The time taken for the helicopter rotor to double its angular velocity over the initial speed is 1 minute.
What is the time of motion?
If the rotor speed changed from 225 rev/min to 300 rev/min in one minute.
This means the change in angular velocity (Δω) is:
Δω = ω2 - ω1 = 300 rev/min - 225 rev/min = 75 rev/min
We are given that the rotor doubles its angular velocity over the initial speed, so ω2 = 2ω1.
Substituting ω2 = 2ω1 into the equation for Δω, we get:
75 rev/min = 2ω1 - ω1
Simplifying, we get:
75 rev/min = ω1
Now we can solve for the time taken for the rotor to double its angular velocity over the initial speed.
Δω = αt
Substituting Δω = 75 rev/min and ω1 = 75 rev/min, we get:
75 rev/min = αt
Now we can solve for t:
t = Δω / α
We need to find α, the angular acceleration.
α = Δω / t = 75 rev/min / 1 min = 75 rev/min²
Now we can substitute the value of α back into the equation for t:
t = Δω / α = 75 rev/min / 75 rev/min² = 1 minute
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1 a Explain the difference between a transverse wave and a longitudinal
wave.
b Give one example of each.
c Draw a diagram of a transverse wave. On your diagram, mark the
wavelength and amplitude of the wave.
The difference between transverse and longitudinal waves is direction of wave motion in relative to direction of the particle motion.
Transverse vs Longitudinal Waves: What's the Difference?The particle motion in a transverse wave is only perpendicular to the wave motion but in longitudinal wave, the particle motion is parallel to the wave motion.
An example of transverse wave is a wave on a guitar string which when plucked, it vibrates back and forth in a direction perpendicular to the direction of the wave traveling along the string.
An example of a longitudinal wave is sound waves which are created when a source like speaker or a musical instrument vibrates back and forth in the same direction as the wave is traveling through the air.
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What are the stages of the sliding filament theory?
The sliding filament theory explains how myosin and actin interact to cause a muscle contraction. There are 5 stages: resting, excitement-contraction, contraction, recharge, and relaxation.
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1 The resting phase is before there is any tension in the muscle, pretty self explanatory.
2 The excitement-contraction phase occurs once the sarcoplasmic reticulum (SR) releases calcium, that binds to troponin, which causes tropomyosin to shift, allowing the myosin cross-bridge to attach to actin. The muscle force is determined by the number of cross bridges involved. When there's an increase in the number of cross-bridges, myofibril and sarcoplasmic reticulum hypertrophy, which result in more actin + myosin and more fuel for the muscle respectively. To increase the power generated in a contraction, there needs to be an increase in the speed of cross bridges. Also make note: at this point, the muscle still hasn't quite contracted.
3 The contraction phase is where the power stroke occurs. ATP undergoes hydrolysis via the enzyme myosin ATPase, and loses a phosphate to become ADP. This allows the myosin head to change shape and pull on the actin, which is referred to as the power stroke. Myosin pulling on actin causes the muscle fiber to shorten.
4 The recharge phase is when the contraction continues and can only occur when calcium, ATP, and myosin ATPase are all still available.
5 The relaxation phase occurs when nerve stimulation stops and those components are no longer available. The calcium returns to the sarcoplasmic reticulum and myosin lets go of actin.
20. An x vs. t graph is drawn for a ball moving in one direction. The graph starts at the origin and at t = 5 s the velocity of the ball is zero. We can be positive that at t = 5 s,
a. the slope of the curve is non-zero.
b. the ball has stopped.
c. the acceleration is constant.
d. the curve is at x = 0, 1 = 0.
We can be positive that at t = 5 s, a. the slope of the curve is non-zero.
How to explain the graphIt should be noted that the graph does not indicate that the ball has stopped, as it only tells us that the velocity of the ball is zero at t=5s. Moreover, the curve is not at x=0,1=0 as this statement is not meaningful.
Therefore, the slope of the curve is non-zero. Since the velocity of the ball is zero at t=5s, the slope of the x vs. t graph must be horizontal at this point. However, it is non-zero because the slope was changing up until t=5s.
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a block weighing 15 newtons is on a ramp inclined at 30.0º to the horizon\tal
what is hookies law of elasticity
Hooke's law of elasticity is a principle in physics that states that the force required to extend or compress a spring by some distance is proportional to that distance. It is named after the English physicist Robert Hooke, who first stated the law in 1678. Hooke's law is often written as F = -kx, where F is the force applied to the spring, x is the distance it is stretched or compressed, and k is the spring constant, a measure of the stiffness of the spring.
