Potential difference is the work done in moving a unit charge to a reference point. The potential difference is 9 volts. Thus option B.
Potential difference is a term that is used to describe the work done in transferring a unit positive charge from infinity to a reference point. While the electric field strength is the number of electric field passing through a unit area in a period.
Tension is an example of contact force which is applicable to extended strings, lines, ropes etc.
Given:
electric field strength = 30 V/m
distance between the two points = 30 cm
= 0.3 m
Potential difference between the points = 0.3 x 30
= 9.0 V
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to keep the voltage drop of a 277v circuit to a maximum of 3%, what would be the maximum allowable voltage drop?
The voltage across the circuit is 277 V. To keep the voltage drop to a maximum of 3%, the allowable voltage drop will be 8.31 V.
What is voltage?Voltage is the potential difference applied between the two opposite terminal of the circuit. The unit of voltage is represented as V. According to Ohm's law voltage in a circuit is the product of current and resistance through the circuit.
The applied voltage cannot be utilised by 100%. There occurs a voltage drop across the circuit. Given that the total voltage applied is 277 V. The maximum allowed voltage drop is 3%.
Thus, maximum allowable voltage drop for 277 v = 277 × 3/100 = 8.31 V.
Therefore, the maximum allowable voltage drop is 8.31 V.
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when electromagnetic energy travels from air into water, the waves are bent due to the density differences between the air and water. what is this bending called?
When a wave travels from one medium to another, its velocity (speed) changes, causing it to bend. This is known as refraction. The wave's frequency remains constant.
Refraction is the bending (and slowing down) of electromagnetic radiation's propagation direction as it passes through two denser substances. Electromagnetic waves transfer energy from one location to another through radiation. Starlight that is going through space could be this energy. Or perhaps your hands are being warmed by a campfire. A molecular substance's surface will curve when it comes into contact with another substance, creating a meniscus. Light slows down and somewhat changes direction as it passes through water from air.
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the weight of a satellite on a planet's surface is w. which is closest to the weight of the satellite when it's in orbit?
The closest to the weight of the satellite when it's in orbit is 0
Because the surface does not apply any force to the body, it appears to have no weight.
All positions are comfortable since a body in a satellite requires no support to be at rest. We refer to this condition as weightlessness.
It will be challenging to control one's movement because, without weight, he will likely tend to drift aimlessly. He will have to push himself away from the walls or other permanent things in order to go from one place to another.
Because everything is falling freely, things are at rest in relation to one another. For example, if a table is removed from underneath an object, the object will stay in place without any support.
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A soccer player takes a free kick from a spot that is 26m from the goal. The ball leaves his foot at an angle of 26˚, and it eventually hits the crossbar of the goal, which is 2.4m from the ground
At what speed did the ball leave his foot?
The speed of the ball when it left his foot is 11.13 m/s.
What is the motion of the projectile?A projectile is an object that is launched or projected into the air and is only subject to the acceleration of gravity. Projectile and trajectory both refer to the same thing: an object.
The given parameters;
distance of the goal, d = 26 m
angle of projection of the ball, = 26°
height of the cross bar, H = 2.4 m
The speed of the projectile will be calculated by applying the formula for maximum height reached by a projectile;
[tex]H=U^{2} sin^{2}/2g[/tex]
[tex]u^{2} =2gh/x=sin^{2}[/tex]
[tex]u^{2} =2*9.8*2.4/sin^{2} 26[/tex]
[tex]u^{2} =81.10[/tex] m/s
u=9 m/s
Thus, the speed of the ball when it left his foot is 9 m/s.
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A proton follows the path shown in (Figure 1). Its initial speed is v0 = 2.2×106 m/s.What is the proton's speed as it passes through point P?Express your answer to two significant figures and include the appropriate units.
The proton's speed as it passes through point P is 1.6×10⁶ m/s.
The proton's speed at point P can be determined by the equation:
KE = PE + ( mv²/2 )
where,
KE= kinetic energy
PE = potential energy
m = mass of the proton
v = speed of the proton.
