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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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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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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Find the tension in the two ropes that are holding the 4. 2 kg object in place.
Rope 1 : θ = 57. 6° with respect to the vertical. Rope 2: θ = 33. 8° with respect to the vertical
The tension in the rope at the 57. 6° angle is 48.58 N, and the tension in the rope at the 33. 8° angle is 36.28 N.
What is meant by angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.Angles with a measurement of zero degrees or zero radians are referred to as zero angles. No of the unit of measurement, the zero angle has a measure of.The tension force exerted by the first rope, T1
The tension force exerted by the second rope, T2
and the force of gravity, mg
T1x = −T1 cos 57.6°
T2x = T2 cos 33.8°
mgx = 0
T1y = T1 sin 57.6°
T2y = T2 sin 33.8°
mgy = −mg
Thus, the x and y components of the resultant force will be:
x:
Rx = T1x + T2x + mgx
Rx = −T1 cos 57.6° + T2 cos 33.8° + 0
Rx = T2 cos 33.8° − T1 cos 57.6° (1)
y:
Ry = T1y + T2y + mgy
Ry = T1 sin57.6°+ T2 sin 33.8° + (−mg)
Ry = T1 sin 57.6° + T2 sin33.8° − mg (2)
The next step is to substitute Rx and Ry in Eq. (1) and Eq. (2) with 0:
Rx = T2 cos 33.8° − T1 cos 57.6°
Ry = T1 sin57.6° + T2 sin 33.8° − mg
↓
0 = T2 cos33.8°− T1 cos 57.6° (3)
0 = T1 sin57.6°+ T2 sin 33.8°− mg (4)
Using these two equations we can easily find T1 and T2.
There are multiple ways in which we can do this. One way would be to first solve Eq. (3) for T2:
0 = T2 cos33.8°− T1 cos 57.6°
T2 cos 33.8° − T1 cos 57.6° = 0
T2 cos 33.8° = T1 cos 57.6°
T2 = T1 cos57.6°/ cos 33.8°
T2 = 0.747T1 (5)
hen, we substitute T2 with 0.735T1 in Eq. (4):
0 = T1 sin 57.6°+ T2 sin 33.8° − mg
0 = T1 sin 57.6° + 0.735T1 sin 33.8°− mg
And we solve it for T1:
0 = T1 (sin 57.6° + 0.747 sin 33.8°) − mg
0 = T1 (0.848) − mg
mg = 0.848T1
0.848T1 = mg
T1 = mg /0.848
T1 = (4.2kg) (9.81 N/kg) / 0.848T
T1 = 48.58 N
Finally, we substitute the value of T1 in Eq. (5) to find T2:
T2 = 0.747T1
T2 = (0.747) (48.58 N)
T2 = 36.28 N
Therefore, the tension in the rope at the 57. 6°angle is 48.58 N, and the tension in the rope at the 33. 8°angle is 36.28 N.
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calculate the wavelength of light that has its third minimum at an angle of 30 degrees when falling on double slits separated by 3
The wavelength of light that is inclined at a specified angle when falling on double slits is calculated to be 428.57 nm.
Angle = 30°
Order of interference m = 3
Distance between the slits d = 3 μ m = 3 × 10⁻⁶ m
We know the relation between wavelength, order of interference and distance as,
λ = d sinθ/(m+1/2)
By putting in the values, we have,
⇒ (3 × 10⁻⁶× sin30°)/(3+1/2) = 4.2857 × 10⁻⁷ m
By converting it to nm, we have,
⇒ 4.2857 × 10⁻⁷ × 10⁹ = 428.57 nm
Thus, the required wavelength of light is calculated to be 428.57 nm.
The question is incomplete. The complete question is 'Calculate the wavelength of light that has its third minimum at an angle of 30.0∘ when falling on double slits separated by 3.00 μm. Explicitly, show how you follow the steps in Problem-Solving Strategies for Wave Optics.'
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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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Help!!! A heat engine receives 1240 J of heat and exhausts 910 J per cycle of the engine what net work does the engine perform during the cycle?
a) 0 J
b) 330 J
c) 910 J
d) 2150 J
Net work the engine perform during the cycle is b) 330 J.
The net work done by a heat engine is the difference between the heat absorbed by the engine and the heat exhausted. Therefore, the net work done by the engine during a cycle is
1240 J - 910 J = 330 J.
How does the temperature of the hot reservoir affect the efficiency of a heat engine?
