(b) The classical kinetic energy underestimates the experimental value by 1% at speed u = 0.115c.
(c) The classical kinetic energy underestimates the experimental value by 5% at speed u = 0.257c.
(d) The classical kinetic energy underestimates the experimental value by 50% at speed u = 0.786c.
Kinetic energy, which may be seen in the movement of an object, particle, or group of particles, is the energy of motion.
The classical kinetic energy is given as:
K(c) = (1/2)mu² = (1/2)mc²(u/c)² = (4.5 × 10 ¹⁶) (u/c)²
The actual kinetic energy of the object is given as:
K(r) = [ (1 /(√1-(u/c)²) - 1]mc² = ( 9 × 10⁶)[ (1 /(√1-(u/c)²) - 1]
(b) The speed at which the classical kinetic energy underestimates the experimental value by 1% is:
K(c) = 0.99K(r)
When (1/2) (u/c)² = 0.990 [ (1 /(√1-(u/c)²) - 1]
Solving this we get,
u = 0.115c
(c) Similarly energy underestimates experiment value by 5% :
K(c) = 0.950K(r)
When u = 0.257c
(d) Energy underestimates experiment value by 50% :
Then,
K(c) = 0.500 K(r) when the speed is u = 0.786c
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a meteoroid changed velocity from 9 to 21 in 13 seconds. What is the acceleration of the meteoroid? (round to the nearest whole number)
Answer:
Acceleration:
a = 1 km/c²
Explanation:
Given:
V1 = 21 km/h
V2 = 9 km/h
Δt =13 s
________________
a - ?
a =(V2 - V1) / Δt = (21 - 9 ) /13 = 12 /13 ≈ 1 km/c²
while driving on a two lane highway, you come across a sharp curve and see a large, slow moving vehicle
Use manual gearbox to lessen the impact of force.
since we have not much space to maneuver we will identify all the possible sources.
through this sources try to minimize the damage as much as possible
Firstly we will try this :
1)
The car would try to slow down as much as it could and avoid the collision if it had a manual gearbox.
Second option could be:
2)
On the other hand, if the automobile has an automatic transmission, try to stop as hard as you can, but just before you strike the truck, to prevent going under it and lessen the force of the contact.
Last resort should be:
3)
The handbrake may also be engaged as a third option, which would cause my car to turn and attempt to avoid hitting the other car.
In case the highway is not barricaded on left side as an emergency measure we could crash off road.
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A model shows that the moon has grown to twice its size, yet it has remained in the same place. In one to two sentences, explain how this would impact the gravity between Earth and the moon
When chromium is added to colorless corundum, a red ruby is born, and a green emerald emerges when chromium is added to colorless beryl.
What is chromium?Chromium is a chemical element with the atomic number 24 and the symbol Cr. It is the initial component of group 6. It is a transition metal that is glossy, steely-grey, tough, and brittle.
Because of its high level of corrosion resistance and hardness, chromium metal is prized. The discovery that steel could be transformed into stainless steel, which is extremely resistant to corrosion and discoloration, was a significant advancement in the manufacture of steel. Together, stainless steel and chrome plating (chromium electroplating) account for 85% of commercial use. Chromium is highly prized as a metal that can be thoroughly polished while retaining its shine. Over 90% of infrared light and nearly 70% of the visible spectrum are reflected by polished chrome.
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A person holds a 0.300 kg pomegranate at the top of a tower that is 96 m high. another person holds a 0.800 kg melon next to an open window 32 m up the tower.
The gravitational potential energy of the pomegranate is 282.24 J
The gravitational potential energy of the melon is 250.88 J
What do you mean by potential energy?Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.
The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are examples of common types of potential energy. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).
Although it has connections to the Greek philosopher Aristotle's concept of potentiality, the phrase "potential energy" was coined by the Scottish engineer and physicist William Rankine in the 19th century. Potential energy is connected to forces that affect a body in such a way that their combined work is only dependent on the body's beginning and ultimate positions in space. At any point in space, these forces, also known as conservative forces, can be represented by vectors that are gradients of a particular scalar function known as potential.
Given;
mass of pomegranate, m₁ = 0.3 kg
height of pomegranate, h₁ = 96 m
mass of melon, m₂ = 0.8 kg
height of melon, h₂ = 32 m
The gravitational potential energy of the pomegranate is calculated as;
P.E₁ = m₁gh₁
P.E₁ = 0.3 x 9.8 x 96
P.E₁ = 282.24 J
The gravitational potential energy of the melon is calculated as;
P.E₂ = m₂gh₂
P.E₂ = 0.8 x 9.8 x 32
P.E₂ = 250.88 J
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Pomegranate has a gravitational potential energy of 282.24 J.
Melon has a gravitational potential energy of 250.88 J.
What is potential energy?Because of its position, an object can store energy. For instance, when kept at an elevated position, the large ball of a demolition machine is storing energy. Potential energy is the name given to this accumulated positional energy. Similar to this, a drawn bow's stance allows it to store energy.
Examples
a boulder perched on a cliff's edge. Potential energy will be transformed into kinetic energy if the rock falls since it will be moving. a longbow with an extended elastic string.
Step by step solution:
Given;
Mass of the pomegranate, m₁ = 0.3 kg
Height of the pomegranate, h₁ = 96 m
Mass of the melon, m₂ = 0.8 kg
Height of the melon, h₂ = 32 m
The gravitational potential energy of pomegranate is calculated as;
P.E₁ = m₁gh₁
P.E₁ = 0.3 x 9.8 x 96
P.E₁ = 282.24 J
The gravitational potential energy of melon is calculated as;
P.E₂ = m₂gh₂
P.E₂ = 0.8 x 9.8 x 32
P.E₂ = 250.88 J
Hence, Pomegranate has a gravitational potential energy of 282.24 J.
Melon has a gravitational potential energy of 250.88 J.
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Review. A global positioning system (GPS) satellite moves in a circular orbit with period 11h 58 min.(a) Determine the radius of its orbit.
The global positioning system (GPS) satellite that moves in a circular orbit with period of 11h 58 min has an orbital radius of: 26.55465166*10^6 m
To solve this problem the orbital radius formula and the procedure we will use is:
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(G* m *T²)/(4 * π²)]
Where:
r = orbital radiusG = Gravitational constantm = Mass of the EarthT = Time period of the satelliteπ = mathematical constantInformation about the problem:
T = 11h 58 minG = 6.67 × 10⁻¹¹ m³/kgs²m= 5.972 × 10²⁴ kgπ = 3.1416r =?By converting the time period of (h) and (min) from (s) we have:
T = (11h *3600 s/ 1 h) + (58 min * 60 s/1 min)
T = 39600 s +3480 s
T = 43080 s
Applying the orbital radius formula we get:
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(G* m *T²)/(4 * π²)]
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][(6.67 × 10⁻¹¹ m³/kgs² * 5.972 × 10²⁴ kg *(43080 s)²)/(4 * (3.1416)²)]
r =[tex]\sqrt[3][/tex][tex]\sqrt[3]{}[/tex][1.8725*10^22 m³]
r= 26.55465166*10^6 m
What is the orbital radius?It is the maximum of the radial distribution curve of the outermost orbital.
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A scientific law seeks to explain why an event occurred.
Answer:
answer explanation
Explanation:
explanation answer
The compounds that make up
plastic are ___________
because they contain carbon and
hydrogen
Answer:
ethylene
Explanation:
ethylene is a compound consist of two double bonded carbon atom and four hydrogen atoms at room temperature is a gas
Answer:
Ethylene
Explanation:
Because Ethylene is a simple molecule composed of two double-bonded carbon atoms and four hydrogen atoms. It's a gas at room temperature. Ethylene molecules can be chemically bonded, end to end, to form a polymer named polyethylene.
An arrow is shot horizontally at 93 m/s, from a height of 0.80 meters. Calculate the amount of time (in seconds) the arrow is in the air. Round to two decimal places.
