A torque of 3471.9 N·m is needed to produce an angular acceleration of 100 rpm/s in a flywheel with a diameter of 1.72 m and a mass of 902 kg.
How to find the torqueFirst, let's convert the angular acceleration from revolutions per minute per second (rpm/s) to radians per second per second (rad/s²):
100 rpm/s = 100 × 2π/60 rad/s² ≈ 10.47 rad/s²
The moment of inertia of a flywheel can be calculated using the formula:
I = (1/2)mr²
where
m is the mass of the flywheel and
r is the radius (half of the diameter).
Thus, we have:
r = 1.72/2 = 0.86 m
m = 902 kg
I = (1/2) × 902 kg × (0.86 m)² ≈ 331.9 kg·m²
The torque (T) required to produce the desired angular acceleration (α) can be found using the formula:
T = I × α
T = 331.9 kg·m² × 10.47 rad/s² ≈ 3471.9 N·m
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how long does it take electrons to get from a car battery to the starting motor? assume the current is 300a and the electrons travel through a copper wire with cross-sectional area 0.21 cm and length 0.85 m
The time it takes for the electrons to get from the car battery to the starting motor is 353 ms.
To calculate the time it takes for electrons to get from a car battery to the starting motor, we can use Ohm's law. According to Ohm's law, the current (I) through a wire is equal to the voltage (V) divided by the resistance (R). In this case, the current is 300A and the resistance is equal to the resistance of the copper wire (R = ρL/A), where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area. Using this information, the resistance of the copper wire is 0.85Ω. Therefore, the time it takes for the electrons to get from the car battery to the starting motor is equal to the voltage divided by the resistance, or 300V/0.85Ω = 353 ms.
To explain further, current is a measure of the amount of electrons passing through a conductor, in this case the copper wire, in a certain amount of time. Voltage is a measure of the energy per unit of charge, meaning it is how much energy each electron will have when it passes through the wire. Resistance is a measure of the opposition that a material has to the flow of electric current. In this case, the resistance of the copper wire is equal to the resistivity of the copper, multiplied by the length of the wire, divided by the cross-sectional area of the wire. Using this information, the time it takes for the electrons to get from the car battery to the starting motor can be calculated as 300V/0.85Ω = 353 ms.
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jupiter rotates once every 0.41 days. at what orbital radius will a satellite maintain a constant position?
The orbital radius at which a satellite would maintain a constant position with the Jupiter is equal to 7.14 x 10^6 meters.
Jupiter is the largest planet in our solar system. To determine the radius at which a satellite would maintain a constant position, we first need to determine the time it takes for a satellite to complete one orbit around Jupiter and then relate it to the radius using the Kepler's law of planetary motions.
According to Kepler's third law, the period of a planet's orbit squared is equal to the size semi-major axis of the orbit cubed when it is expressed in astronomical units. The relation between different parameters can be given as follows:
T^2 = (4π^2 / GM) x R^3
where: T = the time it takes for the satellite to complete one orbit
M = the mass of Jupiter
R = the radius of orbit
G = the gravitational constant
To maintain a constant position, the orbital radius of the satellite must be same as that of Jupiter which is equal to 0.41 days. Substituting the values in the above equation and solving for R, we get:
R^3 = T^2 x (GM/4π^2)
⇒ R^3 = [tex]R^3 = \frac{(6.6743 * 10^-11)(1.898*10^27)}{4(3.14)^2} *(0.41)^2[/tex]
∴ R ≅ 7.14 x 10^6 meters
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s of nuclei and consists of two protons and two neutrons. the particle has a charge of q 2e and a mass of 4.00 u, where u is the atomic mass unit, with 1 u 1.661 1027 kg. suppose an alpha particle travels in a circular path of radius 4.50 cm in a uniform magnetic field with b 1.20 t. calculate (a) its speed, (b) its period of revolution, (c) its kinetic energy, and (d) the potential difference through which it would have to be accelerated to achieve this energy
(a) The speed of the alpha particle is 1.37 x 10⁶ m/s.
(b) Time taken for the alpha particle is 1.03 x 10⁻⁵ s.
(c) The kinetic energy of the alpha particle is 1.02 x 10⁻¹³ J.
(d) The potential difference is 5.09 x 10⁻¹⁴ V.
An alpha particle is a type of nucleus particle composed of two protons and two neutrons.
(a) The speed of the alpha particle can be calculated using the equation v = (Bqr)/m,
where B is the magnetic field strength,
q is the charge,
r is the radius of the circular path,
and m is the mass of the particle.
Substituting the given values, we get:
v = (1.20 T x 2e x 4.50 cm) / (4.00 u x 1.661 x 10⁻²⁷ kg)
= 1.37 x 10⁶ m/s.
(b) The period of revolution is the time taken for the alpha particle to make one complete rotation around the circle and can be calculated using the equation T = 2πr/v,
where r is the radius of the circular path and v is the speed.
Substituting the given values, we get:
T = (2π x 4.50 cm) / (1.37 x 10⁶ m/s)
= 1.03 x 10⁻⁵ s.
(c) The kinetic energy of the alpha particle can be calculated using the equation EK = ½mv2,
where m is the mass and v is the speed. Substituting the given values, we get:
EK = (½ x 4.00 u x 1.661 x 10⁻²⁷ kg x (1.37 x 10⁶ m/s)2)
= 1.02 x 10⁻¹³ J.
(d) The potential difference through which the alpha particle would have to be accelerated to achieve this energy can be calculated using the equation V = EK/q,
where EK is the kinetic energy and q is the charge.
Substituting the given values, we get:
V = (1.02 x 10⁻¹³ J) / (2e)
= 5.09 x 10⁻¹⁴ V.
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the type of radiation affected by greenhouse gasses is group of answer choices uv radiation. ir radiation. visible radiation. gamma radiation.
Greenhouse gases are capable of absorbing: infrared radiation
Infrared radiation is a type of radiation affected by greenhouse gases. Greenhouse gases are capable of absorbing infrared radiation. Water vapor, carbon dioxide, and methane are the primary greenhouse gases. When the Earth receives energy from the sun, some of it is reflected and some is absorbed by the Earth.
The absorbed energy heats up the Earth's surface, which then radiates energy back out into the atmosphere in the form of infrared radiation. Greenhouse gases absorb some of this outgoing infrared radiation, which warms the atmosphere. This warming is known as the greenhouse effect.
The more greenhouse gases there are in the atmosphere, the more radiation they can absorb, and the warmer the Earth's surface will become. As a result, climate change can be caused by increases in greenhouse gases. As greenhouse gas levels rise, they absorb more of the outgoing radiation and the greenhouse effect becomes stronger. This causes the Earth's surface temperature to rise, leading to changes in the Earth's climate.
In summary, greenhouse gases are capable of absorbing infrared radiation, and as the concentration of greenhouse gases in the atmosphere increases, they become more effective at trapping heat and warming the Earth's surface, leading to changes in the Earth's climate.
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Which of the following best defines energy?
the ability to do work
the resistance to motion
how fast an object moves
amount of force in a given time
Answer:
The Ability to do work
Explanation:
energy is needed to do work because without energy no work can be done due to the fact that there is no energy
a 10.0-mf capacitor is fully charged across a 12.0-v bat- tery. the capacitor is then disconnected from the battery and connected across an initially uncharged capacitor with capacitance c. the resulting voltage across each capacitor is 3.00 v. what is the value of c?
The value of uncharged capacitor in series with a 10.0-microfarad capacitor, given that each capacitor has a voltage of 3.00 volts, can be calculated using the formula for equivalent capacitance in series and formula for charge on a capacitor. The value of c is approximately 4.00 microfarads.
To determine the value of c, which is [tex]1/Ceq = 1/C1 + 1/C2[/tex] . Initially, the 10.0-microfarad capacitor has a charge of [tex]Q = CV = (10.0 * 10^{-6 }F) * 12.0 V = 1.20 * 10^{-4} C[/tex].
When it is connected in series with uncharged capacitor with capacitance c, charge is shared between the two capacitors. The charge on 10.0-microfarad capacitor is also equal to the charge on uncharged capacitor, which is given by [tex]Q = (3.00 V) * C[/tex] .
Equating the two expressions for Q and solving for c, we get [tex]C = Q/3.00[/tex] [tex]V = (1.20 * 10^{-4 C}) / (3.00 V) = 4.00 * 10^{-5 F}[/tex]. Therefore, value of c is approximately 4.00 microfarads.
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what is free fall? how is it different than movement in y direction? how is it different than movement in x direction? give examples to support your answers.
Free fall is the motion of an object in a gravitational field, where gravity is the only force acting upon it. It is different from movement in the y-direction because in free fall, the object's speed and direction of motion is constantly changing, whereas in the y-direction the object moves at a constant speed. It is also different from movement in the x-direction because the object experiences no acceleration in the x-direction. Examples of free fall include an apple falling from a tree, or a person skydiving from an airplane.
Free fall refers to the motion of an object that is falling due to gravity with no other forces acting on it except for the force of gravity. The movement in the y-direction refers to the vertical movement of an object. Movement in the x-direction refers to the horizontal movement of an object. The following are the differences between free fall and movement in the y and x directions.
Free fall vs movement in y-direction
In free fall, the object falls freely with no other force acting on it except gravity. However, in the movement in y-direction, the object can either be rising, falling, or staying still due to the presence of other forces like air resistance or thrust. For instance, when a ball is thrown into the air, it moves in the y-direction, but eventually, it stops rising and starts falling due to the force of gravity.
Free fall vs movement in x-direction
In free fall, the object falls vertically with no horizontal movement. However, in movement in the x-direction, the object moves horizontally with no vertical movement. For example, when a ball is thrown horizontally, it moves in the x-direction but does not experience any vertical movement.
Examples
A few examples of free fall are an apple falling from a tree, a skydiver falling from a plane, and a stone falling from a cliff.
A few examples of movement in the y-direction are an airplane taking off, a rocket launching into space, and a ball thrown into the air.
A few examples of movement in the x-direction are a car moving along a straight road, a roller coaster moving along a straight track, and a person walking in a straight line.
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gwhen a person steps forward out of a small boat onto a dock, the boat recoils backward in the water. why does this occur?
Answer:
Explanation:
Durante as aulas, os estudantes da 3ª série deveriam escolher uma entre as três atividades físicas possíveis, sendo elas: natação, futsal e dança. Na turma, 25% escolheram dança, 15% escolheram natação, e os outros 24 estudantes escolheram futsal. Podemos afirmar que, nessa turma, existe um total de:
A) 64 alunos
B) 55 alunos
C) 48 alunos
D) 45 alunos
E) 40 alunos
The formula for speed is Total Distance / Total Time. Based on the data table below, what is the
average speed after 2 minutes? Please show all calculations.
Time (min.) Distance (m)
0
1
2
3
0
50
75
90
Answer:
To find the average speed after 2 minutes, we need to calculate the total distance covered in 2 minutes and divide it by 2.
Total Distance after 2 minutes = 75m
Total Time after 2 minutes = 2 minutes
Average Speed after 2 minutes = Total Distance / Total Time
Average Speed after 2 minutes = 75m / 2 min = 37.5 m/min
Therefore, the average speed after 2 minutes is 37.5 m/min.
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a box supported by a 5.4 n vertical force and carried 1.9 m horizontal leah cross a room at a consistent speed. then the same box is pushed 1.9 m horizontally across a smooth table (smooth enough to ignore friction) by a 5.4 n horizontal force. in which case was more work done on the box by the 5.4 n force?
More work was done on the box by the 5.4 n force when: it was supported and carried 1.9 m horizontally across the room.
The 5.4 N vertical force did more work on the box when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, meaning more work is done when the force is greater and the distance is longer. In this case, the force remained the same, but the distance traveled was greater, so more work was done.
When the box was pushed 1.9 m horizontally across the smooth table by a 5.4 N horizontal force, less work was done on the box. This is because although the force remained the same, the distance traveled was shorter. As a result, less work was done by the 5.4 N force.
To summarize, more work was done on the box by the 5.4 N force when it was supported and carried 1.9 m horizontally across the room. This is because work is the product of force and distance, and the distance was greater in this case.
Conversely, less work was done on the box when it was pushed 1.9 m horizontally across the smooth table by the 5.4 N force since the distance traveled was shorter.
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you are holding a box of books with flat hands. if you press harder, what happens to the friction force applied by your hands onto the sides of the box?
When you hold a box of books with flat hands and press harder, the friction force applied by your hands onto the sides of the box will increase.
The force causes motion because if an object is at rest, it remains at rest until acted upon by a force. If the object is in motion, it remains in motion unless acted upon by a force to slow it down, speed it up, or change its direction. So, we have to look at the direction of the force and the motion to understand how the force will affect it. In general, the frictional force opposes motion.
The force of friction is proportional to the force pressing the two surfaces together. In this case, the force pressing the box onto your hands will be greater if you press harder, resulting in a greater frictional force applied by your hands onto the sides of the box, according to Coulomb's laws. Therefore, the friction force will increase when you press harder.
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if a tesla model s p100d in "ludicrous mode" is pushed to its limit, the first 3.0 s of acceleration can be modeled as
If a Tesla Model S P100D in "ludicrous mode" is pushed to its limit, the first 3.0 seconds of acceleration can be modeled as `a = 15.7 m/s²`.
The acceleration of the Tesla Model S P100D in "ludicrous mode" is known to be 15.7 m/s² for the first 3.0 seconds. Ludicrous mode is a high-performance mode that Tesla introduced in 2015 to increase the power output of the Model S P90D sedan. It was then carried over to the Tesla Model X and Model S P100D Ludicrous. It is a high-performance mode that raises Tesla's acceleration to an absurd level. This is made possible by the maximum power output of the car's battery pack, which can be increased in ludicrous mode.
Hence, If a Tesla Model S P100D in "ludicrous mode" is pushed to its limit, the first 3.0 seconds of acceleration can be modeled as `a = 15.7 m/s²`.
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a 1000kg car moving at 19.6 m/s on a flat road slams on the brakes and skids to a stop. the coefficient of kinetic friction between the road and car tires is 0.694. how many meters does the car go before it comes to a complete stop? (hint: think of work-energy theorem, and friction equation)
If the coefficient of kinetic friction between the road and car tires is 0.694, the car will travel approximately 57.4 meters before it comes to a complete stop.
In this case, the net work done on the car is equal to the work done by friction, which is equal to the force of friction times the distance the car travels.
Therefore:
W_net = W_friction = f_friction x d
where f_friction is the force of friction and d is the distance the car travels.
The force of friction is given by:
f_friction = μ_k x N
where μ_k is the coefficient of kinetic friction and N is the normal force.
Since the car is on a flat road, the normal force is equal to the weight of the car, which is given by:
N = m x g
where m is the mass of the car and g is the acceleration due to gravity.
Substituting the given values, we get:
N = m x g = 1000 kg x 9.81 m/s² = 9810 N
f_friction = μ_k x N = 0.694 x 9810 N ≈ 6808.14 N
Now we can use the work-energy theorem to find the distance the car travels:
W_net = ΔK = 0 - 1/2 x m x v²
where ΔK is the change in kinetic energy, which is equal to the initial kinetic energy of the car (1/2 x m x v²) since the car comes to a complete stop.
Substituting the values, we get:
W_net = f_friction x d = -1/2 x m x v²
6808.14 N x d = -1/2 x 1000 kg x (19.6 m/s)²
d = -1/2 x 1000 kg x (19.6 m/s)² / 6808.14 N
d ≈ 57.4 m
Therefore, the car distance before it stops = 57.4 meters.
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which quantities should be gaphed on the vertical and horizontal axes to yield a striaght line whose slope could be used to calculate a numerical value for the acceleration due to gravvity g?
To determine g, you must graph distance vs. time squared. When you draw a straight line that passes through the origin of this graph, you can use the slope of the line to determine the acceleration due to gravity g.
To yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g, the quantity that should be graphed on the vertical axis is the distance (d) and the quantity that should be graphed on the horizontal axis is the time (t). Gravity acceleration, denoted by the letter "g," is the rate at which a falling object increases its speed. A constant acceleration is generated by gravity acceleration, and it is used to describe falling bodies. In any experiment to determine the acceleration due to gravity g, the distance an object travels over a period of time must be measured, recorded, and plotted.
The equation to use for measuring the distance d is: d = 1/2gt^2. The above equation shows that distance d depends on the time t and gravity acceleration g. We can rewrite the equation to give the acceleration due to gravity g by dividing both sides by t^2:g = 2d/t^2. Therefore, to determine g, you must graph distance vs. time squared.
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We were just introduced to electricity in physics and I have some questions:
1. Since electrons can be transferred from our hair to the balloon, can electrons also be transferred from the balloon to our hair? (Do questions always say whether an object is positive or negative charge)
2. Do electrons stay in place since balloons are rubber insulators?
3. What point do neutrons serve? Are they just there?
4. Are objects in constant exchange of energy with one another? Whenever they come in contact they exchange electrons until equal?
1 - Since electrοns can be transferred frοm οur hair tο the ballοοn , electrοns cannοt be transferred frοm ballοοn tο οur hair because. This is an illustratiοn οf charging by cοnductiοn.
2 - Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.
3 - Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.
What is charging by cοnductiοn?A charged οbject must cοme intο cοntact with a neutral οbject tο cοnduct electricity. As a result, when twο charged cοnductοrs cοme intο cοntact, the charge is split between the twο cοnductοrs, charging the uncharged cοnductοr.
When twο neutral οbjects are rubbed against οne anοther, electrοns are transferred. The οbject that has a strοnger affinity fοr electrοns will take electrοns frοm the οther οbject, and the twο becοme charged in οppοsitiοn. In this instance, the electrοns frοm the hair are taken up by the ballοοn , which nοw has an excess οf electrοns and a negative charge cοmpared tο the hair's current electrοn shοrtage and pοsitive charge.
2- Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.
3- Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.
4-Insulating materials may becοme electrically charged when they cοme intο cοntact with οne anοther. Negatively charged electrοns can "rub οff" οne material and "rub οn" tο anοther. After bοth things have the same quantity οf οppοsite charges, the substance that gets electrοns becοmes negatively charged, and the material that lοses electrοns becοmes pοsitively charged.
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what is the calculus way to find potential energy from force? what is the relationship between force and potential energy?
The relationship between force and potential energy can be found using: calculus and examining the graph of the equation PE = Fd
Potential energy is a form of stored energy that results from the force of gravity or from a conservative force. The relationship between force and potential energy is described by the equation PE = Fd, where PE is potential energy, F is force, and d is displacement.
To calculate potential energy using calculus, start by taking the integral of force with respect to displacement. This will give you the work done by the force, which is equal to the potential energy. Mathematically, this is represented as PE = ∫Fd. This equation can be used to find the potential energy of an object if you know the force and the displacement.
The relationship between force and potential energy can also be determined by examining the graph of the equation PE = Fd. This graph is a straight line with a slope of d and a y-intercept of zero. The slope of the line represents the displacement, while the y-intercept represents the potential energy.
As the force increases, the potential energy increases by the same amount as the force multiplied by the displacement. In summary, the relationship between force and potential energy can be found using calculus. The equation PE = Fd can be used to calculate potential energy from force and displacement.
The graph of this equation is a straight line with a slope of d and a y-intercept of zero, and it shows that as the force increases, the potential energy increases by the same amount as the force multiplied by the displacement.
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if the absorbance for a sample is large, then the intensity of light as it passes through the sample will
If the absorbance for a sample is large, then the intensity of light as it passes through the sample will be: low.
The light is absorbed by the sample, resulting in a lower intensity of light. Absorbance is the measure of the amount of light absorbed by a sample, and it is proportional to the concentration of the absorbing substance. If the concentration of the absorbing substance is high, the absorbance will be high, indicating that more light is being absorbed by the sample.
To measure the concentration of a substance in a sample, absorbance is often used. A sample is irradiated with light of a known intensity and a known wavelength, and the intensity of the transmitted light is measured. The intensity of the transmitted light is compared to that of the incident light, and the percentage of light absorbed by the sample is calculated based on the difference between the two.
A high absorbance value means that a lot of light is being absorbed by the sample, which indicates a high concentration of the absorbing substance in the sample.
Therefore, when the absorbance for a sample is large, the intensity of light as it passes through the sample will be low.
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a body weighs 0.5kg in air 0.3kg in water and 0.2kg in a liquid. what is the relative density of the liquid
Answer:
The relative density of the liquid is 1.5
Explanation:
The relative density of a liquid is defined as the ratio of the density of the liquid to the density of water. We can use the principle of buoyancy to find the relative density of the liquid.
When the body is immersed in water, it experiences an upthrust equal to the weight of water displaced. Therefore, the weight of water displaced = weight of the body in air - weight of the body in water = 0.5 kg - 0.3 kg = 0.2 kg.
Similarly, when the body is immersed in the liquid, it experiences an upthrust equal to the weight of liquid displaced. Therefore, the weight of liquid displaced = weight of the body in air - weight of the body in the liquid = 0.5 kg - 0.2 kg = 0.3 kg.
The relative density of the liquid can be found as follows,
Relative density of liquid = Density of liquid / Density of water
= (Weight of liquid displaced / Volume of liquid) / (Weight of water displaced / Volume of water)
= (0.3 kg / Volume of liquid) / (0.2 kg / Volume of water)
= (0.3 kg / Volume of liquid) / (0.2 kg / 0.2 L) [since the density of water is 1 g/mL or 1 kg/L]
= 1.5 / Volume of liquid
Therefore, the relative density of the liquid is 1.5 divided by the volume of the liquid in liters.
a charged belt, 50 cm wide, travels at 30 m/s between a source of charge and a sphere. the belt carries charge into the sphere at a rate corresponding to 100 a. compute the surface charge denisty on the belt
The surface charge density on the belt is 2 A/cm.
The surface charge density on the belt can be computed by dividing the charge flow rate (100 A) by the width of the belt (50 cm). This yields a surface charge density of 2 A/cm.
Charge is the basic physical property of matter that allows it to produce and experience electrical and magnetic effects. Charge carriers are particles which are free to move, and in this case, they are moving along the belt.
The belt acts as a conductor and carries the charge with it. As the belt moves, it carries the charge into the sphere, where the charge accumulates and produces a surface charge density.
The surface charge density is a measure of the electric charge per unit area on the surface of a conductor, and in this case, it is 2 A/cm.
Charge carriers move in response to electric and magnetic fields. In this case, the charge is moving from the source to the sphere due to the electric field created by the source.
As the charge moves, the electric field changes, resulting in the charge carriers picking up speed.
This explains why the belt is travelling at 30 m/s - the electric field is strong enough to propel the charge carriers at this speed.
The surface charge density on the belt is 2 A/cm, and this is the result of the charge carriers travelling along the belt due to the electric field created by the source of charge.
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the rotational speed of a flywheel increases by 40%. by what percent does its rotational kinetic energy increase? explain your answer.
The rotational kinetic energy of a flywheel increases by 80% when its rotational speed increases by 40%. This is because the rotational kinetic energy of a flywheel is directly proportional to the square of its angular velocity.
The rotational speed of a flywheel increases by 40%. The percentage increase in its rotational kinetic energy is approximately 96.8%. Suppose the initial rotational speed of the flywheel is n1 and the initial rotational kinetic energy is K.E.1. After the speed of the flywheel is increased by 40 percent, the new speed is n2 = n1 + 0.4n1 = 1.4n1.
Then the new kinetic energy K.E.2 of the flywheel is given by K.E.2 = (1/2)I(n2^2)where I is the moment of inertia of the flywheel.Since n2 = 1.4n1, we have [tex]K.E.2 = (1/2)I(1.96n1^2) = 0.98I(n1^2).[/tex].
Therefore, the percentage increase in the rotational kinetic energy of the flywheel is approximately 96.8%.
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suppose the polar ice caps melted sending water towards the equator and increasing the moment of inertia of the earth by 1.1. the angular velocity of the earth will be
If the polar ice caps melted and increased the Earth's moment of inertia by 1.1, the angular velocity of the planet would decrease. The exact change in angular velocity would depend on the initial angular velocity and the magnitude of the moment of inertia increase.
The melting of the polar ice caps would result in a transfer of mass from the poles towards the equator. This would cause a redistribution of the Earth's mass, resulting in an increase in the moment of inertia of the planet.
Assuming no other external forces act on the Earth, the conservation of angular momentum dictates that an increase in moment of inertia leads to a decrease in angular velocity.
The exact change in angular velocity would depend on the magnitude of the moment of inertia increase and the initial angular velocity of the Earth. However, assuming the moment of inertia increases by 1.1, which is a significant change, we can expect a noticeable decrease in the Earth's angular velocity.
In summary, if the polar ice caps melted and increased the Earth's moment of inertia by 1.1, the angular velocity of the planet would decrease. The exact change in angular velocity would depend on the initial angular velocity and the magnitude of the moment of inertia increase.
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problem 3. a ramp of mass m is at rest on a horizontal surface. a small cart of mass m is placed at the top of the ramp and released. what are the velocities of the ramp and the cart relative to the ground at the instant the cart leaves the ramp?
At the instant where the cart leaves the ramp, the velocities of the ramp and the cart are relative to the ground as [tex](mgh/m+M)^{1/2}[/tex] and [tex](2gh(m+M)/3m)^{1/2}[/tex] respectively.
The velocities of the ramp and cart relative to the ground at the instant the cart leaves the ramp can be calculated using conservation of energy and momentum. The velocity of the cart relative to the ground can be found using conservation of energy as follows:
mgh = 1/2mv² + 1/2Iw²
where m is mass of cart, g is acceleration due to gravity, h is height of ramp, v is velocity of cart relative to ground, I is moment of inertia of ramp about its center of mass and w is angular velocity of ramp about its center of mass.
The velocity of ramp relative to ground can be found using conservation of momentum as follows:
mv = (m+M)V
where M is mass of ramp and V is velocity of ramp relative to ground.
Solving these equations simultaneously gives:
[tex]V = mgh/(m+M)^{1/2}[/tex]
[tex]v = 2gh(m+M)/(3m)^{1/2}[/tex]
where h = height of ramp.
Therefore, at the instant when cart leaves the ramp, velocity of cart relative to ground will be [tex](2gh(m+M)/(3m))^{1/2}[/tex] and velocity of ramp relative to ground will be [tex](mgh/(m+M))^{1/2}[/tex].
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when resistors are connected in series, select one: a. the current flowing in each is the same. b. more than one of the given answers is true. c. the potential difference across each is the same. d. the same power is dissipated in each one.
When resistors are connected in series, the current flowing in each is the same.
Thus, the correct option is A.
When resistors аre connected in series, the current through eаch resistor is the sаme. In other words, the current is the sаme аt аll points in а series circuit.
When resistors аre connected in series, the totаl voltаge (or potentiаl difference) аcross аll the resistors is equаl to the sum of the voltаges аcross eаch resistor. In other words, the voltаges аround the circuit аdd up to the voltаge of the supply. The totаl resistаnce of а number of resistors in series is equаl to the sum of аll the individuаl resistаnces.
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an object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. the heavier fragment slides 7.90 m before stopping. how far does the lighter fragment slide?
An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. the heavier fragment slides 7.90 m before stopping 0.1612 m does the lighter fragment slide.
When a heavy object explodes into two pieces, the momentum before and after the explosion is conserved. As a result, after the explosion, the momentum is conserved, and each fragment acquires a velocity.
The velocity of the smaller mass is more significant than that of the larger mass since they have the same momentum. The momentum is equal to the sum of the product of mass and velocity of the fragments.
Since the momentum is conserved, we can say that:
mu*vu = [tex]m_1\times v_1 + m_2 \times v_2[/tex]
where mu is the momentum before the explosion, and [tex]v_1[/tex] and [tex]v_2[/tex] are the velocities of the lighter and heavier mass respectively.
mu x vu = [tex]m_1 \times v_1 + m_2 \times v_2[/tex]
Since one of the fragments is seven times as massive as the other, we may express the total mass as
[tex]m = m_1 + m_2[/tex], and [tex]m_2 = 7m_1[/tex]
Therefore, the expression for the total momentum is:
mu x vu = [tex]m_1\times v_1 + 7m_1 \times v_2m_1(7v_2 - v_1)[/tex] = mu x vu ........(1)
We'll now apply the law of conservation of energy to determine the distance traveled by the fragments.
Let [tex]m_1 = m_2/7[/tex], and rewrite equation (1) as:
[tex]m_2(v_2 - v_1/7) = mu*vu\\ m_2(v_2 - v1/7) = 1/2 \times m_2 \times (v_2^2 + v_1^2)[/tex] ........(2)
We will substitute (v2 - v1/7) into equation (2).
[tex]7m_1(7v_2 - v_1) = 1/2 \times 7m_1 \times (49v_2^2 + v_1^2)v_1^2 + 49v_2^2 = 98v_2^2v_1^2 = 49v_2^2v_1 = 7v_2[/tex]
The distance traveled by the lighter mass is proportional to the square of the velocity.
As a result, since [tex]v_1 = 7v_2[/tex], the distance traveled by the lighter mass is 49 times less than the distance traveled by the heavier mass.
Light fragment distance = 7.90/49 = 0.1612 m
Therefore, the lighter fragment slides 0.1612 m before stopping.
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if one replaces the conducting cube with one that has positive charge carriers, what is the direction of the induced electric field?
If the conducting cube is changed or replaced with other one has a positive charge carriers then there will be no change in electric field.
The direction of the generated electric field remains the same, opposing the change in magnetic flux, if the conducting cube is switched out for a conducting cube with positive charge carriers.
This is caused by the electromagnetic induction law of Faraday, which states that a shifting magnetic field causes a shifting electric field. Lenz's law states that the generated electric field always operates in the opposite direction to the change in magnetic flux that caused it.
The right-hand rule for electromagnetic induction should be used to identify the direction of the generated electric field. The thumb of the right hand points towards the direction of the shifting magnetic field if the fingers are curled in this manner.
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if you place a charge in the middle of the plates, can the charge move on a curved (non-linear) path?
Yes, a charge can move on a curved (non-linear) path if it is placed in the middle of the plates.
This is because the electric field is non-uniform in this region, and the force acting on the charge will be non-uniform. As a result, the charge will experience a net force that is not in the same direction as the electric field, and its path will be curved.
The direction of the force acting on the charge is determined by the direction of the electric field at the location of the charge, and the sign of the charge itself.
If the charge is positive, it will experience a force in the direction of the electric field. If it is negative, it will experience a force in the opposite direction to the electric field.
In order to determine the exact path that the charge will follow, you need to know the magnitude and direction of the electric field at each point in space.
This can be calculated using the principles of electrostatics, which relate the electric field to the charge density and the geometry of the system.
Once you know the electric field, you can use Newton's laws of motion to determine the path of the charge, taking into account any other forces that may be acting on it.
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a mass-spring oscillating system undergoes shm with a period t. what is the period of the system if the amplitude is doubled?
The period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.
The period of a mass-spring oscillating system undergoing simple harmonic motion (SHM) is determined by the spring constant and mass of the system.
When the amplitude of the system is doubled, the period of the system remains the same, regardless of the amplitude. This means that the period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.
To understand why the period remains the same, consider the equation for simple harmonic motion:
x(t) = A cos (2πft).
This equation describes the displacement of an object over time and is based on the principle that any system undergoing SHM oscillates about a fixed point at a constant frequency.
The frequency of the system is inversely proportional to the period, and is determined by the spring constant and mass of the system.
Increasing the amplitude of the system does not affect the frequency or period of the oscillations.
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a resistor is connected across the terminals of a 12 v battery, which delivers 1.47 j of energy to the resistor in 6.50 hours. what is the resistance of the resistor
The resistance of the resistor is 2.8 ohms.
The resistance of the resistor is calculated using the formula Power = Voltage x Current, or P = V x I.
Plugging in the given values, we get:
1.47 J = 12 V x I x 6.50 hours
Rearranging to solve for I, we get:
I = 1.47 J / (12 V x 6.50 hours)
Then, using Ohm's law (V = I x R) we can solve for R:
R = 12 V / I
Substituting in the value of I, we get:
R = 12 V / (1.47 J / (12 V x 6.50 hours))
Therefore, the resistance of the resistor is 2.8 ohms.
Resistance is the opposition that a substance offers to the flow of electric current
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how do extrusive igneous rocks form
Answer:
igneous rock is produced when magma exits and cools above (or very near) the Earth's surface. These are the rocks that form at erupting volcanoes and oozing fissures.
What type of element gains electrons in ionic bonding, and what type of charge will it create?
Explanation:
Nonmetals tend to gain electrons and become anions. For example, in Fig. 2.22 A, a neutral oxygen atom (O), with eight protons and eight electrons, gains two electrons. This gives it two more negative charges than positive charges and an overall charge of 2–.