A block of mass M=5.0 kg is hanging at equilibrium from an ideal spring with spring constant k=250 N/m
a) on the dot below, which represents the block, draw and label the forces (not components) that act on the block. Each force must be represented by distinct arrow, starting on, and pointing away from, the dot.
The block is pulled 0.15 m below is equilibrium position and released from rest.
b) determine the maximum displacement of the mass from equilibrium
c) calculate the elastic potential energy of the spring, just as the block is being released
d) calculate the maximum speed, the block will have during its motion
e) calculate the displacement of the block from equilibrium when the kinetic energy of the block is equal to the elastic potential energy of the spring
The block is brought to rest at equilibrium. The block is then pulled down half the original distance.
f) will the new period for the motion of the block, be greater than, less than, or equal to the original period for the motion of the block?
The maximum displacement of the mass from equilibrium is 0.4 times the square root of the maximum height the block reaches.
What is Displacement?
In physics, displacement is the distance and direction of an object's change in position from its starting point to its end point. It is a vector quantity and is represented by a vector pointing from the object's initial position to its final position. Displacement is different from distance, which is the total path length traveled by an object and is a scalar quantity.
The elastic potential energy of the spring is given by:
U = 1/2 k[tex]x^{2}[/tex]
where U is the elastic potential energy, k is the spring constant, and x is the displacement from equilibrium.
At the instant the block is released, it is pulled 0.15 m below its equilibrium position. Therefore, the initial displacement of the block is x = 0.15 m.
Substituting the given values, we get:
U = 1/2 * 250 N/m * [tex](0.15 m)^{2}[/tex] = 1.875 J
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You are going to put your senses to the test by experimenting with taste and smell. These sensory tests are very simple but will require you to have a few grocery items on hand.
Take the onion and cut it in half. Take the apple and cut it into quarters—you're going to eat one of those apple quarters. Now that your onion is cut, hold it to your nose and breathe in. Breathe a few times to get all the onion smell into your olfactory glands—the scent glands. Breathe just a few more times. You want to have the smell of the onion completely saturated into your sense of smell. Continue to hold the onion under your nose. Think of an onion in your mind. Picture it and keep smelling your onion. Take one of the apple quarters and bite into it and chew.
What do you notice?
What does the apple taste like?
Were your senses tricked?
Why were you asked to bite into an apple? Onions and apples have a similar texture and consistency. Biting into an apple while smelling an onion should have given your brain the sense that it was biting into something of onion-like consistency. It's all a ploy to trick your brain into thinking that you'd just taken a bite and were eating an onion.
When you hold the onion to your nose and breathe in, you will likely smell the pungent and sharp aroma of the onion. As you continue to smell the onion and imagine it in your mind, your brain will start to associate the smell with the taste of an onion.
When you take a bite of the apple quarter, you may initially taste the sweetness of the apple, but because your brain is primed to expect an onion taste, you may notice a slightly onion-like flavor in the apple. Your brain may be tricked into interpreting the apple's texture as being more onion-like, even though the two foods have different textures.
Overall, this experiment plays with the way that our senses of taste and smell work together to create flavor perception. Our brains rely on a combination of taste, smell, and texture to interpret what we're eating, and this experiment shows how our brains can be tricked into expecting a certain flavor based on our sense of smell.
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The population of Las Vegas is estimated to double in size by the year 2030. Of the methods of energy production we learned about the quarter (solar, hydroelectric), which do you think will be the best to supplement our current power grid to meet the power needs of our population by the year 2030?
According to the question Solar energy is the most reliable and sustainable option for supplementing the current power grid in Las Vegas by 2030.
What is power?Power is the ability to influence or control the behavior of people, events, and outcomes. It is an essential element of life, as it is needed to make decisions, shape the environment, and establish order. Power can be wielded by individuals, organizations, and societies. It is often used to gain an advantage or to achieve a desired outcome. Power can either be coercive or consensual, depending on the situation and the parties involved. Coercive power is used to force others to do something, while consensual power is used to gain agreement and cooperation. Power can lead to positive outcomes, such as cooperation and collaboration, but it can also be misused or abused.
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Show that the minimum ratio of cation radius to anion radius at coordination number equal to 8 should be 0.732.
The minimum ratio of cation radius to anion radius at coordination number equal to 8 is 0.732.
In a crystal lattice, the coordination number refers to the number of anions surrounding a cation or the number of cations surrounding an anion. At a coordination number of 8, the cation is located at the center of a cube, and the anions are located at the corners of the cube.
