So the force you have to apply to break the ropes and accelerate the box with a=1 m/s^2 is 2 + √3 + 1 N
Calculating the problem:To determine the force FA that must be applied to break the ropes and accelerate the box with a=1 m/s^2, you can use the equation of motion:
F = ma
where F is the net force acting on the box, m is the mass of the box, and a is the acceleration of the box.
We know that the net force acting on the box is equal to the force applied to it minus the forces of tension in the top and side ropes.
So, F = FA - T1 - T2
and the acceleration of the box is 1 m/s^2
Given that,
FA = m×a + T1 + T2
Substitute the given values for m, a, T1 and T2,
FA = 2 kg × 1 m/s² + √3 N + 1 N
FA = 2 kg × 1 m/s² + √3 N + 1 N
= 2 + √3 + 1 N
What is movement?An object's movement or shift in position in relation to its surroundings over time is referred to as the motion. A subfield of physics that deals with the behavior of physical systems and objects is mechanics, the study of motion.
There are various kinds of motion, such as:
Motion in a line:This is straight-line motion. The linear velocity and acceleration of an object are calculated using the distance and time it takes to travel in a particular direction.
Motion by rotation:An axis is in motion here. When describing an object's rotational motion, the terms "angular displacement," "angular velocity," and "angular acceleration" are utilized.
Rhythmic oscillation: This is a motion that happens over and over again and revolves around a central point. It's called oscillation. A pendulum that swings or a guitar string that vibrates are two examples.
Motion of a projectile: This is the movement of an object that is projected into the air, like a ball that is thrown into the air or a gunshot.
Relational movement: This is how an object moves in relation to a reference point, like how a car moves on a road in relation to the earth.
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can an object be charged negatively with the help of a positively charged object? select all that apply 1. no; negative charges can only be obtained with other negatively charged objects. 2. yes, by letting the two objects touch each other 3. yes, by bringing the positively-charged object near the object to be charged, then discharging the far side 4. yes, by rubbing the two objects together 5. yes, by bringing
Yes, by bringing the positively-charged object near the object to be charged, then discharging the far side.
What is positively-charged?Positively-charged particles, or ions, are atoms or molecules that are missing one or more electrons, giving them a surplus of positive charge. This imbalance between the number of protons and electrons causes the particle to be attracted to objects with a negative charge, such as other ions.
The positively-charged object will cause electrons to be transferred to the object to be charged, thus resulting in a negative charge on the object.
Yes, by rubbing the two objects together. By rubbing the two objects together, electrons can be transferred from one object to the other, thus resulting in negative charge on one object and positive charge on the other.
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expert answer 1 month ago a) determine the distance of the spectrum. write the equation for the diffraction grating for the sodium and substitute the required values to determine the initial angular position of the sodium spectrum of the first order. write the equation for the diffraction grating for the sodium and substitute the required values to determine the final angular position of the sodium spectrum of the first order. determine the angular separation of both closely spaced yellow lines of sodium of the first order. -- b) write the equation for the diffraction grating for the sodium and substitute the required values to determine the initial angular position of the sodium spectrum of the second order. write the equation for the diffraction grating for the sodium and substitute the required values to determine the final angular position of the sodium spectrum of the second order. determine the angular separation of both closely spaced yellow lines of sodium of the second order. -- c) write the equation for the diffraction grating for the sodium and substitute the required values to determine the initial angular position of the sodium spectrum of the third order. write the equation for the diffraction grating for the sodium and substitute the required values to determine the final angular position of the sodium spectrum of the third order. determine the angular separation of both closely spaced yellow lines of sodium of the third order. like 0 the
Where θ 1 is the angle of the first line, and θ 2 is the angle of the second line.
What is angle?Angle is the measure of a turn or displacement between two intersecting lines. Angles are typically measured in degrees, with 360 degrees in a full circle. acute angles are smaller than 90 degrees, while obtuse angles are larger than 90 degrees. Straight angles are exactly 180 degrees, while reflex angles are greater than 180 degrees.
The equation for the diffraction grating for the sodium is:
nλ = d sinθ
Where n is the order of the spectrum, λ is the wavelength of the light, d is the distance of the spectrum, and θ is the angle of the light.
For the first order, the initial angular position is:
nλ = d sinθ
θ = sin-1 (λ/d)
For the first order, the final angular position is:
nλ = d sinθ
θ = sin-1 (λ/d)
The angular separation of the two closely spaced yellow lines of sodium is:
Δθ = θ 1 - θ 2
Where θ 1 is the angle of the first line, and θ 2 is the angle of the second line.
