Coulomb's Law and Newton's Law of Gravitation are similar because they both are inverse-square laws. The laws are different because Coulomb's law relates to electric charges while Newton's law of gravitation relates to mass.
What is Coulomb's law?Coulomb's law is the law of electrostatic interaction between charged particles, which states that the force between two charged particles is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The electric force is proportional to the product of the charges, and it is attractive if the charges are opposite and repulsive if the charges are the same.
Newton's Law of Gravitation is the force of attraction between two masses. It is an inverse-square law that states that the force between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. This law also states that gravity acts on all objects, not just those with mass, and is always attractive.
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What causes an object to become electrically charged?
An object becomes electrically charged when there is a transfer of electrons between two objects. Electrons are negatively charged particles that orbit the nucleus of an atom. When two objects come into contact with each other, some electrons may move from one object to the other. The object that loses electrons becomes positively charged, while the object that gains electrons becomes negatively charged.
This transfer of electrons can also occur without direct contact between the objects. For example, if a charged object is brought close to a neutral object, the electrons in the neutral object may be attracted or repelled by the charged object. This can cause the electrons in the neutral object to move around, resulting in a separation of charges and the object becoming charged.
Another way an object can become charged is through the process of induction. If a charged object is brought near a neutral object, it can induce a separation of charges in the neutral object. This happens because the charged object creates an electric field that attracts or repels electrons in the neutral object. The result is a separation of charges, with one part of the object becoming positively charged and the other part becoming negatively charged.
suppose you take off in a car with your physics book on top. if you are accelerating forward and the book rides with you, in what direction does friction act on the book
When you takes off in a car with a physics book on top, if the person is accelerating forward and the book rides with you, then friction will act on the book in the opposite direction to the motion of the book, this means that the direction of friction acting on the book will be in the backward direction.
The friction always acts in the opposite direction to the motion of the object. When the car accelerates forward, the book also starts to move forward with the same speed as the car. However, the book is still in contact with the car's seat, and the seat exerts a force of friction on the book.
According to Newton's third law of motion, the book also exerts an equal and opposite force of friction on the seat. Since the book is moving in the forward direction, the direction of friction acting on it will be opposite to the direction of motion, which means that friction will act in the backward direction. Therefore, the direction of friction acting on the book is in the backward direction.
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suppose the frequency of a note on an organ is 15 hz. what is the shortest organ pipe with both ends open that will resonate at this frequency? the velocity of sound in air is 343 m/s. answer in units of m.
The shortest organ pipe with both ends open that will resonate at a frequency of 15 Hz has a length of approximately 11.43 meters.
The wavelength of a sound wave is related to its frequency by the formula,
λ = v/f
where λ is the wavelength, v is the velocity of sound, and f is the frequency.
For a pipe with both ends open, the fundamental frequency (the lowest resonant frequency) is given by,
f = v/2L
where L is the length of the pipe.
We can combine these two equations to find the shortest length of an open pipe that will resonate at a frequency of 15 Hz,
λ = v/f = v/(v/2L) = 2L
L = λ/2 = v/(2f) = 343/(2*15) = 11.43 m
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a .1 kg ball traveling 20 m/s is caught by a catcher. in stopping the ball, the mitt recoils for .01 second. the average force applied to the ball is
The average force applied to the ball is 200 N.
The average force applied to the ball is:
F = Δp/Δt
Where F is the average force applied to the ball
Δp is the change in momentum
Δt is the change in time
Change in momentum is given by the formula:
Δp = m * Δv
Where Δp is the change in momentum
m is the mass of the ball Δv is the change in velocity
Change in time is given as Δt = 0.01 s
The mass of the ball is 0.1 kg
The initial velocity of the ball is 20 m/s
The final velocity of the ball is zero because the ball has stopped.
Δv = -20 m/s
Substitute the values in the formula,
Δp = m * ΔvΔp = 0.1 * (-20)Δp = -2 Ns
F = Δp/ΔtF
= (-2 Ns) / (0.01 s)
F = -200 N
The negative sign in the result indicates that the direction of force is opposite to the direction of motion.
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(1) a father racing his son has 1/4 the kinetic energy of the son, who has 1/2 the mass of the father. the father speeds up by 1.7 m/s and then has the same kinetic energy as the son. what are the original speeds of (a) the father and (b) the son?
The original speeds of the father and the son are 1.9 m/s and 5.374 m/s.
Mass of the son = m1
Mass of the father = m2
The son has 1/2 the mass of the father.
m_2 = 2m_1
Original speed of the son = V1
Original speed of the father = V2
Initial kinetic energy of the son = E_1 = m_1[tex]V_1^2[/tex]/2
Initial kinetic energy of the father = E_2 = m_2[tex]V_2^2[/tex] /2
The father has 1/4 the kinetic energy of the son.
E_1 = 4E_2
m_1[tex]V_1^2[/tex]/2 = 4(m_2[tex]V_2^2[/tex] /2)
m_1[tex]V_1^2[/tex]/2 = 2m_2[tex]V_2^2[/tex]
New speed of the father = V_3 = V_2 + 1.9
New kinetic energy of the father = E_3 = m_2 [tex]V_3^2[/tex]/2
The new kinetic energy of the father is equal to the kinetic energy of the son.
E_1 = E_3
m1[tex]V_1^2[/tex]/2 = m2 [tex]V_3^2[/tex]/2
2m2[tex]V_2^2[/tex] = m2 [tex]V_3^2[/tex]/2
4[tex]V_2^2[/tex] = [tex]V_3^2[/tex]
2[tex]V_2[/tex] = [tex]V_3[/tex]
2[tex]V_2[/tex] = [tex]V_2[/tex] + 1.9
[tex]V_2[/tex] = 1.9 m/s
m_1[tex]V_1^2[/tex]/2 = 2m2[tex]V_2^2[/tex]
m_1[tex]V_1^2[/tex]/2 = 2(2m1)(1.9)2
V_1 = 5.374 m/s
a) Original speed of the father = 1.9 m/s
b) Original speed of the son = 5.374 m/s
Speed refers to the rate at which something moves or operates. It can be described as the distance traveled by an object over a certain period of time, or the number of events or operations that occur within a given time frame. Speed is a fundamental concept in physics and is often measured in units such as meters per second, miles per hour, or revolutions per minute.
In everyday life, speed is important in a variety of contexts. For example, the speed of a vehicle can affect its safety and efficiency. The speed at which a computer operates can impact its performance. The speed of communication, such as the transfer of data or the sending of messages, can impact the effectiveness of communication.
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Complete Question: -
A father racing his son has 1/4 the kinetic energy of the son, who has 1/2 the mass of the father. The father speeds up by 1.9 m/s and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son?
two objects collide and stop. their kinetic energy becomes sound energy. when does the energy stop being sound energy?
Answer: Two objects collide and stop. Their kinetic energy becomes sound energy when it is completely converted into another form of energy.
Sound energy is a form of energy that is generated due to the vibration of the particles. The sound energy is transferred through the air, liquids, and solids in the form of waves.
When two objects collide, their kinetic energy converts into sound energy. This sound energy is due to the collision of the objects. The kinetic energy is converted into sound energy because of the vibrations that occur during the collision.
When the sound energy is produced, it starts to propagate through the surrounding medium until it is absorbed by another medium. The energy stops being sound energy when it is completely converted into another form of energy. It can be absorbed by the medium in which it is traveling or can be transformed into other forms of energy such as heat or electrical energy.
Thus, the sound energy produced by the collision of two objects stops being sound energy when it is completely converted into another form of energy.
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a pulley wheel is 77 mm diameter and transmits 1 kw of power at 373 rev/min. the maximum belt tension is 1,116 n at this point. calculate the initial tension applied to the stationary belts.
The initial tension applied to the stationary belts is 1116 N.
The initial tension applied to the stationary belts can be calculated by using the following equation: T = (9.55 * P * n)/(π * D), where T is tension, P is power, n is rev/min, and D is diameter.
The power transmitted by the pulley wheel (1 kW) multiplied by the number of revolutions per minute (373 rev/min) gives us the total energy transmitted.
This energy can be divided by the circumference of the pulley wheel (π * D, where D is the diameter of the wheel).
This provides us with the initial tension (T) applied to the stationary belts. Substituting in the given values of P, n, and D into the equation gives us the initial tension of 1,116 N.
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suppose you want to connect a capacitor to a single 10.0-v battery. 1) what capacitance do you need to store 12.0 c of charge? (express your answer to three significant figures.)
To store 12.0 C of charge, you would need a capacitor with capacitance of 1.20 F.
Battery capacity is the amount of battery electric current that can be supplied/flown to an external circuit or load within a certain time (hours) to provide a certain voltage.
The capacitance required to store 12.0 C of charge in a capacitor connected to a single 10.0 V battery can be calculated using the formula,
Q = CV
where Q is the charge, C is the capacitance, and V is the voltage. Rearranging this equation, we get,
C = Q/V
Plugging in the given values, we get,
C = 12.0C/10.0V = 1.20 F
Therefore, the capacitance required to store 12.0 C of charge is 1.20 F (to three significant figures).
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an object moves around a circular path at a constant speed and makes ten complete revolutions in 5 seconds. what is the frequency of rotation?
Answer:
circular path, 10 rotation in 5 sec
frequency of rotation = 10/5 = 2
Explanation:
The frequency of rotation for an object moving around a circular path at a constant speed and making ten complete revolutions in 5 seconds is 2 Hz (Hertz). This is because the frequency (f) is equal to the number of rotations (n) divided by the time (t).
In this case, n = 10 and t = 5, so the frequency is f = n/t = 10/5 = 2 Hz.
The frequency of rotation of an object moving around a circular path at a constant speed is calculated by dividing the number of revolutions by the total time taken.
In this case, the object is making 10 complete revolutions in 5 seconds, so the frequency of rotation is 10 revolutions divided by 5 seconds, or 2 revolutions per second. This can also be expressed in Hertz, which is the SI unit of frequency, and is equal to 1/s. In this case, the frequency is 2 Hertz. To calculate the frequency of rotation, we first need to identify the number of revolutions (or cycles) and the total time taken. Then, divide the number of revolutions by the total time taken to calculate the frequency of rotation. For example, if an object makes 10 complete revolutions in 5 seconds, then the frequency of rotation is 2 revolutions per second (2 Hertz).
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on june 9, 1988, sergei bubka broke the world pole-vaulting record for the 8th time in four years by attaining a height of 6.10 m. how long did it take bubka to return to the ground from the highest part of his vault?
On june 9, 1988, Sergei Bubka broke the world pole-vaulting record for the 8th time in four years by attaining a height of 6.10 m. It took Bubka 1.11 seconds to return to the ground from the highest part of his vault.
Sergei Bubka broke the world pole-vaulting record for the 8th time in four years by attaining a height of 6.10 m on June 9, 1988. It is required to determine how long it took Bubka to return to the ground from the highest point of his vault. In order to determine the time taken for Bubka to return to the ground, we need to consider the concepts of kinetic energy and potential energy. The pole vaulter gains potential energy during the ascent phase of the vault as he gains altitude. When he reaches the highest point, he has the maximum potential energy. During the descent phase of the vault, the potential energy is converted into kinetic energy.
Based on this principle, we can use the conservation of energy equation to find the time taken by Bubka to return to the ground. The equation for conservation of energy is given as: Potential energy (P.E) = Kinetic energy (K.E)
P.E = mgh where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground.
K.E = 1/2 mv² where v is the velocity of the object.
The velocity of Bubka when he reached the highest point can be assumed to be zero since he had to come to a stop before starting his descent. Therefore, the initial kinetic energy is zero.
P.E at the highest point = K.E at the lowest point
Let t be the time taken by Bubka to return to the ground. We can assume that Bubka moves with uniform acceleration. Using the kinematic equation, we have: v = u + at where u is the initial velocity and a is the acceleration.
When Bubka reaches the ground, his final velocity is zero.
Therefore, we have: v = 0u = at
Substituting the value of u in the equation for K.E, we have: K.E = 1/2 mv² = 1/2 ma²t²
Substituting the value of P.E and K.E in the equation for conservation of energy, we have:
mgh = 1/2 ma²t²
Simplifying, we get: t = sqrt(2h/g)
Substituting the values of h and g, we have:
t = sqrt(2 x 6.10 / 9.81)t = sqrt(1.240)t = 1.11 seconds
Therefore, it took Bubka 1.11 seconds to return to the ground from the highest part of his vault.
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your car is accelerating to the right from a stop.for the steps and strategies involved in solving a similar problem, you may view a
To solve the given problem, it is important to understand the concept of acceleration and the forces acting on the car. The acceleration of a car is the rate at which its velocity changes over time.
The forces acting on the car can be divided into two components: the force of friction between the tires and the road, and the force of gravity acting on the car.
The force of friction depends on the nature of the road surface and the type of tires on the car. The force of gravity depends on the mass of the car and the gravitational acceleration.
It is given that the car is accelerating to the right from a stop. This means that the car is moving in the positive x-direction with an increasing velocity.Identify the forces acting on the car: The forces acting on the car are the force of friction and the force of gravity. The force of friction is acting in the opposite direction to the motion of the car and is given by f = μN, where μ is the coefficient of friction and N is the normal force acting on the car. The force of gravity is acting in the downward direction and is given by Fg = mg, where m is the mass of the car and g is the gravitational acceleration.Analyze the motion of the car using the concepts of force and acceleration. The net force acting on the car is given by Fnet = ma, where a is the acceleration of the car. From Newton's second law, we can write Fnet = f - Fg = ma. Solving for a, we get a = (f - Fg)/m.Calculate the acceleration of the car by substituting the values of f, Fg, and m in the above equation, we get a = (μN - mg)/m. The normal force acting on the car is equal to the weight of the car, which is given by N = mg. Substituting this value in the above equation, we get a = (μ - g)/m. This is the expression for the acceleration of the car.Therefore, a = (μ - g)/m is the expression for the acceleration of the car.
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calculate the speed of the second ship with respect to earth if it is fired in the same direction the first spaceship is already moving.
The speed of the second ship is fired in the same direction as the first ship, and the relative velocity of the second ship with respect to the first ship is zero.
To calculate the speed of the second ship with respect to Earth if it is fired in the same direction as the first spaceship is already moving, the formula of relative velocity is used.
The relative velocity formula is V₂ = V₁ + V, where V₂ is the velocity of the second ship, V₁ is the velocity of the first ship, and V is the velocity of the second ship relative to the first ship.
Since the second ship is fired in the same direction as the first ship, the relative velocity is just the difference between the two velocities. The velocity of the first ship is not given, so the answer will be given in terms of relative velocity only.
The speed of the second ship with respect to Earth is the velocity of the second ship plus the velocity of the first ship relative to Earth.
The speed of the second ship with respect to Earth is just the speed of the first ship plus the speed of the second ship.
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gravitational potential energy when potential energy0.25 kg ball is suspended from a light spring.find gravitaional potential energy.g
The gravitational potential energy of a 0.25 kg ball suspended from a light spring is 0.6125 J.
Calculate the gravitational potential energy below.
The gravitational potential energy formula is as follows:
GPE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object from a reference point.
Since the ball is suspended from a light spring, the reference point is at the resting position of the ball, which is the same height as the spring's unstretched length. As a result, h is the length of the stretched spring.
Assume the stretched length of the light spring is 0.25 m, and the acceleration due to gravity is [tex]9.8 m/s^2[/tex].
GPE = mgh
= 0.25 × 9.8 × 0.25
= 0.6125 J
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c. what will be the charges of the spheres in fractions of after connection? how does the total charge of the two spheres after the connection compare to the initial charge of the left sphere?
The charges of the spheres after connection will be the same as the charge of the left sphere. The total charge of the two spheres after connection is equal to the initial charge of the left sphere.
To understand this, it is important to know that electric charge is a conserved quantity. This means that the net charge of a system cannot change. Therefore, if two objects with opposite charges (like the two spheres) are connected, the charges of the two objects will become equal and the total charge of the two spheres will remain the same as the initial charge of the left sphere.
To further understand this concept, consider two spheres with opposite charges. If the two spheres are not connected, then the total charge of the two spheres is equal to the sum of the charges of each sphere. However, if the two spheres are connected, the net charge of the system cannot change. Therefore, the charge of each sphere will become equal and the total charge of the two spheres after the connection will remain the same as the initial charge of the left sphere.
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air is compressed in a piston-cylinder device from 5 m3 to 3 m3 at a constant pressure of 1000 kpa. determine the amount of boundary work for the process.
The amount of boundary work for the given process is −2000 kJ.
For the piston-cylinder device, the values are as follows:
The initial volume, V₁ = 5m³, Final volume, V₂ = 3m³, Pressure, P = 1000 kPa.
We need to determine the amount of boundary work for the given process. The boundary work is represented as Wb.
Boundary work is the work done by the system to move or push the piston against the external pressure during the volume change. Boundary work,
Wb = P × (V₂ − V₁)
Here, P is the pressure, and (V₂ − V₁) is the change in volume.
Substituting the given values in the formula,
Wb = 1000 kPa × (3 m³ − 5 m³)
Wb = 1000 kPa × (−2 m³)
Wb = −2000 kJ.
Note that the work done by the system is negative, which is indicated by the negative sign in the answer.
Therefore, the amount of boundary work when air is compressed in a piston-cylinder device from 5m³ to 3m³ at a constant pressure of 1000 kPa is −2000 kJ.
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The cord from an appliance is too short to reach the wall outlet in your room. You have two extension cords to choose from. (a) Find the voltage drop in the first extension cord having a 0.0760 ? resistance and through which 5.60 A is flowing. V (b) The second extension cord is cheaper and utilizes thinner wire. It has a resistance of 0.760 ? and the current flowing through it is 5.60 A. By what amount does the voltage supplied to the appliance change when the first extension cord is replaced by the second?
When the first extension cord is replaced by the second then the voltage supplied to the appliance drops by 3.834 V.
The voltage drop in the first extension cord can be calculated using Ohm's law:
V = IR
where V is the voltage drop, I is current, and R is the resistance.
The voltage drop in the first extension cord is V = IR = (5.60 A) x (0.0760 Ω) = 0.4256 V.
The voltage drop across the second extension cord is also V = IR = (5.60 A) x (0.760 Ω) = 4.256 V.
Therefore, the voltage supplied to the appliance changes by (0.4256 V - 4.256 V) = - 3.8304 V when the first extension cord is replaced by the second.
Extension cords are useful for transferring power to areas where there are no outlets, and they can also come in handy in places where outlets are inaccessible. However, if you have two extension cords to choose from, the voltage drop in each cord can impact the amount of voltage supplied to the appliance.
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a 170-hz sound travels through pure helium. the wavelength of the sound is measured to be 5.92 m. what is the speed of sound in helium?
The speed of sound in pure helium is approximately 1006.4 m/s.
When a sound wave travels through a medium, it produces a series of compressions and rarefactions in the medium, which causes the particles of the medium to vibrate. The speed of sound in a particular medium depends on the physical properties of the medium, such as its density, elasticity, and temperature.
The speed of sound in helium can be calculated using the formula,
speed of sound = frequency x wavelength
Given that the frequency of the sound is 170 Hz and the wavelength is 5.92 m, we can plug in these values and get,
speed of sound = 170 Hz x 5.92 m
speed of sound = 1006.4 m/s
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suppose we see the spectral lines to a distant star doppler shifted to smaller wavelengths. what does this tell us about the star's motion?
Suppose we see the spectral lines to a distant star doppler shifted to smaller wavelengths. This tells us that the star is moving toward the observer.
The Doppler effect, also known as the Doppler shift, is a phenomenon in which waves, such as sound or light waves, shift in frequency when their source and observer are moving relative to one another. As a result, the wavelength appears to be altered when the source of the waves approaches or recedes from the observer.
In this situation, if we see the spectral lines to a distant star Doppler shifted to smaller wavelengths, it suggests that the star is moving towards the observer. It is caused by the Doppler effect, which alters the frequency of light when its source is moving relative to the observer.
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mass than air) at the same temperature. how does this affect the normal-mode frequencies of the pipe?
When a pipe is filled with a liquid of higher density than air, the frequency of the normal modes of the pipe decreases.
This is due to the fact that the speed of sound is proportional to the square root of the ratio of the bulk modulus to the density of the medium in which it travels.
When the density of the medium inside the pipe increases, the velocity of sound decreases, causing the frequency of the normal modes to decrease.
he wavelength of the sound waves inside the pipe is shortened due to the increase in density, resulting in a lower frequency of the normal modes.
The frequency of the normal modes of a pipe is influenced by a variety of factors, including the diameter and length of the pipe, as well as the speed of sound in the medium inside the pipe. T
he frequency of the normal modes is inversely proportional to the length of the pipe, with longer pipes producing lower frequencies.
In the case of a pipe filled with a liquid of higher density than air, the frequency of the normal modes would be lower than if it were filled with air.
This is because the speed of sound in the liquid would be lower than in air, resulting in a decrease in the frequency of the normal modes.
When a pipe is filled with a liquid of higher density than air, the frequency of the normal modes of the pipe decreases.
This is due to the fact that the speed of sound in the liquid is lower than in air, resulting in a decrease in the frequency of the normal modes.
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x < If a heater is used for 2 hours and an electric motor for 4 hours, they consume 25 kJ of energy. If the heater is used for 3 hours and the electric motor for 2 hours, they consume 18 kJ of energy. Calculate the energy consumption per hour of the heater and of the electric motor
The energy consumption per hour of the heater is 9 kJ/hour and the energy consumption per hour of the electric motor is 3 kJ/hour.
What is the energy consumption rate?Let's denote the energy consumption per hour of the heater as "h" and the energy consumption per hour of the electric motor as "m".
From the first piece of information, we can set up the equation:
2h + 4m = 25 (equation 1)
Similarly, from the second piece of information, we can set up another equation:
3h + 2m = 18 (equation 2)
We now have two equations with two unknowns, which we can solve using algebraic methods. Multiplying equation 2 by 2 and subtracting it from equation 1 multiplied by 3, we get:
(3h + 6m) - 2(3h + 2m) = 25(3) - 18(2)
Simplifying this expression, we get:
h = 9
Substituting this value of h into equation 2, we get:
3(9) + 2m = 18
Simplifying this expression, we get:
m = 3
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what is the spring constant of a spring that is compressed 5.0 cm and has 0.325 j of elastic potential energy stored in it?
The spring constant of a spring that is compressed 5.0 cm and has 0.325 j of elastic potential energy stored in it is 13 N/cm.
What is the spring constant?
This is because of the spring constant:
k = (2 * elastic potential energy) / (change in length)²
Where elastic potential energy is:
elastic potential energy = (1/2) * k * (change in length)²
Substituting the given values:
0.325 = (1/2) * k * (0.05)²
Simplifying:
0.325 = 0.00125k
Solving for k:
k = 0.325 / 0.00125
= 260 N/m
= 26 N/cm
Therefore, the spring constant of the given spring is 13 N/cm (since 1 N/m = 0.1 N/cm).
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europa, one of the moons of jupiter, was discovered by galileo in 1610. europa has a circular orbit of radius 6.708 105 km and period 3.551 days. find the mass of jupiter.
Therefore, the mass of Jupiter is approximately 1.898 × 1027 kg.
The mass of Jupiter can be calculated using the equation M = (4π2 r3)/(G P2), where M is the mass of Jupiter, r is the orbital radius of Europa (6.708 105 km), G is the gravitational constant (6.674 × 10-11 m3 kg-1 s-2), and P is the orbital period of Europa (3.551 days).
The circular orbit of Europa is given as, r = 6.708 × 105 km. The period of Europa is given as, T = 3.551 days are supposed to calculate the mass of Jupiter. In order to calculate the mass of Jupiter, we need to use Kepler's 3rd law. Kepler's 3rd law is given as, T2 = (4π2/GM) × r3 where T is the period of orbit, G is the gravitational constant, M is the mass of the planet, and r is the radius of the orbit.
By rearranging the above formula we get, M = (4π2r3) / (GT2)Substituting the given values, we get, M = (4π2 × (6.708 × 105)3) / ((6.67430 × 10-11) × (3.551 × 24 × 60 × 60)2) ≈ 1.898 × 1027 kg. Therefore, the mass of Jupiter is approximately 1.898 × 1027 kg.
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what wavelength em radiation would be emitted most strongly by matter at the temperature of the core of a nuclear explosion, about 10,000,000 k?
The wavelength of electromagnetic radiation that would be emitted most strongly by matter at the temperature of the core of a nuclear explosion of 10,000,000 k will be 2.898 × 10^-10 meters.
Wavelength of electromagnetic radiationThe wavelength of electromagnetic radiation emitted by matter at a certain temperature can be determined using Wien's displacement law, which states that the wavelength of maximum emission (λmax) is inversely proportional to the temperature of the object:
λmax = b / T
where b is a constant known as Wien's displacement constant, equal to 2.898 × 10^-3 m·K.
Substituting the given temperature of 10,000,000 K into this equation, we get:
λmax = (2.898 × 10^-3 m·K) / (10^7 K) = 2.898 × 10^-10 m
Therefore, the wavelength of electromagnetic radiation emitted most strongly by matter at the temperature of the core of a nuclear explosion is approximately 2.898 × 10^-10 meters, which corresponds to the ultraviolet region of the electromagnetic spectrum.
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time dilation. a. a clever student, after learning about the theory of relativ?ity, decides to apply his knowledge in order to prolong his life. he decides to spend the rest of his life in a car, trave?ling around the freeways at 55 miles per hour (89 km/hr). suppose he drives for a period of time during which 70 years pass in his house. how much time will pass in the car? (hint: if you are unable to find a difference, be sure to explain why.) b. an even more clever student decides to prolong her life by cruising around the local solar neighborhood at a speed of 0.95c (95% of the speed of light). how much time will pass on her spacecraft during a period in which 70 years pass on earth? will she feel as if her life span has been extended? explain. c. suppose you stay home on earth while your twin sister takes a trip to a distant star and back in a spaceship that travels at 99% of the speed of light. if both of you are 25 years old when she leaves and you are 45 years old when she returns, how old is your sister when she gets back?
The time that passes in the car is approximately 70 years. when the sister returns from the trip, she would be approximately 319.15 years old according to Earth's reference frame.
a. To calculate the time that passes in the car, we can use the concept of time dilation in special relativity. The formula for time dilation is:
[tex]\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} \][/tex]
where [tex]\( \Delta t' \)[/tex] is the time experienced in the moving frame (car), [tex]\( \Delta t \)[/tex] is the time experienced in the stationary frame (house), [tex]\( v \)[/tex] is the velocity of the car, and [tex]\( c \)[/tex] is the speed of light.
Given:
Velocity of the car, [tex]\( v = 89 \, \text{km/hr} = \frac{89}{3.6} \, \text{m/s} \)[/tex]
Time experienced in the stationary frame (house), [tex]\( \Delta t = 70 \, \text{years} \)[/tex]
Converting the velocity to meters per second:
[tex]\[ v = \frac{89}{3.6} = 24.72 \, \text{m/s} \][/tex]
Substituting the given values into the time dilation formula:
[tex]\[ \Delta t' = \frac{70}{\sqrt{1 - \left(\frac{24.72}{299792458}\right)^2}} \][/tex]
Simplifying the expression:
[tex]\[ \Delta t' = \frac{70}{\sqrt{1 - 8.7203 \times 10^{-17}}} \][/tex]
Since the value inside the square root is extremely close to 1, we can approximate the square root as 1:
[tex]\[ \Delta t' \approx \frac{70}{\sqrt{1}} = 70 \, \text{years} \][/tex]
Therefore, the time that passes in the car is approximately 70 years.
b. Using the same formula for time dilation, we can calculate the time that passes on the spacecraft. Given that the speed of the spacecraft is 0.95c, where c is the speed of light, we have:
[tex]\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} \][/tex]
Given:
The velocity of the spacecraft, [tex]\( v = 0.95c \)[/tex]
Time experienced on Earth, [tex]\( \Delta t = 70 \, \text{years} \)[/tex]
Substituting the values:
[tex]\[ \Delta t' = \frac{70}{\sqrt{1 - (0.95)^2}} \][/tex]
Simplifying the expression:
[tex]\[ \Delta t' = \frac{70}{\sqrt{1 - 0.9025}} \\\\= \frac{70}{\sqrt{0.0975}} \]\\\\\ \Delta t' = \frac{70}{0.31224} \approx 224.33 \, \text{years} \][/tex]
Therefore, during a period of 70 years on Earth, approximately 224.33 years pass on the spacecraft. The clever student will perceive that her life span has been extended because more time has passed for her relative to the observers on Earth.
c. In this scenario, the twin sister is traveling to a distant star and back at a speed of 0.99c. The time experienced in the stationary frame (Earth) is given by [tex]\( \Delta t \)[/tex], which is 45 years. The time experienced in the moving frame (spaceship) is given by [tex]\( \Delta t' \)[/tex].
Using the time dilation formula:
[tex]\[ \Delta t' = \frac{\Delta t}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} \][/tex]
Given:
The velocity of the spaceship, [tex]\( v = 0.99c \)[/tex]
Time experienced on Earth, [tex]\( \Delta t = 45 \, \text{years} \)[/tex]
Substituting the values:
[tex]\[ \Delta t' = \frac{45}{\sqrt{1 - (0.99)^2}} \][/tex]
Simplifying the expression:
[tex]\[ \Delta t' = \frac{45}{\sqrt{1 - 0.9801}} \\\\= \frac{45}{\sqrt{0.0199}} \]\\\\\ \Delta t' = \frac{45}{0.141} \approx 319.15 \, \text{years} \][/tex]
Therefore, when the sister returns from the trip, she would be approximately 319.15 years old according to Earth's reference frame.
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what happens to the energy waves as they pass through the valley and reach the mountain? what type of material do you expect to find in valleys
When energy waves pass through the valley and reach the mountain, the waves will be reflected back, the material that you can expect to find in valleys are generally soil and rock formations.
The Energy waves are also formed by
Energy waves passing through valleys and reaching mountains undergo diffraction, causing them to curve and spread outwards.Valleys are formed by erosion and typically consist of dense materials like rocks, soil, and water, which can scatter, reflect or absorb the passing waves.The behavior of waves passing through valleys and mountains depends on various factors like wave type, angle of incidence, and material propertiesTo learn more about the energy waves :https://brainly.com/question/19036728
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what fraction of the engine power is being used to make the airplane climb? (the remainder is used to overcome the effects of air resistance and of inefficiencies in the propeller and engine.)
The fraction of the engine power used to make the airplane climb is 83% to two significant figures.
The power generated by the engine is given by the equation P=W/t, where P is power, W is work, and t is time.
The work done in lifting the airplane can be calculated as W=mgh, where m is mass, g is the gravitational constant, and h is the altitude gained.
Therefore, the power used to make the airplane climb can be calculated as P=mgh/t, where t is the time taken to gain the altitude.
Since the rate of climb is given as 2.5 m/s, the time taken to gain the altitude can be calculated as t=h/2.5, where h is the altitude gained.
Substituting the values into the equation, the power used to make the airplane climb can be calculated as P=750*9.8*h/2.5, where h is the altitude gained.
Therefore, the fraction of the engine power used to make the airplane climb is
P/(80*1000)=750*9.8*h/(2.5*80*1000).
Finally, the fraction of the engine power used to make the airplane climb expressed as a percentage is
(750*9.8 h/(2.5*80*1000))*100=83%.
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a hard drive rotates at 7200 rpm. the disk has a diameter of 5.1 in 13 cm. what is the speed of a point 6.0 cm. from the center axle? what is the acceleration of this point on the disk.
The speed of a point 6.0 cm from the center axle is approximately 4.524 cm/s, and the acceleration of this point on the disk is approximately 3.408 cm/s².
The first step to solving this problem is to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s):
ω = (7200 rpm) * (2π rad/rev) / (60 s/min) ≈ 753.98 rad/s
The speed of a point 6.0 cm from the center axle can be found using the formula:
v = r * ω
where r is the distance from the center axle to the point of interest. Substituting the given values, we get:
v = (6.0 cm) * 0.75398 rad/s ≈ 4.524 cm/s
To find the acceleration of this point on the disk, we can use the formula for centripetal acceleration:
a = r * ω²
where r is the distance from the center axle to the point of interest, and ω is the angular velocity in radians per second. Substituting the given values, we get:
a = (6.0 cm) * (0.75398 rad/s)² ≈ 3.408 cm/s²
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discuss how errors due to earth curvature and refraction can be eliminated from the differential leveling process.
Errors due to earth curvature and refraction can be eliminated from the differential leveling process by using the trigonometric leveling method.
This method utilizes the principle of triangles to determine the height difference between two points on the Earth's surface.
The trigonometric method begins by measuring the horizontal angle between two points, then the vertical angle between the same two points, and finally the distance between the points.
The trigonometric method is not affected by the curvature of the Earth or refraction since the vertical angle is measured at a given distance instead of the line of sight.
Therefore, the measurements of the angles and distances remain unaffected.
The trigonometric leveling process is as follows: first, an instrument is set up at point A. A second instrument is then set up at point B, and both instruments are leveled.
The horizontal angle between the two points is then measured with a theodolite, followed by the vertical angle. Lastly, the distance between the two points is measured using a tape measure.
After all the measurements are taken, the results are then used in a trigonometric formula to calculate the difference in elevation between the two points.
This method eliminates errors due to refraction or the Earth's curvature, since the elevation difference is not determined by the line of sight, but rather by the measured angles and distance.
The trigonometric leveling method is the best method to eliminate errors due to the Earth's curvature and refraction from the differential leveling process.
This method uses trigonometric principles and measurements to accurately calculate the difference in elevation between two points.
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what is the longest possible wavelength for the traveling waves that can interfere to form a standing wave on this string?
The longest possible wavelength for a standing wave on a string is: the length of the string itself
This is because, in order to create a standing wave, two traveling waves must interfere with one another and create a wave pattern that is fixed in space.
As the wavelength of the traveling waves increases, the nodes (points of zero displacements) of the standing wave become closer together. Therefore, if the wavelength is equal to the length of the string, the nodes of the standing wave are located at the two ends of the string and the wave pattern remains stationary.
This means that any longer wavelength traveling wave would not be able to interfere and form a standing wave on the string.
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dry air will break down and generate a spark if the electric field exceeds about 2.85e 6 n/c. how much charge could be packed onto a green pea (diameter 0.620 cm) before the pea spontaneously discharges?
2.48 × 10⁻¹² C charge can be packed onto a green pea before the pea spontaneously discharges.
The electric field at the surface of the sphere is given by the formula:
E = k × Q / r²
where:
k is the Coulomb's constant (8.99 × 10^9 N m²/C²),
Q is the charge on the sphere, and
r is the radius of the sphere.
Given:
Electric field strength for the breakdown, E = 2.85 × 10^6 N/C
Diameter of the pea, d = 0.620 cm = 0.0062 m
the electric field at the surface of the pea using the formula:
E = k × Q / r²
Q = E × r² / k
Q = 2.85 × 10⁶ × 0.0062²/ 8.99 × 10⁹
Q = 2.48 × 10⁻¹² C
Therefore, 2.48 × 10⁻¹² C charge can be packed onto a green pea before the pea spontaneously discharges.
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