The point between Earth and the moon where a space probe will experience no net force would be 384,400 km from Earth.
The point between Earth and the moon where a 50,000 kg space probe experience no net force is called the Lagrangian point. The fifth Lagrangian point (L5) is located about 60 degrees behind the moon, about 384,400 km from Earth. Therefore, the distance between the probe and the Earth is 384,400 km, which is the average distance between the Moon and Earth.
The Lagrangian point is a point in space where the gravitational forces of two major celestial bodies (such as Earth and the moon) or more celestial bodies balance the gravitational forces, allowing a third smaller body to remain in constant position relative to the larger bodies.
L5, the fifth Lagrangian point, is a Lagrangian point in the Earth-Moon system, located about 60 degrees behind the Moon. It is approximately 384,400 km away from Earth, the same as the average distance between Earth and the Moon. It is one of the stable equilibrium points of the Earth-Moon system, as the gravitational forces of the Earth and the Moon balance the centrifugal force acting on a spacecraft at this point.
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what would its landing speed have been in the absence of air resistance? express your answer using two significant figures.
The landing speed of the ball in the absence of air resistance would be 14 m/s.
The landing speed of an object in the absence of air resistance can be calculated by considering the conservation of energy.
The initial energy of the object will be equal to the final energy of the object when it reaches the ground.
A ball falling from a height h with an initial velocity u.
The gravitational potential energy of the ball is given by mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball.
The kinetic energy of the ball is given by 1/2 mu², where u is the initial velocity of the ball.
At the ground level, the gravitational potential energy of the ball will be zero, and the kinetic energy of the ball will be given by 1/2 mv², where v is the velocity of the ball when it reaches the ground.
mgh + 1/2 mu² = 1/2 mv²
Solving for v, we get:
v = sqrt(2gh + u²)
In the absence of air resistance, the ball will continue to fall with an acceleration of g. Therefore, we can assume that the initial velocity u is equal to zero. Thus, the equation reduces to:
v = sqrt(2gh)
g = 9.8 m/s², we can calculate the landing speed of the ball for a given height h. For example, if the ball is dropped from a height of 10 meters, then the landing speed of the ball will be:
v = sqrt(2gh) = sqrt(2*9.8*10) = 14 m/s
Therefore, the landing speed of the ball in the absence of air resistance would be 14 m/s.
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a 4.0 kg body has two times the kinetic energy of an 8.5 kg body. calculate the ratio of the speeds of these bodies.
The ratio of the speeds of these bodies is 2.06
The kinetic energy of an object is equal to 1/2mv^2.
For the 4.0 kg body, the kinetic energy is 1/2 (4.0 kg)v^2
For the 8.5 kg body, the kinetic energy is 1/2 (8.5 kg)u^2
Given that the kinetic energy of the 4.0 kg body is twice the kinetic energy of the 8.5 kg body, we can set up the following equation:
1/2 (4.0 kg)v^2 = 2 * (1/2 (8.5 kg)u^2)
Simplifying the equation, we have:
2 (4.0 kg)v^2 = (8.5 kg)u^2
Solving for the ratio of the speeds, we get:
v^2/u^2 = (8.5 kg)/(2 (4.0 kg)) = 4.25
Therefore, the ratio of the speeds of the two bodies is equal to the square root of 4.25, which is approximately equal to 2.06.
So, the 4.0 kg body is moving at approximately 2.06 times the speed of the 8.5 kg body.
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Hodan carried a box of (5,4)m. The box had a mass of 5kg. Hodan said that over 300J of work was done on the box. Is she correct, explain your answer
Answer:
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calculate the force required to stop a car of mass 1400 kg in 2 seconds if it is moving with a velocity of 10 m/s.
The force required to stop a car of mass 1400 kg in 2 seconds if it is moving with a velocity of 10 m/s is 7000 N in the opposite direction to the car's motion.
Calculate the force required to stop a car of mass 1400 kg in 2 seconds if it is moving with a velocity of 10 m/s.
To solve the given problem, we can use the equation:
F = (m * Δv) / Δt
where F = force
required to stop the carm = mass of the car Δv = change in velocity = final velocity - initial velocityΔt = time taken to stop the car.