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two point charges placed 5 cm aparnt on the xa axis. at what points along the x axis is the potential zero?
The point where the potential is zero is located at [tex]x = 5 cm * k * Q1/(Q1 + Q2)[/tex]
The potential at a point in space due to a point charge is given by the equation:
V = k * Q/r
where V is the potential, k is the Coulomb constant [tex](8.99 x 10^9 N * m^2/C^2)[/tex], Q is the charge, and r is the distance from the point charge to the point where the potential is being calculated.
In this problem, we have two point charges placed 5 cm apart on the x-axis. How about we call the charges Q1 and Q2, and we should assume that Q1 is located at the origin (x = 0) and Q2 is located at x = 5 cm.
The potential at a point along the x-axis is the amount of the potentials due to each of the point charges.
V = k * Q1/r1 + k * Q2/r2
where r1 is the distance from the point to Q1 and r2 is the distance from the point to Q2.
In the event that the potential at a point is zero, the amount of the potential due to each of the point charges is zero.
So, k * Q1/r1 + k * Q2/r2 = 0
To find the points along the x-axis where the potential is zero, we can set the equation above equal to zero and address for x.
r1 = x and r2 = |x - 5 cm|
k * Q1/x + k * Q2/|x - 5 cm| = 0
x = k * Q1/Q2 * |x - 5 cm|
x = k * Q1 * (5 cm - x)/Q2
x = 5 cm * k * Q1/(Q1 + Q2)
In this way, the point where the potential is zero is located at
x = 5 cm * k * Q1/(Q1 + Q2)
This is valid for any point in the x-axis, and these points are called equipotential points.
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a ringing alarm clock is put under a glass jar. the air is slowly removed from the space around it. what will happen as the air is removed?
The level of the sound can be decreased by gradually draining the air from a plastic bottle. The sound about an alarm clock cannot be heard at all since sound cannot travel through a vacuum.
What will occur once the air is drained away?A ringing alarm clock will gradually grow quieter when air is gently drawn out of the area around it and placed beneath a glass jar. Because sound is indeed a mechanical wave that moves across a medium, this is the case.
We can hear the sound because the air molecules in the jar shake as sound waves pass through them. The amount of air particles available to vibrate and convey sound waves declines when air is eliminated, which lessens the sound's strength. There will be so little remaining air to vibrate due to the almost full removal of the air that the sound will be almost undetectable.
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Calculate the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec. Model the dancer as a cylinder (I = MR 2) with a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m.
The angular momentum of the ballet dancer is 14.98 kgm²/s.
What is the angular momentum of the ballet dancer?The angular momentum of the ballet dancer is calculated by applying the following formula as show below.
L = Iω
where;
I is the moment of inertia of the dancerω is the angular speed of the dancer = 1.5 rev/sec = 9.42 rad/sThe moment of inertia of the dancer, I = MR²
I = 62 kg x (0.16 m )²
I = 1.59 kgm²
The angular momentum of the ballet dancer is calculated as;
L = 1.59 x 9.42
L = 14.98 kgm²/s
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Betty was enjoying the warm sunshine in a park. After a few minutes, it became windy. Betty felt cold and put on her jacket. Which component helps a robot detect such a change in its environment?
A. Sensor
B. Motor
C. Actuator
D. Manipulator
The component of robot which helps detect the change in environment is a sensor. The correct option is A.
Robotics is the study area devoted to creating robots and automation, while a robot is a programmable machine that can execute a task. Different robots have varying degrees of autonomy. These levels range from totally autonomous bots that operate independently to bots that are controlled by humans and accomplish tasks.
Robots consist of some sort of mechanical construction. The mechanical part of a robot helps it perform tasks in the environment for which it was designed.
Robots have some degree of computer programming. If a robot didn't have a set of instructions telling it what to perform, it would just be another piece of simple hardware. Programming a robot can teach it when and how to perform a task.
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A projectile of mass 0.419 kg is shot from
a cannon, at height 6.2 m, as shown in the
figure, with an initial velocity v; having a
horizontal component of 6.7 m/s.
The projectile rises to a maximum height
of 1.6 m above the end of the cannon's barrel
and strikes the ground a horizontal distance
past the end of the cannon's barrel.