Given
Proton's initial speed is v₀ = 2.2×10⁶ m/s
By putting the values in the question the solution is as follows so as the Proton's speed at point P can be calculated as:
v = √(2KE/m)
= √(2 ×2.2 × 10⁶ m/s² / 1.67 × 10⁻²⁷ kg)
= 1.6 × 10⁶ m/s
Therefore, the proton's speed as it passes through point P is 1.6×10⁶ m/s.
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two identical cylinders, a and b, contain the same type of gas at the same pressure. cylinder a has twice as much gas as cylinder b. which is true?
If both of cylinders contains same type of gas at same pressure, then a)
([tex]T_A < T_B[/tex]). So, correct option is a.
Gas regulation condition for any gas is as per the following .
PV = n×R×T (defined for n moles of gas )
Let the Pressure , volume , temperature and mole of gas in chamber A be P,V
T₁ and 2n . Pressure , volume , temperature and mole in chamber B will be
P , V , T₂ and n.
Applying Gas regulations , we get
For gas in chamber A
PV = 2n R T₁
For gas in chamber B
PV = n R T₂
Likening these conditions , we get
2n R T₁ = n R T₂
2 T₁ = T₂
or we can say that 2[tex]T_A[/tex]=[tex]T_B[/tex]
Hence, option a is correct.
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(Complete question) is:
Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true? Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true?
a)TA < TB
b)TA >TB
c) TA = TB
d)Not enough information to make a comparison.
When nitrogen and hydrogen gas combine to make ammonia, the chemical equation looks like this:
2N2 + 3H2 => 2NH3
If the hydration energy of 2N2 + 3H2 is equal to + 2251.3 kJ/mol and the lattice energy of 2NH3 is equal to -2343.52 kJ/mol, what is the total energy change of this reaction and is the reaction endothermic or exothermic?
(a) The total energy change of this reaction is -4,594.82 kJ/mol.
(b) The reaction is exothermic.
What is the change total energy change of this reaction?
The total energy change of the given reaction is determined by taking the difference between the energy of the product and the reactant.
ΔH = Hp - Hr
where;
Hp is the energy of the productHr is the energy of the reactantThe given parameters;
energy of the product = -2343.52 kJ/molenergy of the reactant = 2251.3 kJ/molΔH = -2343.52 kJ/mol - 2251.3 kJ
ΔH = -4,594.82 kJ/mol
Based on the negative change in the total energy, the reaction is exothermic.
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the white dwarf at the center of the helix nebula has a mass three times the mass of our sun.
Three times as massive as the Sun is the white dwarf star in the heart of the Helix planetary nebula. False The Chandrasekhar mass, or 1.4 solar masses, is the white dwarf's maximum mass.
White dwarf stars typically last between 100,000 and 10 billion years and have masses between 0.1 and 1.4 that of the Sun. To balance their mass, white dwarf stars no longer produce energy. White dwarf stars, like Sirius B, Procyon B, or Van Maanen, are limited in mass theoretically to 1.4 solar masses.
A star core remnant known as a white dwarf is primarily made up of electron-degenerate materials. A white dwarf is extremely dense; it has a mass similar to that of the sun.
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find the volume of the solid that lies under the plane 4x+6y-2z+15=0 and above the rectangle
The solid that is located above the rectangle and beneath the plane 4x+6y-2z+15 has a volume of 51 liter.
The amount of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. There are 30 unit cubes total in the solid, hence the volume is 2 units. 3 units 30 cubic units from 5 units.
Formula for Solids Volume. Let's have a look at the volumes of all the three-dimensional solid shapes before we answer the problems based on the combination of solids. The formula for volume and surface area for a cuboid with dimensions of length (l), breadth (b), and height (h) is provided by: Volume = lbh.