Given, mass of the car, m = 1400 kg Initial velocity, u = 10 m/s Final velocity, v = 0 m/s Time taken to stop, t = 2 seconds Therefore, Δv = v - u = 0 - 10 = -10 m/s
Substituting the given values in the above equation, we get:
F = (m * Δv) / Δt = (1400 kg * (-10 m/s)) / (2 s) = -7000 N
Here, the negative sign indicates that the force required to stop the car is acting in the opposite direction to the car's motion.
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a 60 kg dancer applies a horizontal force of -800 n on the dance floor. the dancer's acceleration will be
The acceleration of the dancer who applies a horizontal force of -800 N on the dance floor will be 13.33 m/s².
The formula used to calculate acceleration is as follows:F = m × a
where,F is the force,m is the mass, and,a is the acceleration
Substituting the given values in the above formula, we get:
-800 N = 60 kg × a
We can solve this equation for a, which will give us the acceleration of the dancer.
a = (-800 N) / (60 kg) = -13.33 m/s²
Therefore, the acceleration of the dancer will be 13.33 m/s².
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what is the equation to find the equivalent resistance, req, of two resistors in series, r1 and r2? group of answer choices
The equivalent resistance of resistors in series is always greater than the individual resistances. This is because the total resistance of the circuit is the sum of the resistances, and therefore the electric current has to overcome more resistance to flow through the circuit as compared to when a single resistor is used.
To find the equivalent resistance, req, of two resistors in series, r1 and r2, the following equation is used:
Req = R1 + R2
Where Req is the equivalent resistance of the series circuit,
R1 is the resistance of the first resistor,
R2 is the resistance of the second resistor.
Resistors in a circuit are the components that oppose the flow of electric current. When two resistors are connected in series, they are connected end to end so that the electric current flows through one resistor before flowing through the second one.In a series circuit, the equivalent resistance, req, is calculated as the sum of the individual resistances of the resistors connected in series.
Therefore, to find the equivalent resistance of two resistors in series, R1 and R2, we add the resistance values of the two resistors, as shown in the formula above.
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the photo at right was taken through a specroscope. what color was the pigment extract used to produce this spectrum? what colo(s) did this extract absorb?
Light is a form of energy. All the properties of light can be explained by Considering the Wave length and lespuscutar theory.
The Wave Theory states that waves are how light moves across space. When Visible light is passed through a prim it is split up into seven colours which corresponds to definite wave length. a phenomenon Called dispersion. The study of interaction between matter and electromagnetic radiation is defined as spectroscopy.
A spectrophotometer is a device which detect the percentage transmittance of light radiation. When light of certain intensity and frequency range is passed through the Sample Thus the instrument Compare the intensity of the transmitted light with that of the incident light.
A spectroscope is a device that divides light into its individual wavelengths to produce a spectrum.
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a 500g pot of water at room temperature (20c) is placed on a stove. how much heat is required to change this water to steam at 100c
To change 500g of water at room temperature (20°C) to steam at 100°C, you will need to add 1128.500 kJ of heat. This is because water requires a certain amount of heat energy, called the 'latent heat of vaporization', to turn from a liquid to a gas.
Mass of water (m) = 500g
Initial temperature ([tex]T_i[/tex]) = 20°C
Final temperature ([tex]T_f[/tex]) = 100°C
The heat of vaporization ([tex]H_{vap}[/tex]) = 2260 J/g.
To calculate the amount of heat required to convert 500 g of water at room temperature to steam at 100°C, we will use the formula:
[tex]Q = m \times H_{vap}\\Q = 500 g \times 2260 J/g\\Q = 1128500 J[/tex]
Therefore, it would take 1130000 J of heat to change this water to steam at 100°C.
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measurements show a certain star has a very high luminosity (100,000 x the sun's) while its temperature is quite cool (3500 k). how can this be?
The star might be quite large in size, with a much larger surface area than the sun. This would increase its luminosity despite its cooler temperature.
