(a) Total force along y axis,
∑F =ma=0
kx−mg=0 ⇒k= [tex]\frac{mg}{x}[/tex]
The spring constant is, k is
k=(1.5)×(9.8)/(0.020)=14.7/0.020 =735N/m
(b) Frequency f = [tex]\frac{1}{2} \pi[/tex] [tex]\sqrt{\frac{k}{m} }[/tex] ⇒ 4[tex]\pi ^{2}[/tex][tex]f^{2}[/tex] = [tex]\frac{k}{m}[/tex]
[tex]\frac{k}{4\pi ^{2}f^{2} }[/tex]= m ⇒ m = (735)4[tex]\pi ^{2}[/tex](3.0)(0.3)
=(735)×4×(3.75)×(3.75)×(9.0)
=735×4×9.85×9.0=7354×9.85×9.0
=735354.6 N
=2.07kg
The spring constant is the force required to stretch or compress the spring divided by the distance the spring is lengthened or shortened. It is used to determine the stability or instability of a spring and thus the system for which it is intended. It is denoted by k.
Therefore the spring constant is 735 N/m and the mass should be 2.07kg.
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Q|C Spherical waves of wavelength 45.0cm propagate outward from a point source. (b) Explain how the amplitude at a distance of 240cm compares with the amplitude at a distance of 60.0cm.
The difference between the amplitude at a distance of 60.0 cm and 240 cm is I240 = 16×I60
A240=4×I60
Δ∅240=4.Δ∅60
We are given distance of the center of the source for two waves:
D1=240 cm
D2=60.0 cm
b) Calculating how their amplitude compares:
[tex]A_{240} =\sqrt{\frac{I_{240} }{I_{60} } } .A_{60}[/tex]
[tex]=\sqrt{16} .A_{60}[/tex]
[tex]A_{240} = 4. A_{60}[/tex]
How can you determine a wave's phase?
The period, or length of each cycle, is determined by dividing the frequency by 1, so 1/100 corresponds to a period of 0.01 seconds. The phase shift equation is given by ps = 360 * td / p, where td is the time interval between waves, p is the wave period, and ps is the phase shift in degrees.
Phase: The "Phase" of a waveform refers to the location of the moving particle and is expressed in "Radians or degrees."
Phase difference, also known as "Phase angle," is the amount of time that one wave precedes or follows another.
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A scientific law seeks to explain why an event occurred.
Answer:
answer explanation
Explanation:
explanation answer
Suppose you are transported to a planet with twice the mass of earth, but the same radius of earth. Your weight would __________ by a factor of __________.
According to gravitational force, the weight would be greater by a factor of 2.
We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as
F = G.m1.m2 / R²
where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.
From the question above, we know that
m1 = m
m2 = 2m1 = 2m
R1 = R2 = R
Gravitational force is proportional to mass
F1 ~ M
Hence, the ratio of weight is
F2 / F1 = m2 / m1
F2 / F1 = 2m / m
F2 / F1 = 2
Hence, the weight would be greater by factor of 2 .
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A ball starts from rest and rolls down a 5.0m long frictionless ramp. It accelerates at 3.5m/s^. when it reaches the bottom, it rolls across a frictionless horizontal surface at a constant speed for an additional 3.0 s before striking a wall. what is the total distance travelled by the ball
Using uniform motion equation , the total distance travelled by the ball is 22.74m.
It is known as uniform motion when an object moves in a straight path at a constant speed. This indicates that the body's velocity stays constant as it travels the same distance in the same amount of time. The body will not accelerate in the case of uniform rectilinear motion. In this case, the object's average speed will be equal to its real speed.
Using equation of motion ;
[tex]s = ut +\frac{1}{2} at^{2}[/tex]
plugging in the values we get:
s = 22.74m
Therefore, using uniform motion equation , the total distance travelled by the ball is 22.74m.
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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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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
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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If a signal can travel in a cable at 80% of the speed of light, what length of cable, in inches, represents 1 ns?
According to a signal velocity, the cable length is 9.45 inches.
We need to know about the velocity to solve this problem. The velocity can be determined as the total distance divided by the total time. It can be written as
v = d / t
where v is velocity, d is distance and t is time.
From the question above, we know that
v = 80%c = 0.8c = 2.4 x 10⁸ m/s
t = 1 ns = 1 x 10¯⁹ s
The length of cable can be represented by the distance
v = d / t
d = v . t
d = 2.4 x 10⁸ . 1 x 10¯⁹
d = 0.24 m
Convert to inches (1m = 39.37 inches)
d = 0.24 m
d = 0.24 x 39.37 inches
d = 9.45 inches
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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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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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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.
