A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms his angular velocity remains the same. Option e is the correct choice.
When the arms are folded the rotational inertia is lower. When the man extends his arm he is basically increasing his rotational inertia thereby loosing angular velocity using the principle of conservation of angular momentum. This implies less angular distance is covered in the same time giving us negative work.
After pulling arms, the angular velocity increases but moment of inertia of decreases in, such a way that angular momentum remains constant.
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Calculate the distance traveled by an object moving 11 pico-meters per second for 13 Giga-seconds. (pico = 10-12) Answer in milli-meters.
The object would have traveled a distance of 143 mili-meters in 13 Giga-seconds at a speed of 11 pico-meters per second.
To calculate the distance traveled by an object, we need to multiply the object's speed by the time it has been moving.
Distance = speed x time
Recall that:
pico = 10⁻¹²
Giga = 10⁹
mili = 10⁻³
Information available in the problem:
speed = 11 pico-meters = 11 x 10⁻¹² m
time = 13 Giga-seconds = 13 x 10⁹
Hence,
Distance = 11 x 10⁻¹² x 13 x 10⁹
= 143 x 10⁻³ meters
= 143 mili-meters
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Research help further the biological perspective when they demonstrated that electrical
Research helps further the biological perspective when they demonstrated that electrical activity in the brain can predict an individual's behaviour.
What is behaviour?Behaviour is the way in which an individual or group acts and reacts to events, people, and their environment. It is the actions of an individual or group and the reactions they cause in others. Behaviour can be conscious or unconscious, voluntary or involuntary, and is often defined in terms of being either adaptive or maladaptive.
This concept, known as neuropsychology, provides evidence that behavior is largely determined by biological processes and can help explain the complex relationships between the brain and behavior. Neuropsychological research has allowed scientists to better understand the neural basis of behavior, allowing a more.
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Eight gallons of water per minute are flowing at a given time from the 1-inch outlet in the tank shown above. What is the amount of water flowing at that time from the 2inch outlet?
The amount of water flowing at that time from the 2inch outlet is 16 gallons per minute
What is flow rate?Flow measurement, a quantification of bulk fluid movement, is another term for flow rate. The mass of a material that moves per unit of time is known as the mass flow rate. The amount of fluid moving per unit of time is known as the volumetric flow rate.
More ideas on how we arrived at the answer
The 1-inch outlet is flowing at 8 gallons per minute.
Now Because the 2-inch outlet is twice the size of the 1-inch outlet, it is flowing at twice the rate or 16 gallons per minute.
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a golf ball is thrown at and bounces backward from a massive bowling ball that is initially at rest. after the collision, compared to the golf ball, the bowling ball has more
After the collision between the golf ball and the initially at rest bowling ball, the bowling ball will have more momentum, since momentum is conserved in the collision. The golf ball will bounce backward with a momentum equal in magnitude but opposite in direction to the initial momentum of the golf ball.
However, the bowling ball will not have more velocity than the golf ball, since the velocity of the two objects after the collision will depend on their masses and the specific details of the collision. The bowling ball will have a lower velocity than the golf ball due to its larger mass, but it will have more kinetic energy since it has a larger mass and a non-zero velocity after the collision.
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It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero's crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.55 kgf (= 34.8 N) in air and 3.25 kgf (= 31.9 N) in water, determine if the crown is made of pure gold. The density of gold is 19, 300 kg/m^3 Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.
The crown is not made of pure gold as the density of the material is found to be less than gold.
Archimedes observed that every solid, regardless of shape, will experience an upward force when submerged in a liquid that is equal to the weight of the amount of liquid that the solid has extracted.
So, if any body is weighed in air, the normal force will be equal to the gravity force (which we call weight) which can be expressed as follows:
Fg = m g = δ V g = 34.8 N
When submerged in water, the normal force is equal to the difference between the actual weight, and the upward force due to Archimedes' principle, called buoyant force, as follows:
Fn = Fg - Ep = δx. V. g - δH₂O . V. g = 31.9 N
By dividing Fg into Fn and condensing commonly used terminology, we obtain:
δx / (δx - δH₂O) = 34.8 / 31.9 = 1.09
Solving for δx, we get the following value:
δx = 10,900 Kg/m³, less dense than pure gold, so we can conclude that the crown was not made of pure gold.
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An inventor is applying for a patent. He claims his new heat engine can produce 1,200 J of work for every 1,800 J of heat applied to it. In 3–5 sentences, evaluate this claim after solving for η.
will mark brainiest, need help asap
The efficiency, η, of the new engine would be 0.67.
Efficiency calculationBased on the given information, the inventor's new heat engine has an efficiency of:
η = work output / heat input = 1,200 J / 1,800 J = 0.67
This means that for every 1,800 J of heat applied to the engine, only 1,200 J of work can be produced, and the remaining 600 J of heat energy is lost as waste heat.
While an efficiency of 0.67 is relatively high for a heat engine, it is important to note that the practicality and potential applications of the engine cannot be evaluated solely based on its efficiency.
Other factors such as cost, durability, and scalability would also need to be considered in determining the viability of this invention.
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a spherical shell has an inned radius of 3.7 cm and an outer radius of 4.5 cm. if charge is distributed uniformly throughout the shell with a volume density of 6.1x10^-4 the total charge is
The required total charge on a spherical shell whose volume density is specified is calculated to be 1.31 × 10⁻⁹ C.
Using the formula, one can get the total charge.
Total charge = Volume density × Volume of sphere
The charge is said to be distributed uniformly throughout the shell with the volume density 6.1 × 10⁻⁴ C/m³.
The inner radius of the spherical shell is given as 3.7 cm = 3.7 × 10⁻² m.
The outer radius of the spherical shell is given as 4.5 cm = 4.5 × 10⁻² m.
Volume of the sphere is calculated as,
V = 4π/3(outer radius - inner radius)³ = 4π/3 (4.5 × 10⁻² - 3.7 × 10⁻²)³ = 4π/3 (0.8 × 10⁻²)³ = 4π/3 × (0.512 × 10⁻⁶) = 2.14 × 10⁻⁶ m³
So, the total charge can be given as,
⇒ 6.1 × 10⁻⁴ - 2.14 × 10⁻⁶ = 1.31 × 10⁻⁹ C.
Thus, the total charge is calculated to be 1.31 × 10⁻⁹ C.
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If cable AB is subjected to a tension of 916 N, determine the magnitude of the vertical force F (in N). 2 m 6 m с 3 m 1.5 m 0 ות 6 2 m 3 m B
The magnitude of the vertical force F is 882.4 N. Use equilibrium equations of force in direction of y.
To determine the magnitude of the vertical force F, we can use the equilibrium equations of the forces in the y direction.
Summing the forces in the y direction:
[tex]Fsin(60°) - 916 N - 150 N = 0[/tex]
where the 150 N is the weight of the beam CD.
Solving for F, we get:
[tex]Fsin(60°) = 766 N[/tex]
F = 882.4 N
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element x exists as diatomic molecules and the substance has a melting point of 423k and a boiling point of 615k.part a. in the box provided, draw a molecular-level picture to best represents a sample of element x at 500k. be sure to use a key to indicate what you are drawing.
Based on the given information, we can infer that element X is a non-metal that exists as a diatomic molecule.
At 500K, which is between its melting point and boiling point, the substance is in its liquid phase. To draw a molecular-level picture, we can imagine a sample of liquid element X containing diatomic molecules. At 500K, the molecules would be moving around and colliding with each other. Some molecules would have enough kinetic energy to break free from the surface of the liquid and become gas molecules, while others would stick together and remain in the liquid phase.
It's difficult to draw a molecular-level picture, but we can represent a sample of element X at 500K as follows:
_ _
/ \ / \
| X | X |
\_/ \_/
Here, each X represents a diatomic molecule of element X. The wavy lines around the molecules indicate the movement of the molecules due to their kinetic energy. Some of the molecules have enough energy to break free and become gas molecules, while others remain in the liquid phase.
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Write the given number using scientific notation( notice that ^ indicates the power;for example
4245=4.245x 1013 , and 0.005=5x10^-3) 0.0034 = X 10 ^=
0.0034 is equal to 3.4 x 10⁻³, written in scientific notation.
A way of expressing numbers that are either too large or too small (which would usually result in a long string of digits) to be conveniently written in decimal form is called scientific notation. It is commonly used by scientists, engineers, and mathematicians, in part because scientific notation can simplify certain arithmetic operations.
In order to write 0.0034 in scientific notation, first we determine if the exponent for the base 10 is positif or negative. Since 0.0034 is less than 1, the exponent must be negative.
Next, we find the coefficient. It is 3,4 because the base should be a number between 1 and 9, including the non-negative number(s) after, and 3 is the first non-negative number behind the decimal point.
Lastly, we find the exponent itself. It has to be a negative number. Since we moved the decimal point (until we get to the number after 3) three times, the exponent then is -3.
Gathering all the facts and we've got 3,4 x 10⁻³. That is 0.0034 written in scientific notation.
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A pressure vessel that has a volume of 10m3 is used to store high-pressure air for operating a supersonic wind tunnel. If the air pressure and temperature inside the vessel are 20 atm and 300K, respectively:
• What is the mass of air stored in the vessel?
Let us now heat the gas in the vessel. Enough heat is added to increase the temperature to 600 K.
• Calculate the change in entropy of the air inside the vessel.
The mass of air stored in vessel is, 23.7 kg. The change in entropy of the air is 4,451 J/K.
a) Ideal gas law states, PV = nRT, P is pressure, V is volume, n is number of moles, R is gas constant, and T is the temperature.
Solve for n,
[tex]n = \dfrac{20\times 10}{0.08206 \times 300 K}\\n = 818.8 moles[/tex]
Molar mass of air = 28.97 g/mol.
mass = n x molar mass
= 818.8 x 28.97
= 23.7 kg
b) The change in entropy,
[tex]\triangle S = nC_v \ln{\dfrac{T_2}{T_1}} + nR \ln{\dfrac{V_2}{V_1}}[/tex]
where Cv is the specific heat at constant volume, T1, T2 are initial and final temperatures, V1, V2 are the initial and final volumes.
For air, Cv = 20.8 J/(mol K)
R = 8.314 J/(mol K).
Volume is constant, V2/V1 = 1.
[tex]\triangle S = nC_v \ln{\dfrac{T_2}{T_1}}[/tex]
[tex]\triangle S = (818.8\times 20.8) \ln{\dfrac{600}{300}\\ = 4,451\ J/K[/tex]
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Where is information first stored in a human brain?
Answer:
sensory organs
Explanation:
Information processing starts with input from the sensory organs, which transform physical stimuli such as touch, heat, sound waves, or photons of light into electrochemical signals. The sensory information is repeatedly transformed by the algorithms of the brain in both bottom-up and top-down processing.
A car starts from rest on a curve with a radius of 100 m and tangential acceleration of 1.4 m/s2 .Through what angle will the car have traveled when the magnitude of its total acceleration is 2.6 m/s2?
The angle the car will have traveled when the magnitude of its total acceleration is 2.6 m/s2 is approximately 33.0°.
This can be found using the equation a=v2/r, where a is the magnitude of the total acceleration, v is the tangential velocity, and r is the radius of the curve.
Rearranging this equation to solve for theta (θ), we get θ = (v2/a) x (180/π). Plugging in the given values for a, v, and r, we get θ = (1.4^2/2.6) x (180/π) ≈ 33.0°.
Acceleration is the rate of change of velocity measured in meters per second (m/s) squared. It is the rate at which an object's speed and direction of motion change over time. Acceleration can be caused by a variety of forces, such as gravity, friction, or a push or pull. It can also be caused by changes in speed or direction, such as when an object is speeding up or slowing down.
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A student must design an experiment to determine the gravitational mass of an object. Which of the following experiments could the student use? Select two answers. Place the object on one side of a lever at a known distance away from a fulcrum Place known masses on the other side of the fulcrum so that they are also placed on the lever distances from the fulcrum Move the known masses to a known distance such that the lever is in statie brium known Place the object on a surface of negligible friction and pull the object horizontally across the surface with a spring scale at anonconstant speed such that a motion detector can measure how the object's speed as a function of time changes Place the object on a surface that provides friction between the object and the surface. Use a surface such that the coefficient of friction between the object and the surface is known. Put the object horizontally across the surface with a spring scale at a nonconstant speed such that a motion detector can measure how the object's speed as a function of time changes Place the object on the end of a vertically hanging spring with a known spring constant. Allow the spring to stretch to a new equilibrium position and measure the distance the spring is stretched from its original equilibrium position
A. Position the item on one side of a lever, a certain distance from the fulcrum. Position known masses on the other side of the fulcrum so that they are also spaced along the lever at a known distance from the fulcrum.
What constitutes a lever system's fulcrum?The fulcrum is the term used to describe the beam's pivotal point. When force is applied to one end of a lever, a load is applied at the other end.
What in a basic machine is a fulcrum?You push or pull on this portion. The point on which the lever rotates or balances is known as the "fulcrum." Your hand's fingers serve as the fulcrum when using a fork. Scissors are actually two levers combined. Commonly known as a fixed lever, the handle on the toilet flusher.
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The __________ is the mass of the vapor divided by the total mass of a saturated mixture.
The mass of the vapour divided by the total mass of a saturated mixture is known as the vapour mass fraction. This is an important parameter when it comes to understanding the thermodynamic properties of a mixture.
It is also used to calculate the relative humidity of a mixture and the dew point temperature. The vapour mass fraction is determined by dividing the mass of the vapour by the total mass of the saturated mixture. The vapour mass fraction can be determined experimentally by measuring the mass of the vapour and the total mass of the mixture. The vapour mass fraction can also be calculated using the ideal gas law, which states that the mass of the vapour can be determined from the pressure, temperature, and volume of the mixture. The vapour mass fraction is an important parameter for understanding the thermodynamic properties of a mixture and can be used to calculate the relative humidity and the dew point temperature.
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The vapour mass fraction is defined as the mass of the vapour divided by the total mass of a saturated mixture. When attempting to understand the thermodynamic characteristics of a mixture, this is a crucial variable.
It is also used to determine the dew point temperature and the relative humidity of a combination. By dividing the mass of the vapour by the total mass of the saturated mixture, the vapour mass fraction is calculated. By measuring the mass of the vapour and the overall mass of the mixture, the vapour mass fraction can be calculated experimentally. The ideal gas law, which stipulates that the mass of the vapour can be estimated from the pressure, temperature, and volume of the mixture, can also be used to compute the vapour mass fraction. The relative humidity and dew point temperature can be determined using the vapour mass fraction, which is a crucial parameter for understanding the thermodynamic characteristics of a mixture.
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show that the displacement , where c and d are constants, is a solution to the wave equation. then find an expression in terms of c and d for the wave speed.
(a) The displacement with c and d as constants is a solution to the wave equation.
(b) An expression for the wave speed in terms of c and d is undefined, i.e, cannot be defined.
(a)
To show that the displacement, where c and d are constants, is a solution to the wave equation, we need to plug the displacement into the wave equation and see if it satisfies the equation.
The wave equation is:
∂²y/∂x² = (1/v²) ∂²y/∂t²
where y is the displacement, v is the wave speed, x is the position, and t is the time.
Plugging in the displacement, we get:
∂²(c+dx)/∂x² = (1/v²) ∂²(c+dx)/∂t²
Taking the second derivative with respect to x and t, we get:
d²/dx² = (1/v²) d²/dt²
Since d is a constant, the second derivative of c+dx with respect to x and t is 0. So we get:
0 = (1/v²) 0
This equation is satisfied for any value of v.
So the displacement is a solution to the wave equation.
(b)
To find an expression for the wave speed in terms of c and d, we can rearrange the wave equation to get:
v = √(∂²y/∂x²)/(∂²y/∂t²)
Plugging in the displacement, we get:
v = √(d²/dx²)/(d²/dt²)
Since d is a constant, the second derivative of c+dx with respect to x and t is 0. So we get:
v = √(0/0)
This expression is undefined.
So we cannot find an expression for the wave speed in terms of c and d.
Therefore,
a) The displacement with c and d as constants is a solution to the wave equation.
(b) An expression for the wave speed in terms of c and d is undefined, i.e, cannot be defined.
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HELP!! 15 points!!!
Which statements describe a situation in which work is being done? Select three options.
A mover carries a box up a flight of stairs.
A mover carries a box across a room.
Wind blows against a steel table anchored to the ground.
Wind blows a pool chair across the yard.
A weightlifter lifts a barbell off the ground.
A weightlifter holds a barbell above the head.
Answer:
wind blows a pool chair across the yard
Explanation:
The question is asking about forces at work like air resistance wich is pushing the chair across the yard. Work is when a force pushes pulls so when air resistance is pushing the chair because of the big surface area that is doing work.
For the piping system shown below, water is flowing from left to right at steady-state and constant temperature. You may assume the flow is frictionless. The pipe diameter is larger in section A than section B. The diameters of sections A and C are the same. If gravitation and frictional effects are negligible, which of the following relationships is true about the static pressure in sections A and B?
a). PA < PB because pressure builds up when mass is being pushed through a smaller area
b). PA > PB because pressure decreases as velocity increases at steady-state
c). PA = PB because friction is assumed to be negligible
Part B
The reason for this is because:
a. PA = PC because friction is assumed to be negligible and velocities are the same
b. PA > PC because pressure drops in the direction of the flow even though friction is negligible
c. PA < PC because pressure builds up through the smaller area in section B
(a) The correct relationship is: PA < PB because pressure builds up when mass is being pushed through a smaller area. (b) The correct reason is: PA > PC because pressure decreases in the direction of the flow even though friction is negligible.
(a) The correct relationship between the static pressure in sections A and B is: PA < PB because pressure builds up when mass is being pushed through a smaller area. This is because the velocity of the water must increase as it flows through the smaller diameter section B in order to maintain the same mass flow rate, according to the principle of continuity. This increase in velocity is accompanied by a decrease in static pressure, as described by the Bernoulli equation.
(b) The correct reason for the relationship between the static pressure in sections A and C is: PA > PC because pressure decreases in the direction of the flow even though friction is negligible. This is because the water experiences a pressure drop as it flows from the wider diameter section A to the narrower diameter section B, due to the principle of continuity. However, as the flow area expands again in section C, the velocity decreases and the static pressure increases to a value close to that in section A, since frictional effects are negligible.
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The missing figure in the question is attached below
A rescue team is searching for Andrew, a geologist who was stranded while conducting research in the mountains of Colorado. The team uses electronic listening devices in order to detect any shouts for help. The sound waves from his shouts reaching the base camp can be approximated by a sinusoidal wave with a frequency f = 450 Hz and displacement amplitude A = 4.00×10−8 m , where the sound wave properties are valid at the base camp where the measurements are being made. What sound intensity level will the rescue team measure from the frightened researcher? Assume the speed of sound is v=332m/s and the density of air rho = 1.33 kg/m3 .
Calculate the bulk modulus B of air using the given values of the sound speed and air density. Express your answer numerically in Pascals.
1. The sound intensity level will the rescue (that searching for Andrew, a geologist who was stranded while conducting research in the mountains of Colorado) team measure from the frightened researcher = 2.82 x 10–⁶ W/m²
2. The bulk modulus B of air = 1.46 x 10⁵ Pa
The energy of the wave between the order per unit area of the same is what determines how loud a sound is. The energy is computed by integrating the mechanical energy over a period, where's' is the sound wave's amplitude and the mass is affected by density.
The intensity of the wave:
I = 2 π² f²A²v ρ
= 2 π² (450)² (4.00 x 10–⁸)² (332) (1.33)
= 2.82 x 10–⁶
The bulk modulus:
B = v²ρ
= (332)² (1.33)
= 1.46 x 10⁵ Pa
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As you read through the Case Study of Cold Fusion, Cite evidence in the text for or against science.
Answer:Cold fusion: A case study for scientific behavior ... Scientists take into account all the available evidence when deciding whether to accept an idea or not ...
Explanation:
Suppose now that the container for this sample of helium gas develops a leak overnight while it is fixed at a constant volume. If the gauge pressure of the container drops from 9 to 4 atm during this period while the temperature drops from 27 to insulation to be 3° C., then determine the percentage of the original gas still remaining.
To determine the percentage of the original gas still remaining, we need to calculate the change in the number of moles of gas in the container. We can use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.
We can rearrange the equation to solve for n: n = PV/RT.
First, let's calculate the original number of moles of gas, n1, using the initial conditions:
P1 = 9 atm
V1 = constant
T1 = 27 + 273 = 300 K
R = 8.31 J/mol K (the ideal gas constant)
n1 = P1V1/RT1 = (9)(constant)/(8.31)(300) = constant/27.29
Next, let's calculate the final number of moles of gas, n2, using the final conditions:
P2 = 4 atm
V2 = constant
T2 = 3 + 273 = 276 K
n2 = P2V2/RT2 = (4)(constant)/(8.31)(276) = constant/23.12
Finally, we can calculate the percentage of the original gas still remaining:
Percentage = (n2/n1) * 100%
= (constant/23.12) / (constant/27.29) * 100%
= 83.72%
So, the answer is that 83.72% of the original gas is still remaining in the container.
in this tutorial you will examine dihybrid crosses: crosses where alleles at separate loci assort independently into gametes at meiosis. you will also use logic to determine unknown genotypes, phenotypes, and genetic ratios from given data.
When two parents that are heterozygous for both traits are crossed, the resulting offspring can have any combination of the two traits. In this type of cross, the inheritance of one trait is independent of the inheritance of the other trait, as long as the genes for these traits are located on different chromosomes.
The gene for seed color is located on one chromosome, while the gene for pea texture is located on a different chromosome. If we cross two pea plants that are heterozygous for both traits (YySs x YySs), we can use a Punnett square to determine the expected genotype and phenotype ratios of the resulting offspring.
Genotype ratios:
[tex]YYSS: 1/16[/tex]
[tex]YYSs: 2/16[/tex]
[tex]YYss: 1/16[/tex]
[tex]yySs: 2/16[/tex]
[tex]yyss: 1/16[/tex]
Phenotype ratios:
[tex]Yellow smooth: 9/16[/tex]
[tex]Yellow wrinkled: 3/16[/tex]
[tex]Green smooth: 3/16[/tex]
[tex]Green wrinkled: 1/16[/tex]
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find an expression for the rocket's speed at height h if air resistance is neglected. express your answer in terms of the variables fthrust , m , h , and appropriate constants.
The expression for the rocket's speed at height h, neglecting air resistance, is: v = -g * sqrt(2 * g * h) where g is the acceleration due to gravity and h is the height of the rocket.
What does air resistance mean?Air resistance, also known as air drag, is the force that opposes the motion of an object as it moves through the air. It is caused by the frictional force between the object's surface and the air molecules it encounters. Air resistance increases with the speed of the object and the surface area of the object in contact with the air. For objects moving at high speeds, air resistance can significantly affect their motion, causing them to slow down or change direction. In the case of a rocket, air resistance can have a significant impact on its speed and trajectory, and must be taken into account in many real-world situations.
Assuming that air resistance is neglected, the only force acting on the rocket is the force of thrust, which can be expressed as:
fthrust = m * g
where fthrust is the force of thrust, m is the mass of the rocket, and g is the acceleration due to gravity.
At any height h above the ground, the potential energy of the rocket is given by:
PE = m * g * h
where PE is the potential energy of the rocket.
According to the principle of conservation of energy, the total energy of the rocket (kinetic energy + potential energy) remains constant. Therefore, at any height h, the total energy of the rocket is:
E = KE + PE
where E is the total energy of the rocket and KE is the kinetic energy of the rocket.
The kinetic energy of the rocket can be expressed as:
KE = 0.5 * m * v^2
where v is the speed of the rocket.
Therefore,
E = 0.5 * m * v^2 + m * g * h
Since the total energy of the rocket remains constant, we can differentiate this equation with respect to time to obtain:
0 = m * v * dv/dt + m * g * dh/dt
But since air resistance is neglected, the acceleration of the rocket is:
a = fthrust / m = g
Therefore,
dh/dt = v
Substituting this into the previous equation,
0 = m * v * dv/dt + m * g * v
Simplifying this equation, we get:
dv/dt = -g
Integrating both sides with respect to time,
v = -g * t + C
where C is a constant of integration. At time t=0, the speed of the rocket is zero, so
C = 0
Therefore, the speed of the rocket at height h is:
v = -g * t
Substituting dh/dt = v,
dh/dt = -g * t
Integrating both sides with respect to time,
h = -0.5 * g * t^2 + D
where D is another constant of integration. At time t=0, the height of the rocket is zero,
D = 0
Therefore, the height of the rocket at time t is:
h = -0.5 * g * t^2
Combining the expressions for v and h
v = -g * sqrt(2 * g * h)
where g is the acceleration due to gravity and h is the height of the rocket. This is the expression for the rocket's speed at height h, neglecting air resistance.
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Give an example of a machine that increases speed, a
250 J of ene
machine that changes the direction of force, and a machine
ie speed,
that increases force.
A machine that increases force, force direction, and speed, as well as an illustration of each. A bicycle increases speed, an ax changes direction of force, and a car jack increases force.
What is Speed?Machine that increases speed, a machine that increases direction of force, and a machine that increases force. A bicycle increases speed, an ax changes direction of force, and a car jack increases force. contrast the scientific definition of work with it's everyday meaning.
Speed powder may have traces of pink or grey and can range in color from white to brown. It tastes harsh and has a pungent aroma. Also available in pill form.
Therefore, A machine that increases force, force direction, and speed, as well as an illustration of each. A bicycle increases speed, an ax changes direction of force, and a car jack increases force.
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Will a projectile follow a perfectly parabolic path when there is no air resistance?
A projectile will follow a perfectly parabolic path when there is no air resistance because of gravity:
In kinematics, the term "acceleration of a particle" is used to describe the rate at which velocity changes in a given direction and over a given time. When a particle moves vertically, it is sometimes referred to as gravity-induced acceleration.
The acceleration caused by gravity always operates downward in a parabolic path when there is no air resistance, and the velocity vector always acts perpendicular to the path.
At the topmost point, when the acceleration acts downward and the velocity is tangent to the path, it will automatically act in a perpendicular direction to the acceleration, as mentioned in section A concerning the path of the acceleration and the velocity.
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To find the vector components of a vector with respect to two orthogonal vectors, we can use the projection formula. Let's first find the projection of on the vector :
proj = (( · ) / ( · ))
= ((-9)(-6) + (-1)(2)) / ((-9)^2 + (-1)^2)
= -56/82
= -28/41
Now, let's find the vector in the direction of :
in = proj = (-28/41)
To find perpendicular to , we can subtract from :
⊥ = - in
⊥ = [6/41, -28/41]
Therefore, we can write as the sum of two orthogonal vectors:
= in + ⊥
= [-9, -1]
= [-9*(-28/41) , -1*(-28/41)] + [6/41, -28/41]
= [252/41, -28/41] + [6/41, -28/41]
= [258/41, -56/41]
Thus, we have decomposed into two orthogonal vectors, in the direction of and ⊥ perpendicular to.
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Your college town becomes the founding site for a strange new cult that worships the Moon. These true believers gather regularly around sunset and do a dance in which they must extend their arms in the direction of the Moon. Have your group discuss which way their arms will be pointing at sunset when the Moon is new, first quarter, full, and third quarter?
At sunset, the Moon will be in the western horizon and its believers will point their arms towards the west.
During the first quarter, its believers will point their arms towards the southwest.
During the full moon, its believers will point their arms towards the east.
During the third quarter phase, its believers will point their arms towards the northwest.
Directions during the different moon phasesDuring the new moon phase, the Moon is located between the Sun and the Earth, so it rises and sets at approximately the same time as the Sun. Therefore, at sunset, the Moon will be in the western horizon and its believers will point their arms towards the west.
During the first quarter phase, the Moon is located at a right angle to the Earth and the Sun. It rises at around noon and sets at around midnight. Therefore, at sunset, the Moon will be located in the southern horizon, and its believers will point their arms towards the southwest.
During the full moon phase, the Moon is on the opposite side of the Earth from the Sun, so it rises as the Sun sets and sets as the Sun rises. Therefore, at sunset, the Moon will be located in the eastern horizon, and its believers will point their arms towards the east.
During the third quarter phase, the Moon is also located at a right angle to the Earth and the Sun, but on the opposite side of the first quarter. It rises at around midnight and sets at around noon. Therefore, at sunset, the Moon will be located in the northern horizon, and its believers will point their arms towards the northwest.
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A 686 N person standing on a scale in an elevator, is accelerating upward at 4.9 m/s2. Determine the reading on the scale.
Group of answer choices
1372 N
1029 N
343 N
686 N
The reading on the scale will be equal to the normal force exerted by the scale on the person. We can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration:
Net force = mass x acceleration
The person's mass can be calculated using their weight, which is equal to their mass times the acceleration due to gravity (9.81 m/s^2):
Weight = mass x acceleration due to gravity
686 N = mass x 9.81 m/s^2
mass = 70 kg
Now we can use Newton's second law to find the normal force exerted by the scale:
Net force = mass x acceleration
Normal force - Weight = mass x acceleration
Normal force - 686 N = 70 kg x 4.9 m/s^2
Normal force = 1029 N
Therefore, the reading on the scale will be 1029 N. Answer: 1029 N.
If the archerfish spits its water 30 degrees from the horizontal aiming at an insect 1.6 m above the surface of the water, how fast must the fish spit the water to hit its target? The insect is at the highest point of the trajectory of the spit water. Use g = 10 m/s2.
a. 4.0 m/s b. 11 m/s c. 23 m/s d. 5.7 m/s
The answer is not D.
The fish must spit the water with 11 m/s to hit its target. The correct answer is (b).
The vertical component of the water's velocity is zero, so we can use the equation v0y^2 = 2gh to solve for the initial velocity of the water.
To hit the insect, the water must travel a horizontal distance equal to the distance between the fish and the insect. Substituting the given values, we get:
v0^2 = 32 / sin^2(theta)
t = v0 sin(theta) / g
d = v0x * t, we get:
d = v0 cos(theta) * (v0 sin(theta) / g)
d = sqrt(32) * cos(theta) / sin(theta)
Solving further,
d = 8 / tan(theta)
d = 8 / tan(30) = 13.9 m
v0^2 = 32 / sin^2(30) = 128
v0 = 11.3 m/s (approximately)
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How long it takes paint to dry can have an impact on the production capacity of commerce. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time?" To test this suppose we sample five drying times for each of the different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained.
Robot 1 Robot 2 Robot 3 Robot 4
127 144 134 151
137 133 143 142
136 142 138 135
125 146 135 141
135 125 125 146
At the α
=
0.05
level of significance, test to see whether the mean drying time is the same for each type of robot.
Find the p-value.
The sum of squares of error, treatment, within and between four painters are: 330, 692, 110 and 43.25.
The data provided is for the dying time of four different types of paint.
One-way ANOVA can be used to determine whether all the four paints have the same drying time.
Use Excel to perform the one-way ANOVA.
Go to Data → Data Analysis → Anova: Single Factor
A dialog box will open. Select the data. Select "Grouping" as Columns.
Press OK.
The output is attached below.
The required values are as follows:
(1) Sum of Squares of Treatment (Between Subjects):
SST = 330
(2) Sum of Squares of Error (Within Subjects):
SSE = 692
(3) Mean Squares Treatment (Between Subjects):
MST = 110
(4) Mean Squares Error (Within Subjects):
MSE = 43.25
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--The complete question is, Four different paints are advertised as having the same drying time. To check the manufacturers' claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded for each sample. The data obtained follow. Excel File: data 16-21.xls Paint 1 Paint 2 Paint 3 Paint 4 128 137 135 133 144 133 142 146 130 143 137 124 136 141 131a. Use a = .05 to test for any significant differences in mean drying time among the paints. If an amount is zero, enter "0. Test to see whether the mean drying time is the same for each type of paint.--
If the Earth's diameter is 12,756 km (7,922 miles) at the equator, how far is one degree of longitude at the equator (give both miles and kilometers)? First find: the Earth's circumference: (C = 2īr; r = radius, n = 3.14). How many degrees are there in a circle (360)? Divide the Earth's circumference by the number of degrees to get your answer. 2-3. How many miles and kilometers are there in one minute of longitude at the equator? 2-4. How many miles and kilometers are there in one second of longitude at the equator?
One degree of longitude at the equator is 111.32 kilometers (69.17 miles), one minute of longitude is 1.855 kilometers (1.153 miles), and one second of longitude is 0.031 kilometers (0.019 miles).
At the equator, one degree of longitude corresponds to 1/360th of the circumference of the Earth, which can be calculated as:
C = 2*π*r where C is the circumference, r is the radius of the Earth.
The radius of the Earth is half of its diameter, so:
r = 12,756 km / 2 = 6,378 km
Thus, the circumference of the Earth at the equator is:
C = 2*π*(6,378 km) ≈ 40,075 km
So, one degree of longitude at the equator is:
40,075 km / 360 ≈ 111.32 km
Or in miles:
24,901 miles / 360 ≈ 69.17 miles
To find the distance in one minute of longitude, we need to divide by 60:
111.32 km / 60 ≈ 1.855 km/min
69.17 miles / 60 ≈ 1.153 miles/min
To find the distance in one second of longitude, we need to divide by 60 again:
1.855 km/min / 60 ≈ 0.031 km/sec
1.153 miles/min / 60 ≈ 0.019 miles/sec
Therefore, one degree of longitude at the equator corresponds to approximately 111.32 kilometers (69.17 miles), one minute of longitude corresponds to approximately 1.855 kilometers (1.153 miles), and one second of longitude corresponds to approximately 0.031 kilometers (0.019 miles).
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