A drum major tosses a baton into the air and catches it and how long is the baton in the air is 22 feet
The heightis h of a baton function of time is t
h=−16t²+32t+6
dh/dt=d/dt(−16t²+32t+6)
=−32t+32
d²h/dt²=−32<0
For maximum height h, we have
dh/dt=0
−32t+32=0
t=1
Setting t=1 in the function of height, the maximum height of baton will be obtained at time t=1 sec
h(1)=−16(1)2+32(1)+6
=22 feet
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You measure 48 turtles' weights, and find they have a mean weight of 34 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight.
The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is +- 0.634
Given:
The sample size, [tex]n=48\\[/tex]
The mean of the given sample, [tex]x=34\\[/tex]
Population standard deviation[tex]=4.4\\[/tex]
Significance level[tex]=1- confidence \\[/tex]
[tex]=1-0.90\\=0.1[/tex]
The critical value, [tex]z=(n-x)/deviation=\frac{48-34}{4.4}=3.181[/tex]
The closest z value from the z table corresponding to z=3.181 is [tex]z=.99926[/tex]
The margin of error, [tex]E=z* deviation/\sqrt{n} =0.99926*\frac{4.4}{\sqrt{48} }= 0.634[/tex]
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a spring scale shows a net force of 0.8 n acting on a 1.5-kg mass. what happens to the acceleration of the object if the net force is decreased to 0.2 n?(1 point)
If the net force is reduced, the object's acceleration equals 0.13 m/s².
What is an instance of net force?For instance, even though a car is moving when it is continuously moving at 50 mph on the highway, there is no acceleration, so the net force of the car is zero.
Given
0.8 N acting as a net force on a 1.5 kg mass
To 0.2 N, the net force is reduced
Newton's 2nd law
∑F = ma
The 1.5 kg mass used in states 1 and 2 does not change
At state 1
∑F = 0.8N
m = 1.5kg
a = ∑F/m
a = 0.8/1.5
a = 0.53m/s²
At state 2
∑F = 0.2N
m = 1.5kg
a = 0.2/ 1.5
a = 0.13m/s².
The net force is reduced, the object's acceleration equals 0.13 m/s².
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calculate the theoretical magnetic field at the center of the solenoid calculate the percent difference between the theoretical and experimental values for the magnetic field at the center of the solenoid.
The Theoretical Magnetic field at center of solenoid will be ηNi/L with a percentage difference of 50%.
A solenoid is a long wire that has been wound in a helix shape. Using this arrangement, we can create a magnetic field that is reasonably uniform. When the turns are closely spaced, we can think of the solenoid as having a single circular loop for each turn, and the net magnetic field is the vector sum of all the magnetic fields produced by the turns. As the solenoid's length increases, the interior field becomes more consistent.We can think of it as the ideal solenoid when the turns are closely spaced and the length is significantly greater than the turn radius. In this instance, the interior field is uniform over a sizable volume, and the external field is zero. An expression for the magnetic field in a hypothetical solenoid is obtained using Ampere's law.[tex]B=uNi/L[/tex]
[tex]\beta =\int\limits^ {} B\, dx[/tex]
[tex]\beta =Bsin[2\pi -wt]\\\\k=2\pi /y\\\\\frac{B}{e}=c[/tex]
[tex]\int\limits^a_b {B} \, dx =UIc= Flux[/tex]
where u is permeability , N is number of turns , i is current and L is the length of solenoid.
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Nasa’s orion spacecraft, which left earth last week, flew within 81 miles of the surface of which celestial body on monday?.
Nasa’s Orion spacecraft, which left earth last week, flew within 81 miles of the surface of the moon.
