The four equations for acceleration are obtained from the three equations of motion and from second law of motion.
Explanation:
Acceleration is defined as the rate of change of velocity with respect to time. So the change in velocity with respect to time can be determined using the three equations of motions.
So from the first equation of motion, v = u + at , we can determine the value of acceleration if time taken, final and initial velocity is known. The equation can be re-written as [tex]a = \frac{v-u}{t}[/tex]
Similarly, from the second equation of motion, s = ut + 1/2 at², we can determine the equation for acceleration as [tex]a = 2*\frac{s-ut}{t^{2} }[/tex]
So this is second equation for acceleration.
Then from the third equation of motion, [tex]v^{2}- u^{2} = 2* a *s[/tex]
the acceleration equation is determined as [tex]a = \frac{v^{2}-u^{2} }{2s}[/tex]
In addition to these three equation, another equation is present to determine the acceleration with respect to force from the Newton's second law of motion. F = Mass × acceleration. From this, acceleration = Force/mass.
So, these are the four equations for acceleration.
This is may mastering physics homework and I just need help solving the question.
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc's body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 27 rpm when Luc brings his hands in to his chest.
Answer:
Angular speed of the disc after he fold his hands is given as
[tex]\omega_f = 27.5 rpm[/tex]
Explanation:
As we know that the moment of inertia of the solid cylinder is given as
[tex]I_1 = \frac{m_1r_1^2}{2}[/tex]
so we have
[tex]I_1 = \frac{(950/9.81)(0.20)^2}{2}[/tex]
[tex]I_1 = 1.94 kg m^2[/tex]
now moment of inertia of two dumbbell in his hand is given as
[tex]I_2 = 2(m_2 r_2^2)[/tex]
[tex]I_2 = 2(4)(0.85)^2[/tex]
[tex]I_2 = 5.78 kg m^2[/tex]
Now moment of inertia of the disc is given as
[tex]I_3 = \frac{1}{2}MR^2[/tex]
[tex]I_3 = \frac{1}{2}(1500/9.81)(2^2)[/tex]
[tex]I_3 = 305.8 kg m^2[/tex]
Now we can use angular momentum conservation as there is no external torque on it
[tex](I_1 + I_2 + I_3) \omega_i = (I_1 + I_3)\omega_f[/tex]
[tex](1.94 + 5.78 + 305.8) 27 = (1.94 + 305.8) \omega_f[/tex]
[tex]\omega_f = 27.5 rpm[/tex]
Answer: Hello above answerer, Why didn't you add I2 on the other side of the equation?
You just added I1 and I3
Explanation:
Wind blowing sand from one location to another is an example of
erosion
movement
weathering
deposition
Wind blowing sand from one location to another is an example of erosion. Sand being blown by the wind from one place to another is an actual instance of erosion.
When the wind's force moves and displaces loose sand or other sediment particles, the process is known as wind erosion. Sand particles are picked up and carried by the wind as it sweeps across an open surface, where they impact with other items or surfaces.
Rocks, dunes, cliffs, and other geological structures can all be eroded over time as a result of the continuous movement and influence of wind-blown sand on the environment. Deserts and sandy ecosystems are mostly shaped by wind erosion on a global scale.
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Elements have the same number of ______ as you move from left to right
Answer:
protons
Explanation:
Answer:
Electron shells
Explanation:
When the number of electrons striking the anode of an x-ray tube is increased, the ____ of emitted X-Rays increases.
1. density
2. frequency
When the number of electrons striking the anode of an x-ray tube is increased, the density of emitted X-Rays increases.
Option: 1
Explanation:
As the electron speed increases, the heat radiation also increases from thermionic emission, which causes more heat and more X-ray release. X-rays are produced by an a vacuum tube called X-ray tube that uses more voltage to make the electrons accelerate which the hot cathode releases to a high velocity.
This high speed electrons meets in a collision with a metal target which is the anode, and thus create the X-rays. So, the electron number available and the time period set for their release from the filament determines how many x-rays are produced from the anode. Hence, more the number of electrons striking the anode,the more is the emission of x-rays.
When you are running around a track, what kind of energy are you using?
Answer:
kinetic energy
Explanation:
we are using chemical energy in our bodies to produce movement, whitch in turn convents to warmth.
