The 4.8m/s² is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 43 rpm (revolutions per minute) if the wheel's diameter is 36 cm.
What is magnitude ?
In simple terms, magnitude is "distance or quantity." It shows the size or motion of an object, either in terms of absolute size or relative motion. It is a method for describing a phenomenon's size or range. In physics, the term magnitude is frequently used to describe a length or size.
What is acceleration ?
The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.
Therefore, 4.8m/s² is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 43 rpm (revolutions per minute) if the wheel's diameter is 36 cm.
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Why does the area around the equator stay about the same temperature year round?
- it receives about the same amount of direct sunlight year round.
- it remains about the same distance from the sun year round.
The sun shines practically directly down on and near the equator every day of the year, maintaining a constant daytime temperature there.
How does temperature work?
The average kinetic potential of the particles inside an object is measured by its temperature. The velocity of these particles likewise increases as the temperature rises. A thermometer or even a calorimeter is used to determine the temperature.
What does temperature in the SI mean?
Kelvin,According to the World System of Units, Kelvin, denoted by the letter K, is the Si derived unit of temperature. In the fields of science and engineering, the Kelvin scale is commonly acknowledged or utilised.
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4) a child in a tree house uses a rope attached to a basket to lift a 22 n dog into the house with a work done of 103.4 j. how far did the child lift the dog?
The distance up to where the child lift the dog into the house with a work done of 103.4 j is found to be 4.7 m.
What is the straightforward meaning of distance?An object's distance is its overall motion, regardless of direction. The length of time that an object has traveled, regardless of where it started or ended, is referred to as distance.
The work done by a force is equal to:
W = Fd
where,
W is the work
F is the force applied
The force is exerted over the distance (d).
For our case, the mass of the dog is equivalent to the force required to hoist it:
F=22 N
and the work done by the child to lift the dog is 103.4 j.
To calculate the distance is:
W = Fd
d = W / F
= 103.4 / 22
= 4.7 M
Therefore , the dog is moved through a distance of 4.7 m
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A 20,000 kg rocket has a rocket motor that generates 3.0 x 10^5 N of thrust. a. What is the rocket's initial upward acceleration? b. At an altitude of 5.0 Km the rocket's acceleration has increased to 6.0 m/s^2.
What mass of fuel has it burned?
a. Rocket’s initial upward acceleration is 5.2m/s²
b. Mass of fuel has it burned is 1013 kg
Newton's second law of motion said :
∑F = m . a
The difference between the weight and the thrust will be the sum of force.
∑F = T - W
T - W = m x a
a = [tex]\frac{T - W}{a}[/tex]
From the question we know below information
m = 20000 kg = 2 x [tex]10^{4}[/tex]
T = 3.0 x [tex]10^{5}[/tex] N
W = m x g = 20000 x 9.8 = 1.96 x [tex]10^{5}[/tex] N
We just substitute the information above into the formula :
a = [tex]\frac{3.0 x 10^{5} - 1.96 x 10^{5} }{2 x 10^{4} }[/tex]
a = [tex]\frac{1.04 x 10^{5} }{2 x 10^{4} }[/tex]
a = 5.2 m / [tex]s^{2}[/tex]
So, rocket's initial upward acceleration is 5.2m/s²
(b) The mass of the fuel that burned can be calculated as follows:
T = [tex]m_{2}a + m_{2}g[/tex]
T = [tex]m_{2} ( a + g)[/tex]
[tex]m_{2} = \frac{T}{a+g} \\[/tex]
= [tex]\frac{3 x 10^{5} }{6 + 9.8}[/tex]
= 18987 kg
The mass of fuel = 20000 - 18987 = 1013 kg
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lee pushes horizontally with a force of 71 n on a 24 kg mass for 15 m across a floor. calculate the amount of work lee did. answer in units of j.
lee pushes horizontally with a force of 71 n on a 24 kg mass for 15 m across a floor. calculate the amount of work lee did.
The amount of work done by Lee is: W = 71 N * 15 m = 1065 J.