The efficiency of a heat engine is directly related to the temperature of the hot reservoir. The higher the temperature of the hot reservoir, the more thermal energy is available for conversion into work. This means that the efficiency of the heat engine increases as the temperature of the hot reservoir increases. The maximum efficiency of a heat engine is given by the Carnot efficiency, which is only achievable when the temperature of the cold reservoir is 0 K (absolute zero) and the temperature of the hot reservoir is infinite.
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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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a car moves with a total distance of 45.0 meters in 10 seconds while slowing down smoothly with a final speed of 3.00 m/s. a) what is the original speed of the car? (2 points) b) what is the car's acceleration? (2 points)
Answer : Original Speed is 6m/s while acceleration is 0.3m/s^2.
What is speed?
--In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time;
-- it is thus a scalar quantity.
Here in this question we have given final speed , we have to find the intial speed as well as the acceleration of the body.
d = V1 + V2 /2 × t
45 = V1 + 3/2 × 10
V1 = 6 m/s.
Hence initial speed of body is 6m/s .
By using first equation of motion we find the acceleration
we get acceleration is 0.3 .
What is velocity?
-- Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time .
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what is the maximum amount of trans fat as a percentage that could be in this cereal?physics uncertainty and error
The maximum amount of trans fat as a percentage that could be in this cereal should be 0.5%.
This cereal is formulated to be as healthy as possible, which is why we limit the amount of trans fat to 0.5% or less. Trans fat is an unhealthy form of fat that has been linked to several health conditions, so we strive to keep our trans fat content as low as possible. By limiting trans fats to 0.5% or less, we are confident that this cereal is a healthy choice.
This cereal contains no more than 0.5% trans fat, as mandated by the FDA. Trans fat is an unhealthy type of fat that can increase bad cholesterol levels and the risk of heart disease and stroke. To ensure optimal health and safety, this cereal only contains the amount of trans fat that is legally allowed.
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Would the speed of a satellite in close circular orbit about Jupiter be greater than, equal to, or less than 8 km/s?
Due to the satellite's overshooting circular course and movement away from Earth against the pull of gravity, the speed of satellite in such a closed circular orbit would be greater than 8 km/s.
Explain the effect of gravity on satellite in close circular orbit?The direction of gravity always seems to be toward the core of the Earth when a satellite travels around it in a circular orbit.
The satellite will move further before colliding with the Earth if it is assigned speed in either direction that is horizontal to a surface of the planet. This would travel so far if it is provided enough speed that even as it curves it toward the Earth, this should completely miss it. It will circle the Earth if it moves at just the proper pace. An orbit is the term used to describe this kind of motion and indeed the path which a satellite follows.A satellite must move at a speed of 8 km/s (28,000 km/h) or faster to stay its orbit when it is 100 km above the Earth. Satellites do not required to move as quickly at higher altitudes. The higher-altitude, 36,000 km, television communication satellites may fly at a speed of only 3 km/s (11,000 km/h).Thus, due to the satellite's overshooting circular course and movement away from Earth against the pull of gravity, the speed of satellite in such a closed circular orbit would be greater than 8 km/s.
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two narrow slits are separated by a distance d. their interference pattern is to be observed on a screen a large distance l away. (a) calculate the spacing between successive maxima near the center fringe for light of wavelength 500. nm, when l is 1.00 m and d is 1.00 cm. (b) would you expect to be able to observe the interference of light on the screen for this situation? (c) how close together should the slits be placed for the maxima to be separated by 1.00 mm for this wavelength and screen distance?
The spacing between successive maxima near the center fringe for light of wavelength 500. nm, when l is 1.00 m and d is 1.00 cm is 510^-7 m, Yes, observe the interference of light, distance between the slits be placed for the maxima to be separated by 1.00 mm is 0.5 mm.
Describe wavelength?Wavelength is a measure of the distance between consecutive peaks (or troughs) of a wave, such as a sound wave or an electromagnetic wave (like light). It is typically measured in meters (m) or nanometers (nm). The wavelength of a wave determines its color, with shorter wavelengths appearing as blue or violet and longer wavelengths appearing as red. In the case of electromagnetic waves, the wavelength also determines the type of radiation, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
(a) The spacing between successive maxima near the center fringe for light of wavelength 500 nm is given by the formula dsin(θ) = (λ)/d.
Plugging in the given values, we get: dsin(θ) = [tex]\frac{50010^{-91} }{0.01} =510^{-7} m[/tex]
(b) Yes, it would be possible to observe the interference pattern on the screen for this situation.
