Final answer:
The final displacement of the weather balloon, considering its 6 km upward travel and the 10 km north and 8 km east wind displacement, is approximately 14.1 km from its starting point.
Explanation:
The student is asking to find the final displacement of a weather balloon that has been blown by the wind as it travels upwards. To solve this, we can use the Pythagorean theorem since the balloon's movement creates a three-dimensional right-angled triangle with the vertical ascent and the horizontal wind displacement as the perpendicular sides.
The displacement due to the wind is found by using the Pythagorean theorem for the horizontal components: √((10 km)² + (8 km)²) = √(164 km²) which is approximately 12.81 km to the northeast.
The overall displacement of the balloon is the three-dimensional resultant which can be calculated using the Pythagorean theorem again with the 6 km vertical component and the 12.81 km horizontal component:
√((6 km)² + (12.81 km)²) = √(200 km²) which is approximately 14.1 km. This is the balloon's straight-line distance from its starting point.
Starlight is released during which nuclear reaction?
A. Nuclear fission
B. Gamma decay
C. Positron emission
D. Nuclear fusion
Answer:
D. Nuclear fusion
Explanation:
Nuclear fusion is a nuclear reaction where nuclei of atoms( one of low atomic number and another with a higher atomic number) join together to form a much bigger nucleus and release a lot of energy.In the sun, which is a star of course, where light is released,hydrogen is converted to helium and the process releases massive energy into space in form of heat and light.
Answer:
D. Nuclear fusion
Explanation:
Nuclear fusion is reaction in which two or more atomic nuclei having low atomic numbers join together to form a heavier nucleus usually accompanied with a release of energy.
Stars (like our sun) are very large in size because they are made up of millions of hydrogen and helium atoms. They burn because deep in their core, nuclear fusion reactions occur due to the gases heating up as a result of pressure in the star's core.
This nuclear reaction causes a release of vast amounts of energy in the form of visible electromagnetic radiation. This visible electromagnetic radiation is known as Starlight.
Which situation shows where potential energy and kinetic energy are balanced? A stopped bicycle A roller coaster car going uphill A car moving at a steady speed A runner slowing down
Potential energy or stored energy, and kinetic energy, the energy due to motion can be balanced in the process of converting kinetic energy to potential energy during an uphill motion
The correct option for, which situation shows potential energy and kinetic energy are balanced is option;
A roller coaster car going uphill
The reason the selected option is correct is as follows:
Potential energy is the energy that is due to the relative position of an item in relation to a ground or zero state. The formula for potential energy due to the elevation is given as follows;
Potential energy, P.E. = m·g·h
Kinetic energy is the energy that is due to motion. The kinetic energy of an item is given as follows;
Kinetic energy, K.E. = (1/2) × m × v²
The potential and kinetic energy of a body is balanced when we have;
P.E. = m·g·h = K.E. = (1/2)·m·v²
Which gives;
g·h = (1/2)·v²
Therefore, a point is reached as the an body moves up a heal, where the potential energy (the energy due to height of the object) and the kinetic energy (the energy due to current speed) of the object are equal
The correct situation which shows potential energy and kinetic energy are balanced is therefore; A roller coaster car going uphill
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Final answer:
Potential energy and kinetic energy are balanced when a roller coaster car is going uphill, where potential energy increases and kinetic energy decreases as the car ascends. At the peak, the two energies balance out due to the law of conservation of energy, ensuring total mechanical energy remains constant in a closed system.
Explanation:
The situation where potential energy (PE) and kinetic energy (KE) are balanced is when a roller coaster car is going uphill. As the roller coaster car ascends, its PE increases while its KE decreases as it slows down. At the peak of the hill, there's a moment where the car's velocity is zero and all of the KE has been converted into PE. If we assume no energy is lost to friction and we're dealing with a closed system, the law of conservation of energy states that the total mechanical energy (the sum of KE and PE) remains constant. Thus, the roller coaster at the top of the first rise has a certain amount of total mechanical energy, which balances out as it ascends and descends, converting between KE and PE.
For example, if a roller coaster descends 20 m and starts with an initial speed of 5 m/s, whether it was moving uphill or downhill, it will have the same final speed when it reaches a point 20 m below its starting height. This is consistent with the conservation of energy principle, as the total amount of mechanical energy remains the same throughout the ride, despite the continuous conversion between PE and KE.