What is the Orion spacecraft mission?The NASA Artemis 1 mission uses the crewed spaceship Orion, which is largely reusable. On Monday, NASA's Orion spacecraft flew by the moon's far side, coming 81 miles from the surface. There are no people on board the spacecraft. A lunar landing is the goal of the third Artemis 1 mission, which will use the Orion spacecraft and a SpaceX vehicle. Orion's systems will be tested extensively during the spacecraft's six-day stay, giving mission commanders plenty of time to do so.One of the primary goals of the trip is to test that the Orion spacecraft functions as intended .Its goal is also to provide NASA the opportunity to make any necessary modifications and repairs before astronauts embark for the Artemis II mission, which won't launch until at least 2024.To learn more about Orion spacecraft, refer:
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a negatively charged particle has a velocity in the negative z direction at point p. the magnetic force on the particle at this point is in the negative y direction. what is the direction of the magnetic field at point p from this information?
A moving object has a negative velocity when it is moving in the wrong direction. If an object is slowing down, its acceleration vector is pointing away from the direction in which it is moving.
Positive and negative charges move in the polar opposite directions. The positive charges will flow counterclockwise and the negative charges will travel clockwise, for instance, if the field is into this page. Positive charges are subject to an electric force that travels with the electric field. Additionally, negative charges are subject to an electric force that runs counter to the direction of the electric field. When a car is speeding up, the acceleration points in the same direction as the velocity; when it is slowing down, it points in the opposite direction.
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what is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to i0/2?
Complete Question:
Two slits spaced 0.260 mm apart are placed 0.700 m from a screen and illuminated by coherent light with a wavelength of 660 nm. The intensity at the center of the central maximum ( = 0°) is [tex]I_{0}[/tex].
What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to [tex]I_{0}/2[/tex]
The distance on the screen from the center of the central maximum 0.44 mm where the intensity has fallen to [tex]I_{0}/2[/tex]
The two slits are separated by 0.260 mm.
The screen's distance from the slits is 0.700 meters.
The coherent light has a wavelength of 660 nm.
The value of the path difference will equal to [tex]\pi /2[/tex] because the intensity has decreased to [tex]I_{0}/2[/tex].
This path difference's above formula can be expressed as,
[tex]y_{n} = \frac{(2n-1)D\alpha }{2d}[/tex]
D is the distance of the screen to the slits.
[tex]\alpha[/tex] is the wavelength of the light
d is the distance between slits.
The intensity at the center of the central maximum is [tex]I_{0}[/tex]
Now,
[tex]y = \frac{(2*1)D}{d} *\frac{\alpha }{2\pi } *\frac{\pi }{2}[/tex]
Putting all the values in the formula, we get:
y = 0.44 m
Thus, the distance on the screen from the center of the central maximum 0.44 mm.
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if the speed of an object is doubled but the mass stays the same, the momentum of the object will change by a factor of? g
Doubling the mass of the object doubles both the kinetic energy and momentum. The factor that these variables change is 2.
Kinetic energy of an object can be written as:
K.E. = 1/2 m v2
Momentum is given as:
P = m v
when we have a moving object, we will let its mass be m₀
We will let its initial kinetic energy and momentum be:
E₀ =1/2 m₀ v²₀
The momentum is given as: p₀ =m₀v
Now when we double our mass, we have: m = 2m₀
We substitute this into our generalized formulas:
E = 1/2(2m₀)v²
The momentum p = 2m₀v
We can separate the new factors: E =2(1/2 m₀v₂)
The momentum p =(2 )(m₀v)
These are our initial kinetic energy and momentum. Thus we have:
E = 2 E₀
p =2p₀
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which planet detection method would work best for a massive planet that's close to its host star but doesn't pass between us and the star?
The Doppler method is most frequently employed to find extrasolar planets, however it works best for finding extremely large planets that are near to their host star.
Which planet is the hottest?Venus is the hottest planet within our solar system, with average global temperatures hot enough even to melt lead due to the runaway greenhouse effect caused by its thick atmosphere, which traps heat. Venus is around 700°F (390°C) hotter that it would be in the absence of the greenhouse effect.