(c) To find the distance between the slits, we use the same formula and solve for d: d = (λ)/(dsin(θ)) = [tex]\frac{50010^{-91} }{1*10^{-3} } =0.5mm[/tex]
The slits should be placed 0.5 mm apart to have the maxima separated by 1.00 mm for this wavelength and screen distance.
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Help please I've been stuck on this for so long.
Answer:
Explanation:
I think it is the top one as the formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centimetre.
But I'm not 100% sure
a photographer takes a picture with a f/16 stop at 1/30 of a second (as per indicated by her camera). she notices that the subject is a bit blurred so wants to increase the speed to 1/500 of a second. what should the new stop be to have the same exposure level?
To maintain an exposure level equivalent to f/16 at 1/30 of a second, the new stop should be f/5.6. Due to their inverse relationship, the aperture and shutter speed must be adjusted to account for changes in either one by photographer.
When the shutter speed is increased from 1/30 of a second to 1/500 of a second, the aperture must likewise be changed in order to keep the same exposure level. The amount of light entering the camera, which is managed by the aperture and shutter speed, determines the exposure level. The "exposure triangle" describes the connection between aperture, shutter speed, and exposure. The "reciprocal rule," which dictates that if the shutter speed is increased by a factor of 16, the aperture should be reduced by a factor of 4, should be followed by the photographer in order to maintain the same exposure level. In this instance, the new stop should be f/4 since the photographer wishes to raise the shutter speed from 1/30 to 1/500 while maintaining the same exposure level.
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a small source of light at the bottom face of a rectangular glass slab 2.25 cm thick is viewed from above. rays of light totally internally reflected at the top surface outline a circle of 7.60 cm in diameter on the bottom surface. determine the refractive index of the glass.
The refractive index of the glass is 1.16, if the thickness of the glass slab is 2.25 cm, and the diameter of the circle is 7.60 cm.
incident angle of the light,θ = 90°
Let the angle of internal refraction is θ₁
Let the refractive index of the glass slab, = μ₁
Refractive index of vacuum, μ₂ = 1
By Snell's law, μ₁sinθ₁ = μ₂sin90
Radius of the circle, R = 7.6/2 = 3.8 cm
Thickness of the slab, and radius of the circle, R, makes the right angle triangle with hypotenuse(AC). So applying the pythagorus theorem,
AC² = 2.25² + 3.8²
AC = √(2.25² + 3.8²)
AC = 4.42
So sinθ₁ = 3.8/4.42
sinθ₁ = 0.86
μ₁ × 0.86 = μ₂×sin90
μ₁ × 0.86 = 1 × 1
μ₁ = 1/0.86
μ₁ = 1.16
So the refractive index of the glass slab, μ₁ = 1.16
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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 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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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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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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A skier with mass of 62kg is sliding down a snowy slope. Find the coefficient of kinetic friction for the skier if friction is known to be 45. 0
A skier with mass of 62 kg is sliding down a snowy slope. The coefficient of kinetic friction is 0.0738 N
Calculating the problem:The coefficient of kinetic friction can be found using the formula:
Friction = coefficient of kinetic friction × Normal force
We know that the friction force is 45 N and the normal force is equal to the skier's weight, which can be found using the formula
Weight = mass × gravity
Where the mass is 62 kg and the acceleration due to gravity is approximately :9.8 m/s²
So the normal force is: 62 kg × 9.8 = 607.6 N
Therefore, the coefficient of kinetic friction is: Friction / Normal force or approximately
= [tex]\frac{45}{607.6}[/tex] = 0.0738
How does kinetic friction work?The force that opposes the motion of two surfaces in contact as they slide against one another is known as kinetic friction, but other names for it include sliding friction and dynamic friction. The properties of the two surfaces in contact, such as the roughness of their surfaces and the materials they are made of, determine its strength. It acts in the opposite direction of the force applied to an object.
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6
The best way to increase the mechanical advantage of the following second-class lever is
4
Effort
Load
Fulcrum
Class 2 Lever
A To increase the size of the fulcrum
B) To move the load closer to the fulcrum
To increase the effort
D To move the load further away from the fulcrum
The best way to increase the mechanical advantage of the class 2 lever is to move the load closer to the fulcrum.
option B.
What is mechanical advantage?
The mechanical advantage of a simple machine is the ratio of output force to input force. It is also the ratio of load overcame by a simple machine to the effort applied by the simple machine.
Mathematically, the formula for mechanical advantage of a simple machine is given as;
M.A = output force / input force
M.A = Load / effort
Efficiency of machine = M.A/V.R x 100% = ( distance travelled by load x load ) / ( distance travelled by effort x effort )
Thus, to increase the mechanical advantage requires decrease in the distance travelled by the effort.