What is work done?Work done is a term that describes the amount of energy expended in performing a task or activity. It is calculated by multiplying the force applied to an object with the distance that the object is moved. Work done is measured in units of joules (J), where 1 joule is equal to the work done when a force of one newton is applied over a distance of one meter. Work done is an important concept in physics and engineering, as it is used to calculate the amount of energy transferred or transformed in a process.
The amount of work done by Lee is calculated using the formula W = F * d, where F is the applied force and d is the displacement.
Therefore, the amount of work done by Lee is: W = 71 N * 15 m = 1065 J.
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A house uses solar cells that generate 1.5 kw of electrical power to supply some of its energy needs. if the solar panels supply the house with 40 percent of the power it needs, how much power does the house use?
The electric power that the house use is 3.75kW.
According to the question, a house use solar cell that gives 1.5kW of electric power and the solar panels supply the house with the 40% of the power it need.
Voltage, or the potential of a charge to produce energy, and current, or the flow of electric charge, are the two main components of electric power. Any ratio of current and voltage values can provide a given amount of power.
Let there is x kW power that the house use.
Now it is given that 40% of the power is supplied that means
40% of x=1.5
x=[tex]\frac{(1.5)(100)}{40}[/tex]
x=3.75kW
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Unlike a roller coaster, the seats in a Ferris wheel swivel so that the rider is always seated upright. An 80-ft-diameter Ferris wheel rotates once every 24 s.
A. What is the apparent weight of a 90 kg passenger at the lowest point of the circle?
Express your answer with the appropriate units.
B. What is the apparent weight of a 90 kg passenger at the highest point of the circle?
Express your answer with the appropriate units.
The apparent weight of the passenger at the lowest point is 90 kg and at the highest point it changes due to the centrifugal force.
What is centrifugal force?
The centrifugal force is an apparent force that is observed in a rotating reference frame. It is the force that appears to push objects away from the center of rotation. It is not a real force, but rather a pseudo-force that is caused by the inertia of an object in motion. In other words, it is the inertia of an object that makes it appear as if there is a force pushing it away from the center of rotation.
A. At the lowest point of the circle, the rider is at the bottom of the Ferris wheel and moving at the same velocity as the wheel. Therefore, the apparent weight of the passenger is equal to the true weight, which is 90 kg.
B. At the highest point of the circle, the rider is at the top of the Ferris wheel and is moving at a slower velocity than the wheel. Therefore, the apparent weight of the passenger is less than the true weight. This effect is known as the centrifugal force. The formula for the apparent weight at the top of the Ferris wheel is:
Apparent weight = True weight x (1 - (v^2/r^2))
where v is the velocity of the Ferris wheel and r is the radius of the Ferris wheel.
In this case, the velocity of the Ferris wheel is (2πr)/T = (2π40ft)/24s = 4.71 ft/s
The radius of the Ferris wheel is 40ft
So, the apparent weight of a 90 kg passenger at the highest point of the circle is:
90 kg x (1 - (4.71^2 / 40^2)) = 90 kg x (1 - 0.12) = 90 kg x 0.88 = 79.2 kg.
Therefore, due to centrifugal force the apparent weight of the passenger at the highest point of the circle is 79.2 kg.
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you decide to use your garden hose to wash your garage door. the water shoots out at a rate of 10 kg/s and a speed of 16 m/s with respect to the hose. when the water hits the garage, its speed decreases to zero. determine the force that the water exerts on the wall. what assumptions did you make?
The force exerted by the water on the wall will be equal to 160 N. Newton's third law of motion is seen taking place here.
How is force exerted by the water on the wall calculated?The force exerted by the water on the wall is calculated using the impulse-momentum principle. The principle states that the change in momentum of an object is equal to the impulse, or the force applied over a certain period of time. In this case, the change in momentum is equal to the initial momentum of the water (mass flow rate multiplied by velocity) minus the final momentum of the water (mass flow rate multiplied by final velocity) and the time is assumed to be very small.
