Bohr developed an equation for calculating the energy levels of a hydrogen atom. Using this equation, the following can be determined:
The energy level of an electron
The angular momentum of an electron
The radius of the hydrogen atom's orbit
Around the nucleus of the hydrogen atom, the electrons move in circular orbits. Each of these orbits corresponds to a particular energy level.
Bohr's equation calculates these energy levels based on the electron's distance from the nucleus and its angular momentum.
Thus, by using Bohr's equation, we can determine the energy level of an electron, its angular momentum, and the radius of the hydrogen atom's orbit.
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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 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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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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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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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.
the current through a lightbulb is 2.0 amperes. how many coulombs of leectric charge pass through ther luighbu,kb in one minute?
The current through the bulb is 2.0 amperes. Then the electric charge that passes through Luighbu is 120 Columbs.
Given that the current through a lightbulb is 2.0 amperes. To find the coulombs of electric charge that pass through the light bulb in one minute, we need to know the formula that relates current, time, and electric charge:
Q = It
Where Q is the electric charge (in coulombs), I is the current (in amperes), and t is the time (in seconds).
To convert one minute to seconds, we multiply it by 60. Hence, the time t = 1 minute × 60 seconds/minute = 60 seconds.
So, the electric charge that passes through the light bulb in one minute is given by
Q = It = 2.0 A × 60 s
Q = 120 C
Therefore, the number of coulombs of electric charge that pass through the light bulb in one minute is 120 C.
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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 ________________.--
The formula for speed is Total Distance / Total Time. Based on the data table below, what is the
average speed after 2 minutes? Please show all calculations.
Time (min.) Distance (m)
0
1
2
3
0
50
75
90
Answer:
To find the average speed after 2 minutes, we need to calculate the total distance covered in 2 minutes and divide it by 2.
Total Distance after 2 minutes = 75m
Total Time after 2 minutes = 2 minutes
Average Speed after 2 minutes = Total Distance / Total Time
Average Speed after 2 minutes = 75m / 2 min = 37.5 m/min
Therefore, the average speed after 2 minutes is 37.5 m/min.
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g a cat with mass 4.50 kg is running at a speed of 6.70 m/s. what is the kinetic energy of the cat?
The kinetic energy of the cat is 177.15 Joules.
The kinetic energy of the cat can be calculated using the formula K = 0.5mv2, where m is the mass and v is the velocity.
The cat has a mass of 4.50 kg and is running at a velocity of 6.70 m/s, so we can substitute these values into the formula to find the kinetic energy:
K = 0.5 * 4.50 kg * (6.70 m/s)2
K = 177.15 Joules
Kinetic energy is the energy possessed by an object due to its motion. It is calculated by multiplying half of the object's mass by its velocity squared.
The cat has a mass of 4.50 kg and is running at a velocity of 6.70 m/s, so its kinetic energy is 177.15 Joules.
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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 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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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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What is the transfer of thermal energy called?
Answer:
Conduction
Explanation:
The process by which heat energy is transmitted through collisions between neighboring atoms
the speed of sound in air is approximately the same for all wavelengths. what evidence is there that this is true?
The speed of sound in air is approximately the same for all wavelengths.
Step by step Explanation :
The evidence that this is true is the following:
The speed of sound in air is approximately the same for all wavelengths. This is proved by the fact that a sound wave is an atmospheric disturbance that propagates as a longitudinal wave through the air, travelling as a pressure wave that causes areas of compression and rarefaction.
The speed of sound in air is constant and is determined by the average kinetic energy of the air molecules. This is why the speed of sound is the same for all wavelengths.
When the temperature of air is held constant, the speed of sound in air is constant. This is the primary reason why the speed of sound in air is practically constant at a given temperature.
The wavelengths of sound range from about 17 meters for the lowest audible frequency (about 20 Hz) to about 17 millimeters for the highest audible frequency (about 20,000 Hz).
The speed of sound in dry air at room temperature is around 343 meters per second, but it may vary depending on a variety of factors, including humidity, temperature, and pressure.
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what must the charge (sign and magnitude) of a particle of mass 1.45 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 700 n/c ?
The charge (sign and magnitude) of a particle of mass 1.45 g must be for it to remain stationary when placed in a downward-directed electric field of magnitude 700 n/c is -1.029x10⁻⁴ C.
The magnitude of the charge must be equal to the magnitude of the electric field (700 n/c).
Therefore, we can write:-mg = qE
where, m = 1.45g = 1.45 x 10⁻³ kg
E = 700 N/cm = 1.45 x 10⁻³ kg x 9.81 m/s²
= 0.01419 N (Weight of the particle)
q = -1.029 x 10⁻⁴ C
To remain stationary when placed in a downward-directed electric field of magnitude 700 n/c, the charge (sign and magnitude) of a particle of mass 1.45 g must be negative.
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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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a record turntable is rotating at 33 1 3 rev/min. a watermelon seed is on the turntable 7.3 cm from the axis of rotation. (a) calculate the acceleration of the seed, assuming that it does not slip. (enter the magnitude.)
Assuming that it does not slip, the acceleration of the seed is 0.89 m/s².
The acceleration of the seed can be calculated using the formula for centripetal acceleration:
a = (v²) / r
where a is the centripetal acceleration, v is the velocity of the seed, and r is the distance from the axis of rotation to the seed.
To use this formula, we need to first convert the rotational speed of the turntable from rev/min to radians per second. There are 2π radians in one revolution, so:
ω = (33 1/3 rev/min)(2π rad/rev)(1 min/60 s) = 3.49 rad/s
The velocity of the seed can be calculated from the tangential velocity formula:
v = rω
where v is the tangential velocity of the seed.
Substituting the given values, we get:
v = (0.073 m)(3.49 rad/s) = 0.255 m/s
Now we can use the formula for centripetal acceleration:
a = (v²) / r
Substituting the values we have calculated, we get:
a = (0.255 m/s)² / 0.073 m = 0.89 m/s²
Therefore, the acceleration of the seed is 0.89 m/s² assuming that it does not slip.
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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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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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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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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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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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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:
hdjsigosorodcdjjgjejfiroodofohov jdjvjwigioeofe
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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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 stone is thrown down off a bridge with a velocity of 5.6 m/s. what is its velocity after 3 seconds have passed?
The velocity of the stone after 3 seconds have passed can be calculated using the formula v=u + at, where v is the velocity, u is the initial velocity, a is the acceleration (in this case the acceleration due to gravity, which is 9.8 m/s2), and t is the time. Therefore, the velocity of the stone after 3 seconds have passed will be 5.6 + (9.8*3) = 23.4 m/s.
The acceleration due to gravity causes any object to accelerate as it moves. This acceleration is always constant and acts downwards. Therefore, an object thrown with an initial velocity of 5.6 m/s will continue to accelerate and its velocity will increase. After 3 seconds have passed, the object will have an increased velocity of 23.4 m/s. In addition, when the stone is thrown off the bridge, it is subject to air resistance, which works against the stone and causes it to slow down. The magnitude of air resistance is dependent on a number of factors, such as the shape and size of the object. As such, the stone's velocity after 3 seconds might be slightly lower than the calculated value of 23.4 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 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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How long it took for the Moon to revolve once around Earth and how long it took for the Moon to rotate once on its axis?
The time it takes for the Moon to revolve once around Earth and to rotate once on its axis is known as its period of rotation and revolution, respectively. The time it takes for the Moon to complete one revolution around Earth is approximately 27.3 days or 27 days, 7 hours, and 43 minutes. This period is known as the lunar month or synodic month. During this time, the Moon moves through its phases, from new moon to full moon and back to new moon again.
On the other hand, the time it takes for the Moon to rotate once on its axis is approximately 27.3 days. This means that the Moon takes the same amount of time to rotate on its axis as it does to revolve around Earth. As a result, the same side of the Moon always faces Earth, which is why we only see one side of the Moon from Earth.
It's worth noting that the Moon's period of rotation and revolution are almost the same, which is a rare occurrence in the solar system. This is due to the gravitational influence of Earth, which has caused the Moon to become tidally locked with Earth. This means that the Moon's rotation and revolution are in sync with Earth, resulting in the same side of the Moon always facing Earth.
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