The solution would be like this for this specific problem:
The force on m is:
GMm / x^2 + Gm(2m) / L^2 = 2[Gm (2m) / L^2] ->
1
The force on 2m is:
GM(2m) / (L - x)^2 + Gm(2m) / L^2 = 2[Gm (2m) / L^2]
-> 2
From (1), you’ll get M = 2mx^2 / L^2 and from
(2) you get M = m(L - x)^2 / L^2
Since the Ms are the same, then
2mx^2 / L^2 = m(L - x)^2 / L^2
2x^2 = (L - x)^2
xsqrt2 = L - x
x(1 + sqrt2) = L
x = L / (sqrt2 + 1) From here, we rationalize.
x = L(sqrt2 - 1) / (sqrt2 + 1)(sqrt2 - 1)
x = L(sqrt2 - 1) / (2 - 1)
x = L(sqrt2 - 1)
= 0.414L
Therefore, the third particle should be located the 0.414L x axis so that the magnitude of the gravitational force on both particle 1 and particle 2 doubles.
Using Newton's law of universal gravitation, we can set up equations to find the location of the third particle such that the gravitational force exerted on both particle 1 and particle 2 doubles. The third particle should be placed at the position solved from these equations, either closer to particle 1 or further away.
Explanation:The location of the third particle that could double the gravitational force on both particle 1 and 2 can be achieved by using Newton's law of universal gravitation. This law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
For particle 1 and the third particle, if we denote the mass of the third particle as m3 and its position as x3, the gravitational force F1 on particle 1 is given by F1 = G*m*m3/x3^2. Similarly, for particle 2 and the third particle, the gravitational force F2 on particle 2 is also given by F2 = G*2m*m3/(l-x3)^2.
According to the question, both the gravitational force on particle 1 and particle 2 doubles when the third particle is added. Therefore, we can set up the following equations: 2F1 = G*m*m3/x3^2 and 2F2 = G*2m*m3/(l-x3)^2. From the equations, we could solve for x3 to find the location of the third particle.
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The angular speed of the minute hand of a watch is:
The angular speed of the minute hand of a watch is calculated by dividing the total angle of rotation (2π rad) by the period of rotation (3600 s), which equals 0.1047 rad/min. This indicates the degree of the minute hand's rotation per minute. The right-hand rule also designates the angular velocity's direction.
Explanation:The angular speed of the minute hand of a watch refers to the degree of rotation of the minute hand per unit of time. In the particular case of a watch, the minute hand completes one full revolution (360° or 2π rad) in one hour (60 minutes or 3600 seconds). Therefore, the angular speed ω can be calculated as the total angle of rotation (2π rad) divided by the period of rotation, which is 3600 seconds.
Thus, the angular speed is calculated as ω = 2π rad/3600 s. By converting this to radian per minute, which is a more typical unit for a watch, we obtain that the angular speed of the minute hand of a watch is 0.1047 rad/min. This means that in each minute, the minute hand rotates 0.1047 radians.
This concept and calculation is part of what's studied in rotational motion in physics, where the right-hand rule can also be used to determine the direction of the angular velocity vector.
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A state government is trying to decide what type of energy its state should rely on for electricity in the future. Which of the following is a benefit associated with the use of coal power that the government should take into consideration?
A.Coal power plants release toxic chemicals into the air
B.Mining for coal hurts the environment
C.Coal power can be generated both day and night
D.Burning coal releases greenhouse gases
Answer: C. Coal power can be generated both day and night.
Explanation:
Coal is an important form of source of energy. It is a non-renewable source of energy. It is obtain by mining of the surface below the earth crust. Coal plays an important role in generation of electricity worldwide.
It acts as a raw material for the generation of electricity in both day and night. When the coal is turned into a gas. The gas turbine is hot enough to boil the water that can be used to make the steam. The steam spin another type of turbine so as to generate the electricity.
A mixture can be classified as a solution, suspension, or colloid based on the
A. number of particles it contains.
B. size of its largest particles.
C. color of its particles.
D. size of its smallest particles.
Bob is pushing a lawn mower up a hill with the mower tilting slightly to the right. suppose that we wish to use vectors to determine the total force acting on the mower. what forces should be considered?
Answer:
Applied force, weight, normal force and frictional force
Explanation:
Bob is pushing a lawn mower up a hill with the mower tilting slightly to the right. We have to write the forces acting on the mower.
The following are the forces that are acting on the mower.
1. Applied force - The force with which Bob is pushing a lawn.
2. Weight - Its weight is equal to, W = m g
3. Normal force - that balances its weight
4. Frictional force - It always opposes the motion of the mower.
Hence, this is the required solution.
The lawn mower is acted upon by four different forces.
Vector quantities are those quantities that posses both magnitude and direction. Force is a vector quantity. Hence, the resultant force acting on a lawn mover can be obtained as the resultant of the four forces that act on the mower.
The four forces that act on the lawn mower are;
Applied forceFrictional forceWeight of the mowerNormal reactionHence, the lawn mower is acted upon by four different forces.
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Determine the density of a rectangular piece of concrete that measures 3.7 cm by 2.1 cm by 5.8 cm and has a mass of 43.8 grams.