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.
Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value
is 161.4 degrees Celcius.
The melting point of salicylic acid is known very well as 158.6 degrees Celcius.
What is Bubba's percent error?
Bubba-Joe carries out a careful investigation to determine the melting point of salicylic acid, and concludes that the value is 161.4 degrees Celsius. The melting point of salicylic acid is known very well as 158.6 degrees Celsius. Bubba's percent error will be 1.74 %
Percentage error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
estimated value of melting point = 161.4 °C
true value of melting point = 158.6 °C
percent error = ((true value - expected value) / expected value) * 100
= ((158.6 - 161.4 ) / 161.4 ) * 100
= 1.74 %
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Because most particles fired at metal foil passed straight through, rutherford concluded that.
Answer:
Rutherford deduced that atoms were mostly empty space
Explanation:
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:
How long would it take a 1000W heater to melt 1.00kg of ice at -20.0°C, assuming all the energy from the heater is absorbed by the ice? (a) 4.18 s(b) 41.8 s (c) 5.55 min (d) 6.25min(e) 38.4min
Answer:
Heat for -20 to zero = .48 * 1000 = 480 calories
Heat to melt ice = 1000 * 79.7 = 79700 calories
Total calories required = 80,200 calories
80,200 cal * 4.19 J/cal = 336,000 J
336000 J / 1000 J/sec = 336 sec
336 sec / 60 sec/min = 5.6 min
(c - 5.55 min)
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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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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S The intensity of a sound wave at a fixed distance from a speaker vibrating at a frequency f is I . (b) Calculate the intensity if the frequency is reduced to f / 2 and the displacement amplitude is doubled.
The intensity if the frequency is reduced from f to f / 2 and the displacement amplitude doubled is I.
What do you mean by frequency?The frequency of a repeated event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is stated. The period is the reciprocal of the frequency since it is the length of time for one cycle in a repeating occurrence. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).
I=P/4πr²
Given:
Initial frequency, f = f
Initial Intensity, I = I
Final Frequency, [tex]f^{'}=\frac{f}{2}[/tex]
We know that, The intensity of the speaker is,
[tex]I = \frac{1}{2}\rho \omega^{2}S_{max} ^{2}v[/tex]
Substitute the [tex]\omega[/tex] value in the above equation,
[tex]I = \frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v\;\;\;\;-----equation(1)[/tex]
Therefore, Final intensity of the speaker is,
[tex]I^{'} = \frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v\;\;\;\;-----equation(2)[/tex]
By dividing the equation (1) and (2), We get
[tex]\frac{I}{I^{'}} = \frac{\frac{1}{2}\rho (2\pi f)^{2}S_{max} ^{2}v}{\frac{1}{2}\rho (2\pi f^{'} )^{2}S_{max} ^{2}v}[/tex]
By taking constant parameters in to account, We get,
[tex]\frac{I}{I^{'}} = \frac{(f)^{2}(S_{max}) ^{2}}{(f^{'} )^{2}(S_{max} )^{2}}[/tex]
By solving the above equation, We get
[tex]\frac{I}{I^{'}} = \frac{(f)^{2}}{4(f^{'} )^{2}}[/tex]
Substitute the final intensity value in the above equation,
[tex]I^{'} = I[\frac{4(\frac{f}{2})^{2}}{f^{2} }][/tex]
By solving the above equation, We get,
[tex]I^{'} = I[/tex]
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how much work is done while pushing a box mass of 35kg at a distance of 20m?
Answer: 6867 N.m
Explanation:
Work Done= (35*9.81)*20 = 6867 N.m
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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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.
What is the difference between “q” and “Q” in physics?
Answer:
Big Q represents the source charge which creates the electric field. Little q represents the test charge which is used to measure the strength of the electric field at a given location surrounding the source charge.
The source charge, or Big Q, is what generates the electric field. Little q stands for the test charge, that is used to gauge the intensity of the electromagnetic field around the source charge at a certain position.
What is electric charge?Charged material experiences a force when it is exposed to an electromagnetic field because of the physical characteristic of electric charge.
You can have a positive or negative electric charge. Unlike charges attract one another, while like charges repel one another. Neutral refers to an object that carries no net charge.
