0 = {\rm 10.3923\,m/s^2 -(5\,m/s^2)}t_g \\[/tex]
[tex]\rm t_g = \dfrac{\rm 10.3923\,m/s^2}{\rm 5\,m/s^2} = {\rm 2.08\,s} \\[/tex]
Thus, The acceleration of a prοjectile when it reaches its highest point is 0 m/s². And its acceleratiοn just before and just after reaching this point 10.39 m/s² at time 2.08 s.
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A roller coaster car that has a mass of 200 kg is travelling at a rate of 10 m/s at a
height of 5 m above Earth's surface. How much total energy does the car contain at
this point?
The roller coaster car contains a total of 19810 joules of energy at this point.
How to calculate the total energy of the roller coaster car.First, we need to consider its kinetic energy and potential energy.
The potential energy of the car at a height of 5 m above Earth's surface is given by:
PE = m * g * h
Where
m is the mass of the carg is the acceleration due to gravity (9.81 m/s²)h is the heightSubstituting the given values, we get:
PE = (200 kg) * (9.81 m/s²) * (5 m)
PE = 9810 J
The kinetic energy of the car is given by:
KE = (1/2) * m * v²
Where v is the velocity of the car.
Substituting the given values, we get:
KE = (1/2) * (200 kg) * (10 m/s)²
KE = 10000 J
Therefore, the total energy of the roller coaster car at this point is:
Total Energy = KE + PE
Total Energy = 10000 J + 9810 J
Total Energy = 19810 J
Therefore, the roller coaster car contains a total of 19810 joules of energy at this point.
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what is 2x10^-3 as second
Answer: 0.002
Explanation:
Help quick.
Two objects, m1 and m2, have an elastic collision. The initial velocity of m1 is +6.0 m/s and of m2 is +4.0
m/s. After the collision, the velocity of m1 is +5.0m/s. What is the velocity of m2?
Answer:
u
1
=
6.0
m
/
s
u
2
=
4.0
m
/
s
v
1
=
5.0
m
/
s
Explanation:
if a 50 N block is resting on a steel table with a coefficient of static friction
If F = 37 N, the static frictional force between the block and the table and the minimum force required to move it must be equal.
How is the minimum force of static friction determined?It is the force that regulates itself. The value of static friction varies from zero to the smallest force required to initiate motion. The formula for determining static friction is as follows: Normal Force divided by the static friction coefficient is static friction.
Is weight equivalent to static friction?Although the maximum static friction will rise, the frictional force will always be the same as the weight in mg because friction cannot accelerate an object. Because FrN can take any value less than N to balance the weight, this is the case.
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Can i get help please
I believe its A. Tuberculosis
A particle executes simple harmonic motion with an amplitude of 3. 08 cm. At what positive displacement from the midpoint of its motion does its speed equal one half of its maximum speed? Answer in units of cm
The displacement from the midpoint of the motion at which the speed is equal to half of the maximum speed is 1.85 cm.
v = Aω√(1 - (x/A)^2)
v_max = Aω
v = 1/2 v_max = 1/2 Aω
Substituting the given values, we get:
1/2 Aω = 3.08 cm * ω * √(1 - (x/A)^2)
Simplifying and squaring both sides, we get:
(1/4) A^2 ω^2 = 9.4864 cm^2 * (1 - (x/A)^2)
Solving for x/A, we get:
x/A = √(1 - (1/4)(ω^2/A^2) * 9.4864)
x/A = √(1 - (π^2/400))
x/A = 0.6
The displacement from the midpoint of the motion at which the speed is equal to half of the maximum speed is:
x = 0.6 * 3.08 cm = 1.85 cm
Harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium position with a constant frequency and amplitude. It is characterized by a sinusoidal pattern, where the displacement of the object from its equilibrium position is directly proportional to the sine or cosine of the time elapsed since the motion began.
In harmonic motion, the restoring force acting on the object is proportional to its displacement from the equilibrium position, and the object's motion is governed by Hooke's Law. Examples of harmonic motion include the motion of a mass-spring system, the motion of a simple pendulum, and the vibration of a guitar string.
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Question 10 of 25
You replace a 200 W lamp with a more efficient 55 W LED lamp. If you leave
your lights on 24 hours a day, how much energy are you saving each day by
replacing this bulb?
A. 4,752,000 J
OB. 17,280,000 J
C. 12,528,000 J
O D. 21,225,000 J
SUBMIT
The energy used by the 200 W lamp for 24 hours is 17280000 J whereas, the energy used by the 55 W lamp for one day is 4752000. Therefore, by replacing the200 W lamp by 55 W, we save 12,528,000 J of energy.
What is power ?Power is the unit of energy or work done by an object. It measures how much energy used by the object per second to do a work. Hence, power is the work done or energy by time in seconds.
Given that power of one lamp = 200 W
time = 24 hour= 86400 s.
then energy = power × time
200 W × 86400 s = 17280000 J
Similarly the energy consumed by the 55 W lamp for 24 hours is:
86400 s × 55 W = 4752000J
Then, if replace the 200 W lamp by the 55 W LED lamp, we can save an energy of 17280000 J - 4752000 J = 12,528,000 J.
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1. A child rides a bicycle in a circular path with a radius of 3.2 m. The tangential speed of the
bicycle is 2.7 m/s. The combined mass of the bicycle and the child is 54 kg.
What is the magnitude of the bicycle's centripetal acceleration? What is the magnitude of the
centripetal force on the bicycle?
The magnitude of the bicycle's centripetal acceleration can be calculated using the formula:
a = v^2 / r
where v is the tangential speed and r is the radius of the circular path. Plugging in the given values, we get:
a = (2.7 m/s)^2 / 3.2 m
a = 2.27 m/s^2
The magnitude of the centripetal force on the bicycle can be calculated using the formula:
F = m * a
where m is the combined mass of the bicycle and the child. Plugging in the given values, we get:
F = 54 kg * 2.27 m/s^2
F = 122.58 N
Therefore, the magnitude of the bicycle's centripetal acceleration is 2.27 m/s^2, and the magnitude of the centripetal force on the bicycle is 122.58 N.
Answer:
[tex]\huge\boxed{\sf F_c=123.02 \ N}[/tex]
[tex]\huge\boxed{\sf a_c=2.28 \ m/s^2}[/tex]
Explanation:
Given data:Mass = m = 54 kg
Tangential speed = v = 2.7 m/s
Radius = r = 3.2 m
Required:Centripetal force = [tex]F_c[/tex] = ?
Centripetal acceleration = [tex]a_c[/tex] = ?
Formula:[tex]\displaystyle F_c=\frac{mv^2}{r}[/tex]
[tex]\displaystyle a_c=\frac{v^2}{r}[/tex]
Centripetal acceleration:Put the given data in the above formula.
[tex]\displaystyle a_c=\frac{(2.7)^2}{3.2} \\\\a_c=\frac{7.29}{3.2} \\\\a_c=2.28 \ m/s^2\\\\[/tex]
Centripetal force:Put the given data in the above formula.
[tex]\displaystyle F_c=\frac{(54)(2.7)^2}{3.2} \\\\F_c=\frac{(54)(7.29)}{3.2} \\\\F_c=\frac{393.66}{3.2} \\\\F_c=123.02 \ N\\\\\rule[225]{225}{2}[/tex]
Two identical beakers are both half filled with a liquid beaker a contains water and beaker b contains a liquid that is denser than water
The pressure at the bottom of both beakers is the same. The correct answer is D.
The pressure at the bottom of both beakers is the same. The pressure at the bottom of a fluid is determined by the weight of the fluid above it, which is the same for both beakers since they are equally filled with the same amount of liquid. The air pressure on the beakers does not affect the pressure inside the liquid.