The density of the concrete is approximately 0.965 g/cm³. The result does not support the statement that rebar is mostly iron.
Explanation:The density of a substance can be calculated by dividing its mass by its volume. In this case, the mass of the concrete is 43.8 grams and the volume is calculated by multiplying the length, width, and height, which is 3.7 cm x 2.1 cm x 5.8 cm = 45.4014 cm³ (rounded to the nearest 0.0001 cm³). Therefore, the density of the concrete is 43.8 g / 45.4014 cm³ ≈ 0.965 g/cm³.
(b) Since the density of the concrete in (a) is less than the density of iron (approximately 7.87 g/cm³), the result does not support the statement that rebar is mostly iron.
Moving your finger across a textured surface can produce vibrations that are interpreted as texture. these vibrations are defined as _____.
a. temporal cues
b. parietal cues
c. spatial cues
d. olfactory cues
Are all neon lights made up of neon gases
the contribution of Tycho Brahe was primarily his
calculations
observation
inventions
theories
A plucked guitar string produces a sound wave with a wavelength of 0.15 m and a velocity of 10.5 m/s, what is the frequency of the wave?
Using the wave equation, the frequency of the sound wave produced by the guitar string can be calculated by dividing the velocity (10.5 m/s) by the wavelength (0.15 m), resulting in a frequency of 70 Hz.
The student is asking about the frequency of a sound wave produced by a plucked guitar string. To calculate this, we can use the basic wave equation v = f λ, where v is the velocity of the wave, f is the frequency, and λ is the wavelength. Given the wavelengths of 0.15 m and the velocity of 10.5 m/s, we can rearrange the formula to solve for the frequency (f):
f = v / λ
f = 10.5 m/s / 0.15 m
By calculating this, we find that the frequency of the wave is 70 Hz.
Ep-35 if your inboard/outboard boat runs aground, what action should you take in addition to shifting the weight away from the point of impact
If your inboard or outboard boat runs aground, after shifting the weight away from the point of impact, you should stop the engine and lift the outdrive.
What is a gasoline engine?A gasoline engine can be defined as a mechanical system that is primarily designed and developed to only make use of hydrocarbons (organic compounds) such as fuels, in order to enable a vehicle or boat to move from one point to another on a water body.
Generally, an outboard gasoline engine is installed on the outside of a vehicle or a boat while an inboard gasoline engine is typically installed on its inside.
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You push forward on a car with a force of 150 N, but the car does not move. What is the net force on the car?
PLEASE HELP NOW!! Which of the following must be the same for two isotopes of an element?
A. The number of neutrons
B. The atomic number
C. The mass
D. The charge
<<<<<<<<<< B is the answer >>>>>>>
A boy yells in a narrow valley. The sound reflects off of a boulder that is 80 m away. How long will it take to hear the echo if the speed of a sound wave is 320 m/s?
Answer:
0.50 s
Explanation:
you're welcome
What makes science different from other fields of knowledge like art or philosophy?
Which statement is true about magnetic poles?
North and south poles repel each other.
North and south poles attract each other.
Two south poles will attract each other.
Two north poles will attract each other.
North and south poles attract each other.
Explanation;A magnet is a material that has an ability to produce magnetic fields.A magnet has two poles, north pole and a south pole. The north pole is the side which points north when a magnet is freely suspended on air, while south pole is the pole that points south. Based on the basic law of magnetism, like poles repel while unlike poles attract. Therefore, north pole attracts with a south pole, but repels another north pole. Two north poles repel while two south poles also repel.While standing near a bus stop, a student hears a distant horn beeping. The frequency emitted by the horn is 440 Hz. The bus is traveling at 20.0 m/s, and the speed of sound is 330 m/s. What frequency will the student hear at each point in the bus's motion?
A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding
B. 415 Hz while approaching, 440 Hz through the crossing, 468 Hz while receding
C. 440 Hz while approaching, 415 Hz through the crossing, 400 Hz while receding
D. 505 Hz while approaching, 440 Hz through the crossing, 438 Hz while receding
Answer:
A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding
Explanation:
When bus is approaching the stand where boy is standing then the frequency is given as
now we know that
[tex]f_0 = 440 Hz[/tex]
[tex]v = 330 m/s[/tex]
[tex]v_b = 20 m/s[/tex]
frequency is given by
[tex]f_1 = f_0 \frac{v}{v - v_b}[/tex]
now plug in the data in the equation
[tex]f_1 = 440 \times \frac{330}{330 - 20}[/tex]
[tex]f_1 = 468 Hz[/tex]
Now when bus is moving away from the bus stop then frequency is given as
[tex]f_2 = f_0 \frac{v}{v + v_b}[/tex]
[tex]f_2 = 440 \times \frac{330}{330 + 20}[/tex]
[tex]f_2 = 415 Hz[/tex]
so here correct answer would be
A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding
A car accelerates from rest at a constant rate of 2m/s2 for 5s. what is the speed of a car at the end of that time?
You are retrieving your boat from the water. as a courtesy to others, when should you pull your boat into a launch lane?
Explanation:
Traffic jams on boat ramps can be avoided if everyone follows and practices some common courtesy at the ramp. While retrieving the boat from the water surface, it is a common courtesy to place the boat into the launch area only after the towing vehicle has arrived at the ramp. Drop off the driver and then generously wait wait offshore for your turn. Try to clear up the ramp until the trailer arrives at the ramp. This is a most common practice that every body should follow as a common courtesy to others.
Only a _______ technician may wear the ASE insignia on his or her uniform. A. full-time B. certified C. qualified D. dues-paying
Answer:
B. Certified
Explanation: I agree with the other person and i also believe it is correct
What will most likely occur if sulfur forms an ionic bond with another element?
In a collision, the __________ collision is when an unsecured driver strikes the inside of the vehicle.
Answer:
In a collision, the SECOND collision is when an unsecured driver strikes the inside of the vehicle.
Explanation:
When driver in the car is unsecured then it means that the driver is not having his safety seat belt.
Now when collision occurs between the car and some other object then due to the property of inertia of driver it has tendency to move in the direction of his motion.
So the driver will continue his motion and collide with other parts of the car and due to this he may got injured.
So in any car collision there are two types of collision
first is the collision of car with other objects
second collision is between car and the driver inside the car
How do scientists determine the age of the solar system?
In terms of energy, think about what happens when you eat a hot meal. Describe all the different forms of energy that you experience. For example, if you are eating under a lamp, its electromagnetic energy helps you see the food. Explain the source of each form of energy.
Which one of the following does not accurately describe the universal gravitational law? A. Gravitational force is proportional to the square of the distance between the centers of both bodies. B. The object with the smaller mass does most of the moving because the object with the larger mass has too much inertia to move any noticeable amount. C. Gravitational force is proportional to the product of the two masses. D. Every object in the universe that has mass attracts every other object in the universe that has mass.
When you drop a sugar cube in a glass of water, at first the water doesnât taste sweet. later, it tastes very sweet.what causes the change in the waterâs taste?
The velocity of waves having wavelength 0.643 m and frequency 3.25 e 10 hz is
The relationship between velocity (v), wavelength (w) and frequency (f) is expressed as:
v = w f
Plugging in the given values into the equation:
v = 0.643 m (3.25 e 10 Hz)
Where Hz = 1 / s , therefore:
v = 0.643 m (3.25 e 10 / s)
v = 2.09 e 10 m / s
Taking into account the definition of wavelength, frecuency and propagation speed, the velocity of waves having wavelength 0.643 m and frequency 3.25 e 10 Hz is 2.09 e 10 m/s.
What is wavelength, frecuency and propagation speedWavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation: v = f×λ
What is the velocity of waves in this caseIn this case, you know:
f=3.25 e 10 Hzλ=0.643 mReplacing in the definition of propagation speed:
v= 3.25 e 10 Hz× 0.643 m
Solving:
v= 2.09 e 10 m/s
Finally, the velocity of waves having wavelength 0.643 m and frequency 3.25 e 10 Hz is 2.09 e 10 m/s.
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Four students are asked to find the mass of a mineral using a calibrated balance. The results were as follows: 16.009 g, 15.780 g, 16.110 g, and 15.990 g. The known mass of the mineral is 16.100g. Which student's result was the most accurate? The results were _____. 16.009 g 15.780 g 16.110 g 15.990 g
Answer:
16.110 g
Explanation:
Ptolemy's model was __________, with the earth fixed in the center of the universe.
A magnetic field applies forces on:
a.static charges
b.moving charges
c.water flow
Answer:
its b on oddessey ware
Explanation:
Why do you lurch forward in a bus that suddenly slows? why do you lurch backward when it picks up speed? what law applies here?
Final answer:
You lurch forward in a bus that suddenly slows due to Newton's First Law of Motion, or the law of inertia, which suggests an object in motion stays in motion unless acted on by an unbalanced force. When the bus accelerates, inertia causes you to feel pushed back as your body prefers to remain at rest. Understanding this law helps in recognizing the importance of safety measures like seatbelts.
Explanation:
Understanding Movement in a Bus: Newton's First Law of Motion
When a bus suddenly slows down, you lurch forward because of Newton's First Law of Motion, also known as the law of inertia. This law states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Since your body wants to keep moving at the same speed the bus was going before it slowed down, you lurch forward when the bus decelerates.
Similarly, when the bus speeds up, you might feel like you are being pushed back into your seat. This is again due to the law of inertia. Your body wants to remain at its state of rest (or moving at a constant speed if the bus was already moving), so when the bus accelerates, it creates a temporary imbalance, making you feel pushed back.
Using seatbelts or holding onto something stable inside the bus can counteract these effects by providing the necessary force to keep you in place, thereby preventing injury and ensuring safety.
Why Understanding Newton's First Law is Important
The applications of Newton's First Law are seen in everyday life, not just in theoretical physics. It explains a wide range of phenomena, from why it's crucial to wear a seatbelt to the importance of headrests in preventing whiplash injuries. Understanding these principles can help improve personal safety and awareness in moving vehicles.