Classical electrodynamics, the name given to early understanding of how charged particles interact, is still accurate for issues that do not call for taking into account quantum phenomena.
Electric current is a conserved attribute, meaning that the net charge—that is, the sum of the positive and negative charges in an isolated system—cannot change.
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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.
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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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
A particle's location is measured and specified as being exactly at x = 0 , with zero uncertainty in the x direction. How does that location affect the uncertainty of its velocity component in the y direction? (a) It does not affect it. (b) It makes it infinite. (c) It makes it zero.
It does not affect the uncertainty of the velocity component in the y direction.
Any of a number of mathematical inequalities known as the uncertainty principle establishes a fundamental upper bound on the precision with which initial conditions can be used to forecast the values of some pairs of physical properties of a particle, such as location and momentum.
The measured and stated location of a particle is at x = 0 with zero uncertainty in the x direction.
According to the uncertainty principle, positional and velocity uncertainty are related along the same axis. The velocity component's x-directional component is infinitely uncertain due to the zero uncertainty in location along the x-axis, while the y-directional component is unaffected.
The correct option is (a).
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Which equation is perpendicular to the line
(1901
y = 3 and passes through the point (- 1, 3).
a. x = 3
b. y = 3
c. y = -1
d. X = -1
The equation perpendicular to the line is y=3.
The slope of the line [tex]$3 x+y=3$[/tex] is [tex]$m=-3$[/tex]
Hence slope of the perpendicular line is [tex]$\mathrm{m}^{\prime}=\frac{1}{3}$[/tex]
Therefore the equation of a perpendicular line is
Therefore the equation of a perpendicular line is
[tex]$(\mathrm{y}+1)=\frac{1}{3}(\mathrm{x}-3) $[/tex]
[tex](y+3)=\frac{1}{3}(x-1)[/tex]
Switch sides
[tex]\frac{1}{3}(x-1)=(y+3)[/tex]
[tex]$\frac{1}{3}(x-1)=y+3$[/tex]
Multiply both sides by 3
[tex]$3 \cdot \frac{1}{3}(x-1)=3 y+3 \cdot 3$[/tex]
Simplify
[tex]$x-1=3 y+9$[/tex]
Add 1 to both sides
[tex]$$x-1+1=3 y+9+1$$[/tex]
Simplify
[tex]$$x=3 y+10$$[/tex]
y= 3.33 (Approx 3)
The two different lines that cross each other at a 90° angle are called perpendicular lines. Have you observed any similarities between the walls' intersecting corners, such as the letter "L"? They are parallel lines, which are straight lines that cross each other at the proper angle.
If two lines cross at a 90° angle, we say that they are perpendicular to one another.
the vertex's matching angle is a right angle. All crossing lines are not necessarily perpendicular to one another, but perpendicular lines always cross each other. Perpendicular lines have two key characteristics.
In every case, perpendicular lines cross or intersect.
Any two perpendicular lines will always intersect at an angle of 90 degrees.
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The highest speed achieved by a standard non racing sports car is 3.60 x 10² km/h. Assuming that the car accelerates at a constant rate to reach this maximum speed for 25.0 s and covers a distance of 1.50 km while accelerating, what was the initial velocity of the car?
The car has a constant acceleration of 1.95m/s2 and reaches a top speed of 41.0m/s. The boat has a constant acceleration of 6.50m/s2 .
What is acceleration ?When it comes to mechanics, acceleration refers to how quickly an object's velocity changes over time. Acceleration is a vector quantity (in that they have magnitude and direction). The direction of the net force acting on an item determines its acceleration.
According to Newton's Second Law, an object's acceleration is a sum of two factors:
The size of the net balance of all external forces acting on that thing is directly proportional to the net resultant force; the magnitude of the object's mass, depending on the materials from which it was created, is inversely related to the mass.
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Once its rockets have ceased firing, an intercontinental ballistic missile will follow a path that is best described as.
Once its rockets have ceased firing, an Intercontinental Ballistic Missile will follow a path that is best described as an ellipse with the center of the Earth at one focus.
As the ellipse is the set of points, on a plane whose distance from two fixed points sums up to constant, in That describes all free-fall paths near Earth, it got The Major Axis which is the longest diameter and the widest part of the ellipse it basically starts from one side of the ellipse crossing the center to the other side and the Minor Axis which is the shortest diameter and present at the narrowest part of the ellipse.As the ellipse explains all free-fall paths near Earth (free-fall is referred to as the acceleration of objects toward the Earth when dropped at rest)
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