Final answer:
While running around a track, the main type of energy used is kinetic energy, the energy of motion. Gravitational potential energy also plays a role when changing elevation. Energy from food provides the caloric input, but losses to heat and friction during digestion and running result in less energy available for motion.
Explanation:
When you are running around a track, the kind of energy you are using is primarily kinetic energy. This is the energy that an object possesses due to its motion. As you exert force on the ground, for instance when a sprinter's foot pushes off the track, kinetic energy increases, which prevents the runner from slowing down. This aspect of energy in motion is known as work being done on the runner by the force exerted through the ground.
Additionally, when a runner is starting or going uphill, potential energy, specifically gravitational potential energy, comes into play. This type of energy is relative to the position of the runner's body and the Earth's gravitational pull. As they ascend, they gain potential energy, which can be converted into kinetic energy as they descend.
2 characteristics of constant speed
Answer:
it has no acceleration
Explanation:
What is the acceleration of the object?
Answer:
Explanation:
Velocity is changing by a constant amount -10 m/s-in second of time.Anytime an object's velocity is changing,the object is said to be accelerating;it has an acceleration.
Answer:
[tex]\boxed{\mathrm{view \ explanation}}[/tex]
Explanation:
[tex]\displaystyle Acceleration =\frac{change \ in \ velocity}{elapsed \ time}[/tex]
[tex]\displaystyle A=\frac{V_f-V_i}{t}[/tex]
Does reflection occur when a wave bounces off a surface that cannot pass through
Answer: yes
Explanation: bc
Based on the idea of isostasy, which of these statements is NOT correct?
A) Continental crust is less dense than oceanic crust.
B) The depth at which a crustal plate sits is a function of its mass.
C) When more weight is added to the crust, through a process like mountain building, it slowly sinks deeper into the mantle.
D) The formation ice sheets cause the Earth's surface to sink so much that when the ice melts, the crust and mantle does not rebound.
The formation ice sheets cause the Earth's surface to sink so much that when the ice melts, the crust and mantle does not rebound.
Explanation:
The above-mentioned statement is the only false statement
During the Ice ages, large continental parts were covered under thick ice sheets. This imposed a superincumbent additional load on the Earth's crust.
Isostasy refers to the balance that exists between parts of Earth's mantle and crust. Isostatic adjustments are a common phenomenon. As a result of isostatic adjustments, several parts of the world have risen by as much as 900 feet as an adjustment to superincumbent load since ice ages. E.g. Parts of Scandinavian countries have witnessed these activities and also undergoing this process.
Answer: d
Explanation:
A certain microwave has a
wavelength of 0.032 meters. Calculate the frequency of this
microwave
Answer:
[tex]9.375\times 10^{9} Hz[/tex]
Explanation:
Frequency is mathematically defined as the quotient of speed divided by wavelength.
[tex]Frequency= \frac {v}{W}[/tex]
where
v-is the speed of light
-w is wavelength.
Given the speed of the wave as [tex]V=300000000 \ m/s[/tex] and the wavelength [tex]\lambda= 0.032\ m[/tex], we substitute these values in the Frequency function to solve for frequency:
[tex]Frequency=\frac {300000000}{0.032}=9375000000 Hz=9.375\times 10^{9} Hz[/tex]
Hence, the wave's frequency is [tex]9.375\times 10^9\ Hz[/tex]
Microwave has the wavelength of 0.032 meters so, the frequency is [tex]\rm 9.375\times 10^9 \; Hz[/tex] and this will be determined by using the frequency formula.
Given :
Wavelength = 0.032 m
The Formula of Frequency can be used to determine the wavelength of the microwave:
[tex]\rm Frequency = \dfrac{c}{w}[/tex] --- (1)
where, [tex]\rm c = 3 \times 10^8\;m/sec[/tex] is the speed of light and w is the wavelength.
Now, put the values of speed of light (c) and wavelength (w) in equation (1).
[tex]\rm Frequency = \dfrac{3\times 10^8}{0.032}[/tex]
[tex]\rm Frequency = 9.375\times 10^9 \; Hz[/tex]
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A charge of 4.5 × 10-5 C is placed in an electric field with a strength of 2.0 × 104 StartFraction N over C EndFraction. If the charge is 0.030 m from the source of the electric field, what is the electric potential energy of the charge?
Answer:
0.027 J
Explanation:
The electric potential energy of the charge is given by:
[tex]U=qEd[/tex]
where:
q is the magnitude of the charge
E is the strength of the electric field
d is the distance of the charge from the source of the field
In this problem, we have:
[tex]q=4.5\cdot 10^{-5}C[/tex] is the charge
[tex]E=2.0\cdot 10^4 V/m[/tex] is the strength of the field
d = 0.030 m is the distance of the charge
So, its electric potential energy is
[tex]U=(4.5\cdot 10^{-5})(2.0\cdot 10^4)(0.030)=0.027 J[/tex]
Answer:
.027 J
Explanation:
The truck’s motor is creating 500 N of thrust, but air resistance is placing 500 N in the opposite direction
Explain how water freezing and thawing causes weathering and the type of weathering it would be considered.
Final answer:
Water freezing and thawing causes weathering through a process called frost or ice wedging. This leads to the physical weathering of rocks or soil. In areas with frequent freeze-thaw cycles, such as Iceland, this process can gradually break down rocks into smaller pieces.
Explanation:
Water freezing and thawing can cause weathering through a process called frost or ice wedging. When water freezes, it expands by about 9%, exerting pressure on the rocks or soil in which it is trapped. This pressure can cause the rocks to crack or break apart, leading to physical weathering. As the ice thaws, water seeps into the cracks and when it freezes again, it widens the cracks further, gradually breaking down the rock. This type of weathering is known as mechanical weathering. It is a significant process in areas with frequent freeze-thaw cycles.
Example: In regions with colder climates, such as Iceland, freezing and thawing of water can weather rocks over time. The repeated cycles of freezing and thawing cause the rocks to deteriorate and break down into smaller pieces, contributing to the formation of gravel, sand, and clay.
The magnitudes of the vertical and horizontal components of a vector are 11 and 17 centimeters respectively. Find the magnitude of the vector and the angle from the horizontal axis.
Explanation:
let the magnitude of the vector be |A|
|A| = ✓11^2 + 17^2 =
|A| =✓410
|A| = 20.23
theta =Tan^-1(11/17) =32.91°
Explanation: edmentum answer
Suppose a truck has a momentum of 40,120 kg • meters per second and a mass of 1,180 kg. What is the truck’s velocity?
4.7 × 107 meters per second
47 × 107 meters per second
34 meters per second
3.4 meters per second
Final answer:
To find the velocity of a truck given its momentum and mass, divide the momentum by the mass; the truck has a velocity of 34 meters per second.
Explanation:
The question is asking us to calculate the velocity of a truck given its momentum and mass. The formula to find velocity when momentum and mass are known is velocity = momentum / mass.
Plug in the values to get the velocity: velocity = 40,120 kg·m/s ÷ 1,180 kg = 34 m/s. Therefore, the velocity of the truck is 34 meters per second.
To find the velocity of a truck given its momentum and mass, divide the momentum by the mass; the truck has a velocity of 34 meters per second.
Which of the following materials offer the least electrical resistance? Pure water, wood, salt water, glass
Salt water offers the least electrical resistance.
Explanation:
Least electrical resistance indicates that any material which readily allows the electric current through itself, and shows more conductivity.
Here pure water doesn't contain any ions, so it is a bad conductor.
Wood and glass are also bad conductors of electricity.
Salt water contains ions, which conducts electricity which means it shows least electrical resistance.
Answer:
salt water
Explanation:
So
Some lakes, such as the Great Salt Lake, accumulate soluble minerals such as salt. In
those lakes, people find it much easier to float than when they are in fresh water. Why is
this the case?
The reason for people to swim easier in salt water than fresh water is because of buoyancy
Explanation:
In fresh water there is lack of minerals and has fresh water alone. The density of fresh water is 1000 kg/m³. Hence, in fresh water cannot exert the suitable buoyancy for the swimmer to float easier than that of salt water.
But in Salt water due to enrichment of salts and minerals it is found that salt water has more density than fresh water. Here the salt water offers more buoyancy to the swimmer to lift him up in the water surface and to swim faster and easier than fresh water.
It is similar to that egg floats in the salt water and sinks inside the fresh water because of its own body weight.
Compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2.00 m. Assume the electrons have a mass of 9.11 × 10–31 kg and a charge of 1.61 × 10–19 C. Round to two decimal places
Answer:
1) 5.83
2) 1.38
3) 4.22
Explanation:
The electrostatic force exerted tow electrons on each other is equal to 5.83 × 10⁻²⁹ N. The gravitational force is 1.38 × 10⁻⁷¹ N.
What is coulomb's law?According to this law, the force of attraction between two charged particles can be written as the product of their charges on them and is the inverse of the square of the distance by which they are separated.
The magnitude of the electrostatic force between charges is given by:
[tex]\displaystyle F = k\frac{q_1q_2}{r^2}[/tex]
where k has a value of 8.99 × 10⁹ N.m²/C².
Given the charge on one electron, q₁ = q₂ = 1.61 × 10⁻¹⁹
The distance between these two electrons, r = 2.00 m
The magnitude of electric force between the electrons will be:
F = 8.99 × 10⁻⁹ × (1.61 × 10⁻¹⁹)²/ (2.00)²
F = 5.83 × 10⁻²⁹ N
The gravitational force between two electrons is equal to:
[tex]\displaystyle F = G\frac{m_1m_2}{r^2}[/tex]
F' = 6.674 × 10⁻¹¹ × (9.1 × 10⁻³¹)²/ (2.00)²
F' = 1.38 × 10⁻⁷¹ N
F/F' = 4.23 × 10⁴² N
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What circuit that has only one path for the
current to follow?
Answer:
Series circuit
Explanation:
By definition series circuit is a closed circuit in which the flow of electric current follows only one path.
In a simple electrical circuit (which is a series circuit) where electric cell is the source of power, each component is connected in such a way that there is only one pathway current flows from the positive terminal(+) round to the negative terminal(-) via the external circuit.
Current having only one pathway to flow means that when one of the components is removed, there will be no current flow.
What are some physical activities you can do at home to help you with arm strength , as well as
leg strength? Describe the activity ? Describe the amount of reps, and sets you will be doing per activity. 1 paragraph
Answer:
See the explanation below
Explanation:
To improve the strength in the arms can be performed arm push-ups, there are different variants for this exercise. But ideally, perform the known basic exercise, try to touch with the chest the floor and then rise up to the length of the arms using the strength of these. It will be necessary for beginners to perform a routine of 3 sets to 10 repetitions. Rest one day. In the third week you can perform 4 sets to 25 repetitions, resting only one day. This will improve the strength in the arms considerably.
For the legs should stimulate the muscle of the quadriceps, should perform an exercise known as squat, to perform it should be lowered with your back straight until the knees form an angle of 90 degrees, for beginners should perform 3 sets of 15 repetitions a day, resting only one day. In the second week you can perform 4 sets of 25 repetitions a day, resting one day a week.
The circumference of the earth is 40,000 km. The distance from the
North Pole to the equator is 1/4 of the circumference of the earth, which equals __ m.
Answer:
The distance from the North Pole to the equator is [tex]1*10^{7}[/tex]m.
Explanation:
Circumference of Earth = 40,000 km ......................(1)
Distance from the North Pole to the Equator is = 1/4th of the Circumference of Earth ...................... (2)
Let Distance from the North Pole to the Equator be d ,
the equation formed will be ,
d = 1/4 * Circumference of Earth ........(3)......... ( from equation 1 )
put the value of Circumference of Earth in equation (3),
d = 1/4 * 40,000 km
d = 10,000 km
converting km to m ,
d = 10,000 * [tex]10^{3}[/tex] m
d = 1 * [tex]10^{7}[/tex] m
The distance from the North Pole to the equator is [tex]1*10^{7}[/tex]m.
The distance from the North Pole to the equator is 1/4 of the Earth's circumference, which equals 10,000,000 meters.
Explanation:The distance from the North Pole to the equator is 1/4 of the circumference of the earth. Given that the circumference of the earth is 40,000 kilometers, we can calculate this by dividing the circumference by 4. So, 40,000 km ÷ 4 = 10,000 km. To convert this into meters, we multiply by 1,000 (since there are 1,000 meters in a kilometer), thus 10,000 km × 1,000 = 10,000,000 meters. The distance from the North Pole to the equator is 1/4 of the circumference of the earth. The circumference of the earth is 40,000 km, so 1/4 of that distance would be 10,000 km.
1. Identify whether the following statements describe a change in acceleration. Explain your response.
a. A car stopped at a stop sign.
b. A boat traveling east at 10 knots.
c. An airplane traveling north 600 miles per hour.
d. A person running at 5 meters/second along a curving path.
Answers:
a. Change in acceleration
b. Not change in acceleration.
c. Not change in acceleration.
d. Change in acceleration
Explanation:
Let's begin by explaining what acceleration is:
Acceleration [tex]a[/tex] is initially defined as the variation of Velocity [tex]\Delta V[/tex] in time [tex]\Delta t[/tex]:
[tex]a=\frac{\Delta V}{\Delta t}[/tex]
However, we cannot forget acceleration is a vector quantity as well (like velocity) and as a vector it has magnitude and direction.
So, when one of these aspects changes (or both) acceleration changes as well.
In other words: A change in acceleration implies the change in velocity, or a change in direction, or both.
Having this clear, we can identify the statements that describe a change in acceleration:
a. A car stopped at a stop sign.
Change in acceleration, since the car changed its velocity.
b. A boat traveling east at 10 knots.
Not a change in acceleration, since the boat is travelling at a constant velocity and is not changing its direction.
c. An airplane traveling north 600 miles per hour.
Not a change in acceleration, since the airplane is travelling at a constant velocity and is not changing its direction.
d. A person running at 5 meters/second along a curving path
Change in acceleration, since the person is changing its direction in the curving path.
Infrasounds _____.
can be used to view internal organs
are sounds with frequencies below 20 Hz
are sounds with frequencies above 20,000 Hz
travel in transverse waves
Infra sounds are sounds with frequencies below 20 Hz.The popular concept that infra sounds are in audible holds false
Explanation:
Some example of Infrasounds are- some animals such as whales, elephants and giraffes which communicate with each other using infrasound over long distances. Various natural phenomenon such as Avalanches, volcanoes, earthquakes, ocean waves, water falls and meteors also generate infrasonic wavesInfrasound, is sound that is lower in frequency than 20 Hz or cycles per second.Even the human body can generate mechanical vibrations at very low frequencies, which are known as the infrasonic waves. Such low-frequency vibrations/infrasonic waves are produced by physiological processes—such as heartbeats, respiratory movements, blood flow in vessels, and other processes.A car accelerates from 20mi/hr to 60mi/hr. How many times greater is the car's kinetic energy at the higher speed compared to the kinetic energy at the slower speed
Answer:
9 times
Explanation:
Kinetic energy is:
KE = ½ mv²
When we triple the velocity, the kinetic energy increases by a factor of 9.
9KE = ½ m(3v)²
The kinetic energy of the car at 60 m/hr is 9 times greater than the kinetic energy at 20 m/hr.
What do you mean by kinetic energy?Kinetic energy is a form of energy that an object possesses by virtue of its motion and is dependent on the mass and velocity of the object.
The kinetic energy of an object is given by the equation:
KE = (1/2)mv²
Where
KE = is the kinetic energy,
m = is the mass of the object,
v = its velocity.
Here in this question,
The kinetic energy of an object is proportional to the square of its velocity, so if a car accelerates from 20 km/hr to 60 km/hr, its kinetic energy at the higher speed will be:
KE(higher) = 1/2 ×m × v(higher)²
And at the lower speed, the kinetic energy will be:
KE(lower) = 1/2 ×m × v(lower)²
Where
m = the mass of the car.
Now for ratio, we have to divide the two equations:
KE(higher) / KE(lower) = [1/2× m ×v(higher)²] / [1/2 × m × v(lower)²]
The mass of the car cancels out, leaving us with:
KE(higher) / KE(lower) = (v(higher)²) / (v(lower)²)
Now, we get:
KE(higher) / KE(lower) = (60²) / (20²) = 9
Therefore, the kinetic energy of the car which is moving at a speed of 60 m/hr is 9 times greater than the kinetic energy of the car which is moving at 20 m/hr.
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How much force is required to accelerate a 50 kg with a mass at 4 m/s2?
Answer:200N
Explanation:
Mass=50kg
Acceleration=4m/s^2
Force=mass x acceleration
Force=50 x 4
Force=200N
If the vector below is multiplied by 2, what will be its end point?
Answer:
If the scalar is negative, then multiplying a vector by it changes the vector’s magnitude and gives the new vector the opposite direction. For example, if you multiply by –2, the magnitude doubles but the direction changes. We can summarize these rules in the following way: When vector A is multiplied by a scalar c
Explanation:
Answer: (4, -2)
Explanation:
The vector shown in the image is (2, -1)
2. Now, the scalar multiplication for vectors works in the next way:
3. for a scalar c and a vector (x,y)
4. c*(x,y) = (c*x, c*y)
5. In our case, the scalar is 2, and the vector is (2, -1)
6. 2*(2, - 1) = (2*2, -1*2) = (4, -2)
Need help pls (projectiles)
A) 13.13 m (4.13 m above the top of the ramp)
B) 0.92 s, 30.0 m (14.4 m from the top of the ramp)
Explanation:
A)
The motion of the projectile consists of two independent motions:
- A uniform motion along the horizontal direction (constant horizontal velocity)
- A uniformly accelerated motion along the vertical direction (constant downward acceleration)
To find the maximum height, we just analyze the vertical motion.
The initial vertical velocity of the projectile is given by:
[tex]u_y = u sin \theta = (18)(sin 30^{\circ})=9 m/s[/tex]
Where
u = 18 m/s is the initial velocity
[tex]\theta=30^{\circ}[/tex] is the angle of projection
Since this is a uniformly accelerated motion, we can use the following suvat equation:
[tex]v_y^2-u_y^2=2as[/tex]
where:
[tex]v_y=0[/tex] is the final vertical velocity when the projectile reaches the maximum height
[tex]a=-g=-9.8 m/s^2[/tex] is the acceleration due to gravity (negative because it is downward)
s is the vertical displacement
Re-arranging, we find s:
[tex]s=\frac{v_y^2-u_y^2}{2a}=\frac{0^2-(9)^2}{2(-9.8)}=4.13 m[/tex]
However, this is the vertical displacement above the top of the ramp. We see that the ramp is [tex]d=15.6 m[/tex] long in the horizontal direction, so the height of the ramp is
[tex]h=d tan \theta=(15.6)(tan 30^{\circ})=9m[/tex]
So, the maximum height of the projectile is:
[tex]H=h+s=9+4.13 = 13.13 m[/tex]
B)
To find the time at which the projectile reaches the maximum height, we use another suvat equation:
[tex]v_y=u_y + at[/tex]
where:
[tex]v_y=0[/tex] is the vertical velocity at the maximum height
[tex]a=-9.8 m/s^2[/tex] is the acceleration due to gravity
[tex]u_y = 9 m/s[/tex] is the initial vertical velocity
Solving for t, we find the time:
[tex]t=\frac{v_y-u_y}{a}=\frac{0-9}{-9.8}=0.92 s[/tex]
The horizontal position of the projectile instead is given by the equation for uniform motion:
[tex]x(t)=v_x t[/tex]
where:
[tex]v_x = u cos \theta = (18)(cos 30^{\circ})=15.6 m/s[/tex] is the initial horizontal velocity
Substituting t = 0.92 s, we find:
[tex]x=(15.6)(0.92)=14.4 m[/tex]
So, this is the horizontal distance covered from the top of the ramp at the instant of maximum height; and therefore, the horizontal distance from the beginning of the ramp is
[tex]d=15.6+14.4=30.0 m[/tex]
A tuning fork vibrating at 512 Hz is held near one end of a tube of length that is open at both ends, as shown above. The column of air in the tube resonates at its fundamental frequency. The speed of sound in air is 340 m/s. Calculate the length of the tube.
Answer:
Length of the pipe is 33.2 cm
Explanation:
As we know that the frequency of the sound in open end pipe is given as
[tex]f = \frac{v}{2L}[/tex]
so here we will have
f = 512 Hz
v = 340 m/s
so now we have
[tex]512 = \frac{340}{2L}[/tex]
[tex]L = \frac{170}{512}[/tex]
[tex]L = 33.2 cm[/tex]
Final answer:
To calculate the length of a tube open at both ends with a given frequency and speed of sound, we can rearrange the formula ν = v / (2L) and solve for L, giving a length of 0.332 m for a 512 Hz tuning fork.