[tex]4x+6y-2z+15=0\\2z=4x+6y+15\\z=2x+3y+ \frac{15}{2}\\[/tex]
The volume for the given solid is,
[tex]\\V= \int_{-1}^{1 } \int_{-1}^{2} \left ( 2x+3y+ \frac{15}{2} \right ) dy/dx\\V= \int_{-1}^{1 } \left [ \frac{2x^2}{2}+3xy+\frac{15x}{2} \right ]_{-1}^{2}\\V= \int_{-1}^{1 } \left [ x^2+3xy+\frac{15x}{2} \right ]_{-1}^{2}\\V= \int_{-1}^{1 } \left [ 2^2+3*2y+\frac{15*2}{2}-\left ( (-1)^2+3*-1y+\frac{15*-1}{2} \right ) \right ]\\[/tex]
[tex]V= \int_{-1}^{1 } \left [ 4+6y+\15-\left ( 1-3y-\frac{15}{2} \right ) \right ]\\V= \int_{-1}^{1 } \left [ 4+6y+\15- 1+3y+\frac{15}{2} \right ]\\V= \int_{-1}^{1 } \left [ 3+9y+\frac{45}{2} \right ]\\V= \int_{-1}^{1 } \left [ 9y+\frac{51}{2} \right ]\\V= \left [ \frac{9y^2}{2}+\frac{51 y}{2} \right ]_{-1}^{1 }\\V= \left [ \frac{9*1^2}{2}+\frac{51 *1}{2}-\left ( \frac{9*(-1)^2}{2}+\frac{51 *-1}{2} \right ) \right ]\\[/tex]
[tex]V= \left [ \frac{9}{2}+\frac{51 }{2}-\left ( \frac{9}{2}-\frac{51}{2} \right ) \right ]\\V= \left [ \frac{9}{2}+\frac{51 }{2}- \frac{9}{2}+\frac{51}{2} \right ]\\V= \left [ \frac{51 }{2}+\frac{51}{2} \right ]\\V= 51[/tex]
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the nucleus of a uranium atom has a diameter of 1.5×10−14m and a mass of 4.0×10−25kg.
A uranium atom's nucleus measures 1.5 x 10^-14 mm in diameter and weighs of 2.2635 x 10^17 kg.
The Earth's crust contains 2.8 parts per million of uranium, an element that is found naturally. It is virtually always present in little amounts. It is almost the same in abundance as tin, somewhat less abundant than cobalt, lead, or molybdenum, and more abundant than gold, silver, or mercury.
Nucleus density is determined by the ratio of mass to volume.
Proton mass equals nucleus mass.
Nucleus volume is equal to (4/3)*pi*r3. and r is the radius
A uranium atom's nucleus has a mass of 4.0*10^-25 kg and a diameter of 1.5*10^-14 m.
first, locate volume.
Radius is calculated as follows: 1.5*10^-14 m/2 = 7.5*10^-15 m radius
vol is equal to (4/3)*pi*(7.5*10^-15)3 = 1.76715*10^-42 of volume.
Locate density using the formula d=m/vol (kg/m³)
d = 4.0*10^-25 kg / 1.76715*10^-42 m^3
d = 2.2635*10^17 (kg/m³)
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Correct Question:
The Nucleus Of A Uranium Atom Has A Diameter Of 1.5*10^-14 M And A Mass Of 4.0*10^-25 Kg.
the field of science that deals with the practical application of a liquid in motion is called .
The field of science that deals with the practical application of a liquid in motion is called fluid mechanics.
The fluid mechanics is the branch of science that deals with the practical application of a liquid when it is in motion or in rest.
Pascal's law, equation of continuity and Bernoulli's equation all comes under the study of fluid mechanics.
Fluid mechanics is the field of science because of which we are able to make the break of the vehicles hydraulic lift hydraulic press and many more things. We are able to make the Barometer, thermometer and many other things because of the practical applications of fluid mechanics.
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looking for planets orbiting even the nearest stars is like looking from san francisco for pinheads and marbles orbiting a ? in washington dc
Proxima Centauri's third planet can be seen by observing variations in brightness over a period of more than two years. The third planet that orbits Proxima Centauri, the star nearest to the Sun, has been found by astronomers.
What, looking for planets orbiting even the nearest stars?The transit method has so far been used to discover the great majority of planets orbiting other stars.
Therefore, 3 New Planets Found By Kepler Telescope In The “Goldilocks Zone” The planets that circle distant stars are around the size of Earth and are orbiting. At a distance from their suns that keeps the temperatures on their surfaces in the middle.
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how do the escape speeds for two rockets, the first weighing 20 n and the second weighing 20,000 n compare?
Escape velocity doesn't depends on the weight of a rocket.So, The escape velocity for the lighter rocket is the same as that for the heavier rocket.
Velocity:
Velocity is the primary measure of object position and velocity. It can be defined as the distance traveled by an object in unit time. Velocity can be defined as the displacement of an object in unit time.
Speed:
The rate of change of the object's position in any direction. Velocity is measured as the ratio of distance traveled and time traveled. Velocity is a scalar quantity because it has only direction and not magnitude.
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in bohr’s model, the energy of a photon absorbed or emitted by the electron will be equal to:
in Bohr’s model, the energy of a photon absorbed or emitted by the electron will be equal to "The difference in orbital energies associated with the transition".
The Bohr model, also known as the Rutherford-Bohr model, was first proposed by Niels Bohr and Ernest Rutherford in 1913 and describes an atomic system with an orbiting system of electrons and a small, dense nucleus that is similar to the Solar System in structure but is attracted by electrostatic forces rather than gravity.
Bohr's model helped to explain how electrons could only change orbits by exchanging or absorbing energy in fixed quanta. For instance, if an electron jumps into an orbit that is one orbit closer to the nucleus, it will have to expel energy equal to the energy difference between the two orbits.
The energy of energy level is connected to the energy photon that an electron absorbs or emits.
∆E = hf, where f is the frequency of radiation received or released during the electronic transition and h is the plank constant
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If stormy weather were approaching, the pressure tendency would probably be ______. answer choices. falling. rising. steady. none of these.
Option A - Falling is the pressure tendency ,If stormy weather were approaching .
Stormy weather, namely when it includes components like dark clouds, strong winds, thunder, lighting, and rain, is defined as weather that has generated storms or that indicates storms are imminent. It's frequently used in sentences that refer to stormy weather. Low pressure causes active weather. As a result of air rising because it is lighter than the air masses around it, the atmosphere becomes unstable. When the air pressure increases, vapour in the condenses, creating clouds and rain, among other things. Both violent storms and active weather, such as wind and rain, are produced by low pressure systems.
Low-pressure areas have relatively thin atmospheres. Inward winds are a factor in these locations. Low-pressure storms are frequently well-organized.
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a child (32 kg) jumps up and down on a trampoline. the trampoline exerts a spring restoring force on the child with a constant of 5000 n/m. at the highest point of the bounce, the child is 1.0 m above the level surface of the trampoline. what is the compression distance of the trampoline? neglect the bending of the legs or any transfer of energy of the child into the trampoline while jumping.
x =−0.422 m is the compression distance of the trampoline.
What does the term "energy conservation" mean?Energy efficiency a basic rule of physics and chemistry states that despite internal changes, the overall energy in an isolated system remains constant. It is the underlying principle of the first rule of thermodynamics, which is most frequently stated as "energy cannot be generated or destroyed."
How to calculate the compression distance in the trampoline?Given, Mass m = 32 kg
restoring force, k = 5000 n/n
height, h = 1 m
According to the concept of Conservation of energy,
initial total Energy = final total Energy
Ui + Uepe +Ki = Uf + Uepe + Kf
here,
Ui,Uf = initial,final potential energy
Uepe = elastic potential energy
Ki,Kf = initial,final Kinetic energy
mgh+1/2kx²+0 = mgh+1/2kx²+0
32×9.8×1+0+0 = mgx+1/2kx²
313.6 = 313.6x +1/2×5000×x²
0 = 313.6 + 313.6x + 2500x²
x = [313.6± (√313.6² - 4× -2500×313.6)]/2×313.6
x = -0.422 0r x = 0.29
The compressing of the spring should be considered to be represented by the negative figure of x.
x =−0.422 m is the compression distance of the trampoline.
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true or false: for a star moving away from you, you would observe the light to be shifted toward the blue end of the spectrum.
The given statement that a star moving away from us, we observe the light to be shiftest towards the blue end of spectrum is a false statement.
This phenomenon is called doppler effect. Doppler effect of light can be described as the apparent change in the frequency of the light observed by the observer due to relative motion between the source of light and the observer
In the given situation, the source of the waves is the star, which emits light (the waves). The observer is on Earth, and the star (the source of the waves) is moving away from the observer, so, wavelength of the light observed by us is shifted with respect to the original wavelength of the light emitted by the star.
when the star moves away, the wavelength increases, so it shift towards the red end of spectrum. This effect is called red-shifted.
In the given case, the star is moving away from us, so light will shift towards red end of spectrum.hence, The given statement is false.
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a ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building. the height of the point where the ball is thrown is 25 m from the ground. then find a. how height will the ball rise?
B how long will it be before the ball hip the ground?
A ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building. The height of the point where the ball is thrown is 25 m from the ground. The height will the ball rise is 20m. 5s long will it be before the ball hip the ground.
What is velocity ?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.
A. for solving how high will ball go , velocity at the top point will be 0 this gives ,
s = v² - u² / 2a
= 0 - 20² / -2 × 10
= 20m
B. Time to reach maximum height can be obtained from v = u + at
0 = 20 + ( − 10 ) t
t = 2s
s = ut + 0.5at²
= 20 ( 2 ) + 0.5 ( −10 ) ( 2 )²
= 20m
Therefore, the total distance for maximum height is 45 m
s = ut + 0.5at²
45 = 0 + 0.5 ( 10 ) ( t )²
t = 3s
Then,
Total time = 3+2
= 5s
Thus, A ball is thrown vertically upward with a velocity of 20m/s from the top of a multistory building.The height will the ball rise is 20m. 5s long will it be before the ball hip the ground.
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suppose a particle moves back and forth along a straight line with velocity v(t), measured in feet per second, and acceleration a(t). a) what is the meaning of integral 60^120 v(t) dt? b) what is the meaning of integral 60^120 |v(t)| dt? c) what is the meaning of integral 60^120 a(t) dt?
a) In this part of the problem, we are calculating the integral of the velocity function from t = 60 seconds to t = 120 seconds.
b) Next, we have a similar integral. The velocity function is now, however, contained by absolute value bars. Our velocity function will only equal to positive values as a result.
c) The acceleration function is the subject of our last integral.
a) When we integrate a velocity function, we return to the position function. As a result, this integral is determining the particle's displacement by determining the difference in location between these two points.
b) The result of this integration will treat all traveled distances as positive values as well, even if the particle moves backwards. This integral will determine the overall distance travelled during this period, rather than the displacement between 120 and 60 seconds.
c) When we integrate an acceleration function, we return to the velocity function. Thus, this integral will calculate the total change in the velocity between 60 seconds and 120 seconds.
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where in the universe do we see young galaxies? in the local group in the local supercluster in all regions of space billions of light-years away
The Milky Way is a member of the Laniakea Supercluster, which is a member of the Virgo Supercluster, which is a member of the Local Group galaxy group (which includes more than 54 galaxies).
Are the Local Group galaxies relocating away from us?Does the Local Group grow together with the universe as a whole? (Intermediate) The Local Group of Galaxies (Andromeda, Milky Way, etc.) is moving in the direction of the Local Supercluster.
Where can one find young stars in our galaxy?While the cooler red star predominates the bulge, hot young stars are mostly found in the spiral arms of the disk. The galaxy as a whole undergoes a dramatic change in appearance as we go through the various star populations.
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explain the effects of scattering of visible light on optical effects such as sky color and darkness of shadows
The more the scattering of photons by small particles (such as molecules, microscopic water droplets, and dust particles), the shorter their wavelength.
Since short wavelengths dominate in dispersed light, the sky seems blue there while direct sunlight is more yellowish or even reddish when the sun is low in the sky. When light interacts with the environment to produce vivid and colorful displays, this is known as an optical effect. Tiny particles in the atmosphere cause optical phenomena. Sunlight is reflected, refracted, and scattered as it travels through the atmosphere by water droplets, ice crystals, and dust particles. Refraction of light waves can split white light into distinct colors and produce visual effects.
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An adult inhales about 6.0×10^−4 m^3 of fresh air during a breath. only 20% of fresh air is oxygen. assume the pressure in the lungs is 1.0×10^5 pa and the air is at a temperature of 300 k. How many oxygen molecules are in each breath?
Number of oxygen molecules in each breath is 2.9X10^21
Given that the volume of air inside a breath (V) = 6.0×10^−4 m^3
oxygen in fresh air = 20%
volume of oxygen in fresh air = 20/100 x 6.0×10^−4 = 1.2x10-4m^3
pressure in the lungs (P)= 1.0×10^5 pa
Temperature of air (T) =300K
Using ideal gas equation find the number of moles of oxygen
PV = nRT
Then n = 1.0×10^5 x 1.2x10-4 / 8.314 x 300 = 4.8x10-3mol
We know the number of molecules in 1 mol is 6.023x10^23
Then the number of molecules in 4.8x10-3mol of oxygen is =
4.8x10-3molx 6.023x10^23 = 2.9x10^21
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Please Help me! Please show all work!
Jeremiah the Bullfrog rode a roller coaster around a loop. Being a good friend, he took some measurements for you during his journey. The 1.5kg amphibian noted that at the bottom of the loop, the speed of the roller coaster was 33m/s. You know from the informational poster next to the entrance that the loop has a radius of 22m. How much force did the seat exert on Jeremiah at the bottom of the loop?
74.25 N much force did the seat exert on Jeremiah at the bottom of the loop.
What is centripetal force?This is an acceleration technique. When an item is moving in a circle, it is moving ahead while being turned by a consistent force that is directed inward. The Centripetal Force is the name given to this internal resultant force.
Given that,
Mass (m) = 1.5 kg
speed (v) = 33 m/sec
radius (r) = 22m
As we know,
centripetal force (F) = mv²/r
or, F = [1.5 × (33)²] / 22
or, F = 74.25 N
So, 74.25 N much force the seat exert on Jeremiah at the bottom of the loop.
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how might it be helpful to know the difference between force and energy to understand the physics underlying a crash?
Work is the transmission of energy over a specific distance in one direction with the aid of a force. The force that operates at a specific distance is another name for energy.
Both of them fit the definition of a scalar unit. There must be a force and movement from one location to another for labor to take place.
Energy can be transmitted to or from an object when two things interact because of the forces that each one of the items applies to the other. For instance, the gravitational field energy of a system including the Earth and an object grows as energy is transmitted to the system when the object is raised. Power is the amount of work completed in a given amount of time. In order to learn new information and achieve higher exam scores, studying requires a lot of energy.
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A 34.5kg tree branch falls off of a cliff for a total of 12.09 s. What was the displacement of the tree branch?
Answer:
Assuming air resistance is neglected and the only force acting on the branch is the acceleration due to gravity, the answer is 716.709768 meters.
Explanation:
Since the initial velocity is 0, the displacement s, is simply written as :
s = (1/2)gt².
where g is the acceleration due to gravity.
if the distance of a galaxy is 5 mpc, what is its recessional velocity if the hubble constant is 70 km/s/mpc?
The distance of galaxy is given as 5Mpc. and the Hubble's constant is 70(km/s)/Mpc.
To find the recessional velocity of the galaxy
Hubble found that the tendency of recessional velocity is to increase with the distance of galaxy, therefore recessional velocity is directly proportional to the distance of the galaxy
The relation between recessional velocity and the distance of the galaxy can be expressed using Hubble's law.
substituting the values we get
V=70 (km/s)/ mpc [tex]\times[/tex]5Mpc
V = 350km,
Therefore the recessional velocity will be 350 km/s.
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sound waves have a speed of 340 m/s in room-temperature air. what is the wavelength of the sound waves for the musical tone concert a, which has a frequency of 440 hz?
The wavelength of the sound waves for the musical tone concert is 0.772m if frequency of wave is 440Hz.
Wavelength is defined as the distance between two consecutive crest and troughs. Wavelength is measured in meters and it is represented by λ. Frequency is defined as the number of vibrations completed by the wave in per second time. Frequency is measured in Hertz.
We know that for electromagnetic wave, we know that
c=v×λ
where c is the defined as the speed of the light wave
v is defined as the frequency of light wave and
λ is defined as the wavelength of light wave
We have c=340m/sec, v=440Hz and λ=?
So, on putting the values, we get
=>340=440 ˣ λ
=>λ=340/440
=>λ=34/44
=>λ=0.772m
Hence, wavelength of the sound waves is 0.772m
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if the disk is replaced by a hollow, thin-walled cylinder of the same mass and diameter, what will be the angular acceleration of the disk about its center of mass?
