Answer:c hubble's law
Explanation:
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 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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A fireman of mass 80 kg slides down a pole. When he reaches the bottom, 4.2 m below his starting point, his speed is 2.2 m/s. By how much has thermal energy increased during his slide?
Answer:
3099 J
Explanation:
While the fireman slides down, his initial gravitational potential energy is converted partially into kinetic energy, partially into thermal energy, so we can write:
[tex]\Delta U = K + E_t[/tex] (1)
where
[tex]\Delta U [\tex] is the change in gravitational potential energy
K is the kinetic energy gained
Et is the thermal energy
The variation in gravitational potential energy is
[tex] U = mg \Delta h = (80 kg)(9.8 m/s^2)(4.2 m)=3293 J [/tex]
where m=80 kg is the mass of the fireman, g=9.8 m/s^2 is the acceleration of gravity, [tex]\Delta h=4.2 m[/tex] is the change in height of the fireman.
The kinetic energy gained is
[tex] K=\frac{1}{2}mv^2=\frac{1}{2}(80 kg)(2.2 m/s)^2=194 J[/tex]
where v = 2.2 m/s is the speed reached by the fireman at the bottom of the slide
So now solving eq.(1) we find the increase in thermal energy :
[tex] E_t = \Delta U - K = 3293 J - 194 J = 3099 J[/tex]
Answer:
3100 J
Explanation:
Because this scenario using three forms of energy (kinetic, gravitational potential, thermal), we use the conservation of energy formula:
0=ΔKe + Δ Ug + ΔEth
Keep in mind we want to find change in thermal energy, so:
ΔEth = -(ΔKe + ΔUg)
Change in kinetic energy:
ΔKe = Kf - Ki = [tex]\frac{1}{2}(0)^{2} -\frac{1}{2}(80)(2.2)^{2} = 190 J[/tex]
Change in Gravitational potential energy:
[tex]mgy_{f} - mgy_{i} = 0 - (80)(9.80)(4.2) = - 3300 J[/tex]
ΔEth = [tex]-(190 -3300) = 3100 J[/tex]
Change in thermal energy = 3100 J
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
Which explanation of the solar system best fits the observations of the planets and how they orbit the sun?Question options:The gravity of a large, massive star passing the sun ripped off blobs of material from it that formed the planets.A comet hit the sun and sent off fragments that became the planets.The planets formed at the center of a collapsing spinning cloud of gas and dust.The sun and planets formed from a collapsing spinning cloud of gas and dust.
The most accepted theory so far, in relation to the formation of our solar system is that it was originated by the contraction of a cloud of interstellar gas due to its own gravity.
To understand it better:
According to this theory, a cloud of gas and interstellar dust began to shrink due to its own gravity. This led to the increase in the temperature of the system, which began to rotate forming a large gas sphere in the center (the Sun) with a flat disk around it.
This is how the Sun formed from the sphere in the center and the planets formed from the disk orbiting in the same plane.
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:
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 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
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.
Which electron transition in an excited atom results in a release of energy? first shell to the third shell second shell to the fourth shell third shell to the fourth shell fourth shell to the second shell?
Answer:
fourth shell to the second shell
Explanation:
When an electron of an atom moves from a lower energy shell to a higher energy shell (such as 1st shell to the 3rd shell), it absorbs energy through a specific wavelength of electromagnetic wave equivalent to the difference in energy levels of the electron shells.
Conversely, when the electron jumps from a higher electron shell to a lower one (such as in this case) it releases energy, in the form a specific wavelength of electromagnetic wave, equivalent to the difference in energy levels between the two electron shells.
Answer:
fourth shell to the second shell
Explanation:
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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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.
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.
A weather balloon travels upward for 6 km whi le the wind blows it 10 km north and 8 km east. Approximately what is its final displacement from its initial position?
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.
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.
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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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.
What are the names of the four hemispheres of the earth
Explanation:
Northern, Southern, Eastern, and Western.
Which component of the earth’s atmosphere is decreased due to photosynthesis?
An elevator filled with passengers has a mass of 1700 kg. (a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 1.50 s. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of 0.600 m/s2 for 3.00 s. What is the tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?
(a) 18717 N
There are two forces acting on the elevator:
- The tension in the cable, T, upward
- The weight of the elevator+passenger, downward, which is given by
W = mg
where m=1700 kg is the mass and g=9.81 m/s^2 is the acceleration of gravity
According to Newton's second law, the resultant of these forces must be equal to the product between mass and acceleration:
T - mg = ma
where
a = 1.20 m/s^2 is the acceleration, also upward
Solving the equation for T, we find the tension in the cable:
[tex]T=mg+ma=m(g+a)=(1700 kg)(9.81 m/s^2)(1.20 m/s^2)=18717 N[/tex]
(b) 16677 N
In this second part of the trip, the elevator continues at constant velocity. This means that the acceleration is zero:
a = 0
So Newton's second law becomes:
T - mg = ma = 0
Therefore, the tension in the cable will be equal to the weight of the elevator+passenger:
T = mg = (1700 kg)(9.81 m/s^2)=16677 N
(c) 15657 N
In this third part of the trip, the elevator has a deceleration of
a = -0.60 m/s^2
and we use a negative sign since the acceleration is now downward.
Therefore, Newton's second law is
T - mg = ma
And substituting all the data, we find the new tension in the cable:
[tex] T=mg+ma=m(g+a)=(1700 kg)(9.81 m/s^2-0.60 m/s^2)=15657 N[/tex]
(d) 19.35 m, 0 m/s
The distance covered by the elevator in part a) of the trip is
[tex]d_1 = \frac{1}{2}at^2 = \frac{1}{2}(1.20 m/s^2)(1.50 s)^2=1.35 m[/tex]
The final velocity reached in this part is
[tex]v_1 = at=(1.20 m/s^2)(1.50 s)=1.8 m/s[/tex]
In the second part, the elevator moves at constant velocity of
[tex]v_2 = v_1 = 1.8 m/s[/tex]
so the distance covered is
[tex]d_2 = v_2 t = (1.8 m/s)(8.50 s)=15.3 m[/tex]
The distance covered in the third part will be
[tex]d_3 = v_2 t + \frac{1}{2}at^2 = (1.8 m/s)(3.0 s) + \frac{1}{2}(-0.6 m/s^2)(3.0 s)^2=2.7 m[/tex]
While the final velocity is
[tex]v_3 = v_2 + at = 1.8 m/s + (-0.6 m/s^2)(3.0 s)=0[/tex]
and the total distance covered (so, the heigth of the elevator above the ground) is
[tex]d = d_1 + d_2 + d_3 = 1.35 m +15.30 m+2.70 m=19.35 m[/tex]
To calculate the tension in the cable, use the equation Tension = mass x acceleration + weight. To find the height the elevator moved, use the equations of motion.
Explanation:To calculate the tension in the cable, we need to consider the forces acting on the elevator. When the elevator accelerates upward, two forces are acting on it - the force due to its weight and the tension in the cable. The tension in the cable is given by the equation:
Tension = mass x acceleration + weight
Using this equation, we can calculate the tension in the cable for each scenario:
(a) Tension during acceleration = (1700 kg x 1.20 m/s^2) + (1700 kg x 9.8 m/s^2)
(b) Tension during constant velocity = 1700 kg x 9.8 m/s^2
(c) Tension during deceleration = (1700 kg x -0.600 m/s^2) + (1700 kg x 9.8 m/s^2)
To find how high the elevator has moved above its original starting point, we can use the equations of motion. The final velocity of the elevator can be found using the equation:
Final velocity = initial velocity + (acceleration x time)
The displacement can be found by using the equation:
Displacement = (initial velocity x time) + (0.5 x acceleration x time^2)
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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]
Bob is pulling a 30kg filing cabinet with a force of 200N , but the filing cabinet refuses to move. The coefficient of static friction between the filing cabinet and the floor is 0.80.Part AWhat is the magnitude of the friction force on the filing cabinet?Express your answer to two significant figures and include the appropriate units. f =
Answer:
[tex]2.0\cdot 10^2 N[/tex]
Explanation:
The cabinet does not move: this means that the net force acting on it is zero.
Along the horizontal direction, we have two forces:
- The push exerted by Bob, F = 200 N, forward
- The frictional force, [tex]F_f[/tex], which acts in the opposite direction (backward)
Since the net force must be zero, we have:
[tex]F-F_f = 0[/tex]
So solving the equation we can find the magnitude of the friction force:
[tex]F_f = F = 200 N=2.0 \cdot 10^2 N[/tex]
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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What is the orbital period of a spacecraft in a low orbit near the surface of mars? The radius of mars is 3.4×106m.
The orbital period of a spacecraft in low Mars orbit can be calculated using Kepler's Third Law, taking into account the radius of Mars and its gravitational influence.
Explanation:The orbital period of a spacecraft in a low orbit near the surface of Mars can be calculated using Kepler's Third Law, which connects the time period of a planet's orbit (T) with the semi major axis of its orbit (r). It is important to note that the mass of the spacecraft is much smaller than the mass of Mars, and therefore, the mass of the spacecraft can be ignored in the calculation.
The formula for the orbital period is: T = 2π√(r³/μ), where μ (the standard gravitational parameter) is G*M (the gravitational constant, G, times the mass of Mars, M). Substituting the given radius of Mars into the formula we will get the orbital period of a spacecraft in a low orbit near the surface of Mars.
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The answer is: [tex]1.6888 \, \text{hr}.[/tex]
The orbital period [tex]\( T \)[/tex] of a spacecraft in a low orbit near the surface of Mars can be estimated using Kepler's third law, which relates the square of the orbital period of a planet to the cube of the semi-major axis of its orbit. For a circular orbit, the semi-major axis is equal to the radius of the orbit, which in this case is approximately the radius of Mars. Kepler's third law is given by:
[tex]\[ T^2 = \frac{4\pi^2}{G(M + m)}a^3 \][/tex]
where:
- [tex]\( T \)[/tex] is the orbital period of the spacecraft,
- [tex]\( G \)[/tex] is the gravitational constant [tex](\(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\)),[/tex]
- [tex]\( M \)[/tex] is the mass of Mars [tex](\(6.417 \times 10^{23} \, \text{kg}\)),[/tex]
- [tex]\( m \)[/tex] is the mass of the spacecraft (which is negligible compared to the mass of Mars),
- [tex]\( a \)[/tex] is the semi-major axis of the orbit (approximately the radius of Mars, [tex]\(3.4 \times 10^6 \, \text{m}\))[/tex].
Since the mass of the spacecraft [tex]\( m \)[/tex] is much smaller than the mass of Mars [tex]\( M \)[/tex], we can ignore [tex]\( m \)[/tex] in the calculation. The equation simplifies to:
[tex]\[ T^2 = \frac{4\pi^2}{GM}a^3 \][/tex]
Now we can solve for [tex]\( T \)[/tex]:
[tex]\[ T = \sqrt{\frac{4\pi^2}{GM}a^3} \][/tex]
Plugging in the values:
[tex]\[ T = \sqrt{\frac{4\pi^2}{(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2)(6.417 \times 10^{23} \, \text{kg})}(3.4 \times 10^6 \, \text{m})^3} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2}{(6.674 \times 10^{-11})(6.417 \times 10^{23})}(3.4 \times 10^6)^3} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2}{4.276 \times 10^{13}}(3.4 \times 10^6)^3} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2}{4.276 \times 10^{13}}(3.93 \times 10^{19})} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2(3.93 \times 10^{19})}{4.276 \times 10^{13}}} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2 \times 3.93 \times 10^{19}}{4.276 \times 10^{13}}} \][/tex]
[tex]\[ T = \sqrt{\frac{4\pi^2 \times 3.93}{4.276} \times 10^6} \][/tex]
[tex]\[ T = \sqrt{\pi^2 \times \frac{4 \times 3.93}{4.276}} \times 10^3 \][/tex]
[tex]\[ T = \pi \sqrt{\frac{4 \times 3.93}{4.276}} \times 10^3 \][/tex]
[tex]\[ T \approx \pi \sqrt{3.77} \times 10^3 \][/tex]
[tex]\[ T \approx 3.1416 \times 1.94 \times 10^3 \][/tex]
[tex]\[ T \approx 6.08 \times 10^3 \, \text{s} \][/tex]
To convert seconds to minutes, divide by 60:
[tex]\[ T \approx \frac{6.08 \times 10^3 \, \text{s}}{60 \, \text{s/min}} \][/tex]
[tex]\[ T \approx 101.33 \, \text{min} \][/tex]
And to convert minutes to hours, divide by 60 again:
[tex]\[ T \approx \frac{101.33 \, \text{min}}{60 \, \text{min/hr}} \][/tex]
[tex]\[ T \approx 1.6888 \, \text{hr} \][/tex]
A particle travels in a straight line with speed v.
The particle slows down and changes direction. The new speed of the particle is v\2
The new velocity has a component of v\4
in the same direction as the initial path of the particle.
Through which angle has the particle turned?
A 27° B 30° C 45° D 60°
Answer:
D 60°
Explanation:
Using trigonometry:
- The new speed (v/2) of the particle corresponds to the hypothenuse
- The component of v/4 represents the side adjacent to the angle that we want fo find, [tex]\theta[/tex]
So we can write:
[tex]cos \theta = \frac{adjacent}{hypothenuse}=\frac{v/4}{v/2}=\frac{1}{2}[/tex]
So we find the angle
[tex]\theta= cos^{-1} (\frac{1}{2})=60^{\circ}[/tex]
Answer:
D 60°
Explanation:
Using trigonometry in the attached image:
[tex]cos\alpha =\frac{v/4}{v/2}[/tex]
[tex]cos\alpha =\frac{1}{2}[/tex]
[tex]\alpha =cos^{-1} \frac{1}{2}[/tex]
Angle=60°
At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25°
c. what is the standard deviation of the temperature increase?
Answer: 4.33°
Explanation:
The formula to calculate the standard deviation for a uniform distribution for interval [a,b] is given by :-
[tex]\text{Standard deviation}:\sigma=\sqrt{\dfrac{(b-a)^2}{12}}[/tex]
Given : The amount that the water temperature is raised has a uniform distribution over the interval = [tex][10^{\circ},25^{\circ}][/tex]
Then , the standard deviation of the temperature increase is given by :-
[tex]\sigma=\sqrt{\dfrac{(25-10)^2}{12}}\\\\\Rightarrow\sigma=4.33012701892\approx4.33[/tex]
Hence, the standard deviation of the temperature increase is 4.33°.
For a uniformly distributed random variable, calculate the standard deviation using the formula sqrt((b - a)^2 / 12). In this case, the standard deviation of the temperature increase is approximately 4.33 degrees Celsius.
Explanation:In statistics, the standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of values. This question deals with the uniform distribution, so it's a topic in probability and statistics.
For a uniform distribution on the interval [a, b], the standard deviation can be calculated using the formula: sqrt((b - a)^2 / 12). In this case, a = 10 degrees and b = 25 degrees. So, the standard deviation of the temperature increase is sqrt((25 - 10)^2 / 12) = sqrt(225 / 12) = sqrt(18.75) which is approximately 4.33 degrees Celsius.
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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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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.
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.
People benefit by participating in the market because
Answer:
Market participation allows individuals to specialize and, with trade, ultimately consume more.
People benefit from participating in the market as it leads to better or less expensive products for consumers, higher profits for businesses, and increased income for employees. This process is also beneficial to society overall, yielding positive social results defined as the 'invisible hand' by Adam Smith.
Explanation:People benefit from participating in the market for several reasons. Consumers usually get access to better or less expensive products as businesses constantly compete against each other to provide the best products or services. This competition leads to innovation and pushes businesses to find ways to decrease costs and increase the quality of their goods or products.
From the businesses' perspective, the ones able to provide better or cost-effective products realize an increase in their profits. Their employees also benefit through increased income. It is primarily a win-win for all parties involved - consumers, businesses, and employees. The total gains from such market participation usually outweigh the losses, leading to overall economic welfare in the nation.
Furthermore, self-interested behavior in a market can yield positive social results, termed as 'the invisible hand' by the economist Adam Smith. When persons work hard to earn, they contribute to the economic output. Consumers looking for the best deals motivate businesses to offer goods and services catering to their needs, which in turn, tends to benefit the overall society.
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