Find the magnitude of the initial vertical
velocity vector of the cannon-ball at the end
of the cannon's barrel. The acceleration of
gravity is 9.8 m/s².
The projectile's top height is indicated by the number h. Max equals u squared x divided by 2 g. In this case, the initial horizontal velocity is maximized by u square at a rate of 6 meters per second square.
Find height?The projectile's top height is indicated by the number h. Max equals u squared x divided by 2 g. In this case, the initial horizontal velocity is maximized by u square at a rate of 6 meters per second square.
This rate is then multiplied by two to get 9.8 meters per second square, which equals 1.84 meters.
The projectile can only fly as high as this, then. Here, we already know that the projector is located at a distance of h from the ground, which is the height the projectile has reached from ground level. Please excuse the distance, the cannon is h feet above the ground.
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an object of ma 0.40kg attached to the end of a tring i whirled round in an horizontal circle of radiu 2m with a contant peed of 8m/ calculate the angular velocity of the object
Explanation:
angular velocity = w = v/r
w = 8/2
w = 4rad/s
an object travels in a circular orbit. if the speed of the object is doubled, its centripetal acceleration will be
If an object is traveling in a circular orbit where its speed is doubled, then its centripetal acceleration will be quadrupled.
Centripetal acceleration is the acceleration of an object traversing a circular path. Because velocity is a vector quantity, i.e., it has both a magnitude ( the speed and a direction), so when the object travels on a circular path, its direction changes constantly and thus as a result of this its velocity changes, producing acceleration,
For instance, when an object in a circular orbit is moved with double doubled, then it has quadrupled centripetal acceleration.
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a ufo going 64 m/s west suddenly experienced a constant acceleration for 63 s during which its displacement was 21,892.5 m west. determine the final speed of the ufo
The final speed of the UFO after experiencing a constant acceleration for 63 seconds is 351.3 m/s.
What is accelaration?Acceleration is the rate at which an object increases its speed, velocity or rate of change. It is the rate of change of velocity over time, or the rate of change of the position of an object. Acceleration can be either positive, when the speed of an object is increasing, or negative, when the speed of an object is decreasing.
The final speed of the UFO can be determined by using the equation, v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. So, in this case, v = 64 + (21,892.5/63) = 351.3 m/s. Therefore, the final speed of the UFO after experiencing a constant acceleration for 63 seconds is 351.3 m/s.
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a ball is thrown horizontally from the top of a 70.6-m building and lands 188 m from the base of the building. ignore air resistance. how long is the ball in the air?
A ball launch horizontally from the top of a 70.6-m building lands 188 m from the building's base. The ball will fly for 3.79 seconds.
A displacement is a vector whose length is the shortest distance between a moving point's initial and final positions.
The beginning velocity in the problem is described as horizontal, which implies that the initial vertical velocity(u) is zero. In order to solve for the time of flight using the formula, we also have the height of the building, which is a downward displacement.
We know,
[tex]Y = ut + \frac{1}{2}at^{2}[/tex]
Here, Y = height of the building = 70.6m, u = 0, a = g = 9.81m/[tex]s^{2}[/tex]. We have to find the time of flight t.
⇒ [tex]70.6 = 0*t + \frac{1}{2} (9.81)t^{2}[/tex]
⇒ [tex]t^{2} = 14.3934[/tex]
⇒ [tex]t = 3.79 s[/tex]
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if a spring is released x meters from equilibrium, at what distance from equilibrium will it have acceleration equal to half its maximum acceleration?
When the stretch distances are at half of their maximum displacement, the acceleration will be half of its maximum value by Hooke's Law.
F= -kx
In accordance with Hooke's law, a principle of elasticity, for relatively minor deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load The elasticity of an object is likewise governed by Hooke's law; for example, a metal spring can only be stretched so far before being broken by too much effort. A mass that we already have is then expanded out by x. Displacement and acceleration are inversely related. When the stretch distances are at half of their maximum displacement, the acceleration will be half of its maximum value.
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A car is 180 inches long. A truck is 75 percent longer than rhe car. how long is the truck
The length of the truck that is 75 percent longer than the car is 315 inches.
What is the length of the truck?
The length of the truck that is 75 percent longer than the car is determined from the percentage increment of the truck from the car.
The length of the car is given as 180 inches, then the length of the truck that is 75 percent longer than the car is calculated as follows;
Lt = ( 75 % + 100 % ) x Lc
where;
Lt is the length of the truckLc is the length of the carLt = ( 175% ) x Lc
Lt = ( 1.75 ) x 180 inches
Lt = 315 inches
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Mice can hear sounds with frequencies between 1 kHz and 70 kHz but are there frequencies which mice can hear but humans cannot?