A uniform magnetic field is directed along the x axis. For what orientation of a flat, rectangular coil is the flux through the rectangle a maximum? (a) It is a maximum in the x y plane. (b) It is a maximum in the x z plane. (c) It is a maximum in the y z plane. (d) The flux has the same nonzero value for all these orientations. (e) The flux is zero in all cases.
It is a maximum in the y z plane
Theoretically, magnetic field lines must traverse the coil's contained space in order for there to be magnetic flux through the coil. In contrast to the x y and x z planes, where the coils are located, the y z plane is where the magnetic field lines pass through.
How does magnetic flux work?The entire magnetic field that traverses a particular area is measured by magnetic flux. It is a helpful tool for explaining how the magnetic force affects things inhabiting a certain area. The precise area selected will determine how magnetic flux is measured.
When the field is perpendicular to the coil's region, the flux is at its highest level. When the x axis is located in the plane of the loop and there is no magnetic field component perpendicular to the loop, the flux is zero.
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Two science teachers challenge each other to a 100m race across the football field.
The loser will grade the winner's science labs for one month. Mrs. Boulware runs the race in 10.40 s. Mrs. Hill runs the first 25.0 m with an average speed of 10.0 m/s, the next 50.0m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of 11.1 m/s. Who gets stuck grading science labs for the next month?
найдем время, за которые Миссис хилл пробежала первые 25 метров :
T= s/v = T1+T2+T3 + .....
T1=25/10=2.5 секунд - 1/4 от всей дистанции. Найдем T2 по такому же принципу:
T2=50/9.5 = 5.3 секундный - заняли у Хилл, чтоб пробежать следующие 50 метров, найдем T3:
T3=25/11.1=2.25 секунд - последние 1/4 от всей дистанции. Найдем общее время:
T= 2.5+5.3+2.25=10.05 секунд
10.05<10.4, следовательно Мисс Булвер ЛУЗЕР.
The molar specific heat of a diatomic gas is measured at constant volume and found to be 29.1 J/mol .K. What are the types of energy that are contributing to the molar specific heat? (a) translation only (b) translation and rotation only (c) translation and vibration only (d) translation, rotation, and vibration
Answer:- b
Explanation:
The temperature of the diatomic atom's environment will vary the contributing kinetic energies for its heat capacity. At 60 K or below, the main contributor of energy is translational energy only. When the temperature rises up to about room temperature to 600 K, the contribution of rotational energy starts to be significant. When the temperature exceeds 3000 K, vibration energy is contributing to the heat capacity of a diatomic gas.
The formula for the specific heat capacity at constant volume is:
where d is for degrees of freedom.
The translational motion contribute 3 degrees of freedom, meanwhile, the rotational and vibrational motion contributes 2 each for the degrees of freedom. Having 29.1 J/mol-K as the molar heat capacity at constant volume, the equation will be:
Having the degrees of freedom = 7 means that d.) translation, rotation, and the vibration is contributing.
Answer: B
M A uniformly charged ring of radius 10.0cm has a total charge of 75.0μC . Find the electric field on the axis of the ring at from the center of the ring.(c) 30.0cm, and
The electric field on the axis of the ring at the center of the ring at 30.0cm is 6.74×〖10〗^6 N/C
Where a positive charge (q) is given, always note that the charges are pointing away from the electric field. The expression used to calculate the electric field away from the center of the ring is given by the equation below,
E=(K_e×b)/(r^3×Q)
Given that;
E = Electric field
Ke = electric field constant
a = radius of the charge q from the center of the circle
Q = electric charge = 75.0μC
The radius of the charge is a = 10cm= 0.1m
Distance from the electric field is 30cm = 0.3m
Ke is a constant given as 8.99×〖10〗^(9 ) Nm^2/c^2
E=(8.99×〖10〗^(9 ) Nm^2/c^2×0.3)/(〖0.1〗^3×75×〖10〗^(-6) )
E=6.39×〖10〗^6N/C
Therefore, the electric field away from the center of the ring is 6.39×〖10〗^6N/C away from the center of the ring
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a vehicle's consists of components that generate and transmit power to the wheels. a. suspension b. fuel system c. power train
The power train is a vehicle's consists of components that generate and transmit power to the wheels.
What do you mean by power train?The collection of all the parts that propel your car forward is called the powertrain. The engine of your car generates power, which the powertrain then transfers to the wheels on the ground. The engine, transmission, driveshaft, axles, and differential are the main parts of a powertrain. A high-performance sports sedan is frequently described as having smooth steering, acceleration, and braking, as well as great body control and improved driving safety. These methods are crucial, but they are not the "end-all" of a great sports car. Its incredible performance figures, such as its ability to accelerate from zero to one hundred kilometers per hour in just seconds, come exclusively from your powertrain.
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The rest energy of an electron is 0.511MeV. The rest energy of a proton is 938MeV. Assume both particles have kinetic energies of 2.00MeV. Find the speed of (b) the proton.
The speed of proton is 0.063c given that the rest energy of an electron is 0.511MeV and the rest energy of a proton is 938MeV, with both particles having kinetic energies of 2.00MeV.
From the data given,
Rest energy of an electron = 0.511MeV
Rest energy of a proton = 938MeV
Kinetic energies (K) = 2.00MeV
Using the equation.
γ=K/E_0 +1 (1)
Where, γ represents the ratio of total energy to the rest energy of the particle
γ=2.00MeV/938MeV+1
γ=0.002+1
γ=1.002
γ can also be derived as shown below;
γ=1/(√1-v^2/c^2)
Making v which is the velocity the subject of formula we get;
γ^2=1/(1-v^2/c^2) by squaring both sides
Simplifying it we get;
1/γ^2 =1-v^2/c^2
v^2/c^2 =1-1/γ^2
v/c=√1-1/γ^2
v=√1-1/γ^2 ×c (2)
Putting the values into equation 2 we have;
v=√1-1/〖1.002〗^2 ×c
v=√1-0.996×c
v=√0.004×c
v=0.063×c
v=0.063c
The speed of proton is 0.063c.
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If two objects have the same mass which is more
dense?
Answer: If two objects have the same mass but have different sizes, the object with the greatest density will be the smaller of the two objects. Using an example of two cubes.
Explanation:
Answer:
the smaller of the two objects
Explanation:
If two objects have the same mass but have different sizes, the object with the greatest density will be the smaller of the two objects.
Chemical molecules called ___________ are released at the end of the __________, which allows the neuron to communicate with other neurons.
Chemical molecules called neurotransmitters are released at the end of the synaptic junction, which allows the neuron to communicate with other neurons.
In the human body, neurotransmitters are chemical messengers that convey information between neurons.
The main function of these transmitters is to pass on electrical signals from nerve cells to other cells of the body including nerves, muscles, and glands.
Neurotransmitters are the major constituents of the nervous system and play a significant role in communication among different organs.
Moreover, they are also crucial for human development and growth.
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use the drop-down menu to complete the statement. the production of an electric current by a changing magnetic field is known as .
The production of an electric current by a changing magnetic field is known as electromagnetic induction.
The phenomenon when the current is produced due to changing magnetic field is given by Faraday.
And this phenomenon is called the electro-magnetic induction or magnetic induction since the electricity is generated due to the fluctuations or variance in the magnetic field.
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Answer:
electromagnetic induction
Explanation:
How are variations passed on from one generation to the next
Answer:
Inheritance
Explanation:
Passing of genetic material to offspring over the next generations
When two tuning forks are sounded at the same time, a beat frequency of 5 Hz occurs. If one of the tuning forks has a frequency of 245Hz, what is the frequency of the other tuning fork?(a) 240 Hz (b) 242.5 Hz (c) 247.5 Hz (d) 250 Hz (e) More than one answer could be correct.
The frequency of other tuning fork can be 240Hz or 250Hz and hence more than one option is correct
A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.
Given that one tuning fork has a frequency of 245Hz
Additionally, it is stated that a 5 Hz is the beat frequency.
We know the beat frequency formula
[tex]f_ {beat}[/tex] = [tex]f_{2}[/tex] -[tex]f_{1}[/tex]
Suppose that the first tuning fork's frequency is equal to [tex]f_{1}[/tex], then
CASE 1:
5= 245- [tex]f_{2}[/tex]
[tex]f_{2}[/tex] =245+5
[tex]f_{2}[/tex] =250 Hz
CASE 2 :
5= 245 + [tex]f_{2}[/tex]
[tex]f_{2}[/tex] =245-5
[tex]f_{2}[/tex] =240 Hz
Hence there is more than one option is correct in the given question
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An object of mass “15kg” is in free fall in a vacuum where there is no resistance determine the acceleration of the object
An object of mass “15kg” is in free fall in a vacuum where there is no resistance determine the acceleration of the object -9.8 m/s^2
An object of mass “15kg” is in free fall in a vacuum where there is no resistance
During a free fall motion an object acquires acceleration
a = g ( gravity)
a = 9.8 m/s^2
whilst an item dropped in air that experiences no air resistance is stated to be in free fall motionwhen an item is in unfastened fall, the simplest force appearing on the object is gravity.A loose fall with equal acceleration, internet force acting on them is weight, their weight-to-mass ratios are constantly the identical, their acceleration is g, and the acceleration because of gravity.To know more about free fall motion visit :
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For most of history, the lack of observable stellar parallax was interpreted to mean that.
Answer:For most of history, the lack of observable stellar parallax was interpreted to mean that: Earth is stationary at the center of the Universe.
Explanation:
100 points
National Park rangers create public announcements to help prevent accidental wildfires from start. Which is a simple way that accidental wildfires can be prevented in these parks?(1 point)
Ensure people do not have unattended cooking fires while camping.
Ensure people do not create defensible spaces.
Prevent people from thinning dead trees.
Prevent rangers from setting controlled burns.
It is possible to avoid the spread of accidental wildfires in parks when we stop rangers from initiating a burn that is controlled. Option D
What is a wildfire?The term wild fire refers to fires that burn uncontrollably. There are some factors that could lead to the beginning of wild fires. One of the several ways that we could have the emergence of a wild fire is if a fire is set up and then is left unattended.
The effects of this wild fire could be so devastating that large buildings as well as large habitats where organisms live could become permanently damaged from the raging of the wild fire and could now amount to a tremendous damage as well as the loss of biodiversity in the ecosystem.
Thus, It is possible to avoid the spread of accidental wildfires in parks when we stop rangers from initiating a burn that is controlled.
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In the lab, a student is investigating the effects of texting and driving on reaction time. A student determines his/her reaction time by having a friend release a meter stick at random intervals while the driver sends text messages. The student, on average, catches the meter stick after it has traveled 0.64 m.
How far will the student travel in a car moving at 25 m/s horizontally before reacting?
The distance traveled by the student in a car is 9 m.
Reaction time of the student
The reaction time of the student is the time of motion of the meter stick and it is calculated as follows;
t = √(2h/g)
where;
h is the height traveled by the meter stickg is acceleration due to gravityt = √(2 x 0.64/9.8)
t = 0.36 seconds
Distance traveled by the student in a carx = vt
where;
v is the velocity of the cart is the time of motionx = 25 m/s x 0.36 seconds
x = 9 m
Thus, the distance traveled by the student in a car is 9 m.
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a 6.96 nc charge is located 1.82 m from a 4.02 nc point charge. (a) find the magnitude of the electrostatic force that one charge exerts on the other. n (b) is the force attractive or repulsive? attractive repulsive
The electric force is 7.60 x 10¯⁸ N.
We need to know about the electrostatic force to solve this problem. The electrostatic force produced by charges interacting each other, whose strength is given by the equation
F = k.Q1 . Q2/r²
where F is the electrostatic force, Q1 and Q2 is the charge and r is the radius.
From the question above, we know that
k = 9 x 10⁹ Nm²/C²
Q1 =e = 6.96 x 10¯⁹ C
Q2 = e = 4.02 x 10¯⁹ C
r = 1.82 m
The electrostatic force will attract each other when the charges are different and will repel each other when the charges are same.
F = k.Q1 . Q2/r²
F = 9 x 10⁹ . 6.96 x 10¯⁹ . 4.02 x 10¯⁹/1.82²
F = 7.60 x 10¯⁸ N
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think about some of the things physicists have done or discovered. what is something that you would like to see a physicist develop in the future?
In the near future, I hope that physicists will work on the following theories:
A theory for superconductors that operate at high temperatures, like YBCO.
A stochastic Monte Carlo approach, such as the wave function of interacting electrons in alkali metals, that can handle multiple identical fermions.
A hypothesis for iron superconductors, such as FeSe surface layers on a substrate.
A hypothesis explaining dark matter.
What is the future in physics?I believe environmental issues will have a greater impact on physics. Cleaner and greener lab equipment will be used in science. The particle-accelerator laboratories that once took pride in bragging about how much electricity they used to run collision tests will either have to be more discreet or, even better, prioritize energy-saving solutions. Air travel will become less acceptable as the effects of climate change worsen, making it more difficult for physicists on the go to defend their conference flights.
The field of medical physics will keep growing, with new imaging technologies and better radiotherapy procedures. NASA's James Webb Space Telescope should finally take off in astronomy.
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if blinded by an approaching motor vehicle at night, it is best to: stop dim your lights and continue at the same speed slow down and avoid looking directly into the lights of the approaching vehicle leave your lights on bright to offset the glare submit answer
If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.
What is a Vehicle?This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.
In a situation whereby an individual is blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.
This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.
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Trucks carrying garbage to the town dump form a nearly steady procession on a country road, all traveling at 19.7 m/s in the same direction. Two trucks arrive at the dump every 3 min. A bicyclist is also traveling toward the dump, at 4.47 m/s.(a) With what frequency do the trucks pass the cyclist?
The truck passes the cyclist with a frequency of 8.59×10⁻³Hz.
What do you mean by frequency?In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.
According to the question:
Using Doppler effects:
f' = (v+v₀/v-v₁)f
v₀ is the speed of the observer.
v₁ is the speed of the source.
v is the speed of sound in the medium.
Given:
v, speed of truck = 19.7m/s
f, frequency = 1/90Hz
v₀, speed of cyclist = 4.47m/s
v₁, speed of wave from a stationary source.
Putting in the equation:
f' = 8.59×10⁻³ Hz.
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can a car moving towards right have acceleration towards left?
Answer:
Yes it is possible to have acceleration opposing direction of velocity
Explanation:
1) when you brake the car , the velocity will decrease making the the acceleration to decrease ,it is called decelerating
2) if you imagine the effect of a resistive force or a frictional force than the acceleration is in opposite direction is possible.
Review. A proton is at rest at the plane boundary of a region containing a uniform magnetic field B (Fig. P29.59). An alpha particle moving horizontally makes a head-on elastic collision with the proton. Immediately after the collision, both particles enter the magnetic field, moving perpendicular to the direction of the field. The radius of the proton's trajectory is R . The mass of the alpha particle is four times that of the proton, and its charge is twice that of the proton. Find the radius of the alpha particle's trajectory.
The radius of the alpha particle's trajectory is [tex]r_{\alpha } =\frac{3}{4} (R(proton))[/tex].
What is trajectory?The journey through space and time taken by a mass-moving object is referred to as its trajectory or flight path. Since a trajectory is determined by Hamiltonian mechanics using canonical coordinates, a full trajectory in classical mechanics is defined by position and momentum simultaneously.
A satellite or a missile could represent the mass. For example, a planet, asteroid, or comet moves around a major body in a path called an orbit.
A projectile's trajectory, such as that of a ball or rock thrown, is a well-known example of a trajectory. In a greatly simplified model, an object only moves when it experiences a constant gravitational force field.