The weight of both liquids cannot be the same, as the density of the liquid in beaker B is greater than that of water, so it will have a greater weight. The area at the bottom of the beakers may be the same or different, but it is not relevant to the pressure at the bottom. Therefore, the correct statement is D, that the pressure at the bottom of both beakers is the same.
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--The complete question is, Two identical beakers are both equally filled with a liquid. Beaker A contains water. Beaker B contains a liquid that is denser than water. Which statement is true?
A. The air pressure on the beaker containing dense liquid is greater.
B. The weight of both liquids is the same.
C. The area at the bottom of both beakers is the same.
D. The pressure at the bottom of both beakers is the same.--
Explain the relationship between the load on the spring and the length of the spring when the load is increased from 0 to 10N
(I really need an answer plsss)
Since Hooke's law implies linear, i anticipate that the length of a spring will double if the weight hanging on this is doubled. The graph below depicts a spring's ideal Hooke's law graph.
Simple definition of Hooke's law.At the range of the material's elastic limit, according to Hooke's law, the strain is inversely related to the applied stress. The molecules and atoms in elastic materials stretch when they are stretched, distort when under stress, and then return to their original shape once the tension is released.
What other names are given to Hooke's law?In the year 1660, an English british scientist Robert Hooke discovered Hooke's law, commonly known as that of the law of elasticity. According to Hooke's law, the magnitude of the deformation is precisely proportional to a deforming load or force.
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To help lift a television a mover exerts a force of 50 N on a wedge. The wedge applies a
force 480 N to the televsion. What is the mechanical advantage in using this machine?
O 10
O 0.10
O 24,000
O 1.0
10 is the appropriate number. Here, a machine's mechanical advantage. Hence, choice (a) is the appropriate response. Three mechanical advantages exist: force, distance, and speed.
Although though force mechanical advantage is the sole topic covered in the majority of scientific publications, it is nevertheless crucial.
using the mechanical advantage formula.
[tex]MA= \frac{Fo}{Fi}[/tex]
alternative ≠ 480[tex]N[/tex] and [tex]Fi = 50n,[/tex]
[tex]MA = \frac{480n}{50n}[/tex]
simplify [tex]MA[/tex] ≈ 10
The load to effort ratio is used to quantify mechanical advantage of a machine. A machine's mechanical advantage determines its efficiency. Mechanical Advantage is equal to Load / Effort, or F 0 F I which means that is the mechanical energy, is the production force, and corresponds to the input force.
An object having mass changes its velocity in response to a push or pull. Force is an exterior agent that has the power to alter the rest or motion of something like a body. It has magnitude and direction.
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2
Which statement about the relationship between an organism's traits and its genes is true?
A.
An organism's genes are a direct result of its inherited traits.
B. Traits code for the proteins that determine an organism's genes.
C.
Genes code for proteins that determine an organism's traits.
D. Genes code for the DNA that determines an organism's traits.
TO be completely Honest with this, Based of reading the questions and answers it may be D. just off sheer legibility of logic alone, Hope this is not wrong.
How does the creation of a new mountain range in an ecosystem affect an animal population that becomes divided into two groups by the mountains?
A.
The two new animal populations adapt gradually and separately to their new environments on either side of the mountain.
B.
The two new animal populations are not greatly affected by the separation, and they adapt in the same manner.
C.
The new animal populations gradually migrate up either side of the mountain until they are together again.
D.
The new animal population on one side of the mountain is driven to extinction.
A. The two new animal populations adapt gradually and separately to their new environments on either side of the mountain. This options explains how does the creation of a new mountain range in an ecosystem affect an animal population.
Explain the role of mountain range in an ecosystem?
When a new mountain range is created, it can act as a barrier that separates animal populations on either side. Over time, the two populations will adapt to their new environments, which may be different due to differences in climate, vegetation, or other factors.