The star has a high luminosity (100,000 x the sun's) and a cool temperature (3500 K) because of its size.
A star's luminosity is proportional to its size, so if a star is very large, it can have a high luminosity even if it is relatively cool.
Another possibility is that the star is in a phase of its life cycle where it has expanded and cooled, such as a red giant or supergiant, but still retains a high luminosity due to its large size.
These stars have relatively low surface temperatures, but their large sizes give them very high luminosities.
Therefore, this star is likely very large and thus has a very high luminosity despite its low temperature.
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the rotational speed of a flywheel increases by 40%. by what percent does its rotational kinetic energy increase? explain your answer.
The rotational kinetic energy of a flywheel increases by 80% when its rotational speed increases by 40%. This is because the rotational kinetic energy of a flywheel is directly proportional to the square of its angular velocity.
The rotational speed of a flywheel increases by 40%. The percentage increase in its rotational kinetic energy is approximately 96.8%. Suppose the initial rotational speed of the flywheel is n1 and the initial rotational kinetic energy is K.E.1. After the speed of the flywheel is increased by 40 percent, the new speed is n2 = n1 + 0.4n1 = 1.4n1.
Then the new kinetic energy K.E.2 of the flywheel is given by K.E.2 = (1/2)I(n2^2)where I is the moment of inertia of the flywheel.Since n2 = 1.4n1, we have [tex]K.E.2 = (1/2)I(1.96n1^2) = 0.98I(n1^2).[/tex].
Therefore, the percentage increase in the rotational kinetic energy of the flywheel is approximately 96.8%.
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the reason distance has a greater effect on the force of gravity between our earth and moon is because the distance between them is
The reason distance has a greater effect on the force of gravity between our Earth and Moon is because the distance between them is relatively large.
The reason distance has a greater effect on the force of gravity between the Earth and the Moon is because the force of gravity between two objects decreases with the square of the distance between them. This is known as the inverse square law of gravity.
The force of gravity between two objects is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as,
F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In the case of the Earth and the Moon, their masses are fixed, so the only variable that affects the force of gravity between them is the distance. As the distance between the Earth and the Moon increases, the force of gravity between them decreases rapidly, according to the inverse square law.
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--The complete question is, Fill in the blank, the reason distance has a greater effect on the force of gravity between our earth and moon is because the distance between them is ________________.--
in which region are the temperatures and pressures at which it's possible to change the phase of x by raising or lowering the temperature?
The region in which it is possible to change the phase of x by raising or lowering the temperature is: phase transition region.
This region is typically marked by an increase in pressure and a decrease in temperature. Temperature and pressure are inversely proportional to one another within this region, meaning that as pressure increases, temperature decreases and vice versa.
The exact temperature and pressure at which the phase transition occurs depends on the type of material being transitioned and its individual characteristics. For example, water boils at 100°C and 1 atm of pressure while other substances may have different boiling points.
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a ball is thrown upward from the ground with an initial speed of 35 m/s; at the same instant, another ball is dropped from a building 5.0 m high. after how long will the balls be at the same height?
The time taken by both balls to be at the same height is 1.02 seconds.
The time taken by two balls to be at the same heightGiven,Initial speed of the ball that is thrown upward from the ground, u = 35 m/s,Initial height of the ball that is dropped from a building, h = 5.0 m,Finding out the time taken by both balls to be at the same height,Time taken by ball that is thrown upward from the ground, t = ?
For the first ball (that is thrown upward from the ground), the acceleration, a = -9.8 m/s² (negative because it's going against the gravity).Using the formula of motion,S = ut + 1/2 at²where,S = height of the ball above the ground, t = time taken by the ball to reach that height, and u = initial speed of the ball that is thrown upward from the ground.
Here, h = S and u = 35 m/s, and a = -9.8 m/s². Then putting the values we get,h = ut + 1/2 at²5 = (35)t + 1/2 (-9.8)t²5 = 35t - 4.9t²----------------(1)Also, for the second ball (that is dropped from a building), the time taken to reach the ground can be found using the formula, h = 1/2gt². Here, h = 5.0 m.
Therefore,5 = 1/2 × (-9.8) × t²5 = -4.9t²t² = -5/-4.9t² = 1.02t = √1.02
Therefore, the time taken by both balls to be at the same height is 1.02 seconds.
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if two flutists play their instruments together at the same intensity, is the sound twice as loud as that of either flutist playing alone at that intensity? why or why not?
No, the sound wouldn't be twice as loud as that of either flutist playing alone at that intensity. The increase in sound intensity would be less than twice as loud.
This is because when two sound waves coincide, the amplitude of the resulting sound wave is the sum of the amplitudes of the individual sound waves. That is, when two identical sound waves come together, they create a new sound wave that is slightly louder than the original sound wave, but not twice as loud.
Furthermore, sound intensity is affected by the distance from the sound source, and when two flutists are playing together, the sound waves produced have to travel further before they reach the listener, thus reducing the intensity of the sound.
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Two large parallel metal plates carry opposite charges. They are separated by 10 cm and p. D of 500 volts is applied on them. What is the magnitude of electric field strength between them? compute the work done by the field on a change of 2x10^-9 as it moves from higher to lower part?
(a) The magnitude of electric field in the region between the plates is [tex]\mathbf{9 , 2 5 0}$ $\mathrm{V} / \mathrm{m}$.[/tex]
(b) The magnitude of the force the field exerts on a particle with the given charge i[tex]s $2.22 \times 10^{-5} \mathrm{~N}$.[/tex]
(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is[tex]$8.88 \times 10^{-7} \mathrm{~J}$.[/tex]
(d) the change of the potential energy is[tex]$8.88 \times 10^{-7} \mathrm{~J}$.[/tex]
(a) The magnitude of electric field in the region between the plates is calculated as;
[tex]$$\begin{aligned}& E=\frac{V}{d} \\& E=\frac{370}{40 \times 10^{-3}} \\& E=9,250 \mathrm{~V} / \mathrm{m}\end{aligned}$$[/tex]
(b) The magnitude of the force the field exerts on a particle with the given charge is calculated as follows;
[tex]$$\begin{aligned}& F=E q \\& F=9,250 \times 2.4 \times 10^{-9} \\& F=2.22 \times 10^{-5} \mathrm{~N}\end{aligned}$$[/tex]
(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is calculated as follows;
[tex]$$\begin{aligned}& W=F d \\& W=2.22 \times 10^{-5} \times 40 \times 10^{-3} \\& W=8.88 \times 10^{-7} \mathrm{~J}\end{aligned}$$[/tex]
(d) the change of the potential energy is calculated as;
[tex]$$\begin{aligned}& \Delta U=q \Delta V \\& \Delta U=q\left(V_1-V_2\right)\end{aligned}$$$$\text { DeltaU }=2.4 \times 10^{-9}(370)$$$$\Delta U=8.88 \times 10^{-7} \mathrm{~J}$$[/tex]
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Full Question: Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by a distance of 40.0 mm, and the potential difference between them is 370 V
A. What is the magnitude of the electric field (assumed to be uniform) in the region between the plates?
B. What is the magnitude of the force this field exerts on a particle with a charge of 2.40 nC ?
C. Use the results of part (b) to compute the work done by the field on the particle as it moves from the higher-potential plate to the lower.
D. Compare the result of part (c) to the change of potential energy of the same charge, computed from the electric potential.
g a research rocket is launched from boulder straight towards the south. how would the coriolis effect change the path of the rocket?
For a rocket launched southward from Boulder, the Coriolis effect would cause it to drift to the east, leading to a curved flight path rather than a straight one.
The Coriolis effect is an important force to consider when launching a research rocket from Boulder. The Coriolis effect is the result of Earth's rotation and will cause any object moving along the surface of the Earth to veer to the right in the Northern hemisphere and to the left in the Southern hemisphere.
This effect is most noticeable for objects traveling long distances, such as a rocket. As it continues to fly south, the Coriolis force will continue to act upon it, increasing the curvature of its path. The magnitude of the Coriolis force depends on the speed of the object and its distance from the poles. Therefore, the more time the rocket has to travel, the more it will be deflected from its intended path.
The Coriolis effect is an important factor to consider for any research rocket launch. It has the potential to affect the accuracy and success of the mission and must be taken into account when planning a launch trajectory.
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Complete Question:
A research rocket is launched from Boulder straight towards the south. How would the Coriolis effect change the path of the rocket?
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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4. if the electric field of an electromagnetic wave is oscillating along the z-axis and the magnetic field is oscillating along the x-axis, in what possible direction is the wave traveling?
The possible direction in which an electromagnetic wave is traveling if the electric field is oscillating along the z-axis and the magnetic field is oscillating along the x-axis is the y-axis.
An electromagnetic wave is composed of two mutually perpendicular fields that oscillate perpendicular to the direction of the wave's propagation. They are the electric field and the magnetic field. An electromagnetic wave is created when a charged particle is accelerated. These waves can travel through a vacuum or any medium, including air and water, at the speed of light.
In this scenario, the electric field of the wave oscillates along the z-axis, while the magnetic field oscillates along the x-axis. As a result, the wave's propagation direction must be perpendicular to both fields. As a result, the wave must be propagating along the y-axis.This is why it's critical to comprehend the interplay between electric and magnetic fields in the context of electromagnetic waves.
It's also critical to recognize that an electromagnetic wave's direction of propagation is always perpendicular to the oscillation directions of the two fields, which are mutually perpendicular to each other.
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how much heat is lost through a 3' x 5' single-pane window with a storm that is exposed to a temperature differentia
The amount of heat lost through a 3' x 5' single-pane window with a storm that is exposed to a temperature differential is 108 BTU per hour.
The U-factor is a measure of how well a window insulates against heat transfer. The lower the U-factor, the better the window insulates.
The temperature difference is the difference between the inside and outside temperatures.The area of the window is the size of the window.Using these factors, we can calculate the rate of heat loss through the window in units of BTUs per hour.
Assuming a U-factor of 1.2 and a temperature difference of 60°F, the calculation would be:
Heat Loss = 1.2 BTU/(hrft^2F) x 15 ft^2 x 60°F
Heat Loss = 108 BTU/hour
Therefore, the heat lost through the window is 108 BTU per hour.
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Complete Question:
How much heat is lost through a 3' × 5' single-pane window with a storm that is exposed to a 60 Fahrenheit temperature differential?
two balls are connected to 60-cm-long light strings and the other ends of the strings are fixed together as shown in the figure. one of the balls has a mass of 2.0 kg and is raised up and to the right until it is 12.0 cm higher than the other ball, which has a mass of 3.0 kg. the upper ball is released from rest and sticks to the lower ball when they collide. for the subsequent motion find the:
According to the question the speed of the balls just before they collide is 1.81 m/s.
What is collide?Collide is a term used to describe the process of two objects or particles coming into contact with each other, often resulting in a collision. In physics, the term is used to refer to the force of two objects impacting one another. In everyday language, the term is used to describe two things, such as people or ideas, coming together in a way that produces a powerful impact.
The initial energy of the system can be calculated as:
[tex]E_{initial[/tex] = m₁*g*h + 0
where m_1 is the mass of the upper ball (2.0 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the vertical distance between the two balls (12.0 cm).
The final energy of the system can be calculated as:
[tex]E_{final} = (m_1 + m_2)\times v^2[/tex]
where m_1 and m_2 are the masses of the two balls (2.0 kg and 3.0 kg, respectively), and v is the velocity of the lower ball when the two balls stick together.
From these equations, we can solve for v:
[tex]v = sqrt[(m_1\timesg\timesh)/(m_1 + m_2)] = sqrt[(2.0 kg\times9.8 m/s^2\times12.0 cm)/(2.0 kg + 3.0 kg)] = 1.81 m/s[/tex]
Therefore, the velocity of the lower ball when the two balls stick together is 1.81 m/s.
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a load of 12 kg stretches a spring to a total length of 15 cm, and a load of 30 kg stretches it to a length of 18 cm. find the natural (unstretched) length of the spring.
The natural length of the spring is therefore 12.97 cm.
The natural length of the spring is found by calculating the spring constant using the Hooke's law formula. Spring constant (k) = Force (F) / extension (x). The natural length of the spring refers to the length of the spring when it is not carrying any load. Hooke's law states that the force required to extend or compress a spring by a distance x is proportional to that distance. Mathematically, F=kx, where F is the force applied, x is the displacement from the equilibrium position, and k is the spring constant. To find the natural length of the spring, we need to calculate the spring constant.
To do this, we use the data given in the problem. A load of 12 kg stretches the spring to a total length of 15 cm. We can find the force applied by multiplying the load by the acceleration due to gravity (g), which is 9.8 m/s^2. Thus, F = mg = 12 * 9.8 = 117.6 N. The extension of the spring is given as x = 15 cm - x0, where x0 is the natural length of the spring. Thus, x = 0.15 m - x0. Substituting these values into Hooke's law, we get: k = F/x = 117.6/(0.15 - x0)
Similarly, when a load of 30 kg stretches the spring to a length of 18 cm, we can find the force applied as F = mg = 30 * 9.8 = 294 N. The extension is given as x = 0.18 m - x0. Substituting these values into Hooke's law, we get: k = F/x = 294/(0.18 - x0)
Now we have two equations for k, so we can set them equal to each other: 117.6/(0.15 - x0) = 294/(0.18 - x0) Cross-multiplying and simplifying, we get: 117.6(0.18 - x0) = 294(0.15 - x0) 21.168 - 117.6x0 = 44.1 - 294x0 176.4x0 = 22.932 x0 = 0.1297 m
The natural length of the spring is therefore 12.97 cm.
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what is the speed acquired by a freely falling object 5 s after being dropped from a rest position? what is the speed 6 s after?
The speed acquired by the body is 49m/s and 59m/s respectively.
The speed can be calculated using the formula:
v= u + gt, where v= final speed, u= initial speed = 0 for a freely falling body, g= acceleration due to gravity, t= time.
The speed acquired by a freely falling object 5 seconds after being dropped from a rest position is 49 m/s. This is because an object dropped from rest will accelerate at a rate of 9.8 m/s², so after 5 seconds it will be moving at a speed of 5 * 9.8 = 49 m/s.
The speed 6 seconds after being dropped from a rest position is approximately 59 m/s. This is because an object dropped from rest will accelerate at a rate of 9.8 m/s², so after 6 seconds it will be moving at a speed of 6 * 9.8 = 58.8 m/s.
In summary, the speed of an object dropped from rest 5 seconds after being dropped is 49 m/s, and 6 seconds after it is approximately 59 m/s.
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what principle states that the buoyant force experienced by an object is exactly equal to the weight of the fluid displaced?
The principle that states that the buoyant force experienced by an object is exactly equal to the weight of the fluid displaced is known as Archimedes' Principle. What is Archimedes' Principle? Archimedes' Principle is a scientific law that explains how objects behave in fluids (liquids and gases).
The buoyant force of an object in a fluid is equal to the weight of the fluid displaced by the object according to this principle. This principle is valid for any fluid and any object as long as the buoyancy and weight of the object and fluid are calculated correctly.
The force that causes objects to float or sink in fluids is known as buoyancy. The buoyant force on an object is the net upward force exerted by the fluid in which the object is submerged.
When an object is immersed in a fluid, the fluid exerts an upward force on the object. This buoyant force opposes the weight of the object and causes it to float if the buoyant force is greater than the weight of the object.
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an electron and a proton are each placed at rest in a uniform electric field of magnitude 498 n/c. calculate the speed of each particle 44.4 ns after being released.
An electron and a proton are placed at rest in a uniform electric field of magnitude 498 N/C. The speed of electron and proton 44.4 ns after being released is -3.87 × 10⁶ m/s and 2.13 × 10³ m/s respectively.
Given data:
Electric field (E) = 498 N/C,
Time (t) = 44.4 ns = 44.4 × 10⁻⁹ s,
Mass of electron (m₁) = 9.11 × 10⁻³¹ kg,
Mass of proton (m₂) = 1.67 × 10⁻²⁷ kg.
Formula:
The acceleration produced in the electric field is given by a = qE/m, where q is the charge of the particle, E is the electric field strength, and m is the mass of the particle.
From the above formula, we can find the acceleration produced by the electric field on the electron and proton as follows:
For electron (q = -e, where e is the charge of an electron)
a₁ = qE/m₁ = -eE/m₁
= -1.6 × 10⁻¹⁹ × 498/9.11 × 10⁻³¹
= -8.73 × 10¹⁴ m/s²
For proton (q = +e, where e is the charge of an electron)
a₂ = qE/m₂ = eE/m₂
= 1.6 × 10⁻¹⁹ × 498/1.67 × 10⁻²⁷
= 4.80 × 10⁷ m/s²
Using the kinematic equation, v = u + at, where u is the initial velocity, we can find the speed of each particle 44.4 ns after being released as follows:
For electron,
v₁ = u₁ + a₁t = 0 + (-8.73 × 10¹⁴) × 44.4 × 10⁻⁹
= -3.87 × 10⁶ m/s
For proton,
v₂ = u₂ + a₂t = 0 + (4.80 × 10⁷) × 44.4 × 10⁻⁹
= 2.13 × 10³ m/s
Thus, the speed of the electron is -3.87 × 10⁶ m/s and the speed of the proton is 2.13 × 10³ m/s.
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A long solenoid has 100 turns/cm and carries current i. an electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. the speed of the electron is 0.0460c (c speed of light). find the current i in the solenoid.
The current in the solenoid becomes 3.56 A.
How to find current in the solenoid?
Number of turns in the solenoid, n = 100 turns/cm
Radius of the circular path of electron, r = 2.30 cm
Speed of electron, v = 0.0460c, where c is the speed of light
To find: Current in the solenoid, i
Formula used: Magnetic field inside the solenoid,
B = μ0ni Where, μ0 = 4π × 10⁻⁷ T m/A is the permeability of free spaceSolution:
The force on a moving electron in a magnetic field is given by
F = Bev
Where B is the magnetic field, e is the charge of an electron and v is its velocity.
The force acting on the electron provides the necessary centripetal force for the electron to move in a circle of radius r.
So,
Bev = (mev²)/r
where me is the mass of an electron
On simplifying the above equation, we get
Be = (mev)/r
Put the value of B from the formula of magnetic field inside the solenoid, B = μ0ni
we get
μ0ni = (mev)/r
Solve for i,
i = (mev)/(μ0nr)
Substitute the given values and solve
i = (9.109 × 10⁻³¹ kg × 0.0460c × 3 × 10⁸ m/s)/(4π × 10⁻⁷ T m/A × 100 turns/cm × 2.30 cm)i
= 3.56 A
Therefore, the current in the solenoid is 3.56 A.
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a diver jumps off the diving board. he pushes himself downward at a rate of 2 m/s. gravity increases his downward velocity to 6 m/s when he hits tthe water 1.5 seconds later. what is his acceleration?
The diver's acceleration is 2.67 m/s^2.
We can use the formula for acceleration:
a = (vf - vi) / t
where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.
In this problem, the initial velocity (vi) is 2 m/s downward, the final velocity (vf) is 6 m/s downward, and the time (t) is 1.5 seconds.
Plugging in these values, we get:
a = (6 m/s - 2 m/s) / 1.5 s
a = 4 m/s / 1.5 s
a = 2.67 m/s^2
As a result, the acceleration of the diver is 2.67 m/s^2.
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determine the capacitance of a teflon-filled parallel-plate capacitor having a plate area of 1.80 cm2 and a plate separation of 0.020 0 mm.
To determine the capacitance of a teflon-filled parallel-plate capacitor having a plate area of 1.80[tex]cm^{2}[/tex] and a plate separation of 0.0200 mm, we can use the formula for capacitance: C = εo εr A/d, when the values are plugged in, the capacitance is found to be [tex]1.54* 10^{-9}[/tex] Farads.
The capacitance of a teflon-filled parallel-plate capacitor having a plate area of 1.80[tex]cm^{2}[/tex] and a plate separation of 0.0200 mm is determined using the formula C = εo A/d, where C is the capacitance, εo is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
To explain this calculation further, the permittivity of free space is a constant value equal to [tex]8.85 * 10^{-12}[/tex] A/d, which is derived from the equation εo = 1/ (μoc2), where μo is the permeability of free space, and c is the speed of light. The area of the plates is given in the problem statement as 1.80 [tex]cm^{2}[/tex], and the distance between the plates is given as 0.0200 mm.
When these values are plugged into the formula, the capacitance is found to be [tex]1.54* 10^{-9}[/tex]Farads. In conclusion, the capacitance of a teflon-filled parallel-plate capacitor having a plate area of 1.80 [tex]cm^{2}[/tex] and a plate separation of 0.0200 mm is 1.54 x 10-9 Farads.
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you compress a piston full of gas and do 8.4 joules of work on it. if the internal energy (u) of the system increases by 3.3 joules, how much heat (in joules) left the system (give your answer as a positive number)?
The amount of heat that left the system is 11.7 joules (given as a positive number).
When a piston is compressed fully with gas and 8.4 joules of work is done on it, and the internal energy (u) of the system is increased by 3.3 joules, we need to determine the amount of heat that left the system.
To determine the amount of heat that left the system, we need to use the First Law of Thermodynamics, which states that the change in internal energy (u) of a system is the sum of the heat (q) added to it and the work (w) done on it, which can be represented as:
u = q + w
Where, u = Change in internal energy of the system
q = Heat added to the system
w = Work done on the system
From the given information, w = -8.4 J (since work was done on the system), and u = 3.3 J.
Therefore, substituting these values in the above equation, we get:
3.3 J = q + (-8.4 J)3.3 J + 8.4 J
q = 11.7 J
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suppose you have an atwood machine with two different masses m and m. what are the external forces acting on this system?
The external forces acting on this system are: gravity and the tension in the string.
An Atwood machine is a system consisting of two masses, m, and m, connected by a string that passes over a pulley. In this system, the external forces are gravity and the tension in the string. Gravity pulls both masses downward, while the tension in the string acts in opposite directions on the two masses, pulling the heavier one down and the lighter one up.
The tension in the string is determined by the masses m and m and the acceleration of the system. If m is the heavier mass and m is the lighter mass, the tension in the string will be greater than if both masses had the same weight. This is because the tension must balance the gravitational forces on the two masses. The greater the mass, the greater the gravitational force, and the greater the tension in the string must be to balance it.
The acceleration of the system is determined by the masses, the tension in the string, and the amount of friction in the system. The greater the tension, the greater the acceleration, and the smaller the mass, the greater the acceleration. Friction acts against the acceleration, reducing the net acceleration of the system.
In summary, the external forces acting on an Atwood machine with two different masses m and m are gravity and the tension in the string. The tension in the string is determined by the masses and the acceleration of the system, while the acceleration is determined by the masses, the tension in the string, and the amount of friction in the system.
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The sound level produced by one singer is 71.8 dB. What would be the sound level produced by a chorus of 45 such singers (all singing at the same intensity at approximately the same distance as the original singer)? Answer in units of dB.
The sound level produced by a chorus of 45 singers would be approximately 88.3 dB.
How to find the sound level produced by a chorus of 45 singers?Assuming that the sound level of each singer is independent and the same, the sound level produced by a chorus of 45 singers can be calculated using the following formula:
L2 = L1 + 10 log (N2/N1)
where:
L1 = the sound level of one singer = 71.8 dB
N1 = the number of singers in the original group = 1
N2 = the number of singers in the new group = 45
L2 = the sound level of the new group
Substituting the values in the formula, we get:
L2 = 71.8 + 10 log (45/1)
L2 = 71.8 + 10 log (45)
L2 = 71.8 + 16.5
L2 = 88.3 dB
Therefore, the sound level produced by a chorus of 45 singers would be approximately 88.3 dB, assuming all the singers are singing at the same intensity at approximately the same distance as the original singer.
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