To determine the minimum ratio of cation radius to anion radius at this coordination number, we can use the formula:
r_cation / r_anion = √(2) * (coordination number - 1) / (coordination number + 1)
Substituting the coordination number of 8, we get:
r_cation / r_anion = √(2) * (8 - 1) / (8 + 1) = 0.732
As a result, for coordination number 8, the lowest ratio of cation radius to anion radius is 0.732. This means that for a given anion radius, the cation radius cannot be smaller than 0.732 times the anion radius to achieve a coordination number of 8 in a crystal lattice. If the cation radius is smaller than this minimum value, the coordination number would be less than 8, and the crystal structure would be different.
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Newton studied the forces in an interaction between two objects and formulated the third law of motion, which states that to every action there is an equal and opposite reaction. Using this law, identify the action and reaction force involved in the scenarios specified in the table below. Also, add two more scenarios and identify the action and reaction force in them.
10pt
Action and reaction forces:
A book resting on a table
Action: The weight of the book pulling down on the table.Reaction: The table pushing up on the book with an equal force.A person pushing a wall
Action: The force exerted by the person on the wall.Reaction: The force exerted by the wall back on the person with an equal force.A bird flapping its wings
Action: The downward force exerted by the bird's wings on the air.Reaction: The upward force exerted by the air back on the bird's wings with an equal force.Newton's third law of motion states that every action has an equal and opposite reaction. In the scenarios listed, there are pairs of action and reaction forces that can be identified using this law. For example, in the case of the book resting on a table, the weight of the book is the action force, and the force of the table pushing up on the book is the reaction force.
Similarly, in the case of a person pushing a wall, the force exerted by the person on the wall is the action force, and the force exerted by the wall back on the person is the reaction force.
In addition to the given scenarios, two more examples could be:
A hammer striking a nail
Action: The force exerted by the hammer on the nail.Reaction: The force exerted by the nail back on the hammer with an equal force.A swimmer pushing off the edge of a pool
Action: The force exerted by the swimmer's feet on the pool wall.Reaction: The force exerted by the pool wall back on the swimmer's feet with an equal force.A car accelerating forward
Action: The force exerted by the car's wheels on the road.Reaction: The force exerted by the road back on the car's wheels with an equal force.A rocket propelling itself into space
Action: The force exerted by the rocket's engines on the exhaust gases.Reaction: The force exerted by the exhaust gases back on the rocket's engines with an equal force.In each of these cases, there is a pair of forces that are equal in magnitude and opposite in direction. Understanding these action and reaction pairs can help in understanding the motion and forces involved in various scenarios.
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What is the relationship between the Sun's energy and white light? Responses A The Sun's energy is made up of a wide range of wavelengths, including infrared, visible, and ultraviolet, while white light is made up of a single wavelength. B Both the Sun's energy and white light are made up of a wide range of wavelengths, including infrared, visible, and ultraviolet. C The Sun's energy is made up of a single wavelength, while white light is made up of a wide range of wavelengths, including infrared, visible, and ultraviolet. D Both the Sun's energy and white light are made up of a single wavelength.
The correct response is A: The Sun's energy is made up of a wide range of wavelengths, including infrared, visible, and ultraviolet, while white light is made up of a combination of different wavelengths within the visible spectrum.
The relationship between the Sun's energy and white light is The Sun's energy is made up of a wide range of wavelengths, including infrared, visible, and ultraviolet, while white light is made up of a single wavelength.
Hence option A is correct.
What is Visible light ?Visible light spectrum is nothing but the range of wavelength of radiation from 4000 angstrom to 7000 angstrom(Violet to Red). light is a energy packet. Every Photon having different wavelength travels with same velocity c (velocity of light). When we focus numbers of colors from visible spectrum to a point, that point appears as a white light. hence white light is composed of numbers of Colors in it.
When we pass white light through a prism, as white light enters in the prism all the colors having different wavelength travels with different velocity in the prism due to that there is separation of colors from the white light. Therefore we get different colors of white light in the prism this phenomenon is know as dispersion of light.
Hence option A is correct.
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The sum of two point charges is -15µC. They attract each other with a force of 9 x 10-2 N when kept 5m apart. Find their charges.
According to the question the two charges are -7.5 µC and -7.5 µC.
What is charges?Charges are fees or payments for services or goods. Charges can be one-time payments, recurring payments, or fees associated with using a product or service. Charges can be for products, services, or activities. Examples of charges include fees for using a credit card, fees for using a bank account, fees for renting a car, fees for using a mobile phone plan, fees for using a subscription service, fees for using a streaming service, and fees for using a gym membership.