Is it 8 or 9 planets?Our solar system is made up of ten planetary systems, 146 moons, countless comets, meteorites, and other space objects, as well as Pluto and several dwarf planets. In the system, there is just the Sun. The eight planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and finally Neptune.
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a pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. light waves arrive at the two slits in phase. a fringe pattern is observed on a screen 4.8 m from the slits. in the situation above, there are 5.0 bright fringes/cm on the screen. the wavelength of the monochromatic light is closest to:
750 nm is the predicted wavelength. The distance between two successive crests or troughs of a wave is known as its wavelength. It is measured in the wave's direction.
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
= slit separation = 1.8 mm = 0.0018 m
is the monochromatic light's wavelength.
= 4.8 meters from the screen
= first bright fringe's position =
= order = 1
The first bright fringe's position is indicated by
λ = 7.5 x 10⁻⁷ m
λ = 750 nm
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A golfer making a putt gives the ball an initial velocity of v0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole?
[tex]2v_{0}[/tex] speed should he have given the ball.
here,
initial speed of the ball is v₀
let the resistive force be f and the distance of the hole be d
when it cover distance d/4
using work energy theorem
work done grass force = change in kinetic energy
F × d/4 = 0.5 × m × [tex]v_{0} ^{2}[/tex]
F = 2 ×m×[tex]\frac{v_{0} ^{2} }{d}[/tex] (1)
for covering the distance d
let the velocity be v
work done grass force = change in kinetic energy
F ×d = 0.5 × m × [tex]v^{2}[/tex]
putting F from (1)
2 ×m× [tex]\frac{v^{2} _{0} }{d}[/tex]×d = 0.5 ×m × [tex]v^{2}[/tex]
4 × [tex]v_{0} ^{2}[/tex] = [tex]v^{2}[/tex]
v = [tex]2v_{0}[/tex]
What is work-energy theory and how is it supported?
According to the work-energy theorem, the work done by the net force exerted on a body equals the change in kinetic energy. W = kf - ki is the simplest way to express it. The work energy theorem equation is the one shown above. If the body's kinetic energy declines, the net work done W becomes negative.
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A force of 25 newtons east and a force of 25 newtons west act concurrently on a 5. 0-kilogram cart. What is the acceleration of the cart?.
The acceleration of the 5. 0-kilogram cart on applying two equal and opposite force be 0 m/s².
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Given parameters:
One force: F₁ = 25 Newtons acted eastwards.
Another force: F₂ = 25 Newtons acted westwards.
Magnitude of net force acting on the object = (25N -25N) = 0 Newton.
Hence, acceleration of the 5. 0-kilogram cart. be 0 m/s².
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a bat flying in a cave emits a sound and receives its echo 0.1 s later. how far is from the cave wall? (in m)
The distance from the wall is 17 m when a bat flying in a cave emits a sound and receives its echo 0.1 s later.
Given sound wave velocity (s) = 340m/s
Time taken for the sound wave (echo) to travel towards the wall and reflect off the bat = 0.1 s
So the time taken by the sound wave to travel to the wall only (t) = 0.1s/2 = 0.05s
Distance from wall to bat (d) = speed of sound wave(s) * time(t)
The distance between the wall and the bat is = 340 m/s * 0.05 s = 17 m
Thus, the distance from the wall when a bat emits a sound and receives its echo 0.1 s later in a cave is 17 m.
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A man walks toward Carrefour beginning at his home. It takes him 2 hours to cover the 7 kilometers. He spends 1 hour in the store. He then walks 2 km in 1 hour in the same direction to drop the toys off to his niece.
a) What is the man's average speed for the whole journey?
b) What is the man's average velocity for the whole journey?
The average speed of the man for the whole journey is 2.25 km/hr.
The average velocity of the man for the whole journey is 2.25 km/hr.
What is the average speed of an object?The average speed of an object is the ratio of the total distance traveled by an object and the time taken for the journey.
The average speed of an object is given mathematically as follows:
Average speed = tota; distance / total time taken
From the data given:
Total distance traveled = 7 km + 2 km
Total distance traveled = 9 km
Total time taken = 2 + 1 + 1
Total time taken = 4 hours
Average speed = 9 km / 4 hrs
Average speed = 2.25 km/hr
The average velocity of the man for the journey is calculated as follows:
average velocity = change in displacement/change in time
The journey took place in the same direction, hence, the displacement is 9 km.
Average velocity = 9 km / 4 hrs
Average velocity = 2.25 km/hr
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You want to study a biological specimen by means of a wavelength of 20.0 nm and have a choice of using electromagentic waves or an electron microscope.
A. Calculate the ratio of the energy of a 20.0 nm -wavelength photon to the kinetic energy of a 20.0 nm -wavelength electron.
B. In view of your answer to part A, which would be less damaging to the specimen you are studying, photons or electrons?
The electron's K.E. is P 2 /2m=2.4151019 J=1.51 eV. The relationship between the system's energy output and input is referred to as the "energy balance," "energy payback ratio," or "energy ratio."
The balance of energy can be written as. Eo = dE plus Ei. The energy returned by the material to the energy taken in from the environment is known as the yield ratio. Only the primary fuel can speed up growth, but their availability is constrained.
The De Broglie hypothesis states that p= h \s
= \s1∗10 \s−9
6.62∗10 \s−34
\s =6.62∗10 \s−25 \s kg−m/s
No matter if it's an electron or a photon, the value is constant.
(b) λ=1 nm
E = hc / e = 1243.1 eV = 1.24 keV
Momentum, p=h/=6.631025 kgm/s, is shown in (c).
The electron's K.E. is P 2 /2m=2.4151019 J=1.51 eV.
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A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation x^2/500 - y^2/900 = 1 with units in meters. The center of the tower is at the origin. How wide is the tower at the top?50 m92 m100 m184 m
The width of the tower at the top will be 92 m. Then the correct option is B.
Hyperbola-
The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
A cooling tower is 120 meters tall.
The sides of the tower are in the shape of a hyperbola defined by the equation x²/500 – y²/900 = 1 with units in meters.
The center of the tower is at the origin.
Then the width of the tower at the top will be
x²/500 – (120)²/900 = 1
x²/500 – 14400/900 = 1
x²/500 – 16 = 1
x²/500 = 1 + 16
x²/500 = 17
x² = 8500
x = 92.19 ≈ 92 m
Then the correct option is B.
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a high-fidelity sound system may have a frequency range that extends up to or beyond 20,000 hz. what is the purpose of this extended range?
This increased range's objective is to make it easier for the sound to create detectable high frequency noises.
Describe a sound wave:A sound wave is a series of disruptions that are caused by energy that is being transmitted away from the source of the sound. The path of the acoustic waves is parallel of the particle vibration. So, longitudinal waves is what they are called. Atoms move back and forward between instantaneously as they vibrate.
What does sound wave propagation entail?Transverse waves, such as sound waves, spread diagonally to the transmission medium. Sound waves move in a straight line parallel to the transmission medium since they are longitudinal waves. Depending on the temperature, sound waves can move in either a longitudinal or transverse direction. This increased range's objective is to make it easier for the sound to create detectable high frequency noises.
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This increased range's objective is to make it easier for the sound to create detectable high frequency noises.
Describe a sound wave:A sound wave is a series of disruptions that are caused by energy that is being transmitted away from the source of the sound. The path of the acoustic waves is parallel of the particle vibration. So, longitudinal waves is what they are called. Atoms move back and forward between instantaneously as they vibrate.
What does sound wave propagation entail?Transverse waves, such as sound waves, spread diagonally to the transmission medium. Sound waves move in a straight line parallel to the transmission medium since they are longitudinal waves. Depending on the temperature, sound waves can move in either a longitudinal or transverse direction. This increased range's objective is to make it easier for the sound to create detectable high frequency noises.
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g what is the magnitude of the tension ta in rope a? a. 500 n b. 3200 n c. 370 n d. 130 n e. 100 n f. 400 n value: 10 if the axis of rotation is placed on rope a, then the torques of f
The torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
What is torque?
Torque seems to be the rotational equivalent of force in physics and mechanics. Depending on the area of study, it is also known as that of the moment, instant of force, rotational force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion. In his famous adage, "Give me a lever as well as a place to stand, and I'll move the Earth," Archimedes, who studied the use of levers, is credited with developing the idea. A torque could be thought as a twist to the an object around a particular axis, similar to how a linear force is indeed a push or a pull.
The torque of rope F is equal to the product of the force (F) and the lever arm (r). The lever arm is equal to the length of the rope multiplied by the sine of the angle between the rope and the axis of rotation.
Therefore, the torque of rope F = F * r = F * (length of rope) * sin(angle between rope and axis of rotation).
For example, if F = 500 N, the length of the rope = 3 m, and the angle between the rope and the axis of rotation is 30 degrees, then the torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
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a meterstick of uniform density is hung from a string tied at the 11-cm mark. a 0.40-kg object is hung from the zero end of the meterstick, and the meterstick is balanced horizontally. what is the mass of the meterstick?
The meterstick has a mass of 0.40 kg and is suspended from a string that is knotted at the 11-cm point. A 0.40-kg object is suspended from the meterstick's zero end due to its uniform density.
Mass is a physical body's total amount of matter. It also serves as a gauge for the body's inertia, or resistance to acceleration (change in velocity) in the presence of a net force. The strength of an object's gravitational pull to other bodies is also influenced by its mass. The substance's mass per unit of volume is known as its density (volumetric mass density or specific mass). Although the Latin letter D may also be used, the sign most frequently used for density is (the lower case Greek letter rho). Mass is the mathematical definition of density.
M2 = 0.40 Kg
d = 11cm
m1*g*r1 = m2*g*r1
m1*9.8 = 0.40*9.8
m1 = 0.40 kg
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a player catches a ball. consider the action force to the ball against the player's glove. the reaction is the
The reaction is the force applied by the player's glove on the ball.
What is Newton's third law of motion?Newton's third law of motion states that when one body exerts a force on the other body, the first body experiences a force which is equal in magnitude in the opposite direction of the force which is exerted”.
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.
The direction of the force on the first object is opposite to the direction of the force on the second object.
According to this question, a player catches a ball. The action is the force to the ball against the player's glove while the reaction or opposite force will be the player's glove against the ball.
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a boy can raise a rock that weighs 120 n by using a lever and applying a force of 25 n. what is the mechanical advantage of the lever?
The mechanical advantage of the lever is 4.8
What is mechanical advantage?Mechanical advantage is a measure of the ratio of output force (load) to input force (effort applied) in a system, used to analyze the forces in simple machines like levers and pulleys. Changing the forces that are applied, the conservation of energy is still true and the output energy is still equal to the input energy.Mechanical advantage has no unit.
Therefore mechanical advantage is given as Load/Effort
In this case the load is 120N and the effort is 25N
Therefore the mechanical advantage of the lever = 120/25= 4.8N
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a circuit contains an ac generator and a resistor. what haplens to the average power dissipated in the resistor when the frequency is doubled and the rms voltage is tripled?
The average power increases by a factor of 3^2 = 9 since is proportional to the square of the rms voltage.
What is rms voltage?
In the AC waveform tutorial, we briefly looked at the RMS voltage value of a sine wave and said that this RMS value would give the same heating effect as the equivalent DC power. We detail them in terms of RMS voltage and current.
The term 'RMS' stands for 'Root Mean Square'. Most books define this as "the amount of AC power that produces the same heating effect as equivalent DC power" or something along those lines, but the RMS value is much more than that. Mean value of the quadratic function of instantaneous values. The symbols used to define RMS values are VRMS or IRMS.
