what is the relative velocity of the two spaceships? express it as a ratio to the speed of light. let the relative velocity of the spaceships be positive if they are approaching each other and negative if they are moving apart from one another.
Answers
If the 2 spaceships are moving along the line connecting them , then the relative velocity of the two spaceships is 0.548C .
The term Relative Velocity is defined as " the velocity of an object with respect to the another observer " .
it is given that ; u = 0.765C and u' = 0.925C ;
the space ships shoots a missile ,
we have to find the the velocity "v" ;
the equation to find the relative velocity(v) can be found by using the equation ;
u = (v + u')/(1 + vu'/c²)
simplifying further ,
we get ;
v = (u' - u)/(uu'/c² - 1)
substituting the values of u , u' ,
we get ;
v = (0.925C - 0.765C)/(0.765C*0.925C/C² - 1)
Simplifying and solving further ,
we get ;
v = -0.548C , the negative sign indicates that the spaceships are moving away from each other ,
Therefore , the relative velocity of the 2 spaceships is 0.548C .
The given question is incomplete , the complete question is
Two spaceships are moving along the line connecting them , One of the spaceships shoots a missile towards the other , The missile leaves the attacking spaceship at 0.925C and approaches the other at 0.765C . given u = 0.765C and u' = 0.925C ,
What is the relative velocity of the two spaceships ? express it as a ratio to the speed of light. let the relative velocity of the spaceships be positive if they are approaching each other and negative if they are moving apart from one another.
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Related Questions
a car travels in a circle with constant speed. the net force on the car is
Answers
The net force on the car is zero because the car is not accelerating
Three engines operate between reservoirs separated in temperature by 300 K. The reservoir temperatures are as follows:Engine A: Th = 1000 K, Tc = 700 K;Engine B: Th = 800 K, Tc = 500 K;Engine C: Th = 600 K, Tc = 300 K.Rank the engines in order of theoretically possible efficiency, from highest to lowest.
Answers
The order of theoretically possible efficiency, from highest to lowest is Engine C, Engine B, and Engine A.
The theoretical efficiency of a Carnot engine is given by the formula:
Efficiency = 1 - T_{c} / Th
where Th and T_{c} are the temperatures of the hot and cold reservoirs, respectively.
Using this formula, we can calculate the efficiency of each engine.
For engine A, we have:
Efficiency = 1 - T_{c} / Th = 1 - 700 K / 1000 K = 0.3 or 30%
For engine B, we have:
Efficiency = 1 - T_{c} / Th = 1 - 500 K / 800 K = 0.375 or 37.5%
For engine C, we have:
Efficiency = 1 - T_{c} / Th = 1 - 300 K / 600 K = 0.5 or 50%
Therefore, the ranking of engines from highest to lowest theoretical efficiency is: Engine C (50%) > Engine B (37.5%) > Engine A (30%)
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How do seatbelts relate to the first law of motion.
Answers
Answer: Seatbelts relate to Newton's first law of motion because in the case of a car accident, someone in the car would continue forward until they hit somethng else. A seat belt will help prevent this because it will push back on you (action-reaction force).
Explanation:
As part of previous adventures, formerly conjoined identical twin, Sue, is now 13.4 years younger than her identical twin Lou. (The anniversaries of their birth are no longer the same day.) It is Lou's turn to travel, and he goes away and back at 0.96c. During his round trip, Lou ages 1 year. What is the the difference in the twin's ages when he returns.
Answers
Answer:
Difference in Twin's Ages = 12.68 years
Explanation:
Using special theory of relativity's time dilation phenomenon, we first find the time that is passed on earth during Lou's trip.
t = t₀/[√(1 - v²/c²)]
where,
t = time measured by the person in relative motion = 1 year
t₀ = time measured by the person at rest = ?
v = speed of relative motion = 0.96 c
c = speed of light
Therefore,
1 year = t₀/[√(1 - 0.96² c²/c²)]
1 year = t₀/[√(1 - 0.9216)]
(1 year)(0.28 year) = t₀
t₀ = 0.28 year
Let,
y = Sue's age
x = Lou's age
so,
x - y = 13.4 years
but, after this trip Lou has aged 1 year, and on earth only 0.28 years passed so, Sue has aged only 0.28 years. Therefore,
x = x + 1
y = y + 0.28
Therefore,
(x + 1 year) - (y + 0.28 year) = 13.4 years
x - y = 13.4 years - 0.72 year
x - y = 12.68 years
Difference in Twin's Ages = 12.68 years
which affects the electrostatic charge more, charge or distance?
Answers
Answer:
The electric force decrease as the distance increase and vice versa
As it obeys inverse square law that states ththaforce is inversly proportional to square if distance
so if the distance increased to twice the force will be decreased to quarter.
And that is coloumb's law of electrostatic force:
Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.
F=k(Q1.Q2)/r2
So as you increase the distance between charged objects, Force(attraction/repulsion) weakens by the square of their distance.
As you decrease the distance between charged objects, Force strengthens by the square of their distance.
Inverse relationships are common in nature. In electrostatics, the electrical force between two charged objects is inversely related to the distance of separation between the two objects. Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects. And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. Electrical forces are extremely sensitive to distance. These observations are commonly made during demonstrations and lab experiments. Consider a charged plastic golf tube being brought near a collection of paper bits at rest upon a table. The electrical interaction is so small at large distances that the golf tube does not seem to exert an influence upon the paper bits. Yet if the tube is brought closer, an attractive interaction is observed and the strength is so significant that the paper bits are lifted off the table. In a similar manner, charged balloons are observed to exert their greatest influence upon other charged objects when the separation distance is reduced. Electrostatic force and distance are inversely related.
The pattern between electrostatic force and distance can be further characterized as an inverse square relationship. Careful observations show that the electrostatic force between two point charges varies inversely with the square of the distance of separation between the two charges. That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed. So if the separation distance is doubled (increased by a factor of 2), then the electrostatic force is decreased by a factor of four (2 raised to the second power). And if the separation distance is tripled (increased by a factor of 3), then the electrostatic force is decreased by a factor of nine (3 raised to the second power). This square effect makes distance of double importance in its impact upon electrostatic
Answer:
Charge
Explanation:
MY PASSWORD IS CHANGE
Answers
i GOT DISCONNECTED WITH A TUTOR THAT WAS EXPLAING, NEED HELPIna shoots a large marble (Marble A, mass: 0.08 kg) at a smaller marble (Marble B, mass: 0.05 kg) that is sitting still. Marble A was initially moving at a velocity of 0.5 m/s, but after the collision it has a velocity of −0.1 m/s. What is the resulting velocity of marble B after the collision? Be sure to show your work for solving this problem along with the final answer.
Answers
Given that,
The mass of marble A, m₁=0.08 kg
The mass of marble B, m₂=0.05 kg
The initial velocity of marble A, u₁=0.5 m/s
As the marble B was at rest, the initial velocity of marble B is u₂=0 m/s
The final velocity of marble A, v₁=-0.1 m/s
Let the final velocity of marble B be v₂.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total after the collision.
Therefore
\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\)On rearranging the above equation,
\(v_2=\frac{m_1u_1+m_2u_2-m_1v_1}{m_2}\)On substituting the known values in the above equation,
\(\begin{gathered} v_2=\frac{0.08\times0.5+0.05\times0-0.08\times-0.1}{0.05} \\ =\frac{0.048}{0.05} \\ =0.96\text{ m/s} \end{gathered}\)Therefore the
Answer:
See below
Explanation:
Use conservation of momentum (rather than Kinetic Energy ) for collision problems:
Momentum A = mv = .08 * .5 = .04 km m/s
Momentum B = mv = 0
Total Momentum = .04 + 0 = .04 kg m/s
After collision the sum must be the same
A = mv = .08 ( -.1 ) = - .008 kg m/s
B = m vb = .05 vb
.04 = - .008 + .05 vb
vb = + .96 m/s in the same direction as original A direction
A spring is stretched by 0.02m when a mass of 0.1kg is attached to it. What is
the spring constant? (Show working pleaaase)
Answers
Answer:
5
Explanation:
hookes law, f=kx
the force which is the mass,0.1, is equal to the constant multiplied by thd extension,0.02, so
0.1= f×0.02
0.1/0.02=5
when n identical capacitors are connected in series across a battery, the energy stored is u. if the same capacitors were connected in parallel across the same battery, then how much energy would be stored?
Answers
The energy would be stored in capacitors N^2U.
The total capacitance of N identical capacitors in series is
1/Cs = 1/C + 1/C ..... N times = N/C
Cs = C/N
The energy stored in the combination is
U = 1/2 CsV²
V² =2NU/C
Now, the total capacitance of N identical capacitors in parallel is
Cp = C+ C + .... = NC
The energy stored in this combination is
U' = 1/2CpV²
= NCV²/2
Putting the value of V from the series equation
U' = 1/2CpV² = NC/2 × 2NU/C = N²U
When capacitors are connected in series the total capacitance is less than the individual capacitances of the series capacitors. If two or more capacitors are connected in series, the overall effect will be that of a single capacitor with the sum of the plate distances of the individual capacitors.
The energy U C U C stored in a capacitor is electrostatic potential energy and is therefore related to the charge Q and the voltage V across the capacitor plates. A charged capacitor stores energy in the electric field between its plates. An electric field is generated when a capacitor is charged. After disconnecting the capacitor from the battery, the energy stored in the capacitor doubles when the distance between the plates is doubled.
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Which two phrases describe a situation that will cause a stationary object to
start moving?
A. A net force equal to 0
B. A net force greater than 0
C. Unbalanced forces
D. Balanced forces
(two phrases)
Answers
Answer:
A net force greater than 0 is the answer
Explanation:
trust
Answer:
b c
Explanation:
Suppose a computer technical support representative can answer calls from 6 customers in an hour. what is the probability that a customer will be on hold less than 30 minutes?
Answers
The prοbability that a custοmer will be οn hοld fοr less than 30 minutes is 1/3 οr apprοximately 0.3333.
How tο calculate the prοbability that a custοmer will be οn hοld fοr less than 30 minutes?Tο calculate the prοbability that a custοmer will be οn hοld fοr less than 30 minutes, we need tο knοw the average time it takes tο handle a custοmer call. Let's assume the average handling time is 10 minutes.
In οne hοur, the suppοrt representative can handle 6 calls. Therefοre, the tοtal time spent handling calls in an hοur is 6 calls * 10 minutes per call = 60 minutes.
Nοw, let's cοnsider the prοbability that a custοmer will be οn hοld fοr less than 30 minutes. Since each call takes an average οf 10 minutes tο handle, if a custοmer is οn hοld fοr less than 30 minutes, it means their call is answered within the first 20 minutes (30 minutes - 10 minutes).
The tοtal time spent handling calls in an hοur is 60 minutes, and the time interval in which a custοmer can be answered within the first 20 minutes is 20 minutes.
Prοbability = Time interval fοr answering within 20 minutes / Tοtal time spent handling calls
Prοbability = 20 minutes / 60 minutes
Prοbability = 1/3
Sο, the prοbability that a custοmer will be οn hοld fοr less than 30 minutes is 1/3 οr apprοximately 0.3333.
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A. It Implies That M Is Finitely Generated. B. It Implies That M Has Nonzero Elements Of Nonzero Order. C. When Every Non-Null Element Has Null . D. In The Case That The Ring R Is A Body. E. None Of The Above Alternatives Gives A
Which of the following alternatives give a true statement. Justify your answer.
A modulus M over a ring R has a finite basis:
a. It implies that M is finitely generated.
b. It implies that M has nonzero elements of nonzero order.
C. When every non-null element has null .
d. in the case that the ring R is a body.
e. None of the above alternatives gives a true statement.
Which of the following statements are true?
a. If a subset of a module generates that whole module, then the subset cannot be
empty.
b. Every submodule S of a module M verifies the inequality C. Two different subsets of M have to generate two different submodules of M.
d. If S generates a submodule N of the module M, then contains S.
e. Neither statement is true.
Answers
The correct answer is e. None of the above alternatives gives a true statement. None of the statements in options a, b, c, and d are true when it comes to a modulus M over a ring R having a finite basis.
When a modulus M can be formed entirely from a finite set of elements, the modulus M is said to be finitely generated. M's finite basis does not, however, automatically imply that M is finitely generated. A basis is a set of linearly independent elements, and it might not be enough to produce all of the components of the modulus.
According to the assertion in option b, M must include nonzero items of nonzero order if it has a finite basis. This is untrue, though. The smallest positive number k, such that the element raised to the power of k equals the identity element, is referred to as the order of an element.
According to option c, every non-null element in a modulus with a finite basis has a null. Nevertheless, this claim is likewise untrue. It is possible for a modulus with a finite basis to have non-null elements without a null element.
According to option d, a ring R is a body, or a field, and only then can a modulus have a finite basis. However, this assertion is also untrue. Even though the ring R is not a field, a modulus can nonetheless have a finite basis. None of the given alternatives provides a true statement about a modulus M over a ring R having a finite basis.
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when you do a push-up (illustrated below), your feet are the fulcrum and the load being moved is your body mass (shown by the arrow). if someone weighs 60 kg, how much force is being exerted by their muscles in order to push up?
Answers
That a person who weighs 60 kg exerts a force of 588 N when doing a push-up. A push-up is an exercise that involves body movement and weight lifting.
In this case, a person's body weight acts as the load, while the muscles produce the necessary force to move the load. To solve the problem, we use the formula for weight,
Weight = Mass × Gravity (g)
where gravity (g) is equal to 9.8 m/s² and mass is given as 60 kg.
Weight = 60 kg × 9.8 m/s² = 588 N
Therefore, a person who weighs 60 kg exerts a force of 588 N when doing a push-up.
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Examples of increase in pressure due to increase in applied force
Answers
Answer:
injecting
Explanation:
For an object in uniform circular motion, on what parameters does the experimental determination of the centripetal force depend when using F = ma?
Answers
The experimental determination of the centripetal force when employing F = ma depends on the centripetal force parameters for an item in uniform circular motion.
A parameter "beside, subsidiary" is, in general, any attribute that helps define or categorize a particular system. To put it another way, a parameter is a system component that is essential or helpful for identifying the system or evaluating its operation, status, or other properties. The term "parameter" has more specific definitions in several disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic music production. In addition to its technical uses, it also has broader implications, especially outside of the realm of science, where it is employed to indicate defining characteristics or restrictions, as in the expressions "test parameters" or "game play parameters."
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What change slowly occurs during the main-sequence lifetime of a star?.
Answers
The brakes are applied to a moving vehicle, causing it to uniformly slow down. While slowing, it moves a distance of 40.0 m in 7.45 s to a final velocity of 1.50 m/s, at which point the brakes are released.
What was its initial speed (in m/s), just before the brakes were applied?
What was its acceleration (in m/s2) while the brakes were applied? (Assume the initial direction of motion is the positive direction. Indicate the direction with the sign of your answer.)
Answers
The acceleration is 1.03m/s^2 and initial velocity is 6.1735m/s
As it is given that motion is in positive direction and in one dimension, we will use the formulas of motion in one dimension
It is given to us that while slowing vehicle moves 40m
time taken to halt is 7.45s
final velocity is 1.5 m/s
We are required to find initial speed and acceleration
Using the equation v = u + at
v=1.5 , t = 7.45
1.5 = u + a x 7.45
u + 7.45a= 1.5
u =1.5 -7.45a
Now using the equation v^2 -u^2 =2aS
1.5 x 1.5 -u^2 = 2 x a x 40
2.25 - u^2 = 80a`
2.25- 80a = u^2
Now squaring for u in first equation and equation with second ,we get:
(1.5 -7.45 a)^2 = 2.25 -80a
2.25 + 55.50a^2 -22.35a =2.25 -80a
55.5a^2+57.65 a =0
a(55.5a +57.65)=0
a= 57.65 /55.5 =1.03 m/s^2
u = 1.5 - 7.45 x 1.03
=-6.1735 m/s
negative sign implies that initial speed is in opposite direction
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\(r=s^2/t^2\) 1. If s is tripled and t stays constant, r is multiplied by... 2. If t is doubled, and s stays constant, r is multiplies by...
Answers
Answer:
9 and 4
Explanation:
The relation is:
● r = s^2 / t^2
Triplind s means multiplying it by 3. Since it's an equation we should multiply both sides by the same number
Let k be the number we should multiply by r
●k* r = (3s)^2 / t^2
●k* r = 9s^2 /t^2
We have multiplied s^2 by 9 so we should do the same for r.
k = 9
■■■■■■■■■■■■■■■■■■■■■■■■■■
Doubling t means multiplying it by 2.
Let x be the number we shoukd multiply by r.
● x* r = s^2/(2t)^2
● x*r = s^2/ 4t^2
We have multiplied t^2 by 4 so we should do the same for r.
x= 4
A flashlight contains two batteries connected in series with a small bulb. When the switch is closed, the current in the circuit is I. If the circuit is changed so that two identical bulbs are connected in series to the same two batteries, what is the current?
Answers
Given:
The initial value of the current through the circuit is I.
To find:
The current through the circuit after the circuit is changed.
Explanation:
Let us assume that the total voltage supplied by the two batteries to the circuit is V.
And let us assume that the resistance of the bulb is R.
From Ohm's law, the voltage across the circuit is given by,
\(V=IR\)Thus the current will be,
\(I=\frac{V}{R}\text{ }\rightarrow\text{ \lparen i\rparen}\)When the two identical bulbs are connected, the total resistance of the circuit will be R+R=2R.
Thus from Ohm's law, the current through the resistance is given by,
\(I_0=\frac{V}{2R}\)On substituting the equation (i) in the above equation,
\(\begin{gathered} I_0=\frac{I}{2} \\ I_0=\frac{1}{2}I \end{gathered}\)Final answer:
The current in the circuit after the circuit is changed is (1/2) I.
nuisance static charges are more likely to occur when the air is
Answers
Nuisance static charges are more likely to occur when the air is dry.
When the air is dry, it is not able to hold a sufficient amount of moisture or humidity. When the moisture content of the air is low, the air has a low electrical conductivity, which increases the likelihood of static charges.Static electricity can be created by the rubbing of two objects. When these objects are separated after rubbing, they are left with a static electric charge. The strength of the electric charge is determined by the materials used to create the two objects. Some materials are better at holding static charges than others.
Dry air only exacerbates the situation. Static charges can be a nuisance for a variety of reasons. They can cause shocks, interfere with electronic devices, and can even cause damage to sensitive equipment. In order to reduce the occurrence of static charges, it is important to ensure that the air in your environment is sufficiently humid. This can be achieved by using a humidifier or by simply placing bowls of water around the room. Additionally, anti-static products, such as sprays and mats, can be used to reduce the occurrence of static charges.
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Suppose you are sitting in the passenger seat of a parked car. You hear sounds coming from the stereo of another car parked on the opposite side of the street. You can easily hear the low-pitched bass sounds but cannot hear the any high-pitched sounds coming from the parked car. Explain why you think this happens.
Answers
This happen because of what is called Doppler effect and it occur you who is the receiver of the sound waves is in motion and the source of the wave is stagnant.
What is sound waves?Sound waves is a form of transverse waves in which there is vibrations and compression of particles traveling through a medium thereby transferring energy from one medium to another.
Therefore, This happen because of what is called Doppler effect and it occur you who is the receiver of the sound waves is in motion and the source of the wave is stagnant.
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Question 12
If an object is moving in a ____
line, the change in velocity equals the final speed minus the initial speed.
Answers
If an object is moving in a straight line, the change in velocity equals the final speed minus the initial speed.
What is the change in velocity?
The change in velocity of an object moving in a straight line is a measure of how much its speed has changed over time. The change in velocity is equal to the final speed minus the initial speed, and it is a vector quantity, meaning it has both magnitude and direction.
For example, if an object is moving at a speed of 10 m/s at time t1 and has a speed of 20 m/s at time t2, then its change in velocity would be;
20 m/s - 10 m/s = 10 m/s.
The direction of the change in velocity would depend on the direction of the speed change, which could be either positive (increasing speed) or negative (decreasing speed).
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assign each of the given labels to the flask that it correctly describes.
Answers
Python based Flask is a microweb framework that is intended to be straightforward, lightweight, and simple to use. It Flask set of capabilities for creating web applications, such as routing, managing
Python-based Flask is a microweb framework. It offers a simple interface for creating web applications, letting programmers utilise the tools they want without being constrained in their inventiveness. Flask is a well-liked option for both small and big projects since it is portable and simple to use. Flask, which is frequently used for prototyping and creating APIs, enables for simple, effective development because to its modular architecture and tiny codebase. In addition, the huge Flask developer community offers a multitude of tools and plugins for customization and added functionality. For developers searching for a lightweight, adaptable framework for their web development needs, Flask is an excellent option.
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In a ______ solar system, the planets orbit around the sun.
A. Geocentric
B. Monolithic
C. Heliocentric
D. Pericentric
Answers
Have a good day!
a horse weighs 2400n and each hoof has a surface area of 6cm. calculate the pressure when the horse rears onto two legs
Answers
Answer:
200 Pa
Explanation:
pressure = force/area
force = 2400N
area = 6cm^2 per hoof
pressure = 2400/(6x2)
pressure = 200 Pa
What characteristics of the solar system would have to be known or calculated in order to send a
probe to a distant planet, such as Jupiter?
a. the effects due to the light from the distant stars
b. the effects due to the air in the solar system
c. the effects due to the gravity from the other planets
d. the effects due to the cosmic microwave background radiation
Answers
Answer:
A
Explanation:
The effects due to light from distant stars
The characteristics of the solar system would have to be known or calculated in order to send a probe to a distant planet, such as Jupiter, due to the effects of the gravity from the other planets. Hence, option C is the correct answer.
When sending a probe to a distant planet, such as Jupiter, one of the critical factors that would have to be known or calculated is the effects due to the gravity from the other planets in the solar system. The gravitational interactions between the planets can significantly influence the trajectory and path of the probe during its journey. Accurate calculations are necessary to ensure that the probe's trajectory is properly planned and adjusted to reach its destination with precision. Hence, option C is the correct answer.
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a computer's power supply converts mains ac to low-voltage regulated dc power for the internal components of a computer. you are building a new computer. you are deciding which type of power supply to install. which of the following definitions best describes a valid type of power supply?
Answers
In order to prevent overloading of any circuit, dual rail electrical supply includes independent tracks and P C B traces that are used to offset voltage sags between various circuits.
Using conductive paths, tracks, or signal traces etched from copper sheets laminated onto a non-conductive substrate, a printed circuit board, or PCB, is used to mechanically support and electrically link electronic components.
Semiconductors are used by practically all inverters to generate a controlled power output. An input voltage is rectified if the source has an ac input.
It is, therefore, the proper response.
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A steel ball bearing is released from a height H and
rebounds after hitting a steel plate to a height H.
What is true about the collision with the steel plate?
Answers
Answer:
ELASTIC collision
kinetic energy is conservate
Explanation:
As the ball bounces to the same height, it can be stated that the impact with the floor is ELASTIC.
As the floor does not move the conservation of the moment
po = pf
-mv1 = m v2
- v1 = v2
So the speed with which it descends is equal to the speed with which it rises
Therefore the kinetic energy of the ball before and after the collision is the same
Answer:
CORRECT (SELECTED)
It is elastic since kinetic energy was conserved.
Explanation:
A ball of mass m = 1 kg is attached to an unforced spring (F(t) = 0), with spring constant k = 9 N/m and a damping force of of 6 times the velocity. The object starts at equilibrium, with initial velocity 3 m/s upwards. (a) Solve for the position of the ball. (b) Is the spring overdamped, critically damped, or underdamped? (c) Show that the maximum displacement of the ball from equilibrium is a az meters. (d) Sketch the solution.
Answers
The position of the ball attached to the unforced spring with a damping force of 6 times velocity is given by the function \(x(t) = e^{-3}t (sin3t)\). The system is overdamped, and the maximum displacement from equilibrium is 0.1573 meters.
a) Solve for the position of the ball.
The equation of motion of the ball attached to the unforced spring with damping force of 6 times velocity can be written as, \(m(d^{2}x/dt^{2}) + 6(dx/dt) + kx = 0\)
The given values are,
\(m = 1 kg\)\(k = 9 N/m\)\(dx/dt = v = 3 m/s at t = 0\)As we are supposed to find the position of the ball, we will solve the differential equation by assuming the position x as the solution and by integrating the given equation two times.
\(m\left(\frac{{d^2x}}{{dt^2}}\right) + 6\left(\frac{{dx}}{{dt}}\right) + kx = 0\)
This is the standard form of a second order homogeneous linear differential equation. The characteristic equation of this differential equation is, \(m^{2} r^{2} + 6mr + k = 0\)
Solving the above quadratic equation, we get, \(r = -3 \pm \sqrt{9 - \frac{4k}{m^2}} / 2m\)
Here, \(k/m = 9/1 = 9\). So, \(r = -3 \pm \sqrt{9 - 36} / 2 = -3 \pm 3i\)
From the above values of r, we can say that the general solution of the differential equation is, \(x(t) = e^{-3t}(C_1\cos(3t) + C_2\sin(3t))\)
Let's find the values of constants C1 and C2 using the initial values of the ball position and velocity.
At
\(t = 0\), \(dx/dt = v = 3 m/s\) and \(x = 0\)So,
\(C1 = 0\) and \(C2 = v/3 = 1 m\)Substituting these values in the general solution of \(x(t),x(t) = e^{-3}t (sin3t)\)
Therefore, the position of the ball as a function of time is given by, \(x(t) = e^{-3}t (sin3t)\).
b) The damping force in the given equation is, b = 6 times the velocity.Since the damping force is greater than the critical damping force \((2\sqrt{m \cdot k})\), the given spring is overdamped.
c) Show that the maximum displacement of the ball from equilibrium is a az meters. To find the maximum displacement of the ball from equilibrium, we can differentiate the position function with respect to time and equate it to zero.
d). \((x(t)) / dt = e^{-3}t (3cos3t - sin3t)\)
When the above derivative of the position function is zero, the position of the ball is at the maximum or minimum from the equilibrium.
Substituting the values of t in the above equation, we get,cos3t = sin3t
Therefore, \(\tan(3t) = 1 \quad t = \frac{\pi}{12}, \frac{5\pi}{12}, \frac{9\pi}{12}, \frac{13\pi}{12}, \frac{17\pi}{12}, \ldots \quad \text{For } t = \frac{\pi}{12}\), the position of the ball is at maximum from equilibrium.
Substituting this value in the position function,\(x(t) = e^{-3t} \sin(3t) \quad x\left(\frac{\pi}{12}\right) = e^{-3\left(\frac{\pi}{12}\right)} \sin\left(\frac{\pi}{4}\right) = 0.1573 \, \text{m}\)
Therefore, the maximum displacement of the ball from equilibrium is \(0.1573\) meters.
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If a light bulb uses 60J of electrical energy and produces 30 J of light energy, what is the percent efficiency of the light bulb?
Answers
Answer:
50%
Explanation:
If a light bulb uses 60J of electrical energy and produces 30 J of light energy, the percent efficiency of the light bulb is 50%.
What is percent efficiency?The total amount of beneficial work accomplished, excluding waste and spoilage, is known as output or work output.
This pulp creates 30 jewels' worth of light energy, for a total of 60 jewels. So that's the energy output. Let's use E. O. to symbolize it. Those are 30 Jews.
Additionally, we must calculate the light bulb's efficiency %. Therefore, we will start by computing the efficiency, which is defined as the ratio of energy output to energy input in this book.
And 30/60 is the efficiency that we obtain. Moreover, this is 1 x 2.
The straightforward ratio between output and input energy—by 100. And the result is that this is 50%. That is the required efficiency percentage for this light bulb.
Therefore, the percent efficiency of the light bulb is 50%
To learn more about percent efficiency, refer to the link:
https://brainly.com/question/23818307
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