Let the two charges be x and ( -15 - x ) µC.
According to Coulomb's law,
F = (k × x × ( -15 - x ))/r2
Where k is the Coulomb's constant,
k = 9 × 109 N × m2/C2
Given, F = 9 × 10-2 N
r = 5 m
Substituting these values in the equation,
9 × 10-2 = (9 × 109 × x × ( -15 - x ))/252
⇒ x2+ 15x - 4.5 × 10-4 = 0
Solving this equation,
x = -7.5 µC and ( -15 - x ) = -7.5 µC
Therefore, the two charges are -7.5 µC and -7.5 µC.
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14. How are an object's speed and velocity related to an object's kinetic energy and total mechanical energy
Speed and velocity are related to an object's kinetic energy, which is the energy associated with its motion.
What is kinetic energy?Kinetic energy is the energy that an object has due to its motion. It is a form of energy that is associated with the motion of an object, and is calculated by multiplying the mass of the object by the square of its velocity. Kinetic energy is one of the most fundamental forms of energy, and is found in everything from the movement of atoms and molecules to the motion of planets and stars. Kinetic energy is also the energy that is associated with everyday objects, such as a ball that is thrown or a car that is moving. Kinetic energy can be converted into other forms of energy, such as heat or electricity, and can also be used to do work, such as powering a car or a machine. Kinetic energy is a crucial part of the natural world, and is necessary for many of the processes that occur in nature.
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A block on an inclined surface is connected to another block that is hanging over the top edge of the incline, as shown in the following diagram. The blocks in the system are moving in such a way that block A (with a mass of 3 kg) is moving downwards, as block B (with a mass of 2 kg) slides up the ramp. The coefficient of kinetic friction between the ramp and the sliding block is 0.11.
State the acceleration of each block, and the amount of tension in the string.
The acceleration of block A is 2.31 m/s², the acceleration of block B is 3.44 m/s², and the tension in the string is 8.75 N.
To solve this problem, we will apply the principles of Newton's laws of motion. We will consider the forces acting on each block separately.
For Block A:
The only force acting on block A is its weight, which is given by:
FgravityA = mA * g
where mA is the mass of block A, and g is the acceleration due to gravity (which is 9.81 m/s²).
Since block A is moving downwards, we can find its acceleration by subtracting the force of friction from its weight, and then dividing by its mass:
aA = (FgravityA - FfrictionA) / mA
where FfrictionA is the force of friction acting on block A. Since the surface is inclined, we need to resolve the weight of block A into its components parallel and perpendicular to the surface:
FparallelA = mA * g * sin(θ)
FperpendicularA = mA * g * cos(θ)
where theta is the angle of inclination of the surface. The force of friction is then given by:
FfrictionA = friction coefficient * FperpendicularA
where friction coefficient is the coefficient of kinetic friction between the surface and block A. Substituting these values, we get:
FparallelA = mA * g * sin(θ) = 3 * 9.81 * sin(30) = 14.2 N
FperpendicularA = mA * g * cos(θ)= 3 * 9.81 * cos(30) = 25.7 N
FfrictionA = friction coefficient * FperpendicularA = 0.11 * 25.7 = 2.83 N
aA = (FgravityA - FfrictionA) / mA = (3 * 9.81 - 2.83) / 3 = 2.31 m/s²
For Block B:
The forces acting on block B are its weight, the tension in the string, and the force of friction. The tension in the string is equal to the weight of block A minus the component of its weight parallel to the surface:
Ftension = mA * g * cos(θ)- FparallelA
The force of friction is given by:
FfrictionB = friction coefficient * Fperpendicular B
where Fperpendicular B is the perpendicular component of the weight of block B:
Fperpendicular B = mB * g * cos(θ)= 2 * 9.81 * cos(30) = 17.0 N
Substituting these values, we get:
Ftension = mA * g * cos(θ) - FparallelA = 3 * 9.81 * cos(30) - 14.2 = 8.75 N
FfrictionB = friction coefficient * Fperpendicular B = 0.11 * 17.0 = 1.87 N
The acceleration of block B is then given by:
aB = (Ftension - Ffriction B) / mB = (8.75 - 1.87) / 2 = 3.44 m/s²
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26. The city of Detroit has high unemployment. The automobile industry in Detroit has suffered from global competition and has moved much of the remaining production out of Detroit. The population of the city has fallen from a high of 1,850,000 in 1950 to 701,000 in 2013. Some of the highest crime rates in the United States are now those of Detroit, and huge areas of the city are in a state of severe urban decay. The police force and fire service do not have enough money to pay for staff and equipment such as fully operational vehicles. In 2013, Detroit filed the largest municipal bankruptcy case in U.S. history. How does unemployment affect the income of city? Describe how unemployment might lead city bankruptcy. 7
18. A European sports car dealer claims that his car will accelerate at a constant rate from rest to 100 km/hr in 8.00 s. If so, what is the acceleration?