The Millersburg Ferry (m = 13000.0 kg loaded) is travelling at 11 m/s when the engines are put in reverse. The engineproduces a force of 1.0 x 106N for a period of 20.0 seconds.
a)What is the magnitude of the impulse from the engine?
b)What is the new momentum of the ferry?c)What is the new velocity of the ferry?
Explanation:
It is given that,
Mass of Millersburg Ferry, m = 13000 kg
Velocity, v = 11 m/s
Applied force, F = 10⁶ N
Time period, t = 20 seconds
(a) Impulse is given by the product of force and time taken i.e.
[tex]J=F.\Delta t[/tex]
[tex]J=10^6\ N\times 20\ s[/tex]
[tex]J=2\times 10^7\ N-s[/tex]
(b) Impulse is also given by the change in momentum i.e.
[tex]J=\Delta p=p_f-p_i[/tex]
[tex]J=p_f-p_i[/tex]
[tex]p_f=J+p_i[/tex]
[tex]p_f=2\times 10^7\ N-s+13000\ kg\times 11\ m/s[/tex]
[tex]p_f=20143000\ kg-m/s[/tex]
(c) For new velocity,
[tex]v_f=\dfrac{p_f}{m}[/tex]
[tex]v_f=\dfrac{20143000\ kg-m/s}{13000\ kg}[/tex]
[tex]v_f=1549.46\ m/s[/tex]
Hence, this is the required solution.
Answer:
(a) Impulse of the engine = 20*10^6 N.s
(b) New momentum of the ferry = 1985700 kgm/s
(c) The new velocity of the ferry = 1527.5 m/s
Explanation:
In the given problem, we have:
mass (m) = 13000 kg; velocity (v) = 11 m/s; Force (F) = 1.0*10^6 N; period (t) = 20 s.
From the Newton's law of motion, it is know that:
force*time = mass*velocity; and impulse = force*time
Thus:
(a) the magnitude of the impulse from the engine is:
Impulse = 1.0*10^6 * 20 = 20*10^6 N.s
(b) The new momentum of the ferry is equivalent to the difference between the engine momentum and the ferry momentum. Therefore, we have:
New momentum = Engine momentum - Ferry momentum
Ferry momentum = mass*velocity = 13000*11 =143000 kgm/s
Engine momentum = 1.0*10^6 * 20 = 20*10^6 N.s = 20*10^6 (kgm/s^2 *s) = 20*10^6 kgm/s
Therefore:
New momentum = 20*10^6 - 143000 = 1985700 kgm/s
(c) The new velocity of the ferry is:
v = new momentum/mass = 1985700/13000 = 1527.5 m/s
A student swings back and forth from position A to C, as shown. Which of the following happens when the swing moves from Position B to Position A?
[] Both potential energy and kinetic energy of the student increase.
[] Both potential energy and kinetic energy of the student decrease.
[] Potential energy of the student decreases and kinetic energy of the student increases.
[] Kinetic energy of the student decreases and potential energy of the student increases.
Answer:[] Both potential energy and kinetic energy of the student increase.
Explanation:
The thing that will happen when the swing moves from Position B to Position A is that A. Both potential energy and kinetic energy of the student increase.
Potential energy refers to the energy that's stored in an object due to the position of the object. On the other hand, kinetic energy refers to the form of energy that an object has due to the fact that it's in motion.
From the complete question, it should be noted that since the student swings back and forth from his position, there'll be a rise in the potential energy and kinetic energy.
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In which step of the scientific method is information obtained through the senses?
Answer:
observation I believe
Explanation:
you have to observe with your eyes and could listen with your ears .etc
The method of acquiring the information in a scientific method using the senses are the OBSERVATION.
Explanation:
The observation making about the process of scientific research and development is done through the experiment or the survey. The experiment is designed based on the scientific exploration an individual is pursuing and the survey is based on the hypothesis undertaken.
Both these are simple labor done in qualitative as well as quantitative approach. The observation needs sensible inference which could result into the scientific results.
If larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading? the speedometer if larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading? the speedometer will read low. will still read the speed accurately. will read high.