As a result, the two populations may evolve independently of each other, leading to differences in behavior, appearance, and genetic makeup. This process is known as allopatric speciation. It is important to note that while the two populations may become distinct, they may still be able to interbreed if they come into contact again in the future.
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Which of the following correctly lists the substances from highest to lowest pH? о O O A lemon juice, distilled water, milk of magnesia Jhy B. distilled water, milk of magnesia, lemon juice C. lemon juice, milk of magnesia, distilled water D. milk of magnesia, distilled water, lemon juice
Acidity is indicated by pH values lower than 7, while baseness is shown by pH values higher than 7. The pH of water is actually a measurement of the proportion of free ions of hydrogen and hydroxyl that are in the solution.
What is the suggested example?The souls were shown by him. He pointed to the nicely arranged clothing on the nightstand next to the bed. They still lacked one goat, according to a hasty count.
Which value is indicated?The monitored value from the a transaction file that the monitor reported for a known amount of the specified Parameter. Precision is determined by comparing this value to the known quantity known as REAL VALUE.
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PLEEEEEEASE answer as fast as possible, I will give Brainliest to fastest answer.
A sound wave is traveling through a medium. Which statement best describes a situation that will cause the wave speed to increase?
A. Increase the pressure of the substance and the particles will be farther apart.
B. Increase the volume of the medium and there will be more particles to transfer the wave.
C. Increase the size of the particles and they will have more momentum to carry the wave.
D. Increase the density of the substance and there will be more particles to transfer the wave.
Answer: D. Increase the density of the substance and there will be more particles to transfer the wave.
Answer:
D. INCREASE THE DENSITY OF THE SUBSTANCE AND THERE WILL BE MORE PARTICLES TO TRANSFER THE WAVE .
Explanation:
BECAUSE WAVES ARE TRANSFERED
A sign with a mass of 1000.0 kg is suspended from a wall with a cable that is attached to the wall at a point 3.0 m above a horizontal beam that causes the sign to be a distance of 4.0 m from the wall. See the diagram below.
Two or more physical objects which are in contact with each other exert forces on each other. Here the tension of the cable is 16349.96 N.
What is tension?The force along the length of a medium especially a force carried by a flexible medium, such as a rope or cable is defined as the tension. The tension on an object is equal to the product of the mass of the object and the gravitational force added and acceleration.
T = mg + ma
Here W = mg
W = 1000.0 × 9.81 = 9810
using geometry,
tan α = 3/4
α = 36.87°
Tsinα = W
T sin36.87° = 9810
T = 16349.96 N
Thus the tension of the cable is 16349.96 N.
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En un momento dado , la nadadora de una prueba de natación de 100 m espalda está debajo de la cuerda falsa de salida. Indica a) El camino recorrido si acaba de salir b) El camino recorrido si ya ha tocado el final de la piscina c) El desplazamiento de la nadadora en los casos a y b ¿Coincide en algún caso con el camino recorrido?
If at a given moment, the swimmer in a 100m backstroke swimming race then,
a) The distance traveled if she has just started is 0 meter.
b) The distance traveled if she has just started is 100 meters.
c) The displacement is 0 m in case a and 100 m is case b. No they do not coincide.
Since the swimmer has just started, therefore she has not traveled any distance yet.
As it is mentioned that the swimmer has already touched the end of the pool, she has traveled a distance of 100 meters.
The displacement of the swimmer in cases a and b is zero because displacement is the distance between the starting point and the ending point, regardless of the path taken. In case a, the swimmer has not moved from the starting point yet, so the displacement is zero. In case b, the swimmer has returned to the starting point, so the displacement is also zero.
No, the displacement does not coincide with the distance traveled in either case because the swimmer's path is not necessarily a straight line from the starting point to the ending point. The displacement only considers the initial and final positions of the swimmer, while the distance traveled takes into account the length of the path taken by the swimmer.
Therefore, it could be concluded that at the start diatance is 0m and at the end it is 100m and the displacement at starting is 0m and at the end it is 100m. These do not coincide with each other.
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The question is :
At a given moment, the swimmer in a 100m backstroke swimming race is below the false start rope. State :
a) The distance traveled if she has just started
b) The distance traveled if she has already touched the end of the pool
c) The displacement of the swimmer in cases a and b. Does it coincide with the distance traveled in any case?
A dog jumps off the 10 m stairs down onto his doggy house which is 4 m high.
What is the change in gravitational potential energy of this 3 kg dog?
The change in gravitational potential energy of the dog is -176.58 J.
How to find the gravitational potential energy of the dogThe change in gravitational potential energy of an object is given by:
ΔPE = mgh
where
ΔPE is the change in gravitational potential energy
m is the mass of the object
g is the acceleration due to gravity, and
h is the change in height.
In this case, the dog jumps off a 10 m staircase down to his doggy house which is 4 m high. So the change in height,
h = -6 m (negative because the dog is moving downwards).
g = 9.81 m/s^2
m = 3 kg.
Substituting these values into the equation above, we get:
ΔPE = mgh
ΔPE = (3 kg)(9.81 m/s^2)(-6 m)
ΔPE = -176.58 J
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if 1 cubic centimeter of water has a mass of 1 gram then a liter of water has a mass of _ gram(s)
25,000 newtons accelerating 10m/s2
The mass of the object is 2,500 kg according to Newton's second law of motion.
What is Newton's second law of motion?Newton's second law of motion states that the force acting on an object is equal to the product of its mass and acceleration. Mathematically, F = ma, where F is the force, m is the mass of the object, and a is its acceleration.
If a force of 25,000 N is applied to an object, and the object is accelerating at a rate of [tex]10 m/s^2,[/tex] then the mass of the object can be calculated using Newton's second law of motion:
F = ma
where F is the force, m is the mass of the object, and a is its acceleration.
Rearranging this equation, we get:
m = F/a
Plugging in the values given in the problem, we get:
[tex]m = 25,000 N / 10 m/s^2 = 2,500 kg[/tex]
Therefore, the mass of the object is 2,500 kg
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Assignment The U. S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (U. S. Department of Energy website, February 22, 2008). A portion of the data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car: Compact, Midsize, or Large. The column labeled Displacement shows the engine's displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled HwyMPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. The complete data set is contained in the DATAfile named FuelData. Click on the datafile logo to reference the data. DATA file (a) Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement. Let x represent the engine's displacement. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) 34. 669 2. 683 Is there a relationship between Hwy MPG and displacement at the 0. 05 level of significance? Yes How much of the variation in the sample values of Hwy MPG is is explained by this estimated regression equation? If required, round your answer to one decimal places. 53 % JUNI (c) Consider the addition of the dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and o otherwise. Thus, for a compact car, the value of Class Midsize and the value of ClassLarge are both 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement and the dummy variables ClassMidsize and ClassLarge. Let X1 represent engine's displacement. Let x2 represent variable Class Midsize. Let X3 represent variable ClassLarge. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) 27. 9 + 1. 38 X1 + 4. 73 X2+ 2. 14 X3 How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? If required, round your answer to one decimal places. 72. 4 % Eignment (e) Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the car uses premium fuel and o if the car uses regular fuel. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement, the dummy variables Class Midsize and ClassLarge, and the dummy variable FuelPremium. Let x1 represents engine's displacement. Let X2 represents variable ClassMidsize. Let X3 represents variable ClassLarge. Let X4 represents variable FuelPremium. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) X 28. 7 1. 36 4. 21 X2 + 1. 98 X3 + + X1 + 1. 16 X4 How much of the variation in the sample values of HwyMPG does this estimated regression equation explain? If required, round your answer to one decimal places. 74. 1 % ch of the indenendent
The Guide provides estimated fuel economy (in miles per gallon, or MPG) and annual fuel costs (based on national averages of fuel costs and miles driven) for most model year 2022 vehicles for sale in the United States.