What assumptions were made in the calculation of force exerted by the water on the wall?The assumptions made in the calculation of force exerted by the water on the wall are:
The water hits the garage instantaneously.
The water flow rate is constant and no water is lost during the impact.
The water hits the garage uniformly over the entire area and not just at one point.
The garage door is not moving before the impact. These assumptions are made to simplify the calculation and to make it more accurate. It is important to note that in real-world scenarios, these assumptions may not always hold true and the force exerted by the water on the wall may be different.
How do you calculate the force exerted by water on the wall?Force exerted by the wall on the water, F = dP/dt
= (P2 - P1)/dt
= dm*(V2 - V1)/dt
= (V2 - V1) x dm/dt
= (0 - 16) x 10
= -160 N (negative sign indicates force opposes the motion)
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a discus thrower (fig. p4.33, page 104) accelerates a w discus from rest to a speed of 25.0 m/s by whirling it through 1.25 rev. assume the discus moves on the arc of a circle 1.00 m in radius. (a) calculate the final angu- lar speed of the discus. (b) determine the magnitude of the angular acceleration of the discus, assuming it to be constant. (c) calculate the time interval required for the discus to accelerate from rest to 25.0 m/s.
(B) The magnitude of the angular acceleration of the discus is:
α = (ωf - ωi)/t = (7.85 rad/s - 0 rad/s)/1.25 rev = 6.28 rad/s^2 .
What is acceleration ?
Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s2). Acceleration can be either positive or negative depending on the direction of the change in velocity. Positive acceleration indicates an increase in velocity, while negative acceleration indicates a decrease in velocity.
Acceleration is the result of an applied force, such as gravity, friction, or thrust. It is also affected by the mass of an object, as well as the drag force caused by air resistance. Acceleration can be used to calculate the final velocity of an object after a period of time, as well as the distance traveled in that time. It is an important concept in the study of physics and engineering.
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As the temperature of a metallic conductor increases its resistance usually
Answer :
[tex] Hence \ resistance \ increases \ with \\ increase \ in \ the \ temperature. [/tex]
assume that an mx missile goes from rest to a suborbital velocity of 6.50 km/s in 30.0 s (the actual speed and time are classified). what is its average acceleration in m/s2?
216.66 m/s² is average acceleration of mx missile.
Given information:
initial velocity, u = 0m/s
final velocity, v = 6.5km/s = 6500 m/s
time taken, t = 40s
To calculate average acceleration:
a = [tex]\frac{( v - u)}{t}[/tex]
a = [tex]\frac{(6500 - 0)}{30}[/tex]
a = 216.66 m/s²
Acceleration at any moment is defined as rate of change of haste with time. For the entire trip, average acceleration is defined as rate of change in haste with time taken.
When an object peregrination at a vertical speed of about,000 km/ hr or further, it goes into route once it's above the atmosphere. The satellites need to reach that threshold speed (orbital haste) in order to circumvent Earth.
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an archer shoots an arrow with a mass of 32.4g straight up. the arrow reaches a height of 315m. what is the velocity of the arrow when it hits the ground? ignore air resistance
The third law of motion of Newton explains the relationship between action and reply forces. As an outcome, a reply to the force generated by the bowstring striking the arrow is offered.
What does motion entail?Movement is the act of moving or changing places or positions, as in a conductor. the capacity to move with a living person's force. The word "gait" refers to a person's walking style. a movement or change in posture; a gesture.
What does "motion" mean, and what are some examples?The change in an item's location relative to time is known as motion. Motion includes sounds like windows rattling, a book falling off a seat, water coming from the faucet, etc. even the air that we
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A longitudinal wave has a compression to compression distance of 10 m it takes the wave of 5s to pass a point what is the wavelength of the longitudinal wave
The wavelength of the longitudinal wave will be 10meters.