Calculations:
Since, the collision is elastic:
Therefore, momentum will be conserved.
Which means: [tex]m_{p}.v_{p} + m_{\alpha}.v_{\alpha } = m_{\alpha } . v_{0} +m_{p} .v_{po}[/tex]
[tex]m_{p}.v_{p} + m_{\alpha}.v_{\alpha } = m_{\alpha } . v_{0} ......(i)[/tex]
Similarly, for elastic collision:
Additionally conserved is kinetic energy:[tex]KE_{f}[/tex][tex]=KE_{I}[/tex]
=1/2 [tex]m_{p}[/tex][tex]v_{p} ^{2}[/tex]+[tex]1/2 m_{\alpha }.v_{\alpha } ^{2}[/tex]=[tex]1/2m_{\alpha } v_{0} ^{2}[/tex]
For head on collision: ([tex]v_{0} -v_{p0}[/tex])=[tex](v_{\alpha } - v_{p} )[/tex]
[tex]v_{\alpha } +v^{0} =v_{p}[/tex].......(ii)
and,[tex]m_{\alpha } =4m_{p}[/tex].....(iii)
therefore equation(i) becomes.
[tex]5v_{\alpha } =3v_{0} \\v_{\alpha } =\frac{3}{5} v_{0} \\[/tex].......(iv)
From equation (ii) and (iv) [tex]v_{p} = \frac{3}{5} v_{0} +v_{0} =\frac{8}{5} v_{0}[/tex].......(v)
From equation (iv) and (v) [tex]\frac{v_{p} }{v_{\alpha } } =\frac{8}{3}[/tex]
Since, [tex]r=\frac{mv}{qB}[/tex]
R(proton)=[tex]\frac{m_{p} v_{p} }{eB}[/tex]
[tex]r_{\alpha } =\frac{3}{4} (\frac{m_{p}v_{p} }{eB } )[/tex]
[tex]r_{\alpha } =\frac{3}{4} (R(proton))[/tex]
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A = 5 m/s N, B = 7 m/s at -25 degrees, C = 3 m/s N of W at 45 degrees
Find the resultant vector.
The resultant vector will be 29.5° E of N.
A = 5 m/s
B = 7 m/s at 25° NE
C = 3 m/s at 45° NW
To find the resultant vector for these given vectors,
first we need to resolve the vector B and C into X and Y direction respectively.
On resolution, vector gets distributed into its X-axis and Y-axis components.
Vector B has BCos25° as its X component and BSin25° as its Y component
Similarly, Vector C has CCos45° ac its X-axis component and CSin45° as its Y-axis component.
Now, the algebraic sum of the resolved parts of a series of forces in a particular direction is equal to the resolved part of their resultant in the same direction.
Σ along X-axis
= 5 + BCos25° - CCos45°
= 5 + 7(0.92) - 3(0.76)
= 5 + 6.44 - 2.28
Fx = 9.16 m/s
Σ along Y-axis
= BSin25° + CSin45°
= 7(0.38) + 3(0.64)
= 2.66 + 1.92
Fy = 4.58 m/s
The direction of the resultant vector is given by calculating Tan[tex]\alpha[/tex]
Here Tan[tex]\alpha[/tex] = [tex]\frac{P}{B\\}[/tex]
Tan[tex]\alpha[/tex] = [tex]\frac{4.58}{9.16}[/tex]
Tan[tex]\alpha[/tex] = 0.5
[tex]\alpha[/tex] = Tan⁻¹(0.5)
[tex]\alpha \\[/tex] = 29.5° with the X-axis
Magnitude of the resultant vector can be calculated by
= [tex]\sqrt{Fx^{2} +Fy^{2} +FxFyCos\alpha }[/tex]
= [tex]\sqrt{9.16^{2} +4.58^{2}+ 9.16*4.58*Cos29.5 }[/tex]
= 11.93 m/s
Therefore the resultant vector will be having 11.93 m/s as magnitude directing 29.5° from East to North.
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