The applied force for the engine will be 24,450 N.
The applied force produced by the engine for a car weighing 12,500 n starting from rest and accelerating to 83.0 km/h in 5.00 s with a friction force of 1350 n is:
Applied force = (Mass x Acceleration) - Friction force
Applied force = (12,500 N x (83.0 km/h / 5.00 s)) - 1350 N
Applied force = 25,800 - 1350 N
Applied force = 24,450 N
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a 2.35 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0320 m . the spring has force constant 800 n/m . the coefficient of kinetic friction between the floor and the block is 0.350. the block and spring are released from rest and the block slides along the floor. part a what is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (at this point the spring is compressed 0.0120 m .)
The speed of the block when it has moved a distance of 0.0200 m from its initial position is 0.784 m/s.
The speed of the block when it has moved a distance of 0.0200 m from its initial position when it has been released from rest is given by v. The force constant of the horizontal spring is given by k. The block has a mass of m. The distance the spring has been compressed is given by d. The coefficient of kinetic friction between the floor and the block is given by μk.
It is asked to determine the speed of the block. There are different ways to approach this problem, but one of the most common ways is to consider the conservation of energy principle. This principle states that the total energy of a system remains constant if no external work is done on it. In other words, the initial energy of the system is equal to the final energy of the system.
Using this principle, we can write :
Initial energy = final energy
1/2 k x² + m g d = 1/2 m v² + m g d + f k d
where x = initial compression of the spring (0.0320 m), d = compression of the spring at the end (0.0120 m), v = speed of the block f, k = kinetic friction force, mg = weight of the block, k = spring constant of the horizontal spring. By solving this equation for v, we get:
v = sqrt((k/m) x² + 2g(mu_k- d))
where:g = 9.81 m/s²
We can substitute the given values into this equation to get:
v = sqrt((800/2.35) x² + 2*9.81(0.35 - 0.012))v = 0.784 m/s
Therefore, the speed of the block when it has moved a distance of 0.0200 m from its initial position is 0.784 m/s.
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Rank the given speeds of observers relative to a yardstick by the observed length of the yardstick from shortest to longest.
Items (4 items) (Drag and drop into the appropriate area) 0.25c 0.1c 0.5c 0.01c
Items in order Shortest 1 2 3 4 Longest
The required items in order from shortest to longest: 0.01c < 0.1c < 0.25c < 0.5c
The length contraction phenomenon occurs when objects are observed from different reference frames moving at relativistic speeds. According to special relativity, as an object approaches the speed of light (c), its length in the direction of motion appears shorter to an observer in a different reference frame.
In this case, the observer moving at 0.5c would perceive the yardstick to be the shortest, followed by the observer at 0.25c, the observer at 0.1c, and finally, the observer at 0.01c would perceive the yardstick to be the longest. This ranking is based on the relative velocities of the observers with respect to the yardstick and the effect of length contraction at higher speeds.
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what factor does not determine how much gravitational potential energy is in an object-earth system?
The factor that does not determine how much gravitational potential energy is in an object-earth system is the object's mass.
An object-earth system is a system in which an object interacts with the earth by exerting a force of attraction. The object's energy is derived from the work done by gravitational forces when the object is moved away from the earth's surface.
An object in an object-earth system's gravitational potential energy is the work done by gravitational forces on the object when it is moved from a lower position to a higher one in the object-earth system. The factor that does not determine how much gravitational potential energy is in an object-earth system is the object's mass. The gravitational potential energy of an object in the earth-object system is determined by the distance between the object and the earth's surface. The gravitational potential energy of an object increases as the distance between it and the earth's surface increases.
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It costs 2.6 cents to charge a car battery at a voltage of 12 V and a current of 15 A for 120 minutes.
What is the cost of electrical energy per kilowatt-hour at this location?
Express your answer indollars per kilowatt-hour. Express your answer using two significant figures.
To two significant numbers, the cost of electrical energy per kilowatt-hour at this location is roughly 0.072 dollars/kWh.
To start, let's figure out how many kilowatt-hours (kWh) of energy were used:
Convert the time units to hours as follows: 120 minutes / 60 minutes each hour = 2 hours.
Use the following formula to get the energy consumed in kilowatt-hours:
certifies a............... (hours)
Power (kW) is calculated as Voltage (V) x Current (A) / 1000, where 12 V x 15 A / 1000 is 0.18 kW.
Energy (kWh) equals 0.18 kW times two hours, or 0.36 kWh.
Then, using the stated cost of battery charging, we can determine the price of electrical energy per kilowatt-hour:
Price (in dollars) equals 2.6 cents to 0.026 dollars.
Cost per kWh is calculated as Cost/Energy, which is 0.026 dollars/0.36 kWh, or 0.072 dollars/kWh.
Hence, to two significant numbers, the cost of electrical energy per kilowatt-hour at this location is roughly 0.072 dollars/kWh.
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what does fae mean? if it helps this is from the topic forces and elasticity
The meaning of f∝e is that the extension is directly proportional to the force applied of a particular object from Hooke's law.
What connection does there exist between force and elasticity?The extension for a particular spring and other elastic items is inversely proportional to the applied force. For instance, the extension doubles if the force does. This is effective up until the proportionality limit is reached.
According to Robert Hooke's law of elasticity, which holds true for relatively minor deformations of an item, the displacement or amount of the deformation is directly proportional to the deforming force or load. Hooke's law was first discovered in 1660.
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complete question :
What does this mean f∝e?
what is an electric current?obtain an expression for effective resistence of three resistors R1,R2 and R3 are connected in series to 6v battery through voltmeter and ammeter.
R = R1 + R2 + R3 equivalent resistance of 3 resistors in series
I = V / R
in computing the standard error of the mean, the finite population correction factor is used when group of answer choices n/n > 0.05 n/n 0.05 n/n > 0.05 n/n 30
In computing the standard error of the mean, the finite population correction factor is used when the group of answer choices n/n > 0.05. Hence, the correct answer is option A.
The standard error of the mean (SEM) is a statistic that measures the accuracy with which a sample represents the population mean. It indicates how precisely the sample estimate of the mean varies from the real mean of the population.The formula for SEM is as follows:SEM = s / sqrt (n), where s is the sample standard deviation and n is the sample size. When the sample size is large, it is common to assume that the population standard deviation σ is unknown and is therefore estimated using the sample standard deviation s. We do this by dividing s by the square root of the sample size.
When the sample size is a substantial portion of the population, the finite population correction factor (FPC) must be applied to the SEM formula to account for the sample size's effect on the standard error. FPC is the ratio of the population size minus the sample size to the population size minus one, raised to the power of 0.5.In summary, the finite population correction factor is utilized when the ratio n/N is greater than 0.05. If the ratio is less than or equal to 0.05, the FPC can be ignored.
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The three forces (in units of N) given below are acting on a 20 kg mass. Calculate the magnitude of the acceleration of the mass. F1 = 3i F2 = 5j F3 = (i-3j)
A. 0.224 m/s^2 B. 0.1 m/s^2
C. 1.0 m/s^2 D. 0.2 m/s^2
The magnitude of the acceleration of the mass is A. 0.224 m/s^2
To find the acceleration of the 20 kg mass, we can use Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration:
Σ[tex]F = ma[/tex]
Where ΣF is the vector sum of all the forces acting on the object.
In this case, we have three forces acting on the mass:
F1 = 3i NF2 = 5j NF3 = (i - 3j) NThe vector sum of these forces is:
Σ[tex]F = F1 + F2 + F3[/tex]
[tex]= (3i N) + (5j N) + (i - 3j) N[/tex]
[tex]= (4i - 2j) N[/tex]
So the net force on the mass is (4i - 2j) N. Now we can use Newton's second law to find the acceleration of the mass:
Σ[tex]F = ma[/tex]
[tex](4i - 2j) N = (20 kg) a \\\\a = \frac{(4i - 2j) N}{20 kg}[/tex]
To find the magnitude of the acceleration, we can use the Pythagorean theorem:
[tex]|a| =\sqrt{(ax)^2 + (ay)^2}[/tex]
where ax and ay are the x and y components of the acceleration vector. In this case, we have:
[tex]ax = \frac{4 N}{20 kg} = 0.2 m/s^2\\\\ay = \frac{-2 N}{20 kg} = -0.1 m/s^2[/tex]
So the magnitude of the acceleration is:
[tex]|a| = \sqrt{(0.2 m/s^2)^2 + (-0.1 m/s^2)^2} \\|a| = \sqrt{0,04 m/s^2 + 0,01 m/s^2}\\|a| = \sqrt{0,05 m/s^2}\\|a| = 0.224 m/s^2[/tex]
Therefore, the answer is A. 0.224 m/s^2.
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why do astronomers prefer to put infrared telescopes on high-flying airplanes or on satellites in space?
Astronomers prefer to use infrared telescopes on high-flying airplanes or on satellites in space because the atmosphere of the Earth blocks a significant amount of infrared light. By placing these telescopes in the sky or in space, astronomers can get a better view of infrared light from distant objects in the universe.
Airborne telescopes can offer temporary access to the observable range of the electromagnetic spectrum blocked by water vapor and ozone layer.The atmosphere filters out and absorbs some of the infrared light. The atmosphere consists of many layers. Infrared light does not get through the layer of ozone, water vapor, or carbon dioxide that makes up the lower part of the atmosphere. However, the higher atmosphere is transparent to infrared light. So, flying above this layer can give astronomers a much clearer and less obstructed view of the universe.
Satellites can offer a better view of the universe without interference from the Earth’s atmosphere. In space, the telescope is not hampered by the Earth's atmosphere. For example, the Hubble Space Telescope, which orbits about 570 km above Earth's surface, provides a clearer view of the universe in ultraviolet, visible, and near-infrared wavelengths than ground-based telescopes do. It has discovered galaxies, stars, and phenomena far beyond the reach of Earth-based telescopes.
They offer the possibility of carrying bigger and heavier instruments than a ground-based observatory.The weight of an airborne telescope is significantly reduced in comparison to a ground-based telescope because it is placed above the Earth’s atmosphere, and this has the advantage of allowing for more extensive equipment, including larger and heavier telescopes. Satellites have the same advantage as they are not limited by the size of the payload.
Airborne telescopes and satellites can observe celestial objects in the infrared spectrum.Infrared light is absorbed by the Earth's atmosphere. As a result, infrared telescopes that are placed on the ground will be less successful. As a result, astronomers prefer to place them on airborne telescopes and satellites, which are above the Earth's atmosphere. This makes it possible for infrared telescopes to examine the universe and make discoveries that would otherwise be impossible to observe from the ground.
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a square loop of wire carrying a current in a clockwise direction lies in the plane of the paper. the magnetic field inside the loop is directed select one: a. into the paper everywhere. b. into the paper near the wire but out of the paper elsewhere. c. out of the paper everywhere. d. out of the paper near the wire, but into the paper elsewhere.
The magnetic field inside the loop is directed out of the paper near the wire, but into the paper elsewhere. The correct answer is Option D.
What is a loop of wire?A wire loop is a closed-circuit that is often referred to as a coil. A current-carrying loop produces a magnetic field around it, which is used to detect changes in the electric current flowing through the wire by the magnetic field it produces. A loop of wire is used in electric motors, electric generators, and inductors.
How to determine the direction of the magnetic field inside a loop of wire?A wire loop carrying a current produces a magnetic field. A clockwise current flow results in a clockwise magnetic field direction, which is directed out of the paper near the wire but into the paper elsewhere. A counter-clockwise current flow results in a counter-clockwise magnetic field direction, which is directed into the paper near the wire but out of the paper elsewhere.
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the sun is shining on james and has created a shadow that is 8 feet long what is the distance from his head to his shadow
The distance from James's head to his 8-foot long shadow is 8 feet.
To find this, we can use the simple triangle relationship: opposite side (the shadow) is equal to the hypotenuse (the distance between James's head and his shadow) times the cosine of the angle formed by the sun's rays.
The distance from James's head to his shadow can be calculated using trigonometry. The tangent function can be used for this purpose.
To calculate the distance from James's head to his shadow, follow these steps:
Firstly, draw a right triangle with one of its angles adjacent to James's head and the other adjacent to the base of the shadow. The hypotenuse of the triangle is the line between James's head and the tip of the shadow.
Let x be the distance from James's head to the base of the shadow. The hypotenuse is the square root of (x^2 + 8^2).
Use the tangent function to find the value of x. tan(angle) = opposite/adjacent. In this case, the angle is the angle of elevation of the sun, which can be determined from the time of day and the location.
If the angle is not known, it can be assumed to be 45 degrees. tan(45) = opposite/adjacent.
The opposite side is 8, so: x = 8/tan(45) = 8/1 = 8 feet.
Therefore, the distance from James's head to his shadow is 8 feet.
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In the context of the motor control process related to the speed-accuracy trade-off, the _____ phase of movement includes the beginning of limb movement in the direction of a target.
In the context of the motor control process related to the speed-accuracy trade-off, the initiation phase of movement includes the beginning of limb movement in the direction of a target.
What is motor control?Motor control is the ability to regulate and coordinate motor skills to achieve a desired outcome. The central nervous system (CNS) is in charge of regulating these skills. The CNS is divided into two parts: the peripheral nervous system (PNS) and the central nervous system (CNS). Motor skills are regulated by both parts of the nervous system. The CNS, on the other hand, is more involved in higher-level motor control.
A motor control system can be divided into three stages: planning, initiation, and execution. When the central nervous system processes the desired movement, it activates the motor program in the initiation stage, which produces the motor command sent to the muscles. Movement is initiated by the initiation stage. Following that, the movement is executed to meet the task's requirements. The motor program adjusts movement by making corrections based on previous trials and feedback. Therefore, the initiation phase is critical in the context of the motor control process related to the speed-accuracy trade-off.
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What is more important in determining the amount of damage an object sustains in a collision? 1. the total momentum change per unit time 2. the total momentum change 3. Both 1 and 2 4. None of these
3.) the total momentum change per unit of time, and the total momentum change are both important in determining the amount of damage an object sustains in a collision.
The amount of damage an object receives in a collision depends on both the overall momentum change and the momentum change per unit of time. The mass and velocity of the objects colliding determine the total momentum change, which is a measure of the force of impact. The impulse, also known as the change in momentum per unit of time, is equally significant. This gauges how long an impact lasts and how the force is applied throughout that time. Impacts that last longer and exert less force can cause less harm than impacts that last less time and exert more force. The specific factors that contribute to damage will depend on the details of the collision, such as the speed, mass, and shape of the objects involved.
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A circuit consists of a 10.0-ohm resistor, a 15.0-ohm resistor, and a 20.0-ohm resistor connected in parallel across a 9.00-volt battery. What is the equivalent resistance of this circuit?0.200 Ω1.95 Ω4.62 Ω45.0 Ω
The equivalent resistance of this circuit is 4.62 Ω.
What is resistors?
A resistor is an electronic component that is used to resist or limit the flow of electric current through a circuit. It is a passive component, which means it does not require any external power source to function.
Resistors are typically made of materials that have a high resistance to the flow of electric current, such as carbon, metal, or metal oxide
When resistors are connected in parallel, the total resistance can be calculated using the following formula:
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances.
Applying this formula to the given circuit, we get:
1/Req = 1/10 + 1/15 + 1/20
1/Req = 0.1 + 0.0667 + 0.05
1/Req = 0.2167
Taking the reciprocal of both sides gives:
Req = 1/0.2167
Req = 4.62 Ω
Therefore, the equivalent resistance of this circuit is 4.62 Ω.
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A hoop, solid sphere, and a cylinder of equal mass and radius roll without slipping down a ramp with height h. Which has the greatest speed at the bottom of the ramp? A. Solid sphere B. Cylinder OC. All speeds are equal D. Hoop
A. Solid sphere, In comparison to the hoop and cylinder, the solid sphere has the least moment of inertia, which causes the bottom of the ramp to have a higher angular velocity and a higher linear velocity.
This is due to the fact that, among objects of the same mass and radius, the solid sphere has the lowest moment of inertia. With a particular angular velocity, an object's moment of inertia defines how much rotational kinetic energy it contains. The hoop and cylinder will have a smaller linear velocity and a smaller angular velocity when they reach the bottom of the ramp than the solid sphere because they have greater moments of inertia.
The solid sphere will thus be moving at its fastest near the bottom of the slope.
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which method gives a more accurate value of focal length? why is the image distance obtained in method a only approximately equal to the focal length? you may refer to the lens equation in the appendix.
The method of using a screen gives a more accurate value of focal length
The method of using a screen gives a more accurate value of focal length because it is not subject to parallax errors. The image distance obtained in Method A is approximately equal to the focal length because it relies on the angle of incidence and angle of refraction of light, which can be inaccurate if the measurements are not taken precisely. The Lens Equation in the Appendix states that the focal length is equal to the image distance divided by the magnification, which can give a more accurate result than Method A.
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Part A A canoe is designed to have very little drag when it moves along its length. Riley, mass 62 kg, sits in a 21 kg canoe in the middle of a lake. She dives into the water off the front of the canoe, along the axis of the canoe. She dives forward at 1.7 m/s relative to the boat. Just after her leap, how fast is she moving relative to the water? Express your answer with the appropriate units Value Units Submit Request Answer ▼ Part B Just after her leap, how fast is the canoe moving relative to the water? Express your answer with the appropriate units. (c)EValue Units
The speed of Riley relative to the water is 1.7 m/s. and the speed of canoe relative to the water is 0 m/s.
How fast is Riley moving relative to the water?The equation needed to solve the problem is the following:
Final Velocity = Initial Velocity + (Acceleration × Time)
The steps to solve for speed of Riley are the following:
Mass of Riley = 62 kg
Mass of canoe = 21 kg
Speed of leap relative to the boat = 1.7 m/s
By using the equation for conservation of momentum (also known as the center of mass formula):
m₁v₁ + m₂v₂ = (m₁ + m₂)vf
Solve for the unknown variable: vf = (m₁v₁ + m₂v₂) / (m₁ + m₂)
Plugging in the values given, you get: vf = (62 kg × 1.7 m/s) / (62 kg + 21 kg) = 1.2 m/s
Therefore, Riley is moving at 1.2 m/s relative to the water.
Velocity of the canoe relative to the water can be determined by using the equation for conservation of momentum (also known as the center of mass formula):
m₁v₁ + m₂v₂ = (m₁ + m₂)vf
v₂ = [(m₁ + m₂)vf - m₁v₂] / m₂
Plugging in the values given, you get: v₂ = [(62 kg + 21 kg) × 1.2 m/s - 62 kg × 1.7 m/s] / 21 kg = 0 m/s
Therefore, the canoe is not moving relative to the water.
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Find the fourier series of f(x)=x
for 0<=x<=2
The function f(x) = x, where 0 x 2, has the following Fourier series: Given that f(x) has an odd period of 2, we may express its Fourier series as follows: F(x) = A0 + [n=1 to] Ancos (n/x) plus bnsin (n/x).
Since f(x) is an odd function, a0 = 0. We may apply the following formulae to determine the Fourier coefficients: a = (2/1) f(x)cos(nx/1)[0 to 1] dx Bn = (2/1) f(x)sin(nx/1)[0 to 1] dx We may determine the coefficients using the following formulas: an is equal to (2/1) [0 to 1] x*cos(nx/1) dx. Bn is equal to (2/1), [0 to 1]x*sin(nx/1)dx. By integrating in pieces, we obtain: a = (2/π^2) [(1-(-1)^n)/(n^2)] bn = (2/π) [(1-(-1)^n)/(n)] The Fourier series of f(x) = x, where 0 x its Fourier series as follows: F(x) = A0 + [n=1 to] Ancos (n/x) plus bnsin (n/x).2, is as follows: f(x) = Σ(n=1 to ∞) [(2/) (1-(-1)n)/(n))*sin(nx/1)].
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fifty points Hypothesis: Predict how the addition of subatomic particles will affect the structure and properties of an atom. (Example: I predict that adding more neutrons will affect . . .)
Was your hypothesis correct? Why or why not?
Website: https://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html
Open the Phet build-an-atom simulator.
Answer:
Hypothesis: Adding subatomic particles to an atom will affect its structure and properties. For instance, adding more neutrons to an atom will affect its stability and can result in the formation of isotopes.
The hypothesis is correct. Adding subatomic particles such as protons, neutrons, and electrons to an atom will change its structure and properties. The number of protons determines the atomic number and the identity of the element. The number of neutrons affects the stability of the atom and can result in the formation of isotopes. Isotopes have the same atomic number but different mass numbers due to a different number of neutrons. The addition or subtraction of electrons will affect the charge of the atom, resulting in the formation of ions. Therefore, changing the number of subatomic particles will affect the structure, stability, and properties of an atom.
Adding protons, electrons, or neutrons to an atom changes its structure and properties. Adding protons changes its elemental identity, adding electrons changes its charge, and adding neutrons changes the atomic weight and stability and could result in a potentially radioactive isotope.
Explanation:Adding subatomic particles to an atom can have significant impacts on its structure and properties. For instance, adding protons to an atom changes its identity, because the number of protons in an atom determines what element it is. The addition of more electrons can change the atom's charge, resulting in an ion. More specifically, if you add more electrons than protons, it becomes a negatively charged ion (anion), and if there are fewer electrons than protons, a positively charged ion (cation) is formed.
Adding neutrons transforms the atom into a different isotope of the same element. An isotope is a variant of the same element with different numbers of neutrons. This can affect the atomic weight and stability of the atom, and in some cases, isotopes may be radioactive.
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If I heated up a glass of 100 grams of water, and the temperature changed from 25℃ to 31℃, how much heat was needed to do that (in calories)?
Answer:
6° because some heat is released out of surrounding. if 100 over six which is equal to sixtenn point four
Help asaaap it's about doppler effect
The frequency that the bad guy hear is 12000 hz when the police car is moving with speed of 80m/s.
Frequencyfo=fs(vvov), where fo is the observed frequency, fs is the source frequency, v is the speed of sound, vo is the observer's speed, the top sign indicates the observer is approaching the source, and the bottom sign indicates the observer is leaving the source.Equation fo=800(80-65) fo = 12000 after substituting the variablesThe apparent change in frequency of a wave as a result of an observer moving with respect to the wave source is known as the Doppler effect or Doppler shift. It bears the name of the Austrian physicist Christian Doppler, who first described the phenomenon in 1842.For more information on doppler effect kindly visit to
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a skater of mass 70.0 kg initially moves in a straight line at a speed of 4.80 m/s. the skater approaches a child of mass 39.5 kg, whom he lifts on his shoulders. assuming there are no external horizontal forces, what is the skater's final velocity?
The final velocity of the skater (with the child on their shoulders) is 3.08 m/s.
A skater of mass 70.0 kg initially moves in a straight line at a speed of 4.80 m/s.
When the skater lifts a child of mass 39.5 kg onto their shoulders, their final velocity (assuming there are no external horizontal forces) can be calculated using the law of conservation of momentum.
Momentum is defined as the product of mass and velocity. Therefore, the final momentum of the skater and child can be expressed as:
Final Momentum = (70.0 kg x 4.80 m/s) + (39.5 kg x 0 m/s) = 336 kg m/s
To find the final velocity, we must first find the total mass of the skater and child:
Total Mass = 70.0 kg + 39.5 kg = 109.5 kg
Using the law of conservation of momentum and the total mass, the final velocity of the skater can be expressed as:
Final Velocity = Final Momentum / Total Mass = 336 kg m/s / 109.5 kg = 3.08 m/s
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Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is
Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is 8.78 m/s².
What is gravitational force?The reason for this difference in acceleration is that the gravitational force on an object is inversely proportional to the square of the distance between them.
Thus, the further an object is from the Earth's surface, the weaker the gravitational force acting on it. This is why objects in orbit around the Earth experience less acceleration due to gravity than objects on the surface of the Earth.
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a ceiling fan is turned on and a net torque of 2.3 n*m applied to the blades. the blades have a total moment of inertia of 0.39 kg*m^2. what is the angular acceleration of the blades?
The angular acceleration of the blades is 5.897 rad/s². It can be calculated using the formula α as the ratio of torque to moment of Inertia.
The torque is a rotational or twisting force. Angular acceleration is the rate at which the angular velocity of an object changes, measured in radians per second squared (rad/s²).
Given the torque and moment of inertia, we may utilize the following formula to find the angular acceleration of the blades:
[tex]\alpha= \dfrac{Torque}{Moment \; of \; inertia}\\\alpha= \dfrac{\tau}{I}[/tex]
where τ is the torque in newton-meters (N-m),I is the moment of inertia in kg-m², α is the angular acceleration in radians per second squared (rad/s²).
Rearranging the formula to solve for α gives:
[tex]\alpha=2.3/0.39\\=5.897 rad/s^2[/tex]
Therefore, the angular acceleration of the blades is 5.897 rad/s².
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A 10.0 μF parallel-plate capacitor is connected to a 12.0 V battery. After the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates. Part A A voltmeter is connected across the two plates without discharging them. What does it read? Part B What would the voltmeter read if the plate separation were doubled. Part C What would the voltmeter read if the radius of each plate was doubled, but the separation between the plates was unchanged?
Part A: The voltage of the capacitor will remain constant until some external influence acts on it. Which is 12V.
Part B: The voltmeter reading will be 24.0 V.
Part C: The voltmeter reading will be 3.0 V.
Given that,
Charge of the capacitor = C
Voltage of the battery = V = 12.0 V
Part A:
A voltmeter is connected across the two plates without discharging them.
What does it read?
The voltmeter will read the same voltage as the battery voltage i.e., 12.0 V. This is because once the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates.
Part B:
What would the voltmeter read if the plate separation were doubled?
The capacitance of the capacitor is given by,
C=ϵ[tex]_0[/tex] [tex]\frac{A}{d}[/tex]
Where, ϵ[tex]_0[/tex] is the permittivity of free space
A is the area of each plate and
d is the separation between the plates
The capacitance is inversely proportional to the separation between the plates. Doubling the separation will reduce the capacitance by half. T
Therefore, capacitance will become 5.0 μF.
Now the charge on the capacitor is given by,
Q = CV = 10.0 × [tex]10^{-6}[/tex] × 12.0 = [tex]1.2 \times10^{-4}[/tex] C
Now the capacitance is 5.0 μF, therefore,
Q’ = CV’ = Q
⇒ V’ = Q’/C’ = Q/C =1.2 × [tex]10^{-4}[/tex]/ 5.0 × [tex]10^{-6}[/tex] = 24.0 V
Part C:
What would the voltmeter read if the radius of each plate was doubled, but the separation between the plates was unchanged?
The capacitance of the capacitor is given by,
C=ϵ[tex]_0[/tex] [tex]\frac{A}{d}[/tex]
Where, ϵ[tex]_0[/tex] is the permittivity of free space
A is the area of each plate and
d is the separation between the plates
The capacitance is directly proportional to the area of the plates.
Doubling the radius will increase the capacitance by four times.
Therefore, capacitance will become 40.0 μF.
Now the charge on the capacitor is given by,
Q = CV = 10.0 × [tex]10^{-6}[/tex] × 12.0 = 1.2 × [tex]10^{-4}[/tex] C
Now the capacitance is 40.0 μF,
therefore,
Q’ = CV’ = Q
⇒ V’ = Q’/C’ = Q/C = 1.2 × [tex]10^{-4}[/tex] / 40.0 × [tex]10^{-6}[/tex] = 3.0 V
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A 1. 1 kg box drops two meters from a shelf and comes to rest after 0. 021 s on the floor. What force did the box hit the floor
A 1 kg box falls two metres from a shelf and lands on the ground after 0.021 seconds. The box impacted the ground with a force of around 524.7 N.
The box impacted the ground with a force of around 524.7 N.
Explanation: We can determine the force using the equation F = m * (v/t), where m is the box's mass, v is the velocity change (which is the ultimate velocity because the box starts at rest and comes to a halt), and t is the time it takes for the box to stop.
Given that the box falls 2 metres and its terminal velocity is 0 m/s, v = 2 m/s.
524.7 N is equal to F = 1.1 kg * (2 m/s / 0.021 s).
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apply concepts although a lightning rod is designed to carry charge safely to the ground, its primary purpose is to prevent lightning from striking in the first place. how does it do that?
Although a lightning rod is designed to carry charge safely to the ground, its primary purpose is to prevent lightning from striking in the first place. This is done by providing a path of least resistance for the lightning to follow, which directs the electrical current away from the building or structure.
The lightning rod, also known as a lightning conductor, is used to protect structures from being damaged by lightning strikes. It works by providing a pathway for the lightning to follow, which directs the electrical current away from the building or structure, and safely to the ground. The rod is typically made of a metal conductor, such as copper or aluminum, and is attached to the roof of the building or structure.
The top of the rod is designed to be pointed, which allows it to attract the electrical charge of a lightning bolt. When the lightning strikes the rod, the electrical charge is then conducted through the rod and safely into the ground, where it is dispersed harmlessly. In this way, the lightning rod is able to prevent lightning from striking the building or structure in the first place.
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Show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity.
The magnetic field inside an infinite solenoid is given by the expression:
B = μ0N/L where μ0 is the permeability of free space, N is the number of turns per unit length, and L is the length of the solenoid.
What is a magnetic field inside a toroid?The magnetic field inside a toroid is given by the expression:
B = μ0NI
where μ0 is the permeability of free space, N is the number of turns per unit length, and I is the current flowing through the toroid.
To show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity, we can consider a toroid with an infinitely large central radius and a circular cross-section of radius R. In this case, the number of turns per unit length is N = I/2πR and the current through the toroid is I = 2πRN. Substituting these expressions into the equation for B gives:
B = μ0NI
B = μ0N(2πRN)
B = 2πμ0NR2
B = 2πμ0N2R2
Assuming that the length of the solenoid is equal to its cross-sectional radius, L = R, then the equation for B reduces to:
B = 2πμ0N2R
B = μ0N/L
Therefore, in the limit that the central radius of a toroid goes to infinity, the expression for the magnetic field inside a toroid reduces to the expression for the magnetic field inside an infinite solenoid.
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Physics Help Requested Suppose our experimenter repeats his experiment on a planet more massive than Earth, where the acceleration due to gravity is g=30 m/s2. When he releases the ball from chin height without giving it a push, how will the ball's behavior differ from its behavior on Earth? Ignore friction and air resistance. (Select all that apply.)a. It will take more time to return to the point from which it was released.b. It will smash his face. Its mass will be greater.c. It will take less time to return to the point from which it was released. d, It will stop well short of his face.
On a planet with more massive gravity, such as [tex]g = 30 \ m/s^2[/tex], the ball released from chin height will take less time to return to the point from which it was released, due to the increased acceleration due to gravity.
It will take less time to return to the point from which it was released. The acceleration due to gravity is much stronger on this planet, so the ball will accelerate faster as it falls toward the ground. This means that it will reach its lowest point more quickly and then rise back up to its starting point more quickly as well.
Also, the mass of the ball is not affected by the strength of the gravitational acceleration on the planet.
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a rocket starts from rest and moves upward from the surface of the earth for the first 10.0 s of its motion the vertical acceleration of the rocket is given by ay 2.90m s3 t where the y direction is upward. Part A: What is the height of the rocket above the surface of the earth at t = 10.0 s? Part B: What is the speed of the rocket when it is 205 m above the surface of the earth?
At t = 10.0 s, the height of the rocket above the surface of the earth is 200 m. the speed of the rocket when it is 205 m above the surface of the earth is 20.64 m/s.
To calculate height of the rocket, we can use the equation of motion: s = 1/2*a*t^2. Therefore, the height of the rocket is: s = 1/2*2.90m/s^2*(10.0s)^2 = 200 m
To calculate the speed of the rocket when it is 205 m above the surface of the earth, we can use the equation of motion: v^2 = 2as
Therefore, the speed of the rocket when it is 205 m above the surface of the earth is v = sqrt(2*2.90m/s^2*205m) = 20.64 m/s.
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