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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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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 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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The half-life of francium-223 is 20 minutes. If a sample originally contains 10 g of the isotope, how much remains after an hour?
The amount of the mass of the radioactive isotope remaining after 1 hour is 1.25 g.
What is the mass of the sample remaining after an hour?The mass of the sample remaining after an hour is calculated from the half life of the isotope as shown below.
The half life of the radioactive isotope = 10 minutes
The amount of the mass of the radioactive isotope remaining after 1 hour is calculated as follows;
1 hour = 60 minutes
0 half life ---------------------------> 10 g
20 minutes ------------------------> 5 g
40 minutes -----------------------> 2.5 g
60 minutes -----------------------> 1.25 g
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a saturn v rocket is launched straight up with a constant acceleration of 218 m/s . after 150 s, how fast is the rocket moving and how far has it traveled?
After 150 seconds, the rocket is moving at a velocity of 32700 m/s and has traveled 1,623,500 meters.
A constant acceleration is a change in velocity that does not change over time. If a car accelerates by 20 mph one minute and then another 20 mph the next, its average acceleration remains constant at 20 mph per minute.
We can use the equations of motion to calculate the speed and distance traveled of the rocket. The equation for velocity as a function of time is:
v = at
where v is the velocity, a is the acceleration, and t is the time. Substituting in the given values, we get:
v = 218 m/s * 150 s = 32700 m/s
To find the distance traveled, we can use the equation:
d = 1/2 * at^2
Substituting in the given values, we get:
d = 1/2 * 218 m/s^2 * 150 s^2 = 1,623,500 m
So after 150 seconds, the rocket is moving at a velocity of 32700 m/s and has traveled 1,623,500 meters.
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9. two solid spheres, both of radius 5 cm, carry identical total charges of 2 !c. sphere a is a good conductor. sphere b is an insulator, and its charge is distributed uniformly through- out its volume. (i) how do the magnitudes of the electric fields they separately create at a radial distance of 6 cm compare?(a)ea.eb 50(b)ea.eb.0(c)ea5eb.0 (d)0,ea,eb (e)05ea,eb (ii)howdothemagnitudes of the electric fields they separately create at radius 4 cm compare? choose from the same possibilities as in part (i).
(i) The magnitudes of the electric fields they separately create at a radial distance of 6 cm is [tex]E_{a}[/tex]=[tex]E_b}[/tex]. and (ii) The magnitudes of the electric fields they separately create at radius 4 cm is [tex]E_{a} =E_{b}[/tex], so the correct option is option b.
What do you mean by conductor?A conductor refers to a material that allows an electric current to flow through it with ease. In other words, it has a low electrical resistance. Conductors are materials that have a high number of free electrons that are able to move freely through the material. Examples of conductors include copper, aluminum, gold, and silver. These materials are commonly used in the electrical industry to make wires and other electrical components that need to conduct electricity. In addition to materials, a conductor can also refer to a person or an organization that is responsible for directing or leading an orchestra or a choir. In this context, a conductor is in charge of maintaining the ensemble's rhythm and intonation, and interpreting the score in a way that brings out the music's emotional content and intended meaning.
(i) The magnitude of the electric field created by a charged conductor is given by the formula E = [tex]\frac{kq}{r}[/tex], where k is the Coulomb constant, q is the charge, and r is the distance from the center of the sphere.
For a good conductor, like sphere A, the charge will be distributed evenly on the surface of the sphere. So, the electric field at a radial distance of 6cm will be Eₐ = [tex]\frac{kq}{r^{2} }[/tex] = [tex]k\frac{210^{-6} }{(619^{-2} )}^{2} =\frac{k}{72}[/tex]
For an insulator, like sphere B, the charge is distributed uniformly throughout its volume. The electric field at a radial distance of 6cm will be [tex]E_{b}[/tex]= [tex]\frac{kq}{r^{2} }=k\frac{210^{-6} }{(619^{-2} )}^{2} =\frac{k}{72}[/tex]
As we can see, the magnitudes of the electric fields created by both spheres are equal, so the answer is (b) [tex]E_{a} =E_{b}[/tex]
(ii) For the radius of 4cm, the electric field created by sphere A and sphere B will
[tex]E_{a} =\frac{kq}{r^{2} }=k\frac{210^{-6} }{(410^{-2} )^{2} } =\frac{k}{16}\\E_{b} =\frac{kq}{r^{2} }=k\frac{210^{-6} }{(410^{-2} )^{2} } =\frac{k}{16}\\[/tex]
As we can see, the magnitudes of the electric fields created by both spheres are equal at a radius of 4cm, so the answer is (b) [tex]E_{a} =E_{b}[/tex]
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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 24-g bullet moving at 1,200 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s. what is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?
