A hamiltonian function representing an electron in the presence of a stationary positive point charge is
H = (p^2)/(2m) - (e^2)/(4πε_0r)
What is a hamiltonian function?Generally, The Hamiltonian function representing an electron in the presence of a stationary positive point charge is given by:
H = kinetic energy + potential energy = (p^2)/(2m) - (e^2)/(4πε_0r)
where
p = momentum of the electron m = mass of the electron e = charge of the electron (assumed to be negative) ε_0 = vacuum permittivity r = distance between the electron and the positive point charge.Note that the first term represents the kinetic energy of the electron, and the second term represents the potential energy of the electron due to the attractive electrostatic force from the positive point charge.
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what must the charge (sign and magnitude) of a 1.55 g particle be for it to remain balanced against gravity when placed in a downward-directed electric field of magnitude 635 n/c ?
The 1.55 g particle must have a positive charge that is equivalent to 635 N/C times (1.55 g / 9.8 m/s2) = 11.9 C. To maintain equilibrium against gravity.
for a)
a particle's charge must be opposite in sign and magnitude to the electric force acting on it.
mg = qe
1.55 X 10 ⁻³ X 9.81 = q X 635
q = - 0.023 X 10⁻³ C
it willl be negative
We get at q = F / E = 15.09 N / 635 N/C = 0.0237 C after solving for the charge.
This indicates that the particle's charge must be positive and equal to 0.0237 Coulombs in order for it to balance against gravity in the 635 N/C-magnitude downward electric field.
qe = mg
1.6 X 10 ⁻¹⁹ E = 1.67 X 10 ⁻²⁷ X 9.81
E = 1.02 X 10⁻⁷N/C
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suppose a certain heat engine has an efficiency of 35% . a thermodynamic diagram showing a hot reservoir above, a cold reservoir below, and a closed system in between. a thick arrow indicates that heat flows into the system from the hot reservoir. thinner arrows indicate that the system does work and expels heat into the cold reservoir. in order for this heat engine to do 420 j of useful work, how much energy must be taken in as heat from the high-temperature reservoir?
Energy must be taken in as heat from the high-temperature reservoir is 1200 J.
What do you mean by thermodynamics?The science of thermodynamics examines how heat, work, temperature, and energy are related. The flow of energy from one location to another and from one form to another is broadly what thermodynamics is concerned with.
The efficiency of a heat engine is the ratio of the useful work done by the engine to the total heat energy taken in from the hot reservoir. In this case, the efficiency is 35%. Therefore, the useful work done by the engine is 35% of the total heat energy taken in from the hot reservoir.
If the heat engine does 420 J of useful work, we can use the efficiency formula to find the total heat energy taken in from the hot reservoir:
Total heat energy = (Useful work) / (Efficiency) = 420 J / 0.35 = 1200 J
So, in order for this heat engine to do 420 J of useful work, it must take in 1200 J of energy as heat from the high-temperature reservoir.
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what is fetch? multiple choice question. the distance from wave trough to wave crest the distance over water that the wind blows in the same direction a standard measure used for water depth
Fetch: A region of an ocean or lake's surface where wind blows in a direction that is basically continuous, producing waves.
How physically act waves?An energetic disturbance called a wave moves from one place to another. The only thing that changes when a wave moves is energy, not matter. The substance in which a wave passes is known as the medium. Until it lands in the same place, that medium frequently swings back and forth.
What are the three fundamental qualities of waves?But amplitude, wavelength, energy, and speed are characteristics that all waves share. How much a wave's medium moves is described by its amplitude. Wavelength and frequency both refer to the size and frequency of waves. A wave's speed is its rate of movement.
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In an adiabatic process, an ideal gas contracts to a volume that is 1/12
of its initial volume. The initial temperature is 340 K. What is the final temperature? Let y = 1. 67
In an adiabatic process,The initial temperature is 340 K then the final temperature: 95.2K
Adiabatic process :In an adiabatic process, an ideal gas follows the equation P[tex]V^{y}[/tex] = constant, where y is the ratio of the specific heat at constant pressure to the specific heat at constant volume.
Since the initial volume is V1 and the final volume is V2, we can write:
[tex]P_{1} V^{y}[/tex]₁ = P₁[tex]V^{y}[/tex]₂
As the process is adiabatic, no heat is exchanged with the environment, so the internal energy of the gas remains constant.
The internal energy of an ideal gas is , U = 3/2nRT where n is the number of moles, R is the gas constant and T is the temperature in kelvins.
So we can write:
3/2nRT₁ = 3/2nRT₂
As the process is adiabatic, the work done by the gas also remains constant. So the work done on the gas is equal to the work done by the gas.
P( V₂ - V₁) = - P( V₁ - V₂ )
So we can write:
P₁V₁ = P₂V₂
V₂ = V₁/ 12 P₁V₁ = P₂(V₁ /12) T₂
= 340 K × 1/12 ( 1.67 -1 )
= 340 K× ( 1/3.55)
= 95.2 K
Now, combining the above equations we can find the final temperature: 95.2K
What is an ideal gas?An ideal gas is a theoretical gas that is composed of a large number of atoms or molecules that are so small compared to the distance between them, that they do not interact with each other except during rare collisions. The properties of an ideal gas are defined by a set of assumptions that include: The gas is composed of a large number of identical particles (atoms or molecules) that have no volume and no interactions except for instantaneous, elastic collisions.
The gas is considered to be a perfect gas, meaning it follows the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvins.
The gas is considered to be a diatomic gas, meaning it follows the adiabatic index , y = 1.67
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a particle of mass m is located inside a uniform solid sphere of radius r and mass m, at a distance r from its center. (a) show that the gravitational potential energy of the system is (b) write an expression for the amount of work done by the gravitational force in bringing the particle from the surface of the sphere to its center.
The equation for the system's gravitational potential energy is U = − G * (m2 / R). and G * (m2 / R) is the amount of effort the gravitational force must do to move the particle from the sphere's surface to its centre.
(a) The formula U = - G * (Mm / r), where G is the gravitational constant, M is the mass of the sphere, and m is the mass of the particle, may be used to compute the gravitational potential energy of the system. Here, M = m U = - G * (m2 / R)
(b) The particle's initial potential energy when it is on the sphere's surface is Ui = - G * (m2 / R), and its final potential energy when it is in the sphere's centre is Uf = 0. Work completed equals Uf - Ui work completed equals 0 - (- G * (m2 / R)) work completed equals G * (m2 / R).
G * (m2 / R) represents the amount of effort the gravitational force must do to move a particle from the sphere's surface to its centre.
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A 140.0 g sample of water at 20.0 °c is mixed with 100.0 g of a certain metal at 95.0 °c. after thermal equilibrium was established, the temperature of the mixture is 24.6 °c. what is the specific heat capacity of the metal?
The specific heat capacity of the metal can be calculated using the equation: q = mCΔT, where q is the heat transfer, m is the mass of the metal, C is the specific heat capacity, and ΔT is the change in temperature. The heat transfer from the metal to the water can be determined as q = mCΔT = 100 g * C * (24.6 - 95.0) °C. The heat transfer from the water to the metal can be determined as q = mCΔT = 140.0 g * 4.184 J/g°C * (24.6 - 20.0) °C. The specific heat capacity can then be calculated as C = q / (mΔT).
How does the temperature change of the water and metal determine the specific heat capacity of the metal?The temperature change of the water and steel is used to determine the unique warmth capacity of the steel by means of calculating the warmth switch between the two materials. The warmth switch between the water and metal may be calculated using the equation: q = mcΔT, where q is the heat transfer, m is the mass of the substance, c is the precise heat capability, and ΔT is the trade in temperature. By means of the usage of this equation for each the water and metal, the heat switch among the 2 materials may be calculated and the specific heat potential of the steel can be determined.
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The specific heat capacity of the metal is 140 J/kg°C.
What do you mean by Metal?A metal is a chemical element that is typically characterized by its high electrical conductivity, thermal conductivity, and luster. It is usually a dense, malleable, and ductile material that is a good conductor of heat and electricity. Examples of metals include copper, silver, gold, iron, and aluminum.
The specific heat capacity of the metal can be calculated using the formula:
ΔQ = mCΔT
where ΔQ is the heat transferred, m is the mass of the metal, C is the specific heat capacity, and ΔT is the change in temperature.
First, find the heat transferred:
ΔQ = mCΔT = (140.0 g + 100.0 g)(24.6 °C - 20.0 °C) = 240.0 g * 4.6 °C = 1101.6 J
Next, find the heat absorbed by the metal:
ΔQ = mCΔT = 100.0 g * (24.6 °C - 95.0 °C) = -9700 J
Finally, solve for the specific heat capacity:
C = ΔQ / mΔT = -9700 J / 100.0 g * (24.6 °C - 95.0 °C) = -9700 J / 100.0 g * -75.4 °C = 140 J/kg°C
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An object whose mass is 3 kg is fired from a cannon, giving it a forward momentum
of 1050 kg-m/sec. What is its velocity?
The velocity of an object can be calculated using the equation:
velocity = momentum / mass
Given the mass of the object is 3 kg and the forward momentum is 1050 kg-m/sec, we can substitute these values into the equation:
velocity = 1050 kg-m/sec / 3 kg
velocity = 350 m/sec
Therefore, the velocity of the object is 350 m/sec.
How does the velocity of an object affect its momentum?The velocity of an object is directly proportional to its momentum. As the velocity of an object increases, so does its momentum. This relationship is described by the equation p = m * v, where p is the momentum, m is the mass of the object and v is its velocity. This equation shows that the momentum of an object is directly proportional to the velocity of the object. This means that if the velocity of an object is doubled, its momentum will also double. Conversely, if the velocity of an object is halved, its momentum will also be halved. Also, If the direction of motion of an object changes it also changes the direction of momentum but the magnitude of momentum will remain the same.
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An object whose mass is 3 kg is fired from a cannon, giving it a forward momentum has a velocity of 350 m/sec.
Evaluating :The velocity of an object can be calculated using the equation:
velocity = momentum / mass
Given the mass of the object is 3 kg and the forward momentum is 1050 kg-m/sec, we can substitute these values into the equation:
velocity = 1050 kg-m/sec / 3 kg
velocity = 350 m/sec
Therefore, the velocity of the object is 350 m/sec.
Momentum :The velocity of an object is directly proportional to its momentum. As the velocity of an object increases, so does its momentum. This relationship is described by the equation p = m * v, where p is the momentum, m is the mass of the object and v is its velocity. This equation shows that the momentum of an object is directly proportional to the velocity of the object. This means that if the velocity of an object is doubled, its momentum will also double.
Conversely, if the velocity of an object is halved, its momentum will also be halved. Also, If the direction of motion of an object changes it also changes the direction of momentum but the magnitude of momentum will remain the same.
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A ball is thrown straight up into the air, with an initial speed of 28.2 m/s.
How fast is it moving after 1.00 s?
a 2kg ball is dropped from a height of 3m. what is the velocity of the ball when it hits the ground?
The required velocity of the ball when it hits the ground is calculated to be 7.75 m/s.
Mass of the ball = 2 kg
A ball is dropped from a height = 3 m
Velocity = ?
Initial potential energy of the ball Ep = m g h = (2)(10)(3) = 60 J
As the ball reaches the ground, its potential energy becomes zero as it is entirely converted into its kinetic energy Ek.
So, Ek = 60 J
The formula for Ek is said to be 1/2 m v².
Ek = 1/2 m v²
Making v as subject, we have,
v = √(2 Ek/m) = √(2×60/2) = 7.75 m/s
Thus, the velocity of the ball when it hits the ground is 7.75 m/s.
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a ball is moving at 7.0 m/s and has a momentum of 100kg m/s what is the balls mass
Answer: 14,286 kg
Explanation:
Mass and velocity, have a positive correlation to momentum.
The formula to determine momentum is:
Momentum = Mass x Velocity
So, if we want to determine the mass of the object, the formula can be rearranged to look like this:
Momentum/Velocity = Mass
And can be solved by imputing the values given in the question:
Mass = (100 kg*m/s) ÷ (7 m/s)
Mass = 14,286 kg
the water is then released and passes through turbines to produce
The water released from the reservoir and passes through turbines to produce electricity.
What does the water do to the turbine?At the plant level, water flows through a pip also known as a penstock, and then spins the blades in a turbine, which, in turn, spins a generator that ultimately produces electricity.
What are water turbines called?Hydro turbines, it transform moving water's kinetic energy into mechanical energy, and this mechanical energy is converted into electricity using a hydropower generator. Hydropower turbines contain blades, which spin to produce electricity. Hydro turbines work on Faraday's principles.
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When a turbine's blades are turned by water, electricity is produced and sent to the power plant's users.
What occurs as water flows through the turbine? To generate energy, which is then delivered to the power plant's clients, the water can be used to turn a turbine's blades.The inner shaft of the turbine is then turned by water flowing across its blades.Once transferred to a generator, this rotational motion is used to produce energy.Turbines come in a wide variety of designs, each of which is ideally suited for a particular use.Water flow energy is transformed into mechanical energy by a hydraulic turbine.Using a hydropower generator, this mechanical energy is transformed into electricity.Potential energy, often referred to as kinetic energy, is converted to mechanical energy by a hydroelectric dam from a water reservoir behind the structure.To learn more about turbine's blades refer
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ball is thrown veritcally at this speed. how long until it reaches highest point? how long is in the air?
The ball takes 1.22s to reach the highest point. It remains in the air for 2.44 s when it is thrown vertically upwards.
Equations of motion define the behaviour of physical system in terms of the motion as a function of time.
At the topmost point, v = 0.
Gravitational acceleration is equal to a = -g = -9.8 m/s²
We know one of the equations of motion as, v = u + a t
where, v is final velocity
u is initial velocity
a is acceleration
t is time
Putting in the values in the above equation, we have,
0 = 12 -9.8 t
9.8 t = 12
t = 1.22 s
Thus, the ball reaches the highest point in 1.22 s.
To find out the time in which the ball remains in the air is can be calculated by, v² - u² = 2 a s
where, s is the distance
- 12² = 2 × (-9.8) s
19.6 s = 144
s = 7.34 m
The total time taken by the ball to reach the maximum height is 1.22 s and it takes another 1.22 s to reach the ground.
So, the ball remains in the air for 2.44 s.
The question is incomplete. The complete question is 'Ball is thrown vertically at this speed 12 m/s.'
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An automobile traveling initially at a speed of 60 m/s is accelerated uniformly to a speed of 85 m/s in 12 s. How far does the automobile travel during the 12 s interval?
Answer:
870 m
Explanation:
d = Vit + 1/2at²
a = ΔV/Δt = (85 m/s - 60 m/s) / (12 s) = (25 m/s) / 12 s = 2.08 m/s²
d = (60 m/s)(12 s) + 1/2 (2.08 m/s²)(12 s)² = 870 m
Answer:
The automobile traveled 870 meters during the 12 second interval.
Explanation:
We can use this kinematics equation to evaluate how far the automobile traveled.
[tex]\overline v=\frac{\Delta x}{\Delta t}[/tex]
Note
[tex]\overline v[/tex] is the average velocity
[tex]\Delta x[/tex] is the change in position (displacement)
[tex]\Delta t[/tex] is the change in time (time interval)
The formula for average velocity is
[tex]\overline v=\frac{V_f-V_o}{2}[/tex]
We are given
[tex]V_f=85\\V_o=60\\\Delta t=12[/tex]
First lets evaluate the average velocity.
[tex]\overline v=\frac{85-60}{2}[/tex]
[tex]\overline v=72.5[/tex]
Rearranging our kinematics equation to isolate [tex]\Delta x[/tex] we get
[tex]\Delta x=\overline v \Delta t[/tex]
Now lets evaluate [tex]\Delta x[/tex].
[tex]\Delta x=72.5*12\\\Delta x=870[/tex]
There are many different ways you can solve this; I could have used a different equation.
The globe is divided into time zones, so that any given hour of the day in one time zone occurs at a different time in other time zones. For example, New York City is in one time zone and Los Angeles is in another time zone. When it is 8:00 a.m. in New York City, it is only 5:00 a.m. in Los Angeles. Explain how Earth’s motions cause this difference in times.
Answer:
The rotation of the earth on its tilted axis is the reason behind the difference in the length of the day and night time in different parts of the earth throughout the year. The annual motion of the Earth is called revolution. Since the path of the Earth is elliptical, the interval between the Earth and the Sun keeps shifting.
Explanation:
calculate the wave- length of the x-rays that could be produced when these elec- trons strike a solid.
The wavelength of x-rays that could be produced when the electrons strike a solid is given by Bragg's equation. Mathematically, it is represented as, n λ = 2 d sinθ.
The X-angle ray's of incidence, and angle of scattering, are the same when it strikes a crystal surface. Additionally, constructive interference will happen when the path difference, d, is equal to a whole number of wavelengths, n.
As we require wavelength, let us make it as the subject in the above equation. Then we have, λ = 2 d sinθ/n
where,
d is the distance between atoms' planes
θ is the angle of scattering
n is the path difference
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a car makes a trip due north for three-fourths of the time and due south one-fourth of the time. the average northward velocity has a magnitude of 27 m/s, and the average southward velocity has a magnitude of 17 m/s. what is the average velocity (magnitude and direction) for the entire trip?
The magnitude of the average northward velocity is 27 m/s, while the magnitude of the average southbound velocity is 17 m/s. The total journey average speed is 20.25 m/s to the north.
We must determine the weighted average of the northward and southern velocities in order to get the average speed for the whole journey. We may apply the following formula since the automobile drives north for 3/4 of the time and south for 1/4 of the time:
average speed is (3/4) * (27 m/s) + (1/4) * (-17 m/s)
Since the southbound velocity is moving in the opposite direction of the northward velocity, it is given a negative sign.
Calculating the average velocity results in:
Average speed is equal to (3/4) times 27 m/s plus (1/4) times -17 m/s, or 20.25 m/s.
The total journey average speed is 20.25 m/s to the north.
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This states that charge cannot be created or destroyed. However, a charge can be transferred from one object to other
The conservation of charge states that charge cannot be created or destroyed, but can be transferred between objects.
How does the conservation of charge affect the behavior of electric circuits?
The conservation of charge states that charge cannot be created or destroyed, it can only be transferred from one object to another. This principle affects the behavior of electric circuits by ensuring that the total charge in a closed circuit remains constant. This means that the charge flowing into a circuit must equal the charge flowing out of the circuit. If there is an imbalance, the circuit will not function properly.
The conservation of charge also helps to explain the behavior of electric charges in different types of circuits, such as series and parallel circuits.
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(d) A 2.5 kg object is placed avocation X where it has 10 J of potential energy. A person bumps the shelf causing the object to fall to the ground, Describe the Law of Conservation of Energy and how it is demonstrated as the object falls to the ground.
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant.
As the object falls to the ground, its potential energy is converted into kinetic energy. The potential energy is determined by the object's mass and its height above the ground. As the object falls, its height decreases and its potential energy decreases, but this decrease in potential energy is compensated by an increase in kinetic energy. The kinetic energy is determined by the object's mass and its velocity. As the object's height decreases and its velocity increases, its kinetic energy increases.
As the object falls, the total amount of energy remains constant. The initial potential energy of 10 J is equal to the final kinetic energy of the object. This is an example of the Law of Conservation of Energy in action. The object's potential energy is transformed into kinetic energy, but the total amount of energy remains the same.
the rotating armature of an ac generator is connected to its external circuit through ? while a dc generator uses a(n) ? to make the connection.
With the help of slip rings, an AC generator connects the rotating armature to its external circuit.
A slip ring is an electronic device that permits the transfer of electrical currents and energy from a still structure to a spinning one. Any electrical device that needs to rotate while sending energy or currents can employ a slip ring.
A device that generates electrical energy from mechanical energy is an AC generator. Mechanical energy is provided by steam turbines, gas turbines, and combustion engines as the AC generator's input source. Alternating electrical power in the form of current and voltage is the output.
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Explain which movement Jamal should make (which car and which point), and why that movement will result in the largest increase in potential energy. Describe the magnetic force that will act on the vehicle he moves.
Because potential energy increases with separation distance, Jamal should move the toy car with the greatest separation distance.
What do you mean by potential energy ?The term potential energy is defined as stored energy that depends upon the relative position of various parts of a system. Potential energy is energy that cannot be transfer to kinetic energy. It has the capacity to do work but is not presently doing so.
Because magnetic force is inversely proportional to the separating distance between the cars, the magnetic force acting on the vehicles will decrease as he moves the cars away from each other.
Thus, potential energy increases with separation distance, Jamal should move the toy car with the greatest separation distance.
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The denity of water i 997 kg/m3. A wimming pool contain 375 m3 of water. What i the ma of thi water?
Explanation:
ρ = 997kg/m³
v = 375m³
ρ = m/v
m = ρv
m = 997×375
m = 373,875kg
The speed of an object undergoing constant acceleration increases from 8.0 meters per second to 16.0 meter per second in 10 seconds. How far does the object travel during the 10 seconds?
The distance traveled by object is 120 m in given time 10 seconds.
What is kinematic equation?If other information is known, a set of four equations called the kinematic equations can be used to predict unknown information about an object's motion.
The equations can be applied to any motion that can be classified as either a constant velocity motion (with an acceleration of 0 m/s/s) or a constant acceleration motion. They are never permitted to be used over any time frame in which the acceleration is changing.
Four variables are present in each of the kinematic equations. The fquations offer a useful method of predicting details about an object's motion.
The kinematic equation for distance is,
[tex]\boxed{\mathrm{ d = (v +v_0) \dfrac{t}{2} }}[/tex]
Where,
[tex]\mathrm{V_0}[/tex] - initial speed = 8 m/s
V - final speed = 16 m/s
t - time = 10 s
Put the values in formula,
[tex]{\mathbf{ {d = (16+9) \dfrac{10}{2} }}[/tex]
[tex]\mathbf{d=120m}[/tex]
Thus, The distance traveled by object is 120 m in given time 10 seconds.
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a ball is thrown upward. what is its time interval between the release of the ball and the time it reaches its maximum height?
The upward throw of a ball. The gravity acceleration is 9.8 m/s2, and its combination 1 speed is 10.8 m/s. So, 1.10 seconds pass between the ball's release and the moment it reaches its highest point.
What happens to the ball's speed when it is launched upward and returns to the spot from which it was hurled?Gravity's acceleration is constantly downward and constant, however the speed and direction of the acceleration vary. The speed of the ball is zero at its top portion in its trajectory, then it picks up speed again as it descends toward.
Why does an object being hurled upward have a zero final velocity?Because the acceleration caused by the gravitational force is operating constantly downward at the greatest point when a body was thrown vertically upwards, only that point's velocity is zero. As a result, the velocity is zero due to the acceleration.
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PART 1
The figure shows a claw hammer as it pulls a
nail out of a horizontal board. If a force of magnitude 124 N is exerted
horizontally as shown, find the force exerted
by the hammer claws on the nail. (Assume
that the force the hammer exerts on the nail
is parallel to the nail).
Answer in units of N.
PART 2
Find the force exerted by the surface on the
point of contact with the hammer head. Assume that the force the hammer exerts on the
nail is parallel to the nail.
Answer in units of N.
(1) The force exerted by the hammer claws on the nail is 67.54 N.
(2) The the force exerted by the surface on the point of contact with the hammer head is 124 N.
What is the force exerted by the hammer claws on the nail?
The force exerted by the hammer claws on the nail is calculated by applying the following formula.
Fy = W sinθ
where;
θ is the inclination of the claw on the headW is the force exertedFy = 124 N x sin ( 33 )
Fy = 67.54 N
The the force exerted by the surface on the point of contact with the hammer head is calculated as follows;
Fn = W sin (90)
Fn = 124 N
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You and your friend throw balloons filled with
water from the roof of a several story apartment house. You simply drop a balloon from
rest. A second balloon is thrown downward
by your friend 3.4 s later with an initial speed
of 66.64 m/s. They hit the ground simultaneously.
How high is the apartment house? The
acceleration of gravity is 9.8 m/s
2
. Neglect
air resistance.
Answer in units of m. Answer in units of
m.
The height of the apartment is 127.5 m.
What is the height of the apartment?
The height of the apartment is calculated by applying the following equation.
first equation for your throw; h = ¹/₂g(t +3.4)²
second equation for your friend's throw; h = vt + ¹/₂gt²
h = vt + ¹/₂gt²
h = 66.64t + ¹/₂gt²
now equate the two equations;
¹/₂g(t+3.4)² = 66.64t + ¹/₂gt²
¹/₂(9.8)(t² + 6.8t + 11.56) = 66.64t + ¹/₂(9.8)t²
4.9(t² + 6.8t + 11.56) = 66.64t + 4.9t²
4.9t² + 33.32t + 56.64 = 66.64t + 4.9t²
33.32t = 56.64
t = 1.7 seconds
The height of the apartment is calculated as;
h = ¹/₂g(t +3.4)²
h = ¹/₂(9.8)(1.7 +3.4)²
h = 127.5 m
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Three point charges are arranged along the x axis. Charge q1 = -4. 10 nC is located at x= 0. 250 mand charge q2 = 2. 20 nC is at x= -0. 320 m. A positive point charge q3 is located at the origin.
What must the value of q3 be for the net force on this point charge to have magnitude 3. 10 μN ? (ans in nC)
What is the direction of the net force on q3? + or - direction
Where along the x axis can q3 be placed and the net force on it be zero, other than the trivial answers of x=+[infinity] and x=−[infinity]? (ans in m)
q₃ is approximately -7.58 nC. The direction of the net force on 'q₃' is the negative '-' direction. For the net force on 'q₃' to be zero, 'q₃' can be placed at x = -0.079 m or x = -1.881 m
What is the direction of the net force on q3?q₃ is approximately -7.58 nC
The direction of the net force on 'q₃' is the negative '-' direction
For the net force on 'q₃' to be zero, 'q₃' can be placed at x = -0.079 m or x = -1.881 m
1) The force, 'F', between two charged spheres is given as follows;
F = K*q1*q2/r2
By substituting the given values, we have;
F NET = 14117n C *K /320
K = 9 × 10⁹ N·m²·C⁻²
q₃ ≈ -7.58 nC
= -7.58 nC
2) Given that the negative charge, 'q₁' (-4.10 nC), is located at x = 0.250 m, which is on the positive, '+' side of the origin, it will repel the negatively charged 'q₃', to the '-' direction. q₃ will also be attracted to the '-' direction by the positively charged 'q₂' which is at -0.320 m on the negative side of the origin
The net force's direction on q₃ will be in the '-' direction
3) For zero net force, we have;
= K* 2.20 n C /R 1 (2)
The distance between the given point charges, r = 0.250 - (-0.320)) = 0.57 m
Let 'r1' represent the distance between 'q1' and 'q3', therefore, the distance between 'q2' and 'q3' is 0.57 - r1
From which we have;
(r₁)²×4.10 = 2.20 × (0.57 - r₁)²
From the above equation, we have;
95,000·r₁²+ 125,400·r₁-35739 = 0
Solving, using a graphing calculator we get;
r₁ ≈ 0.241 or r₁ ≈ -1.561
Where, 'r₁', is measured from 'q₂', therefore, we have;
r₁ = 0.241 + (-0.320) ≈ -0.079 or r₁ = -1.561 + (-0.320) ≈ -1.881
Therefore, the charge 'q₃' can be placed at x = -0.079 or x = -1.881 for the ne force on it to be zero
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A figure skater begins spinning counter-
clockwise at an angular speed of 3.2 pi rad/s.
During a 4.6 s interval, she slowly pulls her
arms inward and finally spins at 7.7 pi rad/s.
What is her
average angular acceleration
during this time interval?
Answer in units of rad/s?.
The average angular acceleration of the figure skater during the time interval of 4.6 s is 0.99 rad/s².
Define the term Angular Acceleration?We may determine the body's angular acceleration using the second-order derivative from angular displacement. We can indicate the course of the applied net torque by looking at the path of angular acceleration.For this question:
A figure skater starts spinning counterclockwise at 3.2 pi rad/s of angle.She gently draws her arms inside over a 4.6 s gap, eventually spinning at 7.7 pi rad/s.Then,
angular acceleration = Change in angular velocity / time
α = ω2 - ω1 / t
α = 7.7 - 3.2 / 4.6
α = 4.5/4.6
α = 0.99 rad/s²
Thus, the average angular acceleration of the figure skater during the time interval of 4.6 s is 0.99 rad/s².
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A badger is trying to cross the street. Its velocity vvv as a function of time ttt is given in the graph below where rightwards is the positive velocity direction. A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,0) and (1,5). This first line is connected to a second line with endpoints (1,5) and (3,-5). This second line is then connected to a third line of endpoints (3,-5) and (6,-5). A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,0) and (1,5). This first line is connected to a second line with endpoints (1,5) and (3,-5). This second line is then connected to a third line of endpoints (3,-5) and (6,-5). What is the badger's displacement \Delta xΔxdelta, x from t=2\,\text st=2st, equals, 2, start text, s, end text to 3\,\text s3s3, start text, s, end text?
You are given a set of black coordinate axes with '(velocity) v (m/s)' on the vertical axis and 't (s)' on the horizontal axis.
What is velocity?Velocity defines the direction in which a body or object is moving. Velocity is primarily a scalar quantity. Velocity is basically a vector quantity. Rate of change of distance and Rate of change of displacement is called velocity. Speed corresponds to the speed and direction of travel indication (eg 60 km/h north). Velocity is generally defined as a vector value of the speed and the direction of motion. Simply put, velocity is the speed at which something moves in one direction. Both the speed of a car traveling north on a highway and the speed of a rocket launching into space can be measured by velocity.to learn more about velocity from the given link:
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You will get a set of black coordinate axes with "(velocity) v (m/s)" on the vertical axis and "t (s)" on the horizontal axis.
What is speed?
Speed is the direction in which a body or object is moving. Speed is primarily a scalar quantity. Speed is essentially a vector quantity. The rate of change of distance and the rate of change of displacement are called velocity. Speed corresponds to the specification of speed and direction of movement (e.g. 60 km/h to the north). Velocity is commonly defined as a vector value of velocity and direction of motion. Simply put, speed is how fast something is moving in one direction.
The speed of a car driving north on a freeway and the speed of a rocket launched into space can be measured by velocity.
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How high above the ground is a 10 kg boulder that has 2400 J of gravitational potential energy? use g = 10 m/s2 (Hint: PE = mgh which rearranges to h = PE/mg)
Answer: Therefore, the rock that has a mass of 10 kg and a gravitational energy of 2400 J must be at a height of 24 meters.
Explanation:
How high above the ground is a 10 kg boulder that has 2400 J of gravitational potential energy?
Data:
m = 10 kg
Epg = 1200 J
h = ?
g = 10 m/s²
The formula for gravitational potential energy is:
Epg = m * g * hWhere
Epg = Gravitational potential energym=massg = gravityh = heightWe must calculate the height, for which we clear the formula, then
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{Ep_g}{m*g} } \end{gathered}$}}[/tex]
We substitute data in the formula and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ J}{10 \ kg*10\frac{m}{s^2} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ J}{100 \ kg*\frac{m}{s^2} } } \end{gathered}$}}[/tex]
Before continuing to answer, we must work with the units of Joules, so
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ N*m}{100 \ kg*\frac{m}{s^2} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \not{kg}*\not{\frac{m}{s^2}} *m}{100 \not{kg}*\not{\frac{m}{s^2}} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ m}{100} } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h\cong24 \ m } \end{gathered}$}}}[/tex]
Therefore, the rock that has a mass of 10 kg and a gravitational energy of 2400 J must be at a height of 24 meters.
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Answer:
I do not know this one sorry