Answer:
i love you
Explanation:
A circuit maintains a constant resistance. If the current in the circuit is doubled, what is the effect on the power dissipated by the circuit?The power dissipated is doubled.The power dissipated is quadrupled.The power dissipated is reduced by a factor of 2.The power dissipated remains constant.The power dissipated is reduced by a factor of 4.
Answer:
The power dissipated is quadrupled
Explanation:
The power dissipated by a circuit is given by
[tex]P=I^2 R[/tex]
where
I is the current
R is the resistance
In this problem, the resistance is kept constant, while the current is doubled:
I' = 2I
So, the new power dissipated is
[tex]P'=I'^2 R = (2I)^2 R= 4I^2 R=4P[/tex]
So, the power dissipated is quadrupled.
An object is in static equilibrium if __________.
Answer:
An object is in static equilibrium if the following is true:
+ the sum of the forces on it in each direction is zero.
+ the sum of the forces on it in each direction is zero.+ the sum of the torques on it in each direction is zero.
+ the sum of the forces on it in each direction is zero.+ the sum of the torques on it in each direction is zero.+ it's linear momentum is zero (i.e. it's not moving).
An object in static equilibrium will have these attributes;
The total forces acting on it in each of the direction will equal to zero.The summation of the torque on all the particle of the object will be zero.Static equilibrium can be regarded as any system having a summation of zero force acting on the object in each direction as well as zero torque acting on the particles of all the object.In a simple term equilibrium can be explained as system having its parts at rest.Non-moving stationary object of any kind can be seen as an object with static equilibrium Example of an object experiencing static equilibrium is ball kept on the ground,Therefore, when an object is in static equilibrium, the summation of forces on it will be zero.
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What are the names of the four hemispheres of the earth
Explanation:
Northern, Southern, Eastern, and Western.
The weighted average of the masses of the isotopes of an element
Answer:
Atomic mass
Explanation:
The weighted average of the masses of the various isotopes of an element makes the atomic mass. This is why most atomic mass values usually have decimals.
In order to calculate the atomic mass of an element using the weighted average masses, we use the expression below:
Atomic mass = ∑[tex]m_{i}[/tex][tex]α_{i}[/tex]
Where [tex]m_{i}[/tex] is the mass of isotope i
[tex]α_{i}[/tex] is the abundance of isotope i
The abundance or geonormal abundance is the proportion by which each of the isotope occurs in nature.
Light and sound waves both share what characteristic?
They both exhibit the Doppler effect.
Light and sound are both transverse waves.
They both move fastest in water.
Light and sound both require a medium in which to travel.
Light and sound waves both exhibit the Doppler effect, where the frequency of the wave changes relative to an observer in motion. However, they also have differences, with light being a transverse wave that can travel in a vacuum and sound a longitudinal wave that requires a medium.
Explanation:The correct answer is that light and sound waves both exhibit the Doppler effect. The Doppler effect is the change in frequency of a wave in relation to an observer who is moving relative to the source of the wave. It is often heard in a passing siren, as the pitch of the siren changes from high to low as it passes by. Similarly, light waves from a moving source can change frequency, which astronomers use to tell if stars are moving towards us (light is more blue) or away from us (light is more red).
However, it is important to note that there are differences between light and sound waves as well. Light is a transverse wave and can travel through a vacuum, while sound is a longitudinal wave and requires a medium (like air or water) to travel. Light also travels faster than sound.
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Light and sound waves both exhibit the Doppler effect, with differences in their basic nature; sound requires a medium to propagate and is a mechanical wave, while light is an electromagnetic wave that can travel through a vacuum.
Light and sound waves both exhibit the characteristic known as the Doppler effect. This is observed when the source of the waves is moving relative to the observer, causing a change in the observed frequency. Although sound and light share some similarities, they are fundamentally different in their properties. Sound waves are mechanical waves, which means they require a medium, like air or water, to travel through. In contrast, light waves are electromagnetic waves and do not require a medium; they can travel through a vacuum. Another critical difference between the two is that sound waves are typically longitudinal waves, where the vibration of the medium is parallel to the direction of wave travel, while light waves are transverse, meaning the vibration is perpendicular to the direction the wave is moving. So the correct option is first, They both exhibit the Doppler effect.
On a cold day, the speed of sound in air is 330 m/s. A note with a frequency of 1,320 Hz is played on an instrument. What is the wavelength of that sound wave?
Wavelength = (speed) / (frequency)
Wavelength = (330 m/s) / (1320/s)
Wavelength = (330/1320) m
Wavelength = 0.25 m
Wavelength = 25 cm
The wavelength of that sound wave is 0.25 m.
What is the relationship between Wavelength, Speed and Frequency?Wavelength and frequency are inversely proportional to each other.C = fλ , where C = speed , f = frequency and λ = wavelength.What is the wavelength of the sound having frequency of 1320 Hz?C = fλ
∴ λ = C/f
∴ λ = 330 / 1320
∴ λ = 0.25 m.
Thus, The wavelength of that sound wave is 0.25 m.
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A 7.5 cm object is 14 cm from a concave lens, which has a focal length of –7 cm. What is the distance of the image from the lens? Round your answer to the nearest whole number. 5 cm –5 cm 14 cm –14 cm
Answer:
-5 cm
Explanation:
We can use the lens equation:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]
where
f = -7 cm is the focal lenght
p = 14 cm is the distance of the object from the lens
q is the distance of the image from the lens
Solving the equation for q, we find
[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-7 cm}-\frac{1}{14 cm}=-\frac{3}{14 cm}\\q=\frac{-14 cm}{3}=-4.67 cm \sim -5 cm[/tex]
Answer:
-5 cm
Explanation:
Just took it : )
Formulating a Hypothesis: Part I Since the investigative question has two variables, you need to focus on each one separately. Thinking only about the first part of the question, mass, what might be a hypothesis that would illustrate the relationship between mass and kinetic energy? Use the format of "if...then... because when writing your hypothesis
Answer:
If the mass of an object increases, then its kinetic energy will increase proportionally because mass and kinetic energy have a linear relationship when graphed.
Explanation:
A boy swings a ball on a string at constant speed in a horizontal circle that has a circumference equal to 6 m. What is the work done on the ball by the 10-n tension force in the string during one revolution of the ball?
Answer:
Zero
Explanation:
The work done by a force is given by:
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement of the object
[tex]\theta[/tex] is the direction between the force and the displacement
In this problem, the force is the tension in the string, while the object is the ball. The tension is always radial (towards the centre of the circle), while the ball moves tangentially to the circle: this means that the tension and the displacement are always perpendicular to each other, so
[tex]\theta=90^{\circ}, cos \theta = 0[/tex]
and so the work done is zero.
The work done on the ball swung on a string in a horizontal circle due to the tension force of 10 N in the string during one revolution of the ball is zero.
The work done by the tension force on the ball is given by:
[tex] W = F*d*cos(\theta) [/tex] (1)
Where:
F: is the tension force = 10 N
d: is the displacement
θ: is the angle between the force and the displacement
The displacement is given by the circular path of circumference 6 meters.
In one point of the circular path, the direction of the tension force is to the center of the circumference and the displacement is orthogonal to this direction, so the angle between them is 90° (see the picture below).
The work is then (eq 1):
[tex] W = F*d*cos(\theta) = 10 N*6 m*cos(90) = 0 [/tex]
Therefore, the work done on the ball by the tension force is 0 (zero).
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Which statement correctly describes a step-up transformer?
A. It increases the amount of electric energy available.
B. It increases the voltage of an electric current.
C. It changes direct current into alternating current.
D. It has more loops of wire in its primary coil.
Answer:
B. It increases the voltage of an electric current. Same way a step down would decrease the amount of voltage.
Explanation:
Answer:
B. It increases the voltage of an electric current.
Explanation:
In step up transformer the number of turns of the coil on the output side is more than the number of the turns on the input side of the coil
so here the flux on the output side of the coil will be more
hence we will have
[tex]\phi_2 = N_2\phi_o[/tex]
[tex]\phi_1 = N_1\phi_o[/tex]
here we know that
[tex]\phi_o[/tex] = flux linked with one coil
so here we know by Faraday's law
[tex]\frac{d\phi}{dt} = EMF[/tex]
hence the net EMF or voltage of the output side will be more than the voltage on the input side
So we have
B. It increases the voltage of an electric current.
A student uses 0.0821 l• atm/mol • k as the value of the gas constant. What is most likely true about the variables in the ideal gas law?
Answer:
- the pressure is specified in atmospheres (atm)
- the volume is specificied in liters (L)
- the temperature is specificied in Kelvin (K)
- the number of moles is specified in mol (mol)
Explanation:
The ideal gas law states that:
[tex]pV=nRT[/tex]
where
p is the gas pressure
V is the volume
n is the number of moles
R is the gas constant
T is the absolute temperature
It can be rewritten solving for R
[tex]R=\frac{pV}{nT}[/tex]
In this problem, the gas constant is written as
[tex]R=0.0821 \frac{L \cdot atm}{mol\cdot K}[/tex]
this means that:
- the pressure is specified in atmospheres (atm)
- the volume is specificied in liters (L)
- the temperature is specificied in Kelvin (K)
- the number of moles is specified in mol (mol)
The ideal gas law, PV = nRT, requires the units for pressure, volume, moles and temperature to be in atmospheres, litres, moles and kelvins respectively when the gas constant R is 0.0821 l• atm/mol •K. Any variables used must be converted to these units.
Explanation:The ideal gas law equation is given as PV = nRT, where P stands for pressure, V for volume, n for the number of moles, R for the gas constant and T for temperature. The gas constant (R) in the question is given as 0.0821 l• atm/mol • k. Therefore, this implies that the pressure is in atmospheres (atm), volume is in litres (L), number of moles (mol), and the temperature (T) is in kelvins (K). If the student chooses to use the mentioned value of R, the necessary variables to fit into the ideal gas law's units must be converted to fit these units.
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The roller coaster from problem #1 then tops a second hill at 15.0 m/s, how high is the second hill?
91.5 m
79.2 m
80.0 m
68.5 m
Answer:
68.5
Explanation:
The height of the hill is equal to 11.48 m if the speed of the roller coaster is 15 m/s.
What is the law of conservation of energy?According to the law of conservation of law, energy can only be converted from one to another form but can neither be created nor destroyed. In nature, energy can be found in several forms such as heat, electricity, nuclear energy, chemical energy, etc.
The total energy of an isolated system remains constant when all forms of energy are considered. The law of conservation of energy applies to all kinds of energy.
Given the velocity of the roller coaster, v = 15 m/s
From the law of conservation of energy, kinetic energy at the bottom is equal to potential energy at top of the hill.
(1/2) × mv² = m × g × h
h = v²/2g
h = (15)²/2 ×9.8
h = 11.48 m
Therefore, the height of the hill will be equal to 11.48 m.
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A tuning fork labeled 392 Hz has the tip of each of its two prongs vibrating with an amplitude of 0.600 mm. A) What is the maximum speed of the tip of a prong? B) A housefly (Musca domestica) with mass 0.0270 g is holding on to the tip of one of the prongs. As the prong vibrates, what is the fly's maximum kinetic energy? Assume that the fly's mass has a negligible effect on the frequency of oscillation.
To go through one complete wiggle, the tip of the fork has to move outward 0.6mm, then 0.6mm back to the middle, then inward 0.6mm, then 0.6mm back to the middle again. So one complete wiggle of the tip moves it 2.4mm .
It does this 392 times every second. So its AVERAGE speed would be
Speed = (distance) x (frequency)
Speed = (2.4 mm) x (392 Hz)
Speed = (0.0024 m) x (392 / sec) = 0.9408 m/s .
That's the AVERAGE speed of the tip of one prong. That's easy. Sadly, the question is asking us for the MAXIMUM speed. That will be less easy.
Now right here, I'm afraid I will go off the rails for a bit ... I'm going to assert things and do things that I'm not willing to try and explain for 5 points. It may not even be correct, (which would make it a lot harder to explain). So I'm just gonna jump in and DO IT.
The way I see it, the tip of that prong is wiggling in sinusoidal wiggles. Relative to its resting position, its location is something like
x = (0.6 mm) x sin(2π x 392 t) .
and as usual, its speed is the derivative of that mess.
Speed = dx/dt = (0.6 mm) x (2π x 392) cos(2π x 392 t)
The greatest that the cosine alone can be is 1 , so the maximum value of the speed is
(0.6 mm) x ( (2π x 392))
and that's 1,477.8 mm/s or 1.4778 m/s . I think this is the answer to part-a, and now we can go on to consider the hapless fly, stuck by his pads to the wildly oscillating prong.
Part-b is easy. The fly's maximum kinetic energy is just
KE = (1/2) (flymass) (max speed)²
KE = (1/2) (0.027 g) (1.4778 m/s)²
KE = (1.35 x 10⁻⁵ kg) (2.184 m²/s²)
KE = 2.95 x 10⁻⁵ Joule
So there ya go. These are my answers and I'm stickin withum.
A small bouncy ball with a momentum of 8 kg∙m/s to the left approaches head-on a large door at rest. The ball bounces straight back with a momentum of 6 kg∙m/s. What is the change in the momentum of the ball? What is the impulse exerted on the ball? What is the impulse exerted on the door?
Answer:
-14 kg m/s
Explanation:
Taking the direction "to the left" as positive direction, the initial momentum of the ball is
p1 = +8 kg m/s
while the final momentum is
p2 = -6 kg m/s
so the change in momentum is
[tex]\Delta p = p_2 - p_1 = -6kg m/s - (8 kg m/s) = -14 kg m/s[/tex]
According to the impulse theorem, the impulse exerted on the ball is equal to the change in momentum of the ball, so:
[tex]I_1 = -14 kg m/s[/tex] (which means 14 kg m/s to the right)
While the impulse that the ball exerted on the ball is equal and opposite in direction, so:
[tex]I_2 = + 14 kg m/s[/tex] (which means towards the left)
People are constantly being barraged with low-level radiation. Which radiation source below contributes the most low-level radiation exposure to the average person?a) cosmic raysb) medical X-raysc) radond) rocks, soils, and food
I think the answer is C) Radond
Answer:
C) Radon
Explanation:
Humans are terrified of radiation attack but we are unaware that we face radiations from a lot of natural sources which includes food and water. But their level is low and thus do not have any major impact on our body.
As per US Nuclear Regulatory Commission,on an average, an American faces a radiation of 620 millirem each year. Out of this 50% is because of Natural background radiation. Majority of this radiation is due to Radon in the air, with small contribution (around 30 millirem) from Cosmic rays and even smaller contribution from Earth itself.
In Milgram's experiment, compliance, or doing what the experimenter asked,
dropped when:
A. the study was at Yale University.
B. the teacher heard the learner scream.
O
C. the teacher and the learner were in the same room.
O
D. the learner stopped responding.
Answer:
In Milgram's experiment, compliance, or doing what the experimenter asked,
the teacher and the learner were in the same room. -C.
Answer:
Option C
Explanation:
In his experiment, Milgram wanted to test the extent of obedience a person can go as per the instructions of the authority.
In this he concluded the experiment saying that several factor when changed in the second round of experiment led to the dropping of obedience level and these factors are as follows –
a) Conducting the experiment at some ordinary place instead of Yale university campus
b) When the teachers were asked to force the hand of learner to touch the shock plate and they were placed in the same room
c) Two participants in the same room – If one participants showed disobedience then the other participant’s disobedience level will fall automatically
d) When the authority giving instructions is not nearby or is absent
Hence, option C is correct
The particles that are found in the nucleus of an atom are
Answer: Electrons are the smallest of the three particles that make up atoms. Electrons are found in shells or orbitals that surround the nucleus of an atom
Explanation: hope this helps
A stuntman wants to bungee jump from a hot air balloon 60.0 m above a the ground. He will use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass that obeys Hooke's law. In a preliminary test, hanging at rest from a 5.00 m length of the cord, he finds that his body weight stretches it by 1.30 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon. Hint: the spring constant changes with a longer piece of cord.
A) What lenght of cord should he use?
B) What maximum acceleration will he experience?
Answer:
A) 24.7 m, B) 28.9 m/s²
Explanation:
Hooke's law states the force of a spring is equal to the spring constant times the change in length:
F = k ΔL
Solving for k:
k = F / ΔL
The spring constant is inversely proportional to the length:
k ∝ 1/L
Therefore:
k₁ L₁ = k₂ L₂
(F₁ / ΔL₁) L₁ = k₂ L₂
(mg / 1.30) (5.00) = k L
k = (5.00/1.30) (mg / L)
Initial energy = final energy
Initial gravitational energy = final gravitational energy + elastic energy
mgH = mgh + 1/2 k (ΔL)²
mg(H - h) = 1/2 k (ΔL)²
mg(60.0 - 10.0) = 1/2 k (ΔL)²
50mg = 1/2 k (ΔL)²
100mg = k (ΔL)²
The stuntman will fall a distance L and then an additional distance ΔL. We know this distance is equal to 60-10 = 50 m. L + ΔL = 50, so ΔL = 50 - L.
100mg = k (50 - L)²
100mg = k (2500 - 100L + L²)
100mg = (5.00/1.30) (mg / L) (2500 - 100L + L²)
26L = 2500 - 100L + L²
0 = L² - 126L + 2500
L = (126 ± √5876) / 2
L = 63 ± √1469
L ≈ 24.7 m, 101 m
Obviously L can't be more than 50.0 m, so L = 24.7 m.
As a mass on a spring, the stuntman will follow simple harmonic motion, so his maximum acceleration will be experienced at his minimum velocity, or at the very bottom.
∑F = ma
k ΔL - mg = ma
(5.00/1.30) (mg / L) ΔL - mg = ma
(5.00/1.30) (g / L) ΔL - g = a
(5.00/1.30) (9.81 / 24.7) (50.0 - 24.7) - 9.81 = a
a = 28.9 m/s²
The height of a wave or the amount of _____ the wave carries is the amplitude.
Answer:
The height of a wave or the amount of energy the wave carries is the amplitude.
Explanation:
Amplitude is one of the variable properties a wave presents. The amplitude of a wave refers to the maximum of displacement the wave has from its rest position. In other words, the amplitude is the distance from rest position to the wave's crest. The amount of energy the wave carries will affect the amplitude the wave will have as well; as more energy is carries the amplitude will also increase making the distance from rest position to the crest bigger. A high energy wave is characterized with high amplitude as well as a low energy wave is characterized with a low amplitude.
The amplitude of a wave measures the maximum displacement from its equilibrium position, indicating the wave's energy. The height of a wave or the amount of maximum displacement the wave carries is the amplitude.
The height of a wave, or the amount of energy the wave carries, is referred to as the amplitude. In physics, the amplitude is defined as the maximum displacement of the medium from its equilibrium position.
This distance can be measured from the middle rest position of the wave to the top of the crest or the bottom of the trough.
The amplitude is essential because it determines the energy carried by the wave. For example, in an ocean wave, the amplitude corresponds to the height of the wave above the water's calm surface.
Which component of the earth’s atmosphere is decreased due to photosynthesis?
A 20 cm long spring is attached to a wall. The spring stretches to a length of 22 cm when you pull on it with a force of 100 n. What is the spring constant
Answer:
5000 N/m
Explanation:
Hooke's law for the spring is
[tex] F = k \Delta x[/tex]
where here we have
F = 100 N is the force applied to the spring
k is the spring constant
[tex]\Delta x = 22 cm - 20 cm = 2 cm = 0.02 m[/tex] is the stretching of the spring with respect to its equilibrium position
Solving the equation for k, we find the spring constant:
[tex]k=\frac{F}{\Delta x}=\frac{100 N}{0.02 m}=5000 N/m[/tex]
How long does it take for mars to rotate on its axis
Hello There!
It takes the planet Mars around 24 hours, 37 minutes, 23 seconds to rotate on its axis. This is around the same amount of time that it takes our planet to rotate once on its axis.
Who was the first person to circumnavigate the globe
Answer:
Ferdinand Magellan
Explanation:
Ferdinand Magellan was first man to circumnavigate the earth. A Portugese who lived from 1840- 1521. He died on course his voyage around the earth in the year 1521. His exploration of the earth provides the proof that the earth is a round planet and not actually flat. Magellan's expedition strongly bolstered the round earth theory as against the conventional conception in those days that the earth is flat.
His voyage spanned three years between 1519 and 1522.
Answer:
Ferdinand Magellan
Explanation:
Hope this helps
Which of the following is not a physical property of mattera. melting pointb.heat of combustionc. viscosityd. boiling point
Answer:
The Correct Answer is Heat of Combustion
Explanation: