Answer:
Economic growth can be illustrated by:
d. an outward shift of the production possibilities curve.
Explanation:
Economic growth is the process of increasing the economy's ability to produce goods and services. It is achieved by increasing the quantity or quality of resources.
Production Possibilities refers to the ability of a country to produce goods or services given the limited resources and technology. It is therefore possible to increase production of both goods at the same time as long as resources allow it.
The Production Possibilities Curve, also known as the production possibilities frontier, is a graph that shows the maximum number of possible units a company can produce if it only produces two products using all of its resources efficiently. Firstly, and most commonly, growth is defined as an increase in the output that an economy produces over a period of time, the minimum being two consecutive quarters. An increase in an economy's productive potential can be shown by an outward shift in the economy's production possibility frontier (PPF).
Each point on the curve shows how much of each good will be produced when resources shift from making more of one good and less of the other. The curve measures the trade-off between producing one good versus another.PPC or production possibility curve is a curve whose basic purpose is to show the different possible combinations of two goods that can be produced within the given available resource.
The two main characteristics of PPC are: slopes downwards to the right: PPC slopes downwards from left to right. It is because in a situation of fuller utilization of the given resources, production of both the goods cannot be increased simultaneously.
Economic growth is represented by an outward shift of the production possibilities curve, indicating that the economy can now produce more goods and services than before.
Explanation:Economic growth can be illustrated by an outward shift of the production possibilities curve. An increase in the quality or quantity of factors of production, such as labor, capital, and technology, can enhance an economy's ability to produce goods and services, which is represented graphically by the production curve moving outward. This shift indicates that the economy can now produce more than it could before, making previously unattainable levels of production possible.
What is the period of a simple pendulum 47 cm long (a) on the Earth, and ( b) when it is in a freely falling elevator?
Answer:
a)1.37 s
b)∞ ( Infinite)
Explanation:
Given that
L= 47 cm ( 1 m =100 cm)
L= 0.47 m
a)
On the earth :
Acceleration due to gravity = g
We know that time period of the simple pendulum given as
[tex]T=2\pi\sqrt{ \dfrac{L}{g_{{eff}}}[/tex]
Here
[tex]g_{eff}= g[/tex]
Now by putting the values
[tex]T=2\pi \times\sqrt{ \dfrac{0.47}{9.81}}[/tex]
T=1.37 s
b)
Free falling elevator :
When elevator is falling freely then
[tex]g_{eff}= 0[/tex] ( This is case of weightless motion)
Therefore
[tex]T=2\pi\sqrt{ \dfrac{L}{0}[/tex]
T=∞ (Infinite)
(a) The period of a simple pendulum 47 cm long when on the earth = 1.38 seconds
(b) The period of a simple pendulum when it is in a freely falling elevator = infinity (∞)
Period: This can be defined as the time taken for an object to complete one oscillation. The s.i unit is seconds (s)
The formula for the period of a simple pendulum is
T = 2π√(L/g).................... Equation 1
Where T = period of the simple pendulum, L = length of the simple pendulum, g = acceleration due to gravity.
(a) From the question,
Given: L = 47 cm = 0.47 m,
Constant: g = 9.8 m/s², π = 22/7 ≈ 3.14
Substitute these values into equation 1
T = 2(3.14)√(0.47/9.8)
T = 6.284√(0.048)
T = 6.284(0.219)
T = 1.38 seconds
(b) When it is in a free-falling elevator,
Then g = 0 m/s²
T = 2(3.142)√(0.47/0)
T = Infinity (∞)
Therefore, The period of the simple pendulum is (a) 1.38 seconds when it is on the earth and (b) infinity (∞) when it is in a freely falling elevator.
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2. Three charged particles are placed at the corners of an equilateral triangle of side 1.20 m. The charges are +7.0μC, -8.0 μC and -6.0 μC. Calculate the net force on charge 1 due to the other two charges in unit vector notation. Give values for the magnitude and direction of the force, too.
Answer:
0.53 N, 25.6°
Explanation:
side of triangle, a = 1.2 m
q = 7 μC
q1 = - 8 μC
q2 = - 6 μC
Let F1 be the force between q and q1
By using the coulomb's law
[tex]F_{1}=\frac{Kq_{1}q}{a^{2}}[/tex]
[tex]F_{1}=\frac{9\times 10^{9}\times 7\times 10^{-6}\times 8\times 10^{-6}}{1.2^{2}}[/tex]
F1 = 0.35 N
Let F2 be the force between q and q2
By using the coulomb's law
[tex]F_{2}=\frac{Kq_{2}q}{a^{2}}[/tex]
[tex]F_{2}=\frac{9\times 10^{9}\times 7\times 10^{-6}\times 6\times 10^{-6}}{1.2^{2}}[/tex]
F2 = 0.26 N
Write the forces in the vector form
[tex]\overrightarrow{F_{1}}=0.35\widehat{i}[/tex]
[tex]\overrightarrow{F_{2}}=0.26\left ( Cos60 \widehat{i}+Sin60\widehat{j}\right )[/tex]
[tex]\overrightarrow{F_{2}}=0.13 \widehat{i}+0.23\widehat{j}[/tex]
Net force
[tex]\overrightarrow{F}=\overrightarrow{F_{1}}+\overrightarrow{F_{2}}[/tex]
[tex]\overrightarrow{F}=0.48 \widehat{i}+0.23\widehat{j}[/tex]
Magnitude of the force
[tex]F=\sqrt{0.48^{2}+0.23^{2}}[/tex]
F = 0.53 N
Direction of force with x axis
[tex]tan\theta =\frac{0.23}{0.48}[/tex]
θ = 25.6°
To calculate the net force on charge 1 due to the other two charges, we need to find the individual forces between charge 1 and the other charges and then combine them vectorially using Coulomb's law.
Explanation:To calculate the net force on charge 1 due to the other two charges, we need to find the individual forces between charge 1 and the other charges and then combine them vectorially. The magnitude of the force between two charges can be calculated using Coulomb's law:
F = k * (|q1| * |q2|) / (r^2)
Where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
Let's calculate the individual forces:
Force between charge 1 (+7.0μC) and charge 2 (-8.0 μC) can be calculated using the formula:Next, we can calculate the net force on charge 1 by adding the forces vectorially:
Net Force on charge 1 = F12 + F13
Viscosity: Blood is about 4 to 5 times ____________ viscous than water. Viscosity of blood depends upon the amount of dissolved substances in the blood relative to the amount of fluid. Viscosity is ____________ if the amount of substances increases, the amount of fluid decreases, or both.
Answer:more, increased
Explanation:
Blood is four to five times more viscous than water.
Viscosity depends upon dissolved substances in blood and it increases as the amount is increases or if the fluid in the blood decreases.
Viscosity is the resistance offered by liquid to the flow and it also depends upon temperature and it decreases with increase in temperature.
to obtain a multimeter reading of 1 v between b and c in the circuit the value of r2 would have to be.
Complete question:
In the circuit shown in the figure below (See image attached), suppose that the value of R1 is [tex] 500\,k\Omega [/tex]. To obtain a multimeter reading of 1 V between points B and C in the circuit, the value of R2 would have to be.
Answer:
[tex]R2=0.1\Omega [/tex]
Explanation:
First, we are going to the find current trough the circuit, because the resistors are on series the current is the same on each resistor so I=I1=I2. The Ohm's law for the circuit is:
[tex] V=R_{T}*I [/tex] (1) , with V the voltage of the battery (6V), I the current trough the circuit and [tex]R_{T} [/tex] the total resistance of the circuit, but for resistors on series the total resistance is the sum of the individual resistance so [tex] R_{T} = R1+R2[/tex] (2).
Using (2) on (1) and solving for I:
[tex]I=\frac{V}{R1+R2} [/tex] (3)
Ohm's law is true for the individual resistors too so we're going to apply that on R2:
[tex]V2=R2*I2 [/tex], but remember I2=I
[tex]V2=R2*I [/tex] (4), using (3) on (4)
[tex]V2=R2* \frac{V}{R1+R2} [/tex], solving for R2:
[tex] R1*V2+R2*V2=R2V[/tex]
[tex] R1*V2=R2(V-V2)[/tex]
[tex] R2=\frac{R1V2}{V-V2}=\frac{500\times10^{3}\Omega*1V}{6V-1V}[/tex], V2= 1V because we want that reading on the multimeter.
[tex]R2=100\,k\Omega [/tex]
Answer:
10k
Explanation:
After sliding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +3.0 m/s. Miranda runs after her at a velocity of +4.2 m/s and hops on the inner tube.
How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 69 kg and Miranda's is 59 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.
Answer:
Their combined velocity on the inner tube is +3.55 m/s
Explanation:
This question deals with the conservation of linear momentum. The total linear momentum in a closed system is conserved.
Therefore,
P_i = P_f
m₁ v₁ + m₂ v₂ = (m₁ + m₂) v₁₂
where
m₁ is the mass of Ashleym₂ is the mass of Mirandav₁ is Ashley's velocityv₂ is Miranda's velocityv₁₂ is their combined velocityTherefore,
v₁₂ = (m₁ v₁ + m₂ v₂) / (m₁ + m₂)
v₁₂ = ( (69 kg)(3 m/s) + (59 kg)(4.2 m/s) ) / (69 kg + 59 kg)
v₁₂ = +3.55 m/s
Therefore, Ashley and Miranda's combined velocity on the inner tube is +3.55 m/s.
The positive sign shows that the velocity is in the positive direction.
What are the potentially negative impacts of movement corridors?
Answer:
These corridors can decrease the inbreeding in declining populations and enhance the spread of different diseases.
Explanation:
Movement corridors generally will enhance a process such as dispersal which is the spread or distribution of things over a considerably large area. These corridors can decrease the inbreeding in declining populations. They are very vital to species that usually migrate seasonally. On the other day, the movement corridor can be highly harmful in nature due to its ability of enhancing the spread of different diseases. These corridors facilitate the movement of species and allow the spread of harmful diseases.
Through which one of the following mediums is the velocity of a sound wave the greatest?
A. Steel
B. Water
C. Air
D. Lead
Answer: C. Steel
Explanation: When a sound wave travels through a solid body consisting
of an elastic material, the velocity of the wave is relatively
high. For instance, the velocity of a sound wave traveling
through steel (which is almost perfectly elastic) is about
5,060 meters per second. On the other hand, the velocity
of a sound wave traveling through an inelastic solid is
relatively low. So, for example, the velocity of a sound wave
traveling through lead (which is inelastic) is approximately
1,402 meters per second.
A flat, circular, metal loop of radius r = 1 m is at rest in a uniform magnetic field of magnitude B. The plane of the loop is parallel to the page and the magnetic field is directed perpendicular to and out of the page, as indicated by the blue dots. If the magnitude of the magnetic field increases from 2 T to 6 T in 2 s, what is the magnitude of the induced emf within the circular loop?
Answer:
Induced EMF,[tex]\epsilon=6.28\ volts[/tex]
Explanation:
Given that,
Radius of the circular loop, r = 1 m
Time, t = 2 s
Initial magnetic field, [tex]B_i=2\ T[/tex]
Final magnetic field, [tex]B_f=6\ T[/tex]
The expression for the induced emf within the circular loop is given by :
[tex]\epsilon=\dfrac{d\phi}{dt}[/tex]
[tex]\phi[/tex] = magnetic flux
[tex]\epsilon=\dfrac{d(BA\ cos\theta)}{dt}[/tex]
Here, [tex]\theta=90\ degrees[/tex]
[tex]\epsilon=A\dfrac{d(B)}{dt}[/tex]
[tex]\epsilon=A\dfrac{B_f-B_i}{t}[/tex]
[tex]\epsilon=\pi (1)^2\times \dfrac{6-2}{2}[/tex]
[tex]\epsilon=6.28\ volts[/tex]
So, the induced emf in the loop is 6.28 volts. Hence, this is the required solution.
A boy can swim 3.0 meter a second in still water while trying to swim directly across a river from west to east, he is pulled by a current flowing southward at 2.0 meter a second if he ended up exactly across the stream from where he began at what angel to the shore must he swim upstream
Answer:
Angle: [tex]48.19^o[/tex]
Explanation:
Two-Dimension Motion
When the object is moving in one plane, the velocity, acceleration, and displacement are vectors. Apart from the magnitudes, we also need to find the direction, often expressed as an angle respect to some reference.
Our boy can swim at 3 m/s from west to east in still water and the river he's attempting to cross interacts with him at 2 m/s southwards. The boy will move east and south and will reach the other shore at a certain distance to the south from where he started. It happens because there is a vertical component of his velocity that is not compensated.
To compensate for the vertical component of the boy's speed, he only has to swim at a certain angle east of the north (respect to the shoreline). The goal is to make the boy's y component of his velocity equal to the velocity of the river. The vertical component of the boy's velocity is
[tex]v_b\ cos\alpha[/tex]
where [tex]v_b[/tex] is the speed of the boy in still water and [tex]\alpha[/tex] is the angle respect to the shoreline. If the river flows at speed [tex]v_s[/tex], we now set
[tex]v_b\ cos\alpha=v_s[/tex]
[tex]\displaystyle cos\alpha=\frac{v_s}{v_b}=\frac{2}{3}[/tex]
[tex]\alpha=48.19^o[/tex]
An 880 kg cannon at rest fires a 12.4 kg cannonball forward at 540 m/s. What is the recoil velocity of the cannon? (Unit m/s)
Answer:
7.61 m/s backwards
Explanation:
Initial momentum = final momentum
0 = (880 kg) v + (12.4 kg) (540 m/s)
v = -7.61 m/s
The cannon's recoil is 7.61 m/s backwards.
Answer:
The recoil velocity vector of the cannon is [tex](7.609,0,0)\frac{m}{s}[/tex]
Explanation:
We can solve this problem by applying the Momentum Conservation Principle.
The principle of conservation of momentum states that when you have an isolated system with no external forces, we can use the following equation to calculate the final velocity of one object.
[tex]m1.v1=m2.v2[/tex] (I)
Where ''[tex]m1[/tex]'' and ''[tex]v1[/tex]'' are the mass and velocity of the first object.
And where ''[tex]m2[/tex]'' and ''[tex]v2[/tex]'' are the mass and velocity of the second object.
The momentum is a vectorial magnitude.
If we use the equation (I) with the data given :
[tex](880kg).v1=(12.4kg).(540\frac{m}{s})[/tex]
[tex]v1=7.609\frac{m}{s}[/tex]
If we considered as negative the sense of the velocity vector from the cannonball, the cannon's velocity vector will have the same direction but opposite sense that the cannonball's velocity vector (It will be positive).
We can give it a vectorial character like this :
[tex]v1=(7.609,0,0)\frac{m}{s}[/tex]
The velocity vector will be entirely in the x-axis.
A 1.00-kg sample of steam at 100.0 °C condenses to water at 100.0 °C. What is the entropy change of the sample if the latent heat of vaporization of water is 2.26 x 10⁶ J/kg?
Answer:
The entropy change of the sample of water = 6.059 x 10³ J/K.mol
Explanation:
Entropy: Entropy can be defined as the measure of the degree of disorder or randomness of a substance. The S.I unit of Entropy is J/K.mol
Mathematically, entropy is expressed as
ΔS = ΔH/T....................... Equation 1
Where ΔH = heat absorbed or evolved, T = absolute temperature.
Given: If 1 mole of water = 0.0018 kg,
ΔH = latent heat × mass = 2.26 x 10⁶ × 1 = 2.26x 10⁶ J.
T = 100 °C = (100+273) K = 373 K.
Substituting these values into equation 1,
ΔS =2.26x 10⁶/373
ΔS = 6.059 x 10³ J/K.mol
Therefore the entropy change of the sample of water = 6.059 x 10³ J/K.mol
The entropy change of the sample of steam is equal to 6,058.98 J/Kmol.
Given the following data:
Mass = 1.00 kgTemperature = 100°C to Kelvin = [tex]273+100=373\;K[/tex]Latent heat of vaporization of water = [tex]2.26 \times 10^6\;J/kg[/tex]To determine the entropy change of the sample of steam:
Mathematically, entropy change is given by the formula:
[tex]\Delta S = \frac{\Delta H}{T}[/tex]
Where:
[tex]\Delta H[/tex] is the enthalpy change.T is the absolute temperature.Substituting the given parameters into the formula, we have;
[tex]\Delta S = \frac{2.26 \times 10^6\times 1}{373}[/tex]
Entropy change = 6,058.98 J/Kmol.
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2 litre of water at is poured into a plastic bucket containing 10 litre of water at 20 degree Celsius.What is the final temperature of water?(Density of water=1kg/litre)
Answer:[tex]30^{\circ}[/tex]
Explanation:
Given
[tex]v_1=2 liter[/tex]
volume of water in bucket [tex]v_2=10 liter[/tex]
density of water [tex]\rho =1 kg/liter[/tex]
thus [tex]m_1=\rho \cdot v_1=2 kg[/tex]
[tex]m_2=\rho \cdot v_2=10 kg[/tex]
[tex]T_2=20^{\circ}C[/tex]
suppose [tex]T_1=80^{\circ}C[/tex]
Conserving heat energy i.e. heat lost by water is gained by water in bucket
[tex]m_1cT_1+m_2cT_2=(m_1+m_2)T[/tex]
where T=final Temperature
[tex]T=\frac{m_1T_1+m_2T_2}{m_1+m_2}[/tex]
[tex]T=\frac{160+200}{12}[/tex]
[tex]T=30^{\circ}C[/tex]
Which of the following explains why international travelers need to use special adapters when plugging a device designed to operate in the U.S. into a wall outlet in Europe?
The increased voltage causes the device's resistance to increase, and the device won't work.
The increased voltage causes the device's resistance to decrease, and the device will over-heat.
The increased voltage causes an increase in power usage, and the device will over-heat.
The increased voltage causes a decrease in power usage, and the device won't work.
Answer:
The answer is: The increased voltage causes an increase in power usage, and the device will over-heat.
Explanation:
First, we must consider the variables of the electrical system that will allow us to respond. In this case, power, current and voltage, which are related by
[tex]P=VI[/tex]
Where P=Power, V=Voltage, I=Current.
In the equation it can be observed that power is directly proportional to the system voltage. Thus, if the voltage increases as in this case, the power will also increase, which overheats the device and can cause damage to it.
If a 4.5-meter wave traveled at a speed of 15 m/s, what would its frequency be?
Answer:
The frequency of the wave = 10 Hz.
Explanation:
Wave: A wave is a disturbance that travels through a medium a transfer energy from one point to another in the medium without causing and permanent displacement of the medium itself.
V = λf .................. Equation 1
making f the subject of the equation,
f = V/λ.................... Equation 2
Where V = velocity of the wave, λ = wavelength of the wave, f = frequency of the wave.
Given: V = 15 m/s², λ = 4.5 m.
Substituting these values into equation 2,
f = 15/1.5
f = 10 Hz.
Therefore the frequency of the wave = 10 Hz.
Answer:
The frequency of the wave = 10 Hz.
Explanation:
the guy below gave a good explanation
A drone traveling horizontally at 110 m/s over flat ground at an elevation of 3000 meters must drop an emergency package on a target on the ground. The trajectory of the package is given by x = 110 t , y = − 4.9 t 2 + 3000 , t ≥ 0 where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.
Answer:
The horizontal distance of the target should be 2721,4 meters.
Explanation:
First of all we need to find the time that the emergency package hits the ground after the moment of release:
y=0 (because when it hits the ground it is on the level of 0m);
[tex]0=-4,9*t^2+3000\\t=24,74[/tex]
The emergency package hits the ground after 24,74 seconds from release.
Lets assume that package preserves his 110 m/s horizontal speed during the free fall. The targets horizontal distance is:
[tex]110*24,74=2721,4[/tex]
2721,4 meters
A box is 25 kg with a kinetic force of .35 is pushed horizontally. What force must you continue continue to exert if you want to accelerate the box at a rate of 2.5 m/s squared
The force required is equal to 148.33 N.
Why?
To answer your question, I'll assume that the value of 0.35 is referring to the coefficient of kinetic friction. So, we can solve the problem using the following equations:
[tex]F-F_{f}=m*a\\\\FrictionalForce=\mu *m*g\\\\F_{f}=0.35*25kg*9.81m\frac{m}{s^{2}}=85.83N[/tex]
Now, substituting, we have:
[tex]F-F_{f}=m*a\\\\F=25kg*2.5\frac{m}{s^{2}}+85.83N\\\\F=62.5N+85.83N=148.33N[/tex]
Hence, we have that the force required to accelerate the box at a rate of 2.5 m/s2 is 148.33N.
Have a nice day!
A person is riding on a Ferris wheel. When the wheel makes one complete turn, the net work done on the person by the gravitational force ____________.
Answer:
0
Explanation:
m = Mass of person
g = Acceleration due to gravity = 9.81 m/s²
d = Vertical height from the ground
F = Force = Weight = mg
Net work done would be
[tex]W_n=W_{up}+W_{down}\\\Rightarrow W_n=Fdcos180+Fdcos0\\\Rightarrow W_n=-mgd+mgd\\\Rightarrow W_n=0[/tex]
Hence, the work done on the person by the gravitational force is 0
A tradesman sharpens a knife by pushing it with a constant force against the rim of a grindstone. The 30-cm-diameter stone is spinning at 200 rpm and has a mass of 28 kg. The coefficient of kinetic friction between the knife and the stone is 0.20. If the stone slows steadily to 180 rpm in 10 s of grinding, what is the force with which the man presses the knife against the stone?
Answer:
F = -2.205N
Explanation:
First, we have to find the angular aceleration due to the knife following the next equation:
W = Wo + at
where W is the final angular velocity and Wo is the initial angular velocity, a the angular aceleration and t the time.
Now, we will change the angular velocity to rad/s as:
Wo = 200 rpm = 20.94 rad/s
W = 180 rpm = 18.84 rad/s
Replacing in the previus equation, we get:
18.84rad/s = 20.94rad/s + a(10s)
solving for a:
a = -0.21rad/s^2
Now, we have to find the moment of inertia of the grindstone using:
I = [tex]\frac{1}{2}MR^2[/tex]
Where M is the mass of the stone and R the radius of the stone. Replacing values:
I = [tex]\frac{1}{2}(28kg)(0.15m)^2[/tex]
I = 0.315 kg*m^2
Adittionally:
T = Ia
where T is the torque, I the moment of inertia and a the angular aceleration.
so:
[tex]U_kFd = Ia[/tex]
where [tex]U_k[/tex] is the coefficient of the kinetic friction, F is the force with which the man presses the knife and d the lever arm. So, replacing values, we get:
[tex](0.2)F(0.15m) = (0.315)(-0.21rad/s^2)[/tex]
solving for F:
F = -2.205N
it is negative because the stone is stopping due of this force.
Compare the Lagrangian method with the Newton-Euler method in detail.
The comparison of the Lagrangian and Newton methods are explained. Explanation:
The Newton-Euler Method is derived by Newton's Second Law of Motion, that describes the dynamic systems in terms of force and momentum.
It deals with concentration of particles to calculate the overall diffusion and convection of a number of particles.
The Lagrangian Method the dynamic behavior is described in terms of work and energy.
It deals with individual particles to calculate the trajectory of each particle separately.
The Lagrangian method and the Newton-Euler method are two approaches used to solve problems in classical mechanics involving Newton's laws of motion. The Newton-Euler method relies directly on Newton's second law and free-body diagrams, while the Lagrangian method is based on the principle of least action and the Euler-Lagrange equations. The choice between the two methods often depends on the complexity and nature of the physical system in question.
Explanation:When comparing the Lagrangian method with the Newton-Euler method, it is important to understand that both approaches are used to solve complex problems in classical mechanics, which often involve the application of Newton's laws of motion. The Newton-Euler method is more traditional and is founded upon direct application of Newton's second law, F=ma (force equals mass times acceleration), and the related concepts for rotary motion. This method involves creating a free-body diagram, identifying all the forces acting on the object, and applying Newton's second law to find the accelerations and subsequently the positions and velocities of the object in question.
Contrastingly, the Lagrangian method is a more modern approach, which is grounded in the principle of least action. Instead of focusing on forces, it involves the calculation of the Lagrangian, which is the difference between an object's kinetic and potential energies, and applying the Euler-Lagrange equations to find the equations of motion. This method is particularly powerful in systems where the forces are conservative and can be derived from a potential energy; the Lagrangian method is also more convenient when dealing with complex constraints and coordinate systems that are not Cartesian.
While the Newton-Euler method is practical and straightforward, especially in simple scenarios with few forces or when numerical solutions are required, the Lagrangian approach offers more flexibility and can simplify calculations in systems with symmetries or non-standard geometries. Understanding the application of these methods is an integral part of a problem-solving procedure when using Newton's laws of motion, and both methods reinforce concepts useful across various areas of physics.
A compressed spring in a toy is used to launch a 5.00-gram ball.
If the ball leaves the toy with an initial horizontal speed of 5.00 meters per second, the minimum amount of potential energy stored in the compressed spring was:
a) 0.0125 J
b) 0.0250 J
c) 0.0625 J
d) 0.125 J
Answer:
c) 0.0625 J
Explanation:
How the mechanical energy is conserved, then ball’s kinetic energy is equal to stored energy in compressed spring.
Then:
[tex]K = U_{e}[/tex]
Where K: kinetic energy
[tex]U_{e}[/tex]: elastic potential energy
[tex]K = \frac{mv^{2} }{2}[/tex]
[tex]K = \frac{(0.005)(5)^{2} }{2}[/tex]
K = 0.0625 J
and
[tex]U_{e}[/tex] = 0.0625
Electrical wire with a diameter of .5 cm is wound on a spool with a radius of 30 cm and a height of 24 cm.
a) Through how many radians must the spool be turned to wrap one even layer of wire?
b) What is the length of this wound wire?
Answer:
a) # lap = 301.59 rad , b) L = 90.48 m
Explanation:
a) Let's use a direct proportions rule (rule of three). If one turn of the wire covers 0.05 cm, how many turns do you need to cover 24 cm
# turns = 1 turn (24 cm / 0.5 cm)
# laps = 48 laps
Let's reduce to radians
# laps = 48 laps (2 round / 1 round)
# lap = 301.59 rad
b) Each lap gives a length equal to the length of the circle
L₀ = 2π R
L = # turns L₀
L = # turns 2π R
L = 48 2π 30
L = 9047.79 cm
L = 90.48 m
The spool needs to be turned through 2π radians to wrap one even layer of wire. The length of the wound wire can be calculated using the circumference formula.
Part a: To wrap one even layer of wire around the spool, the spool must be turned through an angle of 2π radians because one complete revolution is equal to 2π radians.
Part b: To calculate the length of the wire wound on the spool, we find the circumference of the spool using the formula: circumference = 2πr, where r is the radius of the spool (30 cm). The length of the wound wire is the product of this circumference and the height of the spool (24 cm).
A Styrofoam cooler has outside dimensions of B = 84.0 cm, W = 47.0 cm, and H = 59.0 cm. The thickness of each wall of the cooler, t, is 8.0 cm. Styrofoam has a density, rho, of 1.0 kg/m3. (a) What is the volume of the Styrofoam used in cubic inches? (b) What is the mass in lbm? (c) How many gallons of liquid could be stored in the cooler?
(a) The volume of the Styrofoam used is 14214.37 in3.
(b) The mass is 9.6 lbm.
(c) The number of gallons of liquid that could be stored in the cooler is 1058.54 gal.
Answer:
a) [tex]V_s=4989.7895\ in^3[/tex]
b) [tex]mass=0.1803\ lb[/tex]
c) [tex]V_i=39.93\ gallons[/tex]
Explanation:
external breadth of cooler, [tex]B=84\ cm[/tex]external width of cooler, [tex]W=47\ cm[/tex]external height of cooler, [tex]H=59\ cm[/tex]∵ thickness of each wall is, [tex]t=8\ cm[/tex]Therefore,
internal breadth of cooler, [tex]B_i=76\ cm[/tex]internal width of cooler, [tex]W_i=39\ cm[/tex]internal height of cooler, [tex]H_i=51\ cm[/tex]a)
External volume of the structure:
[tex]V=B.H.W[/tex]
[tex]V=84\times47\times59\div 2.54^3[/tex]
[tex]V=14214.3828\ in^3[/tex]
Internal volume of the structure:
[tex]V_i=B_i.H_i.W_i[/tex]
[tex]V_i=76\times 39\times 51\div 2.54^3[/tex]
[tex]V_i=9224.5932\ in^3[/tex]
∴Volume of Styrofoam used:
[tex]V_s=V-V_i[/tex]
[tex]V_s=14214.3828-9224.5932[/tex]
[tex]V_s=4989.7895\ in^3[/tex]
b)
given that density of Styrofoam, [tex]\rho=1\ kg.m^{-3}=3.613\times 10^{-5}\ lb.in^{-3}[/tex]
we know,
[tex]\rm mass= density \times volume[/tex]
[tex]mass=4989.7895\times 3.613\times 10^{-5}[/tex]
[tex]mass=0.1803\ lb[/tex]
c)
Volume of liquid it can hold [tex]=V_i[/tex]
[tex]V_i=39.93\ gallons[/tex]
The volume of the Styrofoam used is 14214.37 in³. The mass is 9.6 lbm. The number of gallons of liquid that could be stored in the cooler is 1058.54 gal.
Explanation:To find the volume of the Styrofoam used in cubic inches, we need to convert the outside dimensions from centimeters to inches, subtract the volume of the cooler, and divide by the thickness of each wall. The volume of the Styrofoam used is 14214.37 in³.
To find the mass in lbm, we need to convert the density from kg/m³ to lbm/in³ and multiply by the volume of the Styrofoam used. The mass is 9.6 lbm.
To find the number of gallons of liquid that could be stored in the cooler, we need to convert the volume of the cooler from cm³ to gallons. The number of gallons of liquid that could be stored in the cooler is 1058.54 gal.
How do the source regions of polar and tropical air masses differ
Answer:
Maritime polar and tropical which are cool/humid and warm/humid respectively. Continental polar and tropical which are dry/cold and dry/hot respectively. The maritime is associated with water while the continental is associated with land.
Explanation:
Maritime/polar air masses are humid and cool in nature. They move toward the top at the continental tropical air masses which are also humid but warm at the bottom. In addition, the maritime is associated with water while the continental is associated with land. We can have maritime polar and tropical which are cool/humid and warm/humid respectively. Furthermore, we can have continental polar and tropical which are dry/cold and dry/hot respectively.
Final answer:
Polar air masses form in high-latitude, cold regions and can be dry (continental) or moist (maritime), while tropical air masses form near the equator in warm regions and are generally moist (maritime) or dry (continental).
Explanation:
The source regions of polar and tropical air masses differ mainly in terms of their geographical locations and their temperature and humidity characteristics, which are influenced by whether they form over land or water. Polar air masses originate in high-latitude regions around 60° north or south, and are typically cold with continental polar air masses being dry while maritime polar air masses are somewhat moist. In contrast, tropical air masses form closer to the equator, between 15° and 35° north and south latitude, and are warm, with maritime tropical air masses being moist and continental tropical air masses being dry due to the deserts they often originate from, such as the Sahara and Australian deserts.
Read the false statement. In an atom, protons and electrons are in the nucleus, which is surrounded by neutrons. Which option rewords the false statement so it is true?
1. In an atom, protons and neutrons are in the nucleus, which is surrounded by electrons.
2. In an atom, electrons and neutrons are in the nucleus, which is surrounded by protons.
3. In an atom, electrons and neutrons are in the nucleus, which is surrounded by photons.
4. In an atom, electrons and photons are in the nucleus, which is surrounded by neutrons.
Answer: A.
In an atom, protons and neutrons are in the nucleus, which is surrounded by electrons.
Explanation:
It must first be noted that an atom consists of protons, neutrons and electrons.
The proton and neutron is contained in the atom while the electron is found in the outer most shell of the atoms. It can be concluded then that in an atom, protons and neutrons are in the nucleus, which is surrounded by electrons.
Answer:
A
Explanation:
Jumping up before the elevator hits. After the cable snaps and the safety system fails, an elevator cab free-falls from a height of 36.0 m. During the collision at the bottom of the elevator shaft, a 85.0 kg passenger is stopped in 5.00 ms. (Assume that neither the passenger nor the cab rebounds.) What are the magnitudes of the (a) impulse and (b) average force on the passenger during the collision
Answer:
a) I = -2257.6 Kg*m/s
b) F = -451,520N
Explanation:
part a.
we know that:
I = [tex]P_f-P_i[/tex]
where I is the impulse, [tex]P_f[/tex] the final momentum and [tex]P_i[/tex] the initial momentum.
so:
I = [tex]MV_f-MV_i[/tex]
where M is the mass, [tex]V_f[/tex] the final velocity and [tex]V_i[/tex] the initial velocity.
Therefore, we have to find the initial velocity or the velocity of the passenger just before the collition.
now, we will use the law of the conservation of energy:
[tex]E_i=E_f[/tex]
so:
mgh = [tex]\frac{1}{2}MV_i^2[/tex]
where g is the gravity and h the altitude. So, replacing values, we get:
(85kg)(9.8m/s^2)(36m)= [tex]\frac{1}{2}(85kg)V_i^2[/tex]
solving for [tex]V_i[/tex]:
[tex]V_i = 26.56m/s[/tex]
Then, replacing in the initial equation:
I = [tex]MV_f-MV_i[/tex]
I = [tex](85kg)(0m/s)-(85kg)(26.56m/s)[/tex]
I = -2257.6 Kg*m/s
Then, the impulse is -2257.6 Kg*m/s, it is negative because it is upwards.
part b.
we know that:
Ft = I
where F is the average force, t is the time and I is the impulse. So, replacing values, we get:
F(0,005s) = -2257.6 Kg*m/s
solving for F:
F = -451520N
Finally, the force is -451,520N, it is negative because it is upwards.
What happens when a main-sequence star exhausts its core hydrogen fuel supply?
Explanation:
when a main-sequence star exhausts its core hydrogen fuel supply the core starts to shrink ( lack of fusion reactions) and the rest of the star starts to expands. The fusion reaction leaves the main sequence and begin to fuse helium in a shell outside the core. This mass stars become red supergiant and then evolve to become blue super giant.
Answer: Their temperature decreases dramatically, but their luminosity increases only slightly.
Explanation: This is exact from Plato
A 84.5 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 38.9 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.613 kg, and the astronaut throws the wrench with a speed of 24.9 m/s. How long does it take the astronaut to reach the ship? Answer in units of s.
Answer:
215.35736 seconds
Explanation:
[tex]m_1[/tex] = Mass of astronaut = 84.5 kg
[tex]m_2[/tex] = Mass of wrench = 0.613 kg
[tex]v_1[/tex] = Velocity of astronaut
[tex]v_2[/tex] = Velocity of wrench = 24.9 m/s
In this system the linear momentum is conserved
[tex]m_1v_1=m_2v_2\\\Rightarrow v_1=\dfrac{m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.613\times 24.9}{84.5}\\\Rightarrow v_1=0.18063\ m/s[/tex]
Time is given by
[tex]Time=\dfrac{Distance}{Speed}[/tex]
[tex]Time=\dfrac{38.9}{0.18063}=215.35736\ s[/tex]
The time it will take the astronaut to get back to the ship is 215.35736 seconds
A 1100 kg automobile is at rest at a traffic signal. At the instant the light turns green, the automobile starts to move with a constant acceleration of 5.0 m/s2. At the same instant a 2000 kg truck, traveling at a constant speed of 7.0 m/s, overtakes and passes the automobile. A)How far is the com of the automobile-truck system from the traffic light at t=3.0 s? B)What is the speed of the com then?
Answer:
a ) 21 m b) 7 m/s
Explanation:
For this case, we can consider for our reference system, that point zero (this is, at the rest of the traffic signal) is when X₀ = 0, and direction of movement is from left to right (positive sign)
For the car:
a= acceleration is constant = 5 m/s² m1 , mass = 1100 Kg , V = not constant
This is an uniformly accelerated rectilinear movement, and applicable formulas are:
V = V₀ + at , X = X₀ + V₀t + 1/2at²
For the truck:
V = speed is constant = 7 m/s , mass = 2000 Kg, a = 0
This is an uniform rectilinear movement, and the applicable formula is:
X = X₀ + Vt
a) At t = 3.0 sec, we can use the formula for the track, considering that X₀ = 0 (when it pass the rest of the traffic signal)
X = 0 + (7 m/s)x(3 s) = 21 m
So, at 3 sec, truck will be at 21 m from the rest of traffic light and, as truck has a constant speed; at that exact second; truck and car will be together as a com, so both will be 21 m away from point zero
b) At the exact time (3 sec, or in distance words, 21 m) car and truck will be together as a com, so they will both have the exact speed, hence, speed of car at that point will be 7 m/s
As a result of cancer, Mike had to have part of his cecum removed. Mike is probably at less risk for nutrient absorption problems than he would be if part of his _____ had been removed.
Answer: Small intestine
Explanation: This is because the small intestine is the place where absorption of minerals and nutrients from food takes place.
The small intestine is also known as small bowels, it is located between the large intestine and the stomach where the pancreatic duct supplies it with pancreatic juice and bile that helps digestion.
Suppose we had two speakers, one placed some distance directly behind the other andboth pointing along the same direction, facing us. Now, we connect the speakers tothe same source and turn them on producing a single continuous tone of 440Hz. If thespeed of sound in air is about 343m/s, then how far would we have to put the backspeaker behind the front one so that weneverhear the tone when standing anywheredirectly in front of the speakers?
Answer:
d= 0.3898 m
Explanation:
given,
frequency of the wave = 440 Hz
speed of the sound = 343 m/s
wavelength of the wave = ?
v = λ x f
[tex]\lambda = \dfrac{v}{f}[/tex]
[tex]\lambda = \dfrac{343}{440}[/tex]
λ = 0.7795 m
distance where he should be standing
if you line them up you will see the waves have cancelled each other out
if two speaker are lined together
The speed of sound in the air has no relevance on this question as it would not matter how fast the waves traveled but only that they travel at the same speed as each other.
The distance of half a wavelength in this case is
d = λ/2
d = 0.7795/2
d= 0.3898 m
Final answer:
To ensure silence in front of two speakers emitting a 440Hz tone due to destructive interference, the back speaker must be positioned an odd multiple of half the wavelength of the sound away from the front speaker, with the minimum distance being half the wavelength, 0.38975 meters.
Explanation:
To achieve silence in front of the speakers by exploiting destructive interference, the back speaker must be placed at a distance corresponding to an odd multiple of half the wavelength of the sound produced. Given that the sound has a frequency of 440Hz and the speed of sound in air is approximately 343m/s, we can calculate the wavelength using the formula \(\lambda = \frac{v}{f}\), where \(\lambda\) is the wavelength, \(v\) is the speed of sound, and \(f\) is the frequency. Substituting the given values, we find that the wavelength is \(\lambda = \frac{343 m/s}{440 Hz} = 0.7795 m\). To achieve destructive interference, the distance should be an odd multiple of half this wavelength, i.e., \((2n+1)\frac{\lambda}{2}\) where \(n\) is an integer starting from 0. Thus, the minimum distance required to never hear the tone directly in front of the speakers is \(0.7795 m / 2 = 0.38975 m\), which is half the wavelength.