How do you check the fuel efficiency of a car?The simplest approach to determine your gas mileage is to divide the number of miles traveled by the number of gallons of petrol consumed by your car. In total, it is the number of miles travelled divided by the number of gallons of gas consumed.
Fuel economy is a rating that indicates how far a vehicle can go on a given quantity of gasoline. The higher the fuel efficiency, the less gasoline the vehicle consumes. The conventional metric of fuel efficiency in the United States is miles per gallon (mpg). This metric relates to how far a vehicle can go on a single gallon of fuel.
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. Predicting Water is nearly incompressible.
Air is easily compressed. Predict what will
happen when an air-filled balloon is pulled to
the bottom of a swimming pool.
someone help
Plesde
name five example of derived qualities
Answer:
velocity, power, energy, force and density
Explanation:
Un objeto pequeño que tiene una carga dd -5x10^-9C experimenta una fuerza hacia debajo de 20x10^-9 N cuando se coloca en determinado punto un campo electrico ¿cual es el campo de dicho punto?
El signo negativo indica que el campo eléctrico apunta en la dirección opuesta a la fuerza experimentada por la carga. Por lo tanto, el campo eléctrico en ese punto es de -4 N/C.
F = qE
En este caso, la carga es de -5x10^-9 C y la fuerza es de 20x10^-9 N. Por lo tanto, podemos despejar el valor del campo eléctrico:
E = F/q = (20x10^-9 N) / (-5x10^-9 C) = -4 N/C
A charge is a fundamental property of matter that describes the amount of electric energy that a particle possesses. It is a scalar quantity, meaning it has only magnitude and no direction. The charge can be either positive or negative and is measured in Coulombs (C).
Charged particles can interact with each other through electromagnetic force, which is one of the four fundamental forces of nature. Like charges repel each other while opposite charges attract. Electric fields are generated by charged particles, and the force they exert on other charged particles is proportional to the magnitude of their charges.
A charge is conserved in isolated systems, meaning that the total amount of charge in a closed system cannot be created or destroyed, but can only be transferred from one object to another.
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The volume of a given mass of gas is 273cm²³ at 0 degree Celsius what is the volume at 237°c if its Pressure remains Constant
A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10. 6m. In 1. 00 ms, this laser produced 9. 50 MW of power. How many photons were produced?
To calculate the number of photons produced by the carbon dioxide laser, we need to use the formula relating the energy of a photon to its frequency or wavelength.
The formula is: E = hf = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J s), f is the frequency, c is the speed of light (3 × 10^8 m/s), and λ is the wavelength. First, we need to calculate the energy of one photon with a wavelength of 10.6 μm: E = hc/λ = (6.626 × 10^-34 J s) × (3 × 10^8 m/s) / (10.6 × 10^-6 m) = 1.862 × 10^-20 J. Next, we need to calculate the total energy produced by the laser in 1.00 ms: Energy = Power × Time = 9.50 MW × 1.00 × 10^-3 s = 9.50 × 10^3 J. Finally, we can calculate the number of photons produced by dividing the total energy by the energy of one photon: Number of photons = Energy / E = (9.50 × 10^3 J) / (1.862 × 10^-20 J) = 5.098 × 10^23 photons. Therefore, the carbon dioxide laser produced 5.098 × 10^23 photons when it emitted infrared radiation with a wavelength of 10.6 μm and a power of 9.50 MW for 1.00 ms.
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You have a ball with mass 2.5 kg tied to a rope, and you spin it in a circle of radius
1.2 m. You know that the rope can withstand a tension of 130 N before it breaks.
How fast can you safely spin the ball without the rope breaking?
Answer:
Approximately [tex]7.2\; {\rm m\cdot s^{-1}}[/tex] (rounded up), assuming that this circle is vertical and [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Explanation:
Let [tex]v[/tex] denote the tangential speed of the ball, and let [tex]r[/tex] denote the radius of the circle. Since the ball is in a circular motion, the acceleration on this ball would be equal to the centripetal acceleration [tex]a = (v^{2} / r)[/tex]. The net force on this ball would be [tex]F_{\text{net}} = m\, a = (m\, v^{2} / r)[/tex].
The net force on this ball is also the vector sum of the tension [tex]T[/tex] in the rope and the weight of the ball [tex]m\, g[/tex]:
[tex]F_{\text{net}} = (\text{weight}) + T[/tex].
[tex]T = F_{\text{net}} - (\text{weight})[/tex].
Note that:
[tex]\| T \| = \|F_{\text{net}} - (\text{weight})\| \le \|F_{\text{net}} \| + \| (\text{weight})\|[/tex].
In other words, the magnitude of tension [tex]T[/tex] is at most equal to [tex]\|F_{\text{net}} \| + \| (\text{weight})\| = (m\, v^{2} / r) + (m\, g)[/tex], which happens when weight and net force are in opposite directions.
When the speed of the ball is maximized, the magnitude of tension [tex]T[/tex] would be at the largest possible value of [tex]130\; {\rm N}[/tex]. Rearrange the equation and solve for speed [tex]v[/tex]:
[tex]\displaystyle \frac{m\, v^{2}}{r} + m\, g = \|T\|[/tex].
[tex]\begin{aligned}v^{2} = \frac{r}{m}\, (\|T \| - m\, g) = \frac{r\, \|T\|}{m} - r\, g\end{aligned}[/tex].
[tex]\begin{aligned}v &= \sqrt{\frac{r\, \|T\|}{m} - r\, g} \\ &= \sqrt{\frac{(1.2)\, (130)}{2.5} - (1.2)\, (9.81)}\; {\rm m\cdot s^{-1}} \\ &\approx 7.2\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Which requires more work, lifting a 90 kg bag up 6 m in 4 minutes, or lifting a 45 kg bag up 12 m in 2 minutes?
Answer:
W = m g h increase in PE due to lfting bag
W1 = 90 kg * 9.8 m/s^2 * 6 m
W2 = 45 kg * 9.8 m/s^2 * 12 m
W2 / W1 = 1 the work is the same in both cases
The power required is different
P = W / t
Since t is smaller for W2 and the work output is the same the power required to produce W2 is twice as great
As of the time our textbook went to press, 118 different elements had been discovered. All of the ones with atomic number over 92 have been made in physics laboratories. When element 119 (one that has not yet been identified) is found, provided it is like the other artificially made elements, it will:
A
have only protons, no neutrons at all
B
soon be used in industry to make new kinds of plastics
C
have one of the smallest nuclei known
D
only remain stable for an extremely small fraction of a second
E
eventually be found in the Sun (with very high quality spectrometers)
Answer:
Option D is the most likely answer: element 119 will only remain stable for an extremely small fraction of a second.
This is because all elements with atomic numbers greater than 92 (i.e., the actinides) are unstable and undergo radioactive decay, with their isotopes having extremely short half-lives. As element 119 would have an atomic number greater than 92, it is highly likely that it too would be unstable and undergo radioactive decay, making it difficult to observe and study.
Option A is not possible, as all elements require neutrons in their nuclei to have stable isotopes. Option B is unlikely, as the properties of element 119 are unknown and it would need to be studied extensively before any industrial applications could be developed. Option C is also unlikely, as elements with large atomic numbers tend to have larger nuclei. Option E is also unlikely, as it is not clear how element 119 could be produced in the Sun, given that it is a highly unstable element.
a sound wave strikes a wall normally what is the angle of reflection of sound wave
a 90°
b 60°
c 45°
d 0°
Answer:
C
Explanation: