The battery’s negative terminal is attached to the chassis or metal body in automobiles. A single wire is used to connect the positive terminal to multiple electrical appliances.
The chassis is next connected to the negative terminal of the gadgets, completing the circuit for the current flow.
What happens if a battery’s terminals are connected?There will be a low resistance path for the current to travel when a wire is connected directly between a battery’s two terminals.
The battery will swiftly deplete, and the wire will become slightly heated (the amount of heat depends on the wire’s diameter; the smaller the diameter, the more heat).
Why is it necessary to connect a battery’s terminals?A battery can generate power when it is included in a circuit. The positive terminal (cathode) and the negative terminal are the two ends of a battery (anode).
A circuit is created by connecting the two terminals with wire. A current of electricity is created as electrons move across the wire.
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a boat can travel at a speed of 8 km/h in still water on a lake. in the flowing water of a stream, it can move at 8 km/h relative to the water in the stream. if the stream speed is 3 km/h, how fast can the boat move past a tree on the shore when it is traveling.
Relative velocity of the river with respect to shore, V = 20 km/h.
Relative velocity of the river with respect to shore ,V = 10 km/h
Velocity of the shore = 0 km/h
Relative velocity of the river with respect to shore:
[tex]V = V_{r} - V_{s}[/tex]
Velocity of the river [tex]V_{r}[/tex] = 10 km/h
Relative velocity of the boat with respect to river ,V'= 10 km/h
[tex]V^{'} = V_b} -V_{r}[/tex]
Velocity of the boat [tex]V_b}[/tex] = 20 km/h
Relative velocity of the boat with respect to shore, V":
[tex]V_{"} = V_{b} - V_{s}[/tex]
Relative velocity of the boat with respect to shore is 20 km/h.
What is Relative velocity?It is the pace at which one object's relative location changes in relation to another object over time.
Think about two trains that are traveling in the same direction and at the same pace. Even though the tracks, buildings, and trees on each side of the railway indicate that both trains are moving, to the observer of one train, the other train appears to be stationary. The other train seems to be moving at a constant speed.
The speed at which one thing moves in relation to another is known as the relative velocity of the two objects.
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Photons of wavelength 0.024 a are incident on free electrons. (a) find the wavelength of a photon which is scattered 3
When Photons of wavelength 0.024 a are incident on free electrons, the wavelength of a photon which is scattered 30° is 0.0576 x [tex]10^{-11}[/tex] and for the one scattering at 120° is 0.38 x [tex]10^{-11}[/tex] A.
How can the Compton effect be used to determine the energy of scattered photons?The incident photon’s energy is equal to the scattered photon’s energy minus the total of the recoil electron’s kinetic energy and binding energy.
Compton scattering causes the loss of an electron and ionization of the absorbing atom, just like photoelectric absorption does.
What is the scattered photon’s wavelength?After the scattering event and before, the photon’s wavelength varies by ∆λ = (h/mc) (1-cosφ). Here, c is the speed of light, m is the rest mass of the electron, and is the angle at which the photon is scattered. H is the Planck constant.
Given photon wavelength λ = 0.024A
φ = 30°
From the Compton effect we know that
∆λ = λ1 - λ = h/mc (1-cosφ)
λ1 = [tex]\frac{6.62*10^{-34}}{9.1}[/tex] x [tex]10^{-3}[/tex] x 3 x [tex]10^{8}[/tex] (1- cos30°) + 0.024A
= 0.0576 x [tex]10^{-11}[/tex] A
And then calculating the same for
φ = 120°
we get,
λ1 = 0.38 x [tex]10^{-11}[/tex]A
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Complete Question
Photons of wavelength 0.024A are incident on free electrons.
(a) Find the wavelength of a photon which is scattered 30° from the incident direction and the kinetic energy imparted to the recoil electron
(b) Do the same if the scattering angle is 120°.
From his observations of the phases of venus, galileo concluded that the ptolemaic model of planetary motion was wrong because it predicted.
Galileo’s telescopic discoveries of the moons of Jupiter are often mentioned. But they did not amount to proof that the Ptolemaic system was incorrect.
It's hard to tell you how big a shakeup this caused in astronomy at the time. Thanks to Galileo, we now knew that planets weren't perfect, ethereal lights in the sky. That things could orbit them, same as (most astronomers thought) things did around Earth, making Earth less special, and providing evidence that maybe that heliocentric theory wasn't that out there.
Basically, before Galileo, astronomers were looking at an unchanging, heavenly firmament, separate from Earth by its very heavenly nature.
After, they were studying planets - actual worlds like ours - and moons and the physical (as opposed to heavenly) reality of their place in the universe.
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PLS HELPPP I NEED IT
FITT principle:
Frequency-is how regular or often a person does the plan of a target health-related physical activity. It depends on how determined you want to accomplish your target. The more often you train, the faster the result.
Intensity - is how hard a person exercise during a physical activity period. It can be measured in different ways, depending on the health-related component. For example, monitoring heart rate is one way to measure the intensity during aerobic endurance activities, but does not indicate intensity during flexibility activities. The harder you work, the faster your heart beats.
Time - is the duration of the physical activity. Together with the other aspects of the FITT principle, time varies depending on the target health-related fitness component. For example, in developing flexibility, stretching may take 10-30 seconds for each activity, while the minimum time for performing an aerobic exercise is 20 minutes of continuous action.
Type - refers to the physical activity chosen to improve a specific component of health-related fitness. Different events require different training programs. For example, if a person wants to increase core muscles, he or she must do exercises that target the oblique muscles, while another person wishing to improve his or her cardiovascular endurance needs to jog, run, swim or perform some other aerobic activities.
The FIIT plan required for different type of workout is shown in the image attached.
FIIT plan is used to monitor one's workout routine. It also helps to create workout routines that helps one's fitness goal which might differ from each person. It works based on four elements i.e., Frequency, Intensity, Time and Type.
Frequency refers to how often a workout needs to be done. Intensity refers to how hard a workout must be done. Time refers to the amount of time spent on the workout. Type refers to the king of exercise which suits one's final goal.
Therefore, the FIIT plan required for different type of workout is shown in the image attached.
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Is there any formula to calculate the height a ball will reach depending on the bounce number and it’s initial height? Alternatively, can any formula calculate the amount of times a ball will bounce without going into infinity?
Answer:
yeas
Explanation:
beac×high ×sides and after you fins tims you need to add beac+high and add the sides together and add what did you got from beac,high and sides and thin you will add every thing together
Flying from LA to New York is a 3,944,000 meter trip. What order of magnitude is this measurement?
The order of magnitude of the distance between Los Angeles (LA) to New York (NY) is determined as 6.
What is the order of magnitude of a measurement?
An order of magnitude of a measurement is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one.
Also, the order of magnitude can be defined as the power of 10 a number is raised to when it's in scientific notation.
The given measurement;
m = 3,944,000 m
The measurement in scientific notation;
3,944,000 m = 3.944 x 10⁶ m
Thus, the order of magnitude of the distance between Los Angeles (LA) to New York (NY) is determined as 6.
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After Thanksgiving, Kevin and Gamal use the turkey's wishbone
to
make a wish. If Kevin pulls on it with a force 0.17 N a larger than
the force Gamal pulls
with in the opposite direction, and the
wishbone has a mass of 13
g, what is the wishbone's initial
acceleration?
According to the given statement the wishbone's initial acceleration is 13.08 m/s².
How does acceleration work?Velocity's rate of change with time, both in terms of speed and direction. A point or item going straight ahead is accelerated when it increases or decelerates. Even if the speed remains constant, motion on a circular accelerates so because direction is always shifting.
Briefing:In this task, we calculate the acceleration for a given force and the mass on which the force was applied.
F[tex]_n_e_t[/tex] = 0.17 N
m = 13g
m = 1.3 × 10⁻² kg
a =?
F = m × a
a = F/m
a=0.17 N/1.3× 10⁻² kg
a=13.08 m/s²
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When jumping, a flea accelerates at an astounding 1500 m/s2 , but over only the very short distance of 0.44 mm . if a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?
When the flea jumps straight up, and if air resistance is neglected, the height of the flea will be 0.089m.
What is air resistance?Air resistance acts as a force on objects moving through the atmosphere. This force acts in the opposite direction when a body is travelling through the air. Air resistance causes the moving body to experience frictional force. A body's speed decreases as it goes due to air resistance.
It should be noted that the equation of kinematics will be illustrated thus:
V = ✓(2 × 1500 × 0.44mm)
Therefore, h = V² / 2g
= (✓(2 × 1500 × 0.44mm)² / (2 × 9.8)
= 0.089m
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We have that the flea goes as high as
h=0.0889m
How high does the flea go?From the Question, we are told that
Acceleration =1500ms^2
Distance d=0.47mm
Generally, the equation for height is mathematically given as
h=\frac{u^2}{2 g}
Where
u^2=2 * 1500 * 0.44 * 10^{-3}
u=1.32ms
Therefore
h=\frac{1.32^2}{2 * 9.8}
h=0.0889m
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Prompt: Explain how your physical, emotional, and mental state affects your performance in your exercise. Use specific examples from your experience
Being physically, emotionally, and mentally healthy can keep you healthy and help you avoid significant health issues during exercises.
How to illustrate the information?Exercise boosts mental health by lowering anxiety, depression, and depressive symptoms, as well as by raising self-esteem and increasing cognitive abilities. Additionally, it has been discovered that exercise helps with symptoms including poor self-esteem and social withdrawal.
Exercise on a regular basis can significantly improve symptoms of sadness, anxiety, and ADHD. Additionally, it lowers stress, enhances memory, promotes sound sleep, and uplifts your mood in general. It should be noted that it's important to be in the right state of mind during exercise to prevent injuries.
Therefore, being physically, emotionally, and mentally healthy can keep you healthy and help you avoid significant health issues during exercises.
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The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition what does cognition mean
The social cognitive perspective of personality focuses on social factors such as your parents guardians and teachers and cognition means how we as individuals process and store information.
What is Cognition?This is referred to as the process in which information is stored and processed through the use of our senses, experience etc and is common to all individuals.
The social cognitive perspective of personality on the other hand focuses on social factors such as parents and also in which cognition is among and it is influenced by genetic and environmental factors which therefore makes it the most appropriate choice.
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A coin lies under a glass filled with water.
Explain that you cannot see the coin
Refraction is the cause of this. We perceive an object when light reflects off of it and travels to our eyes. The penny appears to vanish because light is refracted as it passes through the glass's edges and the water, never reaching our eyes.
Refraction in physics is the change in direction that results from a wave's change in speed as it passes through a medium. The electromagnetic waves that make up light are bent due to their different speeds as they pass past the boundary of one transparent medium and into another.
When partially submerged in water and viewed from an angle other than 90° to the surface, a straight stick seems bent. When travelling from air to glass, a ray of light of a single wavelength (various wavelengths appear as different colours to the human eye) is refracted, or bent, in a way that relies on the speeds of the two mediums.
A straight stick appears bent when partially submerged in water and viewed at an angle other than 90° to the surface. A light ray of a single wavelength—different wavelengths appear as different colors to the human eye—is refracted, or bent, in a way that depends on the speeds of the two media when it travels from air to glass.
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a future space explorer has been kidnapped and is held prisoner on a planet in our solar system. with nothing else to do, our prisoner amuses herself by dropping her watch from eye level (170 cm) to the floor. she observes that the watch takes 0.95 s to fall. ignore air resistance.
The acceleration due to gravity of Jupiter is found to be 24.5m/s².
What is free fall?Any motion of a body in which gravity is the sole force acting on it is referred to as free fall in Newtonian physics. A body in free fall has no force acting on it according to general relativity, where gravity is reduced to a space-time curvature.
When gravity and the resulting acceleration are the only forces acting on an object, this is referred to as freefall in physics. A body falling freely due to the earth's gravity is what the phrase "freefall" refers to. Gravitational acceleration will result from this motion.
F = (G x m1 x m2)/r2
F = (6.67 x 10-11) (1.9 x 1027) (185) / ( 7.18 x 107)2
= 4547.8 N
Since the probe is on Jupiter's surface and the force we just discovered is the force of gravity on the surface between the two, this would also be the probe's weight.
Since F = mg:
4547.8 = 185g
24.58 m/s² = g
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A train travelling at 22m/s accelerates uniformly at 0.85 m/s^2 for 25s. Calculate the distance travelled by the train at this time.
The distance travelled by the train travelling at 22 m/s, which accelerates uniformly at 0.85 m/s² for 25s is 815.62.
What is Second equation of motion?
The second equation of motion is used to calculate the distance traversed by the body moving with uniform velocity. Mathematically -
S = ut + 1/2 at²
Given in the question is a train travelling at 22 m/s accelerates uniformly at 0.85 m/s² for 25s. From this, we can write -
Initial velocity [u] = 22 m/s
acceleration [a] = 0.85 m/s²
time taken [t] = 25 s
In order to find the distance travelled by the train, we will use the second equation off motion -
S = ut + 1/2 at²
S = 22 x 25 + 1/2 x 0.85 x 25 x 25
S = 815.62 meters
Therefore, the distance travelled by the train travelling at 22 m/s, which accelerates uniformly at 0.85 m/s² for 25s is 815.62.
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the 25-m crane boom ao lies in the yz plane. determine the maximum permissible tension in cable ab if the absolute value of moments about the coordinate axes of the force exerted on a by cable ab must be |mx|≤ 61.6 kn·m, |my|≤ 13.6 kn·m, |mz|≤ 9.6 kn·m.
The maximum permissible tension in cable AB is 3.11 kN
Given that,
I [tex]M_{x}[/tex] I ≤ 61.6 kN.m
I [tex]M_{y}[/tex] I ≤ 13.6 kN.m
I [tex]M_{z}[/tex] I ≤ 9.6 kN.m
OC = √ [tex]OA^{2}[/tex] - [tex]AC^{2}[/tex]
OC = √ [tex]25^{2}[/tex] - [tex]15^{2}[/tex]
OC = 20 m
[tex]r_{A}[/tex] = 15j + 20k
AB = √ [tex]2.5^{2}[/tex] + [tex]15^{2}[/tex] = 15.2069 m
P = P AB / AB = ( P ) 2.5i - 15j / 15.2069
P = 0.164399P i - 0.98639P j
[tex]M_{o}[/tex] = [tex]r_{A}[/tex] * P = [tex]\left[\begin{array}{ccc}i&j&k\\0&15&20\\0.163499P&-0.98639P&0\end{array}\right][/tex]
[tex]M_{o}[/tex] = ( 19.7828P ) i + ( 3.2700P ) j - ( 2.4525P )k
I [tex]M_{x}[/tex] I ≤ 61.6
19.7828P ≤ 61.6
P ≤ 3.11 kN
I [tex]M_{y}[/tex] I ≤ 13.6
3.2700P ≤ 13.6
P ≤ 4.16 kN
I [tex]M_{z}[/tex] I ≤ 9.6
2.4525P ≤ 9.6
P ≤ 3.91 kN
Tension is the act of stretching. It is a force transmitted through a object when pulled by forces across opposite sides.
Therefore, the maximum permissible tension in cable AB is 3.11 kN
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A boy and a girl are biking down a hill. The boy and the girl weigh the same, and they are using bikes that weigh the same. If the boy and girl are biking at the same speed, which child has more motion energy (kinetic energy)?
Answer:
neither.
they both are going at the same speed
Explanation:
Answer:
They have the same Kinetic Energy
Explanation:
KE = 1/2 m v^2 if the velocities are the same and the masses are the same .....then the Kinetic energies are the same
When is simple observation more appropriate than experimenting in a controlled laboratory?
Simple observation more appropriate than experimenting in a controlled laboratory when the results can be gotten solely by using our sense organs.
What is Experiment?This is referred to as a part of a scientific method and it is performed by scientists to test a hypothesis so as to know whether it will be accepted or refuted.
This is usually performed by different people from all over the world so as to ascertain its authenticity before it becomes a theory or law. This doesn't involve only sense organs alone as different techniques are required to arrive at a conclusion in this process.
Observation on the other hand requires the use of sense organs such as the eyes, nose etc to determine the results and may not need the use of experiments which is therefore the reason why it was chosen as the correct choice.
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Photons are shone on a piece of metal and one electron is ejected for each absorbed photon. What happens when the wavelength of light is decreased?.
The ejected electrons would have greater kinetic energy if the wavelength of light is decreased when Photons are shone on a piece of metal and one electron is ejected for each absorbed photon.
What is Kinetic energy?This is referred to as the type of energy which is possessed by a body by virtue of its motion and it has an inverse relationship with the wavelength of light.
This therefore means that as the wavelength of light is decreased, the kinetic energy of the ejected electrons will increase and vice versa which is therefore the reason why it was chosen as the most appropriate choice.
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J. J. Thomson used a cathode-ray tube to calculate the charge-to-mass ratio of the electron. Which of these suggested the presence of a negative particle?.
J. J. Thomson used a cathode-ray tube to calculate the charge-to-mass ratio of the electron. The deflection of cathode rays towards the positively charged surface proved that they are negatively charged particles.
In 1897, J.J Thomson performed a cathode ray tube experiment to determine the charge-to-mass ratio of electrons.
Due to high flow of voltage, a beam of particles was allowed to flow from the negatively charged end to the positively charged end of the tube.
An end of the tube was painted with phosphorous and when electrons struck that end, a green spark was observed which confirmed the presence of negatively charged particles i.e. electrons.
To put it simply, cathode rays came from the cathode tube and deflected towards a positively charged plate showing that they are negatively charged particles.
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daniel harris has always enjoyed eating tuna fish. unfortunately, a study of the mercury content of canned tuna in 2010 found that chunk white tuna contains 0.6 ppm hg0.6 ppm hg and chunk light tuna contains 0.14 ppm.20.14 ppm.2 the u.s. environmental protection agency (epa) recommends no more than 0.1 μg hg/kg0.1 μg hg/kg body weight per day. a person weighs 69 kg69 kg . how often may the person eat a can containing 6 ounces6 ounces (16 oz
One 6 oz can of chunk light tuna is to be consumed every four days.
How to find the number of days interval?The mercury content in 2010:
White tuna chunks weigh 0.6 ppm in total.
A piece of light tuna has a mass of 0.14 ppm.
The body weighed 63 kg, and the tuna weighed 6 oz.
The maximum quantity of mercury that the body should ingest each day is advised to be no more than 0.1 micrograms.
Solution:
Let's first convert the tuna's mass to grams.
As 1 oz equals 28.3495 g
The tuna weighs 6 oz, or 28.3495 g.= 170.097 g
The maximum daily mercury (Hg) intake for a 63 kg body weight is equal to 63 0.1.
6.3 micrograms per day
But the mass of the mercury (Hg) = concentration (Hg) mass of the tuna
= 0.6 × 10⁻⁶ × 170.097 g
= 1.0206 × 10⁻⁴ g
= 102.06 μg (micrograms)
The interval needed to consume one 6 oz can of chunk white tuna = 102.06/6.3
= 16.2 days
≅ 16 days
An average of 16 days must pass between consuming one 6 oz can of chunk white tuna.
the mass of the mercury (Hg) is equal to the product of the concentration (Hg) and
the mass of the tuna (0.14 106 170.097 g = 2.4814 105 g = 23.814 g).
= 23.814/6.3
= 3.78
As a result, it takes 3.78 days plus 4 days to consume one 6 oz can of chunk white tuna.
Approximately every four days, a single 6 oz can of chunk light tuna is consumed and the total 6-ounce tuna can be consumed in 16 days.
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A bicyclist starts from rest and accelerates along a straight path to a speed of 12. 15 m/s in a time of 4. 5 seconds. What is the bicyclist’s acceleration to the nearest tenth of a m/s2?.
Answer:The cyclist's acceleration to the nearest tenth is: C. 2.7 .
Given the following data:
Initial velocity = 0 m/s (since the cyclist starts from rest).
Final velocity = 12.5 m/s.
Time = 4.5 seconds.
To find the cyclist's acceleration to the nearest tenth:
Acceleration is calculated by subtracting the initial velocity from the final velocity and dividing by the time.
Mathematically, acceleration is given by the formula;
Where:
A is the acceleration.
V is the final velocity.
U is the initial velocity.
t is the time measured in seconds.
Substituting the given parameters into the formula, we have;
Acceleration, A = 2.7
Therefore, the cyclist's acceleration to the nearest tenth is 2.7 .
Explanation:
HELP ASAPP PLEASE!!! I know that I got one correct but i’m not sure what the other one is.
Answer:
Replace distance with "direction"
Explanation:
a uniform electric field exists in the region between two oppositely charged plane parallel plates. a proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cmcm distant from the first, in a time interval of 3.80×10−6 ss .
The magnitude of the electric field is
[tex]1.29 \: \times 10 ^{ - 24} \: N/C.[/tex]
The time interval is t.
[tex]t = 3.8 \times 10 ^{ - 6} \: s[/tex]
The distance of the second proton from the first proton is d.
[tex]d = 1.60 \: 10^{ - 2} \: m[/tex]
[tex]∆x = \frac{1}{2} at ^{2} [/tex]
The magnitude of the electric field is,
[tex]E = \frac{ F}{e}[/tex]
[tex]E = \frac{ma}{e} [/tex]
[tex] = \frac{2 \: ∆x \: m}{e \: t ^{2} } [/tex]
[tex] = 2 \times \frac{(1.6 \times 10 ^{ - 2} )(1.9 \times 10 ^{ - 3}) }{(1.6 \times 10 ^{ - 19})(3.8 \times 10 ^{ - 6} ) ^{2} } [/tex]
[tex] = 1.29 \: \times 10 ^{ - 24} \: N/C[/tex]
Therefore, the magnitude of the electric field is
[tex]1.29 \: \times 10 ^{ - 24} \: N/C.[/tex]
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Imagine the following objects in deep space, separated by a kilometre. which pair of objects experiences the largest gravity force? a proton and an electron an apple and a brick two apples an apple and a proton
The pair of objects that experiences the largest gravity force is an apple and a brick
An object will be weightless in outer space, away from the gravitational field of Earth (or another massive planet), yet it will still have mass and consequently resistance to a given force.
When one body has a higher mass than another, it is said to be more massive. The electron, with a mass of about 9.11 10-31 kg, is one of the Universe's least massive things. Hence, the combination of a proton and electron would experience the least gravity force. The combination of an apple and a brick has the most mass hence would experience the largest gravity force. Two apples or an apple and a proton are less massive compared to an apple and a brick thus incorrect.
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Can a car that has been traveling at different speeds in a straight line east have accelerated west?.
Yes. If a car is traveling eastward and slowing down, its acceleration is opposite to the direction of travel: its acceleration is westward.
A car that has been traveling at different speeds is already accelerating.
Now suppose it is traveling at different speeds means some force is applied to that car.
It is traveling in a straight line in the east and traveling at a different speed, which means the speed keeps on changing so sometimes it can be possible that acceleration can also be in the opposite direction to that in which it is traveling, so here it can be in the west as it is an easterly course of travel direction so no north or south direction movement.
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define a system you interact with every day. is the system open, closed, or isolated? how do matter and energy flow into, out of, or within the system?
In daily life the common example of isolated system, closed system and open system is themosteel bottle , human body and ecosystem respectively.
Water in a thermos, or thermosteel bottle is an example of isolated system where no transfer of energy neither transfer of matter takes place between the system and surroundings. Although no system is perfectly isolated, after some instant there a hear loss takes place by some means.
There are three types of system in thermodynamics,
Open system – system which allows transfer of heat and matter between system and surroundings. For example- Ecosystem.Closed system – system which allows transfer of heat but no transfer of matter between system and surroundings. For example- human body. Isolated system – no transfer of energy neither transfer of matter takes place between the system and surroundings For example – thermosteel bottle.Thermodynamics is the branch of science is which we study about the heat, temperature, work and their relation to energy.
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in example 2.6, we considered a simple model for a rocket launched from the surface of the earth. a better expression for a rocket's position measured from the center of the earth is given by
The expression for velocity is [tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
The expression for acceleration is [tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex]
The expression for the rocket's position as measured from the center of the earth is
[tex]y(t)=[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{2}{3}[/tex]
Let
[tex]x(t)=R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t[/tex]
We have,
[tex]y(t)=[x(t)]^\frac{2}{3}[/tex]
The velocity of the rocket as a function of time is given by
[tex]v(t)=\frac{\mathrm{d} y(t)}{\mathrm{d} t}=\frac{2}{3}[x(t)]^{-\frac{1}{3}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]v(t)=\frac{\mathrm{d} y(t)}{\mathrm{d} t}=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
Since
[tex]x(t)=R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t[/tex]
We have,
[tex]\frac{\mathrm{d} x(t)}{\mathrm{d} t}=3\sqrt{\frac{g}{2}}R_{E}[/tex]
[tex]v(t)=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]v(t)=\frac{2}{3}\frac{1}{\sqrt[3]{x(t)}} X 3 \sqrt{\frac{g}{2}}R_{E}=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
[tex]v(t)=\frac{\sqrt{2g}}{\left ( R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t \right )^\frac{1}{3}}R_{E}[/tex]
[tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex] .......(i)
The acceleration as a function of time is given by
[tex]a(t)=\frac{\mathrm{d} v(t)}{\mathrm{d} t}[/tex]
[tex]a(t)=\frac{\mathrm{d}}{\mathrm{d} t}\left (\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}\right )[/tex]
[tex]a(t)=\frac{\mathrm{d}}{\mathrm{d} t}\left ({\sqrt{2g}}R_{E}[x(t)]^{-\frac{1}{3}}\right )[/tex]
[tex]a(t)=\sqrt{2g}R_{E}\frac{\mathrm{d}}{\mathrm{d} t}[(x(t)]^{-\frac{1}{3}}[/tex]
[tex]a(t)=-\frac{1}{3}\sqrt{2g}R_{E} [(x(t)]^{-\frac{4}{3}}\frac{\mathrm{d} x(t)}{\mathrm{d} t}[/tex]
[tex]a(t)=-\frac{1}{3}\sqrt{2g}R_{E} [(x(t)]^{-\frac{4}{3}}3\sqrt{\frac{g}{2}}R_{E}[/tex]
[tex]a(t)=-gR_{E}^2 [(x(t)]^{-\frac{4}{3}}[/tex]
[tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[x(t)]^\frac{4}{3}} \right )[/tex]
[tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex] .......(ii)
Therefore, the expression for velocity is [tex]v(t)=\frac{\sqrt{2g}}{\sqrt[3]{x(t)}}R_{E}[/tex]
& the expression for acceleration is [tex]a(t)=-\left ( \frac{gR_{E}^{2}}{[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{4}{3}} \right )[/tex]
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In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by [tex]y(t)=[R_{E}^{\frac{3}{2}}+3\sqrt{\frac{g}{2}}R_{E}t]^\frac{2}{3}[/tex]
where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2).
(a) Derive expressions for v(t) and a(t).
(Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)
A Plastic fork has a mass of 5g and a volume of 5.2cm³. What is the density of the plastic fork?
Answer: 0.96153846153846 g/cm3
Explanation:
Find the electrical energy expended by an electric lamp labelled 100 W in 8 seconds.
5. What is Deviation?
6. a) Why don't walkers usually have a problem with deviation?
b) When might deviation be a problem for a walker trying to use a compass?
7. Why can deviation be a problem in ships?
8. Describe two ways of correcting for deviation in a ship.
A gait deviation is a a physiotherapy term. It refers to change in the gait cycle that affects the trunk, hip, knee, or ankle joint. Increased age and/or certain disorders might cause gait abnormalities. These diseases can be either musculoskeletal or neurological in origin.
Why don't walkers usually have a problem with deviation?Walkers don't usually have problem with gait deviation because, walking in itself helps to correct problems with gait deviation. Walking correctly exercises the muscles and skeletons associated with gait hence preventing deviation.
When might deviation be a problem for a walker trying to use a compass?Deviation might be a problem for a walker trying to use a compass if the walker is having or experiencing a Spastic Hemiparetic Gait.
It is distinguished by unilateral leg extension and circumduction, in which the paretic limb moves laterally (circumducts) during the swing phase. This is sometimes referred to as circumductory gait.
The compass can hardly be maintained pointed in the appropriate direction with this configuration.
Why would deviation be a problem when travelling in a ships?Sea travel is known to produce gait changes or deviation.
The reason for this is not far-fetched. Ships don't travel on smooth terrain.
The open sea is characterized by complex, oscillating motion of ships in three translational dimensions (surge, sway, and heave) and three rotational dimensions (roll, pitch, and yaw).
The ship is the base of support or ground surface for passengers and crew: body control must be changed to accommodate for the ship's 6 degrees of freedom oscillatory motion.
Changes in stride that define those who have fully acclimated to living at sea are one of the most well-known characteristics of this compensation.
Anecdotal evidence focuses on a "rolling gait" that is prominent enough to be seen by casual onlookers.
What are two ways of correcting for deviation in a ship?The two ways of correcting deviation are:
In other circumstances, physical therapy may be necessary to enhance balance, strength, and flexibility. You should also undergo fall prevention training.Maintaining good foot alignment may need the use of in-shoe splints or leg braces. In circumstances of uneven leg length, a shoe raise may be useful.Learn more about physiotherapy :
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A 28.5 g sphere is added to a graduated cylinder containing 45.50 ml of water. The water level rises to the 49.10 ml mark. What is the volume of the sphere? What is its density? Based on its density, what type of metal is it?
According to this question, a 28.5 g sphere is added to a graduated cylinder containing 45.50 ml of water. The water level rises to the 49.10 ml mark.
This means that the volume of the sphere can be calculated as follows: 49.10mL - 45.50mL = 3.6mL.
The density can be calculated by dividing the mass by its volume as follows:
Density = 28.5g ÷ 3.6mL = 7.92g/mL
Based on the density of the sphere, it is incoloy.
Therefore;
The volume of the sphere that weighs 28.5g is 3.6mLThe density of the metal sphere is 7.92g/mL.Learn more about density at: https://brainly.com/question/6107689
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