In contrast to the human hearing range of 20 Hz to 20 kHz, mouse hearing extends into the ultrasonic region and ranges from 1 to approximately 100 kHz7,9.
What frequency is too high for human hearing?Our hearing is most sensitive in the frequency range between 2000 and 5000 Hz, however the range of absolute human hearing is 20 to 20,000 Hz. Humans normally have a hearing range of 0 dB and above in terms of loudness.In contrast to the human hearing range of 20 Hz to 20 kHz, mouse hearing extends into the ultrasonic region and ranges from 1 to approximately 100 kHz7,9.The bulk, elasticity, muscles, ligaments, bones, fluid, and inner ear structures all play a role in determining how the ear reacts to sounds. Low frequency noises are resisted by elastic forces, whereas high frequency sounds are resisted by greater masses of force. In this way, frequency range is constrained by mass and elasticity.To learn more about frequency refer to:
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a small metal sphere has a mass of 0.15 g and a charge of - 23.0 nc. it is 10.0 cm directly above an identical sphere that has the same charge. this lower sphere is fixed and cannot move. if the upper sphere is released, it will begin to fall. what is the magnitude of its initial acceleration?
The magnitude of the acceleration is |8.1 * 10^5| m/s^2 = 8.1 * 10^5 m/s^2
What is meant by acceleration?In mechanics, rate of change of velocity of an object with respect to the time is called as acceleration.
As it is known, F = k * (q1 * q2)/r^2
where F is force, k is Coulomb's constant (9 x 10^9 N * m^2/C^2), q1 and q2 are charges of the two spheres, and r is distance between the two spheres.
As we know that , F = m * a
a = F/m
a = (k * (q1 * q2))/r^2) / m
a = (9 * 10^9 N * m^2/C^2 * (-23 * 10^-9 C)^2) / (10^-2 m)^2
Acceleration of the upper sphere is a = -8.1 * 10^5 m/s^2. The negative sign indicates that acceleration is in opposite direction to the force, as expected, since the force is repulsive.
The magnitude of the acceleration is |8.1 * 10^5| m/s^2 = 8.1 * 10^5 m/s^2
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the internal resistance of a battery is 2 ohms. when a resistance of 10 ohms is connected to the battery, it draws 0.6 amp current. the emf of the battery is
The emf of the battery is 7.2 volts when the internal resistance of a battery is 2 ohms. when a resistance of 10 ohms is connected to the battery, it draws a 0.6 amp current.
Given,
Internal resistance, r = 2 ohms
Resistance connected, R = 10 ohms
Current, i = 0.6 amp
let emf = V
Using ohm's law in the circuit
V = i(r+R)
or V = 0.6(2+10) = 0.6 x 12
V = 7.2 volts
Therefore, the emf of the battery is 7.2 volts when the internal resistance of a battery is 2 ohms. when a resistance of 10 ohms is connected to the battery, it draws a 0.6 amp current.
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what is your instantaneous speed at the instant you turn around to move in the opposite direction? (a) depends on how quickly you turn around; (b) always zero; (c) always negative; (d) none of the above.
The instantaneous speed at the instant you turn around to move in the opposite direction is (b) always zero.
We know that the average speed for a given time interval is the total distance traveled divided by the total time taken. As this time interval approaches zero, the distance traveled also approaches zero. But the limit of the ratio of distance and time is non-zero and is called the instantaneous speed. To understand it in simple words we can also say that instantaneous speed at any given time is the magnitude of instantaneous velocity at that time.Instantaneous velocity is defined as the rate of change of position for a time interval which is very small (almost zero). Measured using SI unit m/s. Instantaneous speed is the magnitude of the instantaneous velocity. It has the same value as that of instantaneous velocity but does not have any direction.To know more about speed visit:
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a 9500 pf capacitor holds plus and minus charges of 16.5 x 10e-8 c. what is the voltage across the capacitor?
According to the problem the voltage across the capacitor is 1.73 V.
What is capacitor?A capacitor is an electrical component that stores energy in the form of an electrostatic field. It is composed of two conducting plates separated by an insulating material called a dielectric. When a voltage is applied to the plates, the dielectric stores an electrical charge. Capacitors are used in a variety of electronic devices and are essential for the operation of many electrical and electronic systems.