Therefore, the average power increases by a factor of 3^2 = 9 since is proportional to the square of the rms voltage.
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You are given two converging lenses of focal lengths 3.5 cm and 2.0 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.
The separation between the objective and the eyepiece should be -7.368 cm to get the desired magnification of 30.
Magnification - For a compound microscope, the magnifying power is given by M = Me × Mo where Me = 1 + (d/fe ), is the magnification due to the eyepiece and Mo is the magnification produced by the objective.
According to the given information : fe = 3.5 cm ; fo = 2.0 cm ;
d = 25 cm (d = The normal distance of clear vision of the human eye) and M = 30
Let L be the distance between the objective and the eyepiece.
M = -L/fo (1 + d/fe)
30 = -L/2.0 cm (1 + 25 cm/3.5 cm)
L = -7.368 cm
The separation between the objective and the eyepiece should be -7.368 cm to get the desired magnification of 30.
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what does the resulting slope imply about the relation between the heat lost by the warm water and the heat gained by the cold water?
The outcome was a slope that was upwards. Heat is received at a rate that is inversely proportional to the quantity of heat lost.
Describe heat using an example.Simply said, temperature is an object's heat or cold, and heat is the energy that moves from a hotter to a cooler thing. If you stick your thumb around a cup of coffee, it might feel warm to the touch, for instance. It is warm because the coffee's heat has been transmitted to the cup.
Why do we use the term "heat"?The transfer of energy at a high pace from an energy source to a medium or an object, or the opposite, is known as heat. These three techniques for transferring energy include radiation, conduction, and convection.
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an aluminum rod with a initial length of 15 m and a diameter of 37 mm is subjected to an axial tensile load of 65 kn. calculate its elongation (mm). 0.2390.02390.0023923.9
The elongation of the aluminium rod subjected to an axial tensile load is 0.00239 mm. So, the 3rd option is correct.
It is given to us that -
Initial length of the aluminium rod = 15 mm
Diameter of the aluminium rod = 37 mm
Axial tensile load on the aluminium rod = 65 kN
We have to find out the elongation of the aluminium rod in mm.
The deformation (in this case, elongation) of an aluminium rod with specific length and diameter which is subjected to an axial tensile load can be represented in the form of an equation given by -
δ = [tex]\frac{P*L}{A*E}[/tex] ----- (1)
where,
δ = Deformation of the rod
P = Axial tensile load
L = Length of the rod
A = Area of the rod
E = [tex]2*10^{5}[/tex] [tex]N/mm^{2}[/tex]
According to the given information, we have
P = 65kN = [tex]65*10^{3}[/tex] N
L = 15 mm
A = [tex]\frac{\pi }{2} d^{2}[/tex] where d is diameter of rod
Substituting these values in equation (1), we have
δ = [tex]\frac{P*L}{A*E}[/tex]
=> δ = [tex]\frac{65*10^{3}*15}{\frac{\pi }{2} (37)^{2}*2*10^{5}}[/tex]
=> δ = 0.00239 mm
Thus, the elongation of the aluminium rod subjected to an axial tensile load is 0.00239 mm. So, the 3rd option is correct.
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what is solar activity? describe key features including sunspots, solar prominences, solar flares, and coronal mass ejections.
Solar activity includes coronal mass ejections, high-speed solar winds, solar energetic particles, and solar flares.
Explain about the Solar activity?The magnetic fields become tangled, stretched, and twisted due to the Sun's perpetual gas movement. Solar activity, or solar activity as it is also known, is produced by this motion on the Sun's surface. The Sun's surface occasionally exhibits intense activity. The atmosphere can change from time to time.
In actuality, the lengthier, 22-year cycle of solar activity is divided in half by the 11-year sunspot cycle. The magnetic field of the Sun associated with sunspots reverses polarity with each upswing and downswing in the number of sunspots, and the northern and southern magnetic hemispheres of the Sun alternate in their orientation. There is an 11-year cycle between solar activity maxima as determined by the quantity of sunspots.
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What acceleration will you give to a 24. 3 kg box if you push it horizontally with a net force of 85. 5 n?.
3.325m/s^2 acceleration will you give to a 24.9 kg box if you push it horizontally with a net force of 82.8 N.
What is Newton's second law?
Following Galileo, Isaac Newton investigated the motion of various substances and came up with his three famous laws, the first of which defines force and the second of which analyzes it. When an object's mass is constant under certain circumstances, the force is theoretically equal to the sum of the body's mass and the acceleration it experiences.
Data Given
- Mass of the box[tex]$m=24.9 \mathrm{~kg}$[/tex]
- Net horizontal force on the box[tex]$F=82.8 \mathrm{~N}$[/tex]
As per Newton's second law
[tex]$$\begin{aligned}& F=m a \\& a=\frac{F}{m} \\& a=\frac{82.8 \mathrm{~N}}{24.9 \mathrm{~kg}} \\& a=3.325 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]
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if the distance between two charges is doubled, what will happen to the force between the charges? (4 points) to answer this question, perform the calculation first with a r value of 1 and then a second calculation with a r value of 2.
If the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.
What is force?
A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Force between two charge particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Therefore, if the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.
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a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. over what vertical distance does the hanging mass move in 3.0 seconds? ignore friction and drag forces, and assume that the string does not slip.
a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. vertical distance does the hanging mass move in 3.0 seconds is 18.27 m
distance can be calculate as follows:
Suspended mass, m = 1.09 kg
Pulley mass, M=4.22 kg
pulley radius, r = 1.04 m
now,
Let's put some tension on the "T" string
For this,
vertical net force
mg - T = ma …………(1)
Where,
g is the gravitational acceleration
a is the acceleration of the suspended mass.
Pulley torque = Iα
I is the moment of inertia of the pulley
α is the angular acceleration
Pulley torque is due to string movement
therefore,
Torque = T x r
Also
α = a/r
and I = (Mr²/2) (for circular discs)
Substituting the values of the above relationship for torque, we get
T × r = (Mr²/2) × (a/r)
T = (Ma)/2 …………(2)
from 1 and 2
mg - [(Ma)/2] = ra
mg= a(M + r)
2
(1.09x9.8) = a( 4.22 + 1.04)
2
a= 4.06
now we know that
s= ut+1/2 at²
where s is the distance traveled
u is the initial velocity = 0 (in this case)
t is time = 3 seconds
So if you replace the value
s= (0x3)+ 1/2 4.06 (3)²
s = 18.27 m
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a car goes around a curve of radius r at a constant speed v. the coefficient of static friction between the tires and the surface is µ. what is the maximum value of the car’s velocity in order to prevent the car from skidding off the road?
The maximum value of the car’s velocity in order to prevent the car from skidding off the road is (urg)^(1/2)
What is meant by velocity ?The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second (m/s) is the accepted unit of velocity magnitude (also known as speed).
The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
The pace at which an object's position changes in relation to a frame of reference is known as its velocity, and it depends on time. The definition of velocity is the specification of a moving object's speed and direction (for example, 60 km/h to the north).
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a car is accelerating from rest at to meters per second squared and travels 400 mi how fast is it going at the end
The ideals that we place Our time is equivalent to 20 seconds since S is 400 meters and an is four meters per second squared.
By accelerating, what do you mean?Car's acceleration was gradual. To move through the grades more quickly than is typical: to follow a sped-up educational curriculum. The rate of change has accelerated in recent months.
With examples, what does the term "acceleration" mean?Any alteration in an object's velocity might take the form of a change in direction of motion or a speed increase or reduction. The moon orbiting the earth, an apple falling to the ground, and a car stalled at a stop sign are a few instances of acceleration.
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