a. 3.47 m/s²
b. 6.82 m/s²
c. 11.4 m/s²
d. 17.4 m/s²
The acceleration of a sports car is (a) 3.47 m/s² when it goes from 0 to 100 km/hr in 8.00 s.
Define acceleration ?
Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, which means that it has both magnitude (a numerical value) and direction (either positive or negative).
First, we need to convert the final velocity from km/hr to m/s, since the SI unit of acceleration is m/s²:
100 km/hr * (1000 m/km) / (60 s/hr) ≈ 27.78 m/s
Using the formula for acceleration, which relates acceleration, final velocity, initial velocity, and time:
acceleration = (final velocity - initial velocity) / time
where initial velocity is 0 since the car starts from rest, we can plug in the values given in the problem:
acceleration = (27.78 m/s - 0 m/s) / 8.00 s ≈ 3.47 m/s²
Therefore, the answer is (a) 3.47 m/s².
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Use the graph to answer the following questions
1.) About how long is one half-life for Element 1? (Hint: how long does it take for half of it to decay?)
2.) A scientist finds a bone that has about 15% Element 1 left. About how old is the bone?
3.) A scientist finds a rock with about 75% of its Element 1 left. About how old is the rock?
4.) A scientist drops all his samples and is trying to figure out where to classify them. He thinks a sample is from about 9,000,000 years ago. If he tests the sample, how much of element 1 should be left in it?
5.)A paleontologist finds a skeleton that he thinks is about 1,000,000 years old. How much Element 1 should she expect to find in the sample if her guess is correct?
1. The half-life for element 1 is 3000000 years
2. The age of the bone is 8220000 years
3. The age of the rock is 1230000 years
4. The amount of element 1 remaining is 12.5%
5. The amount of element 1 she would find is 79.55%
1. How do i determine the half-life?The half-life of a substance is the time taken for half the substance to decay.
From the above diagram, we can see that the original amount of element 1 is 100 g. Thus, half of 100 is 50.
Looking at the diagram, the time for 50 g is 3000000 years.
Therefore, we can conclude that the half-life of element 1 is 3000000 years
2. How do i determine the age of the bone?First, we shall determine the number of half lives that has elapsed. This is obtained as follow:
Original amount (N₀) = 100%Amount remaining (N) = 15%Number of half-lives (n) =?2ⁿ = N₀ / N
2ⁿ = 100 / 15
2ⁿ = 6.67
Take the log of both sides
Log 2ⁿ = Log 6.67
nLog 2 = Log 6.67
Take the log of both sides
n = Log 6.67 / Log 2
n = 2.74
Finally, we shall determine the age of the bone. Details below
Half-life of element 1 (t½) = 3000000 yearsNumber of half-lives (n) = 2.74 Age of bone (t) =?t = n × t½
t = 2.74 × 3000000
t = 8220000 years
Thus, the age of the bone is 8220000 years
3. How do i determine the age of the rock?First, we shall determine the number of half lives that has elapsed. This is obtained as follow:
Original amount (N₀) = 100%Amount remaining (N) = 75%Number of half-lives (n) =?2ⁿ = N₀ / N
2ⁿ = 100 / 75
2ⁿ = 1.33
Take the log of both sides
Log 2ⁿ = Log 1.33
nLog 2 = Log 6.67
Take the log of both sides
n = Log 1.33 / Log 2
n = 0.41
Finally, we shall determine the age of the rock. Details below
Half-life of element 1 (t½) = 3000000 yearsNumber of half-lives (n) = 0.41 Age of bone (t) =?t = n × t½
t = 0.41 × 3000000
t = 1230000 years
Thus, the age of the rock is 1230000 years
4. How do i determine the amount remaining?We shall first obtain the number of half lives that will elaspe during the time. Details below:
Half-life of element 1 (t½) = 3000000 yearsTime (t) = 9000000 yearsNumber of half-lives (n) =?n = t / t½
n = 9000000 / 3000000
n = 3
Finally, we shall determine the amount remaining. Details below:
Original amount (N₀) = 100Number of half-lives (n) = 3Amount remaining (N) = ?N = N₀ / 2ⁿ
N = 100 / 2³
N = 100 / 8
N = 12.5%
Thus, we can conclude that the amount remaining is 12.5%
5. How do i know how much of the element she would find?We shall first obtain the number of half lives that will elaspe during the time. Details below:
Half-life of element 1 (t½) = 3000000 yearsTime (t) = 1000000 yearsNumber of half-lives (n) =?n = t / t½
n = 1000000 / 3000000
n = 0.33
Finally, we shall determine the amount she would find. Details below:
Original amount (N₀) = 100Number of half-lives (n) = 0.33Amount found (N) = ?N = N₀ / 2ⁿ
N = 100 / 2^0.33
N = 79.55%
Thus, the amount she would find is 79.55%
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22. In figure 8, there are two equal block of the same volume but different mass. If Block A weight 4.5 kg and block B weight 2.8 kg in air. Take pw = 1000 kg/m³ Determine the density of block B. A 3 kg Figure 8 B 1 kg [2]
A rock is thrown straight up with an initial speed of 22 m/s.
A. Graph the vertical position, velocity, and acceleration of the rock on the axes provided.
B. Draw a motion map for the trip.
C. How long will it be in the air before it returns to the thrower?
The rock will be in the air for 4.48s before it returns to the thrower.
Initial velocity of the rock, u = 22 m/s
Vertical acceleration of the rock, a(y) = -9.8 m/s²
Vertical displacement, Sy = 0
Applying equations of motion,
Sy = ut + 1/2 a(y)t²
0 = 22t - 4.9t²
Time,
t = 22/4.9
t = 4.48 s
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Attaching the image file here.
A crate hangs from a rope that is attached to a metal ring. The metal ring is suspended by a second rope that is attached overhead at two points, as shown. What is the angle if the tension in rope 1 is 1.52 times the tension in rope 2?
Explanation:
vertical tensions in each side of rope 2
2 x mg cos Φ and this equals 1.52 tension in rope 1
2 x mg cos Φ = 1.52 mg 'divide out ' mg
2 cosΦ = 1.52
cosΦ = 1.52/2
arccos ( 1.52/2) = Φ = 40.5 degrees
A cart of mass M is on a level, horizontal track. The cart is attached to one end of an ideal spring, and the other end of the spring is attached to a vertical support. The spring has a spring constant k. The cart is pulled to the right, stretching the spring a distance d, as shown above, and released from rest at time t = 0. The cart-spring system begins to oscillate, and the position x of the cart as a function of time t is given by the equation x(t) = d cos(ωt) , where x is in meters, ω is in rad/s , and t is in seconds. Assume the mass of the cart’s wheels to be negligible.
(a) Derive an equation for the velocity of the cart v as a function of time t .
(b) On the axes below, sketch a graph of the velocity v of the cart as a function of time t for two complete oscillations. On the graph, T represents the time for one complete oscillation. Explicitly label asymptotes, maxima, or minima with algebraic expressions, as appropriate.
(c) Express all answers in part (c) in terms of ω, t, M, d, k, and physical constants, as appropriate.
i. Determine an expression for the kinetic energy K of the system as a function of time t.
ii. Determine an expression for the potential energy U of the system as a function of time t.
iii. Using the equations from parts (c)i and (c)ii, show that the rate of change of the total energy of the system dE/dt is zero.
Two springs identical to the spring above are attached to each side of the cart of unknown mass M, as shown in Figure 1 above. The cart is on a level, horizontal track of negligible friction. A piece of clay is added to the top of the cart so that it will stick to the cart. The cart is displaced to the left a distance d and released from rest, as shown in Figure 2 above. The period of oscillation is recorded. This procedure is repeated for several different pieces of clay of different masses. In each trial, the cart is displaced the same distance d. The data are shown below on the linear graph of T2 as a function of mC , where T is the period of oscillation and mC represents the mass of the clay.
(d) From the graph, determine the following.
k, the spring constant of each spring
M, the mass of the cart
(e) The experiment is repeated, but in a second set of trials, the cart is pulled back a distance D, where D > d . Describe any changes that will occur for the straight line on the graph in part (d).
Justify your answer.
An equation for the velocity of the cart v as a function of time t is v(t) = -dw sinwt
What is velocity?Velocity, a physical entity quantifying the rate at which an object alters it's location over a precise duration, stands as a vector quantity with both magnitude and direction.
Conventionally expressed in meters per second (m/s) or equivalent units of stretch distance versus duration, average velocity is worked out by partitioning an object's displacement over the time taken to complete said displacement. The formula for the same is quite simple:
Average Velocity = Displacement / Duration
Wherein, Displacement reflects the alteration in position of an object, and span denotes the interval consumed during that change.
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A kettle of water gets boiled. It takes 3 minutes to boil 1.0 kg of water. A student empties it
and puts in 2.0 kg of water. How long will it take to boil?
It will take 6 minutes to boil 2 kg of water in the kettle.
The given information states that the kettle takes 3 minutes to boil 1 kg of water. Therefore, to boil 2 kg of water, we can multiply the boiling time of 1 kg water by 2. So, it will take 3 x 2 = 6 minutes to boil 2 kg of water in the kettle.
The reason it takes longer to boil 2 kg of water instead of 1 kg is that more water means more energy is required to raise the temperature to the boiling point. This means that the kettle needs more time to heat up the water to the required temperature.
Therefore, after the student empties the kettle and fills it with 2 kg of water, the boiling process will take 6 minutes.
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Calculate r.m.s. value for the maximum-voltage (+220 V) and current (5 A)?
The RMS value for the maximum-voltage and current is 155.56 V and 3.54 A, respectively.
Define RMS ?
RMS stands for Root Mean Square. It is a mathematical formula used to determine the effective or average value of a set of values, particularly those that vary over time, such as voltage and current in electrical circuits. RMS takes into account both the magnitude and duration of each value, and provides a value that is equivalent to the DC value of the signal that would produce the same amount of power in a resistive load.
To calculate the RMS (Root Mean Square) value for voltage and current, we use the following formulas:
RMS Voltage = Max Voltage / √2
RMS Current = Max Current / √2
Using these formulas, we can calculate:
RMS Voltage = 220 V / √2 = 155.56 V
RMS Current = 5 A / √2 = 3.54 A
Therefore, the RMS value for the maximum-voltage and current is 155.56 V and 3.54 A, respectively.
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A 2000 kg car moves along a horizontal road
at speed v0 = 19.6 m/s. The road is wet,
so the static friction coefficient between the
tires and the road is only µs = 0.176 and
the kinetic friction coefficient is even lower,
µk = 0.1232.
The acceleration of gravity is 9.8 m/s
2
.
Assume: No aerodynamic forces; g =
9.8 m/s
2
, forward is the positive direction.
What is the highest possible deceleration of
the car under such conditions?
Answer in units of m/s
2
.
The highest possible deceleration of the car under these conditions is 1.725 m/s².
The maximum deceleration of the car occurs when the force of friction is equal to the maximum force of static friction, which is given by;
fs = µs × N
where N is the normal force, which is equal to the weight of the car, mg;
N = mg = 2000 kg × 9.8 m/s² = 19600 N
So, the maximum force of static friction is;
fs = 0.176 × 19600 N = 3449.6 N
The deceleration of the car is given by;
a = -fs / m
where m is the mass of the car. Substituting the given values, we get;
a = -(0.176 × 19600 N) / 2000 kg = -1.725 m/s²
Therefore, the highest possible deceleration of car is 1.725 m/s².
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Someone help fast (will mark Brainlist)
The work done by a piston is measured to be 1000 J. If the pressure is a constant 1000 Pa, what is the change in volume of the piston?
Is the process described in #10 isovolumetric? Explain.
The change in the volume of the piston is 1 m³.
What is the change in volume of the piston?The change in volume of the piston is calculated by applying the first law of thermodynamic as shown below;
W = PΔV
where;
W is the work done by the pistonP is the constant pressure of the pistonΔV is the change in volume of the pistonThe change in the volume of the piston is calculated as follows;
ΔV = W/P
ΔV = 1000 J / 1000 Pa
ΔV = 1 m³
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How much energy is required to change a 42 g ice cube from ice at −13◦C to steam at 114◦C? The specific heat of ice is 2090 J/kg · ◦ C, the specific heat of water is 4186 J/kg · ◦ C, the specific heat of stream is 2010 J/kg · ◦ C, the heat of fusion is 3.33 × 105 J/kg, and the heat of vaporization is 2.26 × 106 J/kg. Answer in units of J.
The energy required to change a 42 g ice cube from ice at −13°C to steam at 114°C will be 129964.96 J.
To calculate the energy required to change a 42 g ice cube from ice at −13°C to steam at 114°C, we need to consider the following processes:
Heating the ice from −13°C to 0°C
Melting the ice at 0°C
Heating the water from 0°C to 100°C
Boiling the water at 100°C
Heating the steam from 100°C to 114°C
calculate the energy required for each step:
Heating the ice from −13°C to 0°C:
The specific heat of ice is 2090 J/kg · ◦C. We have 42 g of ice, which is 0.042 kg. The temperature difference is 0◦C - (-13◦C) = 13◦C.
The energy required to heat the ice is:
Q₁ = (0.042 kg) x (2090 J/kg°C) x (13°C) = 1151.04 J
Melting the ice at 0°C:
The heat of fusion of ice is 3.33 × 105 J/kg. The energy required to melt the ice is:
Q₂ = (0.042 kg) x (3.33 × 105 J/kg) = 14046 J
Heating the water from 0°C to 100°C:
The specific heat of water is 4186 J/kg°C. The mass of water is still 42 g. The temperature difference is 100°C - 0°C = 100°C.
The energy required to heat the water is:
Q3 = (0.042 kg) x (4186 J/kg°C) x (100°C) = 17607.72 J
Boiling the water at 100°C:
The heat of vaporization of water is 2.26 × 10 J/kg. The energy required to boil the water is:
Q₄ = (0.042 kg) x (2.26 × 106 J/kg) = 94920 J
Heating the steam from 100°C to 114°C:
The specific heat of steam is 2010 J/kg°C. The mass of steam is the same as the mass of water, which is 0.042 kg. The temperature difference is 114°C - 100°C = 14°C.
The energy required to heat the steam is:
Q₅ = (0.042 kg) x (2010 J/kg°C) x (14°C) = 1239.24 J
The total energy required is the sum of all the energies:
Qtotal = Q₁ + Q₂ + Q₃ + Q₄ + Q₅ = 129964.96 J
Therefore, the energy required to change a 42 g ice cube from ice at −13°C to steam at 114°C is 129964.96 J.
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If a student were to measure the ball's speed at each position above, at which position would
the ball be traveling the fastest?
A
B
C
D
Physics Question: Find The Displacement
A jet is taking off from an aircraft carrier. It starts from rest, speeds up constant acceleration (31 m/s²) and reaches a velocity of 64 m/s. Find the displacement.
The displacement of the jet of acceleration is 31 m/s² is 7.51 m.
What is displacement?Displacement is defined as the change in position of an object.
To calculate the displacement of the jet, we use the formula below
Formula:
s = (v²-u²)/2a.................. Equation 1Where:
s = Displacement of the jetv = Final speed of the jetu = Initial speed of the jeta = Acceleration of the jetFrom the question,
Given:
v = 64 m/sa = 31 m/s²u = 0 m/s (From rest)Substitute these values into equation 1
s = (31²-0²)/(2×64)s = 961/128s = 7.51 mHence, the displacement is 7.51 m.
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a body of mass 0.5kg is taken up an inclined plane the length 10m and height 8m and then allowed to slide down to the bottom again the coefficient of friction between the body and the plane is 0.12. what is work done by gravitational force over the ground trip?,work done by applied force over the up work trip?, work done by frictional force over the round trip? and kinetic energy of the body at the end of the trip?
According to the question Work done by gravitational force over the ground trip: Gravitational force does not do any work over the ground trip since the body is not moving.
What is gravitational force?Gravitational force is the attractive force between two masses. This force is the result of the curvature of spacetime caused by the presence of mass. Gravitational force is what keeps the planets in orbits around the sun, and what keeps the moon orbiting the Earth.
Work done by applied force over the up work trip: The work done by the applied force over the up work trip is given by,
W = F * d * cosθ
= (0.5 kg * 9.81 m/s2) * 10 m * cos(45°)
= 71.4 J
Work done by frictional force over the round trip: The work done by the frictional force over the round trip is given by,
W_f = F_f * d
= (0.5 kg * 9.81 m/s2 * 0.12) * 10 m
= 5.88 J
Kinetic energy of the body at the end of the trip: The kinetic energy of the body at the end of the trip is given by,
KE = 0.5 mv2
= 0.5 * 0.5 kg * (2 * 9.81 m/s2 * 8 m)2
= 611.52 J
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PLS HELP!! I’LL GIVE 25 POINTS TO WHOEVER ANSWERS
IMA of the pulley system is 3.
The length of the effort arm of a lever divided by the length of the resistance arm represents the ideal mechanical advantage, IMA.
IMA = Resistance force/Effort force
IMA = Fr/Fe
Calculating IMA involves measuring the number of ropes present in the pulley system.
Therefore, IMA = 3
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