The voltage across a capacitor is given by V = Q/C, where Q is the charge on the capacitor, and C is the capacitance.
In this case, the charge on the capacitor is 16.5 x 10-8 C, and the capacitance is 9500 pF = 9.5 x 10-8 F.
Therefore, the voltage across the capacitor is V = 16.5 x 10-8 C / 9.5 x 10-8 F = 1.73 V.
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how much natural gas (1019 btu/ ft3) is needed to generate the electricity needed to keep a 100- watt (w) light bulb lit for one (1) year if the overall efficiency of the generating station is 40%?
Only about 40 percent of the thermal energy in coal is converted to electricity, so the electricity generated per ton of coal is 0.4 x 6,150 kWh or 2,460 kWh/ .
Define natural gas?
Natural gas is an odorless, gaseous mixture of hydrocarbons—predominantly made up of methane (CH4). It accounts for about 30% of the energy used in the United States.It is, as the name suggests, a naturally occurring flammable gas that can be used as a fuel or source of energy for a wide range of purposes like cooking, heating, transportation, and power generation.It is formed when layers of decomposing plants and animals are subject to intense heat from the Earth and pressure from rocks. All this pressure, heat and millions of years turned the natural material into coal, petroleum and natural gas.
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A positive charge is brought close to a fixed neutral Which of the figures best represents the charge distribution on the inner and outer walls of the conductor that has a cavity. The cavity is neutral; that is, there is no net charge inside the cavity. Which of the figures best represents the change distribution on the inner and outer walls of the conductor?
The correct option: (e) There is a negative charge on the surface of the cavity, and a positive charge on the outer surface of the conductor.
State the Gauss law for the conductor?Any extra charge on the a conductor will be located on its surface, according to Gauss' Law.
According to Gauss' Law, the surface's electric field and internal charge are related. The charge encapsulated by any surface on the inside of a conductor equals zero since there is no electric field there. Any charge here on conductor must therefore be located on its surface. There wouldn't be an electric field inside the conductor's vicinity if a cavity was cut out of it, and there wouldn't be any charge inside the cavity either. Therefore, the hollow wouldn't have an electric field. Because of electric field should be perpendicular to its surface and the conductor's internal electric field is zero, no flux can penetrate the conductor.Thus, on the cavity's surface there is a negative charge, while the conductor's outer surface has a positive charge.
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The complete question is-
A positive point charge is placed in a cavity inside a neutral conductor without transferring charge to the conductor. What is the sign of the charge on the surface of the cavity and the outer surface of the conductor?
(a) There is no charge on the surface of the cavity or the outer surface of the conductor.
(b) There is a positive charge on the surface of the cavity, but no charge on the outer surface of the conductor.
(c) There is a negative charge on the surface of the cavity, but no charge on the outer surface of the conductor.
(d) There is no charge on the surface of the cavity, but a positive charge on the outer surface of the conductor.
(e) There is a negative charge on the surface of the cavity, and a positive charge on the outer surface of the conductor.
a 6 kg object starts from rest. it is then pushed by a 10 n force for 8 seconds. how much momentum does it have afterward?
The momentum of the object afterwards will be 80 Kgms-1.
Given the following data as per the question:
Mass of the object is given as 6 Kg
Force is given as 10 N in the question
Time is given as the following 8 sec
The value of the Momentum is same as impulse.
So, the formula of impulse is given as:
I = Ft
Where
I is the impulse
F is the force
and t is the time
From the given information,
F = 10 N
t = 8 secs
Therefore,
I = 10 × 8
I = 80 Ns.
Momentum is 80 Kgms-1.
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35. an object of mass 3.00 kg, moving with an initial velocity of 5.001 m/s, collides with and sticks to an object of mass 2.00 kg with an initial velocity of -3.00j m/s. find the fi- nal velocity of the composite object. brainly
The final velocity of the composite object after collision is 1.8002 m/s in the direction of the first object.
Initial velocity of the first object, v₁ = 5.001 m/s
Mass of the first object, m₁ = 3.0 kg
Initial velocity of the second object, v₂ = -3.001 m/s (In opposite direction)
Mass of the second object, m₂ = 2.0 kg
Let the final velocity of the composite object, = V
Mass of the composite object, = (3.0 + 2.0) = 5.0 kg
By the law of conservation of momentum,
m₁v₁ + m₂v₂ = (m₁ + m₂) × V
V = (m₁v₁ + m₂v₂)/(m₁ + m₂)
V = (3 × 5.001 + 2 × (-3.001))/(2 + 3)
V = 9.001/5
V = +1.8006 m/s
Positive sign indicates that the direction of the velocity will be the same as that of the first object.
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A new planet is discovered orbiting a star with a mass 3. 5 × 10^31 kg at a distance of 1. 2x10^11 m. Assume that the orbit is circular. What is the gravitational acceleration on this new planet?
The gravitational acceleration of this new planet is [tex]24.3 * 10^{9} G m/s^{2}[/tex].
Any object located in the field of the planet experiences a gravitational pull. Gravitational acceleration is described as the object receiving an acceleration due to the force of gravity acting on it. It is represented by ‘g’ and its unit is m/s2. Gravitational acceleration is a quantity of vector, that is it has both magnitude and direction.Using the following equation, the gravitational acceleration acting on anybody can be explained. When the object is on or near the surface of the body, the force of gravity acting on the object is almost constant and the following equation can be used:g = GM/R^2
Here,
G = the universal gravitational constant (G = gravitational constant of planet)
M = Mass of planet = [tex]3.5*10^{31} kg[/tex]
R = Radius = 1.2*10^11 m
Putting these values in above equation we get: g= [tex]24.3 * 10^{9} G m/s^{2}[/tex].
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if the average speed of a helium atom at a certain temperature is 1100 m/s, what is the speed in miles per hour? (1 mi
The average speed of a helium atom at a certain temperature is 1100 m/s expressed in miles per hour is: 2460.63 mi/h
What is unit conversion?It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.
To solve this problem the we have to convert the units with the given information.
Information about the problem:
v= 1100 m/sv= mi/h?1 mi= 1609.34 m1 h= 3600 sBy converting the speed units from (m/s) to (mi/h) we have:
v= 1100 m/s * 1 mi/1609.34 m * 3600 s/1 h
v= 2460.63 mi/h
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if 300 waves pass a point in one minute, the frequency is
when 300 waves pass a point in one minute, the frequency is 5 Hz.
What is frequency?Frequency can be defined as, the no.of waves that pass in a unit of time through a fixed point. frequency is measured hertz (Hz)
Define wave and wavelength.Wave: The propagation of disturbances that have place in a medium is referred to as a wave.
There are two types of waves.
1.Longitudinal waves
2.Transverse waves
Wavelength(λ): The distance between two peaks or two troughs can be used to define a wavelength. It is measured in meters (m), centimeters (cm) or millimeters (mm).
Wavelength Formula: λ=ν/f,
where ν is velocity, f is frequency .
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A frequency of 5 Hz is achieved when 300 waves pass a place in one minute.
How can one determine a wave's frequency? A frequency of 5 Hz is achieved when 300 waves pass a place in one minute.By counting how many wave crests—or high points—pass a particular place in a second or other time interval, one may determine the frequency of the waves.More specifically, the frequency of the waves increases with increasing quantity.The number of waves that pass by in a second makes up a wave's frequency, which is expressed in Hertz (Hz).A sound wave, for instance, might be 450 Hz in frequency.Frequency is the measure of how many waves traverse a spot in one second.The total number of occurrences at the conclusion of the observation period serves as the frequency.Count the instances of the behavior that took place throughout the observation period.By how long the activity was noticed, divide the count by that amount.
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a 3500 pf air-gap capacitor is connected to a 22-v battery. if a piece of mica is placed between the plates, how much charge will flow from the battery?
The amount of charge that will flow from the battery is 77000pC
A capacitor is a device that stores electrical charge. The amount of charge stored in a capacitor is proportional to the voltage applied across it, according to the equation Q = C*V.
where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage in volts.
In this case, the capacitance of the air-gap capacitor is 3500pF (pico-farads) and the voltage is 22V, so the charge stored in the capacitor is:
Q = 3500pF * 22V = 77000pC (pico-coulombs)
When a piece of mica is placed between the plates, it reduces the space between the plates, which will increase the capacitance of the capacitor. The increase in capacitance will result in an increase in the amount of charge stored in the capacitor.
It's worth noting that the charge that flows from the battery is equal to the initial charge stored in the capacitor. Since the initial charge stored in the capacitor is 77000pC, this is the amount of charge that will flow from the battery.
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at what angular velocity is the centripetal acceleration 10.5 g if the rider is 12.5 m from the center of rotation? give your answer in rad/s.