The kinetic energy of the block of wood would be 1148 m/s. The result is obtained by using the law of conservation of momentum.
What is the law of conservation of momentum?
The law of conservation of momentum states that the momentum of a closed system before and after the collision is constant. A closed system means there is no external force acting on the system. The formula would be:
∑p initial = ∑p final
p₁ + p₂ = p₁' + p₂'
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Where
∑p initial is momentum before the collision.∑p final is momentum after the collision.m₁ and m₂ is the mass of objectv₁ and v₂ is the speed of object before collisionv₁' and v₂' is the speed of object after collisionA bullet moving through a block of wood that is at rest. It has
Mass of bullet, m₁ = 24 gSpeed of bullet, v₁ = 1,200 m/sMass of wood, m₂ = 1 kgSpeed of wood, v₂ = 0Find the kinetic energy of the block that results from collision!
If a bullet moving through a block of wood, it means that the bullet will be united with the block of wood. Then, the speed of both bullet and wood after collision is the same, v'.
The speed of the bullet is
m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
m₁v₁ + m₂v₂ = (m₁ + m₂)v'
v' = (m₁v₁ + m₂v₂)/(m₁ + m₂)
v' = (24(1200) + 1(-100))/(24 + 1)
v' = (28800 - 100)/25
v' = (28700)/25
v' = 1148 m/s
The kinetic energy of the block of wood would be
KE₂ = ½m₂v₂'
KE₂ = ½(1)(1148)²
KE₂ = 13,171,904 Joule
Hence, after the collision, the kinetic energy of the block of wood is 13,171,904 Joule.
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a car is driving on a curve on the interstate when, all of the sudden, the car encounters ice - reducing the friction to zero. assuming the curve has a radius of 20-m and the interstate is banked at an angle of 10 to the inside, what is the maximum velocity the car can travel to avoid sliding off the interstate
The maximum amount of static friction that the tyres can generate on the road can be used to calculate the maximum speed at which the car can go without slamming off the interstate.
The only force acting on the car when friction is eliminated is gravity, which pulls the vehicle towards the curve's centre.
The formula for calculating the maximum static friction force is
f_max = μ_s * m * g, where
μ_s = coefficient of static friction
m = mass of the car
g = acceleration due to gravity (9.8 m/s^2)
The maximum static friction force can be computed as follows using an assumed static friction coefficient of 0.7:
f_max = 0.7 * m * 9.8 = 6.86 * m N
The formula for the gravitational force is:
f_gravity = m * g * sin(θ), where
θ = bank angle (10°)
The difference between the gravitational force and the maximal static friction force is the net force operating on the automobile. The car won't skid off the road if the net force is zero.
The formula for calculating the maximum velocity is:
v = sqrt(R * g / sin(θ))
where
R = radius of the curve (20 m)
By substituting the values, we get:
v = sqrt(20 * 9.8 / sin(10)) = 26.51 m/s = 94.91 km/h
As a result, the maximum speed at which the car may move without swerving off the highway is roughly 94.91 km/h.
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A proton is moved so that its electric potential energy increases from 2. 0 × 10-18 J to 6. 0 × 10-18 J. The magnitude of the charge on a proton is 1. 602 × 10-19 C.
The electric potential difference through which the proton moved, to the nearest whole number, is ____V
The electric potential difference through which the proton is moved is [tex]2.49 * 10^-18[/tex]V.
How to calculate electric potential difference?The electric potential difference through which the proton is moved can be calculated using the formula:
V = ΔU/q
Where V is the electric potential difference, ΔU is the change in electric potential energy, and q is the charge of the proton.
Given that the electric potential energy increases from [tex]2.0 * 10^-18[/tex] J to [tex]6.0 * 10^-18[/tex] J and the charge of the proton is 1.602 x 10^-19 C, we can substitute these values into the formula to find the electric potential difference:
V = (6.0 x 10^-18 J - 2.0 x 10^-18 J) / 1.602 x 10^-19 C
V = 4.0 x 10^-18 J / 1.602 x 10^-19 C
V = 2.49 x 10^-18 V
Therefore, the electric potential difference through which the proton is moved is [tex]2.49 x 10^-18[/tex] V.
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