Fnet=mTacom, where Fnet is the net external force acting on the system and mT is the system's total mass, can be used to quickly compute the acceleration of the center of mass.
As a result, the system's center of mass accelerates by 2/3 ms2. The fixed point of rotation for things is their center of mass. There is no angular acceleration when a force is applied to the center of mass because the torque produced is zero. 12.5 radians per second squared is the size of the disk's angular acceleration. The position of the point in relation to the axis of rotation affects the rigid body's linear speed and acceleration at any given moment. Think about the disk's point B once more.
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Santa Claus entered the North Pole Annual Elf Throwing Competition. He fired his elf with a
horizontal speed of 25 m/s from the top of an iceberg of height 110 m. What was the elf's range and
time of flight?
Answer:
To find the range and time of flight of the elf, we need to use the equations of motion under the influence of gravity. The range is the horizontal distance covered by the elf and the time of flight is the total time that the elf is in the air.
The initial velocity of the elf in the x-direction (horizontal direction) is 25 m/s and the initial velocity in the y-direction (vertical direction) is 0 m/s, since the elf is thrown horizontally from the top of the iceberg. The acceleration due to gravity is -9.8 m/s^2 in the downward direction.
Using these values, we can find the range and time of flight of the elf using the following equations:
Range:
x = x0 + v0x*t
Where x is the range, x0 is the initial position (in this case, x0 is 0 since the elf is thrown from the top of the iceberg), v0x is the initial velocity in the x-direction (25 m/s), and t is the time of flight.
Time of flight:
y = y0 + v0y*t + (1/2)at^2
Where y is the vertical position of the elf, y0 is the initial position (in this case, y0 is 110 m since the elf is thrown from the top of the iceberg), v0y is the initial velocity in the y-direction (0 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight.
We can solve for t in the second equation and then substitute it into the first equation to find the range.
Solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Where y is the vertical position of the elf (0 m since the elf lands on the ground), y0 is the initial position (110 m), v0y is the initial velocity in the y-direction (0 m/s), and a is the acceleration due to gravity (-9.8 m/s^2).
Substituting this expression for t into the first equation:
x = x0 + v0x*((-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a))
Plugging in the values:
x = 0 + 25*((-0 + sqrt(0^2 - 4*(-9.8)(110))) / (2(-9.8)))
Simplifying:
x = 25*(sqrt(5832) / -19.6)
x = 25*(sqrt(5832) / -19.6)
x = (25*74.6) / -19.6
x = 1865.4 / -19.6
x = -95.1 m
So, the range of the elf is approximately -95.1 m. This means that the elf lands 95.1 m to the left of the starting point (the top of the iceberg).
The time of flight can be found by solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Plugging in the values:
t =
Explanation:
for each of the following cases, indicate whether the work done on the second object in each example will have a positive or a negative value. a. the road exerts a friction force on a speeding car skidding to a stop. b. a rope exerts a force on a bucket as the bucket is raised up a well. c. air exerts a force on a parachute as the parachutist falls to earth.
a) The work done by frictional force on the skidding car is negative.
b) Positive work is accomplished by the rope's force on the bucket.
c) The work done by the force exerted by the air on the parachutist is negative.
W = F * d = F d cos gives the amount of work done.
where, force is F and displacement is d
a) The road exerts a frictional force on a speeding car skidding to a stop.
In this instance, the frictional force F works in opposition to the direction of motion and opposes the motion itself. The angle between displacement and frictional force, which is in the opposite direction and equals 180°.
So, the work done by the frictional force on the skidding car is negative.
b) A bucket is being raised up a well while being pulled by a rope.
The bucket is raised upward by the rope's upward force F. The force and displacement are in the same direction, and their angle is equal to zero.
So, the work done by the force exerted by the rope on the bucket is positive.
c) As a parachutist falls to the ground, air pulls on a parachute.
The air opposes the parachutist's descent with a force F as they both plummet to the ground under the influence of gravity. The force exerted by the air is in a direction opposite to the motion of the parachutist. The force of air and displacement have an angle of 180 degrees.
So, the work done by the force F exerted by the air on the parachutist is negative.
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