What is wavelength?The wavelength is described as the spatial period of a periodic wave which is the distance over which the wave's shape repeats.
wavelength = v/frequency
frequency = 1/T
frequency = 1/5
velocity= 10/5 = 2m/s
Therefore the wavelength of the longitudinal wave = 2/ 0.2
wavelength = 10meters
The wavelength is the distance between two wave crests, and it will be the same for troughs.
The frequency is the number of vibrations that pass over a given spot in one second, and it is measured in cycles per second Hertz.
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alana drew a diagram to compare the life cycles of low-mass and high-mass stars. a venn diagram with 2 intersecting circles. the left circle is labeled low-mass stars and the right circle is labeled high-mass stars. there is an x in the low-mass stars circle, z in high-mass stars circle and y in the intersecting areas. which labels belong in the areas marked x, y, and z?
Low mass stars vary in that they have longer life cycles and develop into white dwarfs. Supernova explosions occur in high mass stars, which also have shorter life cycles.
What should be said about a Venn diagram?Circles are used in a Venn diagram to depict the relationships between individual items or small groups of things. Circles that overlap have certain qualities, but circles that do not overlap do not. Venn diagrams help you to more easily see the relationships and differences between two ideas.
What should be said about a Venn diagram?Circles are used in a Venn diagram to depict the relationships between individual items or small groups of things. Circles that overlap have something in common, but circles that don't share nothing.
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two 3.8 g bullets are fired with speeds of 42.4 m/s and 62.1 m/s, respectively. a) what is the kinetic energy of the first bullet? answer in units of j.
The second one, which has more mass, will have more KE. Explanation: We are aware that KE = E=12mv2 where m Represents mass & v = movement velocity.
What does velocity vs. speed mean?As contrasted to speed, velocity describes the speed and direction of an object's motion because it travels along a path. So speed seems to be a scalar quantity, however velocity is a vector.
Why does velocity formula exist?According to the equation v = s/t, velocity (v) is a scalar quantity that quantifies displacement (or a shift in position, s), over change in time (t).
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To keep your vehicle from rolling into the street when parking downhill on the right with a curb, set the parking brake after
Answer:
Below
Explanation:
....after turning the wheels to face into the curb
a driver in a car traveling at a speed of 26.8 m/s sees a deer 100 m away on the road. calculate the minimum constant acceleration that is necessary of the car to stop without hitting the deer (assuming the deer does not move). group of answer choices -3.6 m/s2 -1.7 m/s2 -4.2 m/s2 -2.8 m/s2
The minimum constant acceleration that is necessary for the car to stop without hitting the deer is -3.6 m/s^2.
What does the term "constant acceleration" mean?
A change in velocity that does not alter over time is referred to as a constant acceleration. A car's average acceleration stays constant at 20 mph per minute even if it increases its speed by 20 mph in one minute and another 20 mph the next.
Is speed constant at constant acceleration?An item travelling with steady acceleration gains speed over a particular period of time.
By continual acceleration, what do you mean?Constant acceleration indicates the velocity keeps rising continuously, increasing at the same rate of acceleration every second. Additionally, because acceleration is a vector quantity, the direction of motion does not change. A moving object can occasionally alter its velocity by the same amount every second.
Given:
Speed v = 26.8 m/s
Distance d = 100 m
Minimum constant acceleration,
[tex]v^2-u^2=2ad[/tex]
[tex]0-26.8^2=2ad[/tex]
[tex]a=(-718.24/200)[/tex]
[tex]a=(-3.6m/s^2)[/tex]
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The current through the 3 Ω resistor is A. 6 A B. 5 A C. 3 A D. 1 A 3Ω
The current through resistor of 3 ohm is currently receiving 3 A of current. It can be calculated by Ohm's Law.
It can be calculated by Ohm's Law which states that the current through a resistor is equal to the voltage across the resistor divided by the resistance. Since the resistance is given as 3 Ω, and if we assume that the voltage across the resistor is also 3 V, then the current through the resistor would be 3 A (3 V / 3 Ω = 1 A).
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nitrogen . oxygen . reflects radio waves . amount of radiation reflected . amount of solar radiation reaching ground . carbon dioxide . absorbs ultraviolet rays
Nitrogen- 78% of atmosphere; oxygen- 21% of atmosphere; reflects radio waves- ionosphere; amount of radiation reflected- 40%; amount of solar radiation reaching ground- 40%.
What does the total radiation that a surface reflects have a name?Albedo, which is typically given as a percentage or a decimal value, is the amount of solar radiation that a surface reflects, with 1 being the ideal reflector and 0 completely absorbing all incoming light.
Detailed answer of the given question.nitrogen- 78% of atmosphere
oxygen- 21% of atmosphere
reflects radio waves- ionosphere
amount of radiation reflected- 40%
amount of solar radiation reaching ground- 40%
carbon dioxide- needed for photosynthesis
absorbs ultraviolet rays-ozonosphere
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how long does it take light to cross the diameter of the milky way galaxy? the diameter of the milky way galaxy is 80,000 light-years.
It would approximately take 200,000 years at Light Speed in order to cross the Milky Way.
What is the Milky way?The Milky way may be defined as a broad band of light that can be frequently observed in the night sky and that is caused by the light of a very large number of faint stars.
It is found that the diameter of the milky way galaxy is 80,000 light-years. So, according to the speed of light, it is calculated that it would approximately take 200,000 years at Light Speed in order to cross the Milky Way. It is a large spiral system consisting of several hundred billion stars, one of which is the Sun.
Therefore, it would approximately take 200,000 years at Light Speed order to cross the Milky Way.
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Karla, Matthew, Daneisha, Vince, and Sergio all have carts of different masses. In their lab, they each
apply a different amount of force to the carts, resulting in different accelerations. However, they did
not label their data table and are now trying to backtrack and identify all of their data.
Your task: using the clues below and your understanding of Newton's 2nd Law of Motion, help
each student determine the mass of their cart, the acceleration of their cart, and the force
they each gave to their cart.
What the students know: the carts had masses of 6kg, 4.5 kg, 9kg, 10 kg, and 12 kg and accelerations
of 5 m/s², 3 m/s², 2 m/s², 4 m/s², and 2.5 m/s².
Clues:
1. Karla's cart is half the mass of Daneisha's.
2. Vince's cart's mass is neither the smallest nor the largest.
3. The mass of Sergio's cart is greater than Vince's.
4. Daneisha's acceleration was half of Sergio's
5. The force Vince applied to his cart was larger than Matthew's.
6. Matthew's acceleration was greater than Vince's.
7. Karla applied less than 18 N of force.
8. Sergio applied more than 40 N of force.
9. Daneisha's force was greater than 27 N.
10. Vince's acceleration was greater than Daneisha's.
11. Karla had less acceleration than Vince.
12. Karla applies the least amount of force.
13. Vince's cart had twice the mass of Matthew's.
The mass of Karla's cart by Newton's second law on applying force will be 12 kg.
What does Newton's second law mean?A detailed explanation of how a force can alter a body's motion is given by Newton's second law. According to this, a body's momentum changes at a rate that is equal to the force acting on it over time in both magnitude and direction.
We know that according to Newton's second law force=mass×acceleration
Now the force needed to push Danielle's cart is 15N.
So, Danielle's car mass is-
In light of the fact that Karla's cart is twice as heavy as Danielle's, Karla's cart's mass can be calculated by multiplying 6 by 2.
So, the mass of Karla's cart is =2×6=12kg.
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A latent function is the intended and recognized consequence of some element of society. Please select the best answer from the choices providedT/F
The statement is False.
A latent function is the unintended and unrecognized consequence of some element of society. It is the hidden or unconscious benefit or outcome that results from an action or element of society, rather than the intended or recognized consequence.
An example of a latent function of going to school is that it allows children to socialize with their peers and learn how to interact with others. While this is not the intended or recognized consequence of going to school, it is a benefit that results from it.
On the other hand, Manifest functions are the intended and recognized consequence of some element of society.
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a bar magnet is falling vertically through a horizontal loop of wire with the south magnetic pole entering the loop first. what is the direction of the induced current (viewed from above) as the south pole enters the loop? group of answer choices clockwise counterclockwise zero
The direction of the induced current as the south pole enters the loop is clockwise direction.
Induced current - what is it?If a conducting loop is subjected to a fluctuating magnetic field, a current can be induced in the loop. If a conducting loop is subjected to a fluctuating magnetic field, a current can be induced in the loop.
What are EMF and induced current?Current is the flow of electrons via a conductor in a closed circuit, whereas induced EMF is the change in potential difference brought on by a change in a coil's magnetic flux.
How can you tell which way an induced current is flowing?If the thumb and forefinger are pointing in the directions of the conductor's velocity and magnetic field, respectively, the center finger will point in the direction of induced current in the conductor.
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what are the two best ways to measure the distance to a distant, isolated spiral galaxy, and how would it be measured
The two best ways to measure the distance to a distant, isolated spiral galaxy are by using the redshift of the galaxy and/or by using the Cepheid variable star method.
What is distance?Distance is a numerical measurement of how far apart two objects, points, or locations are. It is a measure of space in terms of length, width, or height. Distance can be measured in a variety of units including miles, kilometers, yards, and feet. Distance can also be measured in time, such as the amount of time it takes to travel from one location to another. Distance is an important concept in many areas of life, from transportation to navigation to sports.
The redshift of a galaxy is a measure of the expansion of the universe, and is determined by the Doppler Effect. It is calculated using the wavelength of a galaxy's light and the frequency of that light. Redshift can be used to measure the distance of a galaxy by comparing the redshift of the galaxy with the redshift of a standard reference. The further away a galaxy is, the greater its redshift will be.
The Cepheid variable star method is also a reliable way of measuring the distance of a distant spiral galaxy. Cepheid variable stars are stars that pulsate at a regular period, and they can be used as a “standard candle” of sorts, because their luminosity is related to their period. By measuring the period and luminosity of Cepheid variable stars in a distant spiral galaxy, astronomers can calculate the distance to that galaxy.
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in which position would you assist a woman to put her feet in the stirrups and to slide forward to position her buttocks near the edge of the table?
How would you help a woman get her feet into the stirrups and go forward till her buttocks were close to the edge of the desk Lithotomy The ideal setting for the
What in physics is position?
In physics, position refers to a thing looks location and is typically represented by an integer on an axes. Learn about vectors, real numbers, position-time networks, and how to plot a stance graph while exploring the definition and applications of position. Current: 11/05/2021 Position: Where are you at this moment? How many different ways can you respond to that?
What is something's initial position?
The origin of something is where it first began. An x-y graph's origin is the intersection of the two
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A microwave oven draws 0.62kW at an electrical energy rate of 6.8 cents per kWh. Using the GRASS method, calculate the cost of using the microwave for 30 minutes every day for 9 days. Show your work. Round your answer to the nearest cent. You may write out your answer on paper and upload the image. [3 pts]
G
R
A
S
S
Answer: The cost of using the microwave oven for 30 minutes every day for 9 days is $0.57
Explanation: The GRASS method is used to calculate the cost of using an appliance by multiplying the power rating of the appliance (in kW) by the hours of use, and then multiplying that by the rate per kWh.
Here's the calculation:
Power rating: 0.62 kW
Time of use: 30 minutes/day for 9 days = 30/60*9 = 13.5 hours
Cost per hour = 0.62 * 6.8 / 100 = 0.04236
Total cost = 0.04236 * 13.5 = $0.57
Select all that apply: During which 3 periods of time is this object getting faster? This is an all of nothing question so be sure to select exactly 3 of the answers
1) 0s to 2s, 2) 4s to 5s, 3 ) 9s to 10s are 3 periods of time in which this object is getting faster. An identifiable grouping of matter that may be bounded by an identified boundary is referred to as a physical body or physical object.
What does a physical object mean?An object is a discernible grouping of stuff that may move as a unit in three dimensions via translation or rotation and may be contained by a discernible boundary.
What are an object's characteristics?Based on the information perceived, learning and reasoning are used to deduce an object's attributes. Using Occam's razor, an object can be defined as a mental construct that is consistent with the data offered by our senses.
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State the basic assumptions of the kinetic theory.
a certain 48 v electric forklift can lift up to 7000 kg at a maximum rate of 75 meters per minute. what is its power? round your answer to the nearest hundreds.
In this case the power is 703.8 kW and rounding to the nearest hundreds gives 700 kW.
What is power?
Power is the ability to influence or control people, events, and outcomes. It can be seen when one person or group is able to make decisions, set standards, and enforce boundaries. Generally, power is associated with authority, control, and influence; however, it can also refer to the capacity to do work or generate energy.
The power of the forklift can be calculated using the formula: Power = (Load x Velocity) / Time.
In this case, the power is (7000 kg x 75 m/min) / 1 min = 525,000 kg•m/min. Converting to watts, this is 525,000 kg•m/min / 746 = 703.8 kW.
Rounding to the nearest hundreds gives 700 kW.
In this case the power is 703.8 kW and rounding to the nearest hundreds gives 700 kW.
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Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1.
What is the ratio Uc1/Uc2.
Where would I start with this problem and what equation would I use?
You can start the problem by using the formula for capacitance, C = Q/V, where C is the capacitance, Q is the charge stored on the capacitor, and V is the potential difference across the capacitor.
What are capacitors?A capacitor is a passive electrical component that stores electrical energy in an electric field. It consists of two conductive plates, separated by an insulating material called the dielectric. When a voltage is applied across the conductive plates, an electric field is created, which stores energy in the dielectric. The ability of a capacitor to store electrical energy is measured in farads (F).
Given that Capacitor 2 has half the capacitance and twice the potential difference as Capacitor 1, you can express the capacitance and potential difference of Capacitor 2 in terms of those of Capacitor 1.
C₂ = 1/2 × C₁ V₂ = 2 × V₁
You can use these equations to find the ratio of the stored energy in the two capacitors. The stored energy in a capacitor is given by the formula U = 1/2CV², where U is the stored energy, C is the capacitance, and V is the potential difference.
Uc1 = 1/2C₁V₁² Uc2 = 1/2C₂V₂²
By substituting the values of C₂ and V₂ in terms of C₁ and V₁, you can find the ratio of the stored energy in the two capacitors:
Uc1/Uc2 = (1/2C₁V₁²) / (1/2×(1/2C₁) (2V₁) ²) Uc1/Uc2 = 1/8
The ratio of stored energy in the two capacitors is 1/8.
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A particle is located at coordinates x = 2.0 m, y = 3.0 m. What is the magnitude of the torque about the origin when the particle is acted upon by a force of magnitude 5.0 N in (a) the positive x direction, (b) the positive y direction, and (c) the negative x direction?
The positive x direction is 0 Nm, positive y direction is 10 Nm, negative x direction is 0 Nm.
What is torque?The torque, also known as the moment of force, is given by the cross product of the position vector (r) and the force vector (F).
The magnitude of the torque is given by the magnitude of the cross product, which is equal to the product of the magnitudes of the vectors (r and F) multiplied by the sine of the angle between them.
In the case of (a) positive x direction, the torque about the origin is given by:
τ = r x F = (2.0 m) x (5.0 N) x sin(90°) = 3.0 m x 5.0 N = 0 Nm.
In the case of (b) positive y direction, the torque about the origin is given by:
τ = r x F = (3.0 m) x (5.0 N) x sin(90°) = 2.0 m x 5.0 N = 10 Nm.
In the case of (c) negative x direction, the torque about the origin is given by:
τ = r x F = (2.0 m) x (-5.0 N) x sin(90°) = 3.0 m x 5.0 N = 0 Nm.
So, the positive x direction is 0 Nm, positive y direction is 10 Nm, negative x direction is 0 Nm.
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