Explanation:
A tuning fork vibrating at 512 Hz is held near one end of a tube of length that is open at both ends. The tube resonates at its fundamental frequency. To calculate the length of the tube given the speed of sound in air is 340 m/s, we use the formula for the fundamental frequency of a tube open at both ends, which is ν = v / (2L), where ν is the frequency (512 Hz), v is the speed of sound (340 m/s), and L is the length of the tube we are looking for.
Rearranging the formula, we get L = v / (2ν). Plugging in the numbers, L = 340 m/s / (2 × 512 Hz) = 0.33203125 meters, which can be rounded to 0.332 m or 33.2 cm.
Two equal and opposite charges separated by a distance, d, experience an attractive force, F. If each charge is doubled in magnitude, what should be the new distance between them so that the force remains unchanged?
If the each charge is doubled in magnitude and force remains unchanged then the distance between the charged particle is four times the original distance.
Explanation:
The force between two charged objects are shown by Coulomb's law.
In the scalar form, this law is represented as:
[tex]F = k \frac{q_1 q_2}{d^2}[/tex]
where,
k = coulomb's constant
q₁ and q₂ are the magnitude of charged objects
d = distance between the charges.
According to the question,
Case1:
charge on object 1 = +q₁
Charge on object 2 = -q₂
Distance between the charges = d
[tex]Force, F = k\frac{+q_1 X -q_2}{d^2} \\\\F = k\frac{-q_1q_2}{d^2}[/tex]
Case 2:
Charge on object 1 = +2q₁
Charge on object 2 = -2q₂
Force between the objects is same
New distance, dₓ = ?
If both the forces are equal then,
[tex]k\frac{-q_1q_2}{d^2} = k\frac{+2q_1 X -2q_2}{d_x^2} \\\\[/tex]
On simplifying the equation we get,
[tex]\frac{-1}{d^2} = \frac{-4}{d_x^2} \\\\d_x^2 = 4d^2[/tex]
So, if the each charge is doubled in magnitude and force remains unchanged then the distance between the charged particle is four times the original distance.
If the charges are doubled and the force is to remain the same, the new distance between the charges should be the initial distance multiplied by the square root of 2.
Explanation:The force experienced by two equal and opposite charges separated by a distance d can be calculated using Coulomb's Law: F = k*q1*q2/d^2, where F is the force, k is a constant, q1 & q2 are the charges, and d is the distance between them. If the magnitude of each charge is doubled, the equation becomes F = k*2q1*2q2/d'^2, where d' is the new distance. If we want the force to remain unchanged, we have the equation: k*q1*q2/d^2 = k*2q1*2q2/d'^2. Solving for d', we get d' = sqrt (2) * d. Therefore, the new distance between the charges should be sqrt (2) times the initial distance to keep the force the same when the magnitude of the charges is doubled.
Learn more about Coulomb's Law here:https://brainly.com/question/32002600
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one cubic foot of water can store 312btu. a home requires 100,000 what is the volume
Volume of water required to store 100,000 Btu of thermal energy is [tex]320.51foot^{3}[/tex] .
Explanation:
The complete question is : One cubic foot of water can store 312 Btu of thermal energy. On a cold winter day a well-constructed home may require 100,000 Btu of nighttime space heating. What is the volume of water required to store this energy? In this question , it's given that One cubic foot of water can store 312 Btu of thermal energy or 312 Btu takes 1 cubic foot of water ,So
1 Btu takes [tex]\frac{1}{312}[/tex] cubic foot of water
Therefore, 100,000 Btu takes:
⇒ [tex]volume = \frac{1}{312}(100,000)[/tex] [tex]foot^{3}[/tex]
⇒ [tex]volume = \frac{100,000}{312}[/tex] [tex]foot^{3}[/tex]
⇒ [tex]volume = 320.51[/tex] [tex]foot^{3}[/tex]
∴ Volume of water required to store 100,000 Btu of thermal energy is [tex]320.51foot^{3}[/tex] .