The angular velocity of the rider is 2.9 rad/s. The result is obtained by using the formulas in circular motion.
What is circular motion?Circular motion is a motion of an object along a circular path. When an object moves with an acceleration, it has a centripetal acceleration calculated by
ac = v²/r
Where
ac = centripetal acceleration (m/s²)v = linear velocity (m/s)r = radius (m)In circular motion, an object moves with linear and angular velocity. The relationship between both velocities is
v = ωr
Where
ω = angular velocity (rad/s)A rider moves in a circular motion with
Centripetal acceleration, ac = 10.5gRadius, r = 12.5 mFind the angular velocity! (ω = ?)
We find the centripetal acceleration in m/s².
ac = 10.5g
ac = 10.5 × 9.8 m/s²
ac = 102.9 m/s²
The linear velocity is
ac = v²/r
102.9 = v²/12.5
v² = 102.9 × 12.5
v² = 1,286.25
v ≈ 35.9 m/s
Use the equation of relationship between linear and angular velocity!
v = ωr
35.9 = ω (12.5)
ω ≈ 2.9 rad/s
Hence, the rider has the angular velocity of 2.9 rad/s.
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A 1400 kg car traveling at 13.5 m/s to the south collides with a 6400 kg truck that is initially at rest at a stoplight. The car and truck stick together and move together after
the collision. What is the final velocity of the two-vehicle mass? Assume that North is positive. Answer in units of m/s. Answer in units of m/s.
The final velocity of the two-vehicle mass is 2.42m/s.
What is Momentum?Momentum is defined as the product of mass and velocity of an object which is a vector quantity, which has a magnitude and a direction. If m is the mass of an object and v is its velocity, then p is the momentum of the object: [tex]\mathbf{p} = m \mathbf{v}.[/tex]
For above given information,
[tex]m_1= 1400kg\\m_2= 6400kg\\v_1_i=-13.5 m/s\\v_2_i= 0m/s[/tex]
Formula for this is:
[tex]m_1.v_1_i+m_2.v_2_i= (m_1+m_2)v_f[/tex]
(1400.-13.5)+ (6400.0) = (1400+6400).[tex]v_f[/tex]
-18900=7800.[tex]v_f[/tex]
-18900/7800=[tex]v_f[/tex]
[tex]v_f= 2.42m/s[/tex]
Thus, the final velocity of the two-vehicle mass is 2.42m/s.
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Korbel pushes a 15 kg chair for a distance of 30 meters. How much
work did he do?
The work that has been done by the Korbel is 4.41kJ.
What is the work done?We have to note that we define work in physics as the product of the force and the distance. In the case of the chair in the question, we have been told that Korbel pushes a 15 kg chair for a distance of 30 meters.
The force in this case would be the weight of the chair that we have and we can write that;
W = mgh
m = mass
g = acceleration due to gravity
h = height
Thus
W = 15 * 9.8 * 30
W = 4.41kJ
Thus a work of about 4.41kJ is done.
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a car drives straight off a flat cliff that is 57 m high (its initial velocity is purely horizontal). the point of impact is 130 m from the base of the cliff. how fast was the car traveling when it went over the cliff?
The speed of the car traveling when it went over the cliff is 38.12 m/s.
The equation of motion for calculating the displacement of a moving object is given as
[tex]S = ut + \frac{1}{2} at^{2}[/tex]
u = initial velocity
t = time taken
a = acceleration of the object
S = displacement of the object
The above equation can be used to find out the speed of the car.
In this case, the initial velocity, u, is zero because the car falls under gravity. The acceleration, a, will be considered as acceleration due to gravity (g). The time taken is the 'time of flight' taken as 't' and S is taken as the height (h) of the flat cliff.Therefore, the above equation can be written as
[tex]h = \frac{1}{2} gt^{2}\\t = \sqrt[]{\frac{2h}{g} } \\t = \sqrt[]{\frac{2(57)}{9.8} } \\\\t = 3.41 s[/tex]
Therefore, the time of flight = 3.41 s.
If the point of impact from the base of the cliff is 130 m and the time of flight is 3.41 s.
Then, the velocity of the car traveling over the cliff is calculated as
[tex]v = \frac{point of impact}{t} \\\\v = \frac{130}{3.41} \\\\v = 38.12 m/s[/tex]
The velocity of the car traveling when it went over the cliff is 38.12 m/s.
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