The Taylorsville Volunteer Organization participating in the community is the subject of a key motion.
What is motion?The motion of an object is the change in its position over time. It can be measured in speed, velocity, and acceleration. Speed is how fast an object is moving, velocity is speed in a particular direction, and acceleration is the rate of change of velocity. Motion can be linear, circular, or oscillatory. Linear motion is the movement of an object in a straight line, circular motion is the movement of an object in a circle, and oscillatory motion is the movement of an object back and forth. Motion can also be described in terms of forces like gravity, friction, and momentum.
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If there is no change in the velocity of the object then it is known to be in ______
a) constant speed
b) uniform acceleration
c) uniform motion
d) non-uniform motion
OPTION (C) IS CORRECT
ANSWER - UNIFORM MOTION
If there is no change in the velocity of the object then it is known to be in UNIFORM MOTION.
EXPLORE MORE:-
EXAMPLE - A CAR COVERS A DISTANCE OF 15 KM WE'D EVERY 2 HOURS
FOR AN UNIFORM MOTION, ACCELERATION IS ZERO , AS THERE IS NO CHANGE IN VELOCITY....
-THANKS.!!
(10%) Problem 2: The frequency range for AM radio is 540 to 1600 kHz. The frequency range for FM radio is 88.0 to 108 MHz.
188m - 556m is the wavelength range for AM radio.
2.77 - 3.40m is the wavelength range for FM radio.
1) For AM radio
f(max) = 1600 × 10³ Hz
f(min) = 540 ×10³Hz
c = fλ
λ = c/f where,
c = speed of light
f = frequency
λ= wavelength
So,
λ(min) = 3 × [tex]10^{8}[/tex] / 1600 × 10³ = 188 m
λ(max) = 3 × 10⁸/540 ×10³ = 556 m
So wavelength range of AM radio is 188 m - 556m
2) For FM radio
f(max) = 108 × 10⁶ Hz
f(min) = 88 × 10⁶ Hz
λ(min) = 3 × 10⁸ / 108 × 10⁶ = 2.77 m
λ(max) = 3 × 10⁸ / 88 × 10⁶ = 3.40 m
So wavelength range of FM radio is 2.77m - 3.40m
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An electron moving through an electric field is observed to have an acceleration of 1.20 1016 m/s2 in the x direction. What is the magnitude and the direction of the electric field that produces this acceleration
The magnitude is 5.69 × 10^4 N/C and the direction is opposite to the acceleration of electron.
Equation of force on a charge is -
F = ma
→ qE = ma
The acceleration of an electron is 1.201016 m/s².
→ E = ma/q
plug in the values
E = 9.11 × 10^-31 kg × 1×10^16 m/s² i / -1.6 × 10^-19 C
E = 5.69 × 10^4 N/C (-i)
so, magnitude is 5.69 × 10^4 N/C and field is along negative x-axis
Thus, it has opposite direction to the acceleration of electron.
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A sound wave traveling through dry air has a frequency of 16 hz, a
wavelength of 22 m, and a speed of 350 m/s. when the sound wave passes
through a cloud of methane, its wavelength changes to 28 m, while its
frequency remains the same. what is its new speed? (the equation for the
speed of a wave is v= f * 1.)
Answer:
[tex]\huge\boxed{\sf v = 448\ m/s}[/tex]
Explanation:
Given data:Frequency = f = 16 Hz
Wavelength = λ = 28 m
Required:Speed = v = ?
Formula:v = fλ
Solution:Put the givens.
v = (16)(28)
v = 448 m/s
[tex]\rule[225]{225}{2}[/tex]
A bowling ball accidentally falls out of the cargo bay of an airliner as it flies along in a horizontal direction. As seen from the ground, which path would the bowling ball most closely follow after leaving the airplane?
The path the bowling ball would most closely follow after leaving the airplane is horizontal direction.
Path of the bowling ball
Based on the law of inertia, which is the reluctance of an object to stop moving once in motion or start moving when it is at rest.
The bowling ball will maintain the path of the airline in the first few seconds of fall, after which it will change its path to vertical direction.
Thus, the path the bowling ball would most closely follow after leaving the airplane is horizontal direction.
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A box of mass 8 kg slides across a frictionless surface at an initial speed 1.5 m/s into a relaxed spring of spring constant 69 N/m.
Time for which box will remain in contact with spring is 1.1 sec
Given:
mass of box = 8 kg
initial speed of box = 1.5 m/s
spring constant = 69 N/m
To Find:
time for which box will remain in contact with spring
Solution: The time taken to complete one oscillation is called the time period. where m is the mass, and k is the spring constant.
Time period is given as
t = π √m/k
t = 3.14 √8/69
t = 1.1 sec
So time for which box will remain in contact with spring is 1.1 sec
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How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 26.0 cm in diameter to produce an electric field of 1440 N/C just outside the surface of the sphere
a metaphor for generosity and joy and joy and joy and joy organised a large wedding guests had to choose their meal from beef chicken tikka and a kind young women in the streets of St
The number of excess electrons needed to be distributed uniformly in the sphere to produce the given electric field is 1.69*10^(10).
What is an electric field?
The electric force exerted on a unit charge is called the electric field.
For a sphere of uniform charge density, the magnitude of the electric field on its surface is given by,
E=k*q/r^2
where E is the magnitude of the electric field, k is the coulomb's constant which has a value of 9*10^9 N m^(2) C^(-2), and q is the total charge of the sphere, and r is the radius of the sphere.
The radius of the sphere is half of the diameter. Given the diameter of the sphere is 26.0 m, the radius of the sphere r=26.0/2 cm or r=13.0 cm.
It is given that E=1440 N/C, r=13.0 cm, and the value of k is 9*10^9 N m^(2) C^(-2). Substitute these values in the formula of the electric field and solve it to get the value of the total charge on the sphere.
Note: 1 cm = 0.01 m.
1440 (N/C)= (9*10^9 N m^(2) C^(-2))*q/( 13 cm)^2
1440 (N/C)= (9*10^9 N m^(2) C^(-2))*q/( 13*0.01 m)^2
1440 ( N/C)= (532.54*10^(9) N C^(-2))*q
q=1440/(532.54*10^(9)) C
q=2.704*10^(-9) C
Since the charge is quantized, the total charge inside the sphere is the integral multiple of an elementary charge. In the given case, the value of that elementary charge is 1.6*10^(-19) C. The total charge is then given by,
q=ne
where q is the total charge, n is the number of elementary charges and e is the value of the elementary charge.
The value of q is 2.704*10^(-9) C and the value of e is 1.6*10^(-19) C.
Substitute these values in the formula of total charge and solve it to get the number of elementary charges.
2.704*10^(-9) C =n*1.6*10^(-19) C
n=2.704*10^(-9)/ 1.6*10^(-19)
n=1.69*10^(10)
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A laser is shone through a double slit and a particular interference pattern is observed on a screen some distance away. If the separation between the openings is increased, the distance between the fringes will
If the separation between the openings in a laser is increased, then the distance between the interference fringes decreases
What is Interference fringe ?Interference fringe refers to bands caused by different lights which can be found in phase or not each other.
Distances between laser fringes are short which is due to light wavelength.The interference fringes can be estimated by knowing slit separation and wavelength.In conclusion, if the separation between the openings in a laser is increased, then the distance between the interference fringe decreases
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A 2. 0mc charge in an external field of 20n/c, north (direction) will experience a force of: ___0. 04____________ newtons, the direction of the force is __north___________
2. 0 mc charge in an external field of 20n/c, north (direction) will experience a force of 0.4 newtons, the direction of the force is north
Force in an electric field = charge * electric field
given
charge = 2* [tex]10^{-3}[/tex] C
electric field = 20 N/C
Force in an electric field = 2* [tex]10^{-3}[/tex] * 20
= 0.04 N
since , external field is in north direction then the force must be in north direction because the direction of an electric field at a point is the same as the direction of the electric force acting on a positive test charge
hence, 2. 0 mc charge in an external field of 20n/c, north (direction) will experience a force of 0.4 newtons, the direction of the force is north
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An 80-N crate is pushed a distance of 5.0 m upward along a smooth incline that makes an angle of 30o with the horizontal. The force pushing the crate is parallel to the slope. If the speed of the crate increases at a rate of 1.5 m/s2, find the work done by the force. Group of answer choices 260 J 200 J 1 J 200 kJ 140 J
The work done by the force is 140 J.
Calculation:
It is given that, an 80-N crate is pushed a distance of 5.0 m upward along a smooth incline that makes an angle of [tex]30^\circ[/tex] with the horizontal. The force pushing the crate is parallel to the slope and the acceleration is 1.5 [tex]\text{ m/s}^2[/tex].
It is required to find the work done by the force.
The free-body diagram is shown below,
Here, W=80 N, a=-1.5 [tex]\text{ m/s}^2[/tex]
We can write the net force equation as,
[tex]\begin{gathered}F-W \sin 30^{\circ}=m a \\F-m g \sin 30^{\circ}=\left(\frac{W}{g}\right) a\end{gathered}[/tex]
Here W is the weight of the object, m is the mass of the body, and F is the applied force.
Thus,
[tex]\begin{aligned}F-(80 \mathrm{~N}) \sin 30^{\circ} &=\left(\frac{80 \mathrm{~N}}{9.8 \mathrm{~m} / \mathrm{s}^{2}}\right)\left(-1.5 \mathrm{~m} / \mathrm{s}^{2}\right) \\F &=27.755 \mathrm{~N}\end{aligned}[/tex]
It is known that the work done by the force is calculated as the multiplication of the applied force and the displacement.
Thus the work one is,
[tex]\begin{aligned}W &=(27.755 \mathrm{~N})(5 \mathrm{~m}) \\& \approx 140 \mathrm{~J}\end{aligned}[/tex]
Thus the last option is the correct one.
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A radar receiver indicates that a pulse return as an echo in 20 μs after it was sent. How far away is the reflecting object? (c = 3.0 × 10^8 m/s)
A radar receiver indicates that a pulse return as an echo in 20 μs after it was sent. The reflecting object would be 3000 m away .
Phenomenon of hearing back our own sound is called an echo. It is due to successive reflection of sound waves from the surfaces or obstacles of large size. To hear an echo, there must be a time gap of 0.1 second in original sound and the reflected sound.
Given
time = 20 μs = 20 * [tex]10^{-6}[/tex] s
let distance to the reflecting surface be = x
total distance travelled by pulse will be = 2x
speed = 3.0 × [tex]10^{8}[/tex] m/s
distance = speed * time
2x = 3.0 × [tex]10^{8}[/tex] * 20 * [tex]10^{-6}[/tex]
x = 3000 m
The reflecting object would be 3000 m away
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Medical applications of ultrasound use frequencies up to 2.00 × 10^7 hz. What is the wavelength of this frequency in 20 °c air?
The wavelength of the ultrasound wave in 20 °c air is 1.715 * 10⁻⁵ m.
What is the relationship between wavelength and frequency of a wave?The frequency of sound is the number of complete oscillations per second.
The wavelength is the distance between successive positions in the wave.
Velocity of sound is the distance covered per second.
The frequency and wavelength of a wave are related by the formula given below:
Velocity = frequency * wavelengthThe velocity of sound in 20°C air = 343 m/s
frequency of the sound wave = 2.00 × 10⁷ hz or 2.00 × 10⁷ s⁻¹
wavelength = velocity/frequency
wavelength = 343 / 2.00 × 10⁷
wavelength = 1.715 * 10⁻⁵ m
In conclusion, the wavelength of the ultrasound wave is determined from the ratio of the velocity and the frequency of the sound.
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In the absence of a strong magnetic field), what is the chief factor that determines what type of electromagnetic radiation objects give off:____.
The chief factor that determines what type of electromagnetic radiation that objects give off in the absence of a strong magnetic field is their temperature.
What is the radioactive activity?The radioactive activity refers to the energy that a atomic nucleus can release in a given period of time due to the emission of different types of radiation.
This activity (radioactive activity) increases as temperature rises due to a higher collision of subatomic particles that form molecules.
In conclusion, the chief factor that determines what type of electromagnetic radiation in the absence of a magnetic field is temperature.
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A brick and a feather fall to the earth at their respective terminal velocities. Which objectexperiences the greater force of air friction?
Answer:
Under the reasonable assumption that the brick has more mass than the feather, the brick experiences a greater force of air friction.
Explanation:
Objects at terminal velocity, only under the influence of gravity, have maximized their speed and have an acceleration of zero. Thus, neither object is accelerating.
Recall Newton's second law: [tex]\sum {\vec {F}}=m \vec {a}[/tex]
Since acceleration for each object is zero, the sum of the force acting on each of those objects must also be zero.
Since the only forces acting on the objects are gravity and the force of air friction, in order to zero out, the force of air friction must be equal in magnitude and opposite in direction to the force of gravity.
Recall that near the surface of the earth, [tex]F_{gravity}=mg[/tex], so the Force of Gravity acting on an object is directly proportional to the object's mass. (A similar argument could be made even if this were not taking place on the surface of the earth, so long as the objects were the same distance from the object providing gravitational influence).
If the masses of the objects are different, the object with the greater mass will experience a larger force of gravity, and hence a larger force of air friction at terminal velocity.
Under the reasonable assumption that the brick has more mass than the feather, the brick experiences a greater force of air friction.
Compared with a car moving at some original speed, how much work must the brakes of a car supply to stop a car that is moving twice as fast? how will the stopping distances compare?.
It takes four times the work and four times the stopping distance.
Given:
original speed of car = x
brakes applied so final speed = 0
moving speed of another car = 2x
To Find:
work done to stop the car
Solution: Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.
Work done is given by
W = KE(final) - KE(initial)
W = 1/2m(v)^2 - 1/2m(u)^2
W = 1/2m(0 - (x)^2)
W = 1/2m(4x^2)
W = 4(1/2mx^2)
W = 4W
So, work done will be 4 times initial work
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Upon inspiration, what is the name of the air in the conducting zone that is not available for gas exchange?.
Dead space is the name of the air in the conducting zone that is not available for gas exchange.
What is conducting zone?
The conducting zone consists of all of the structures that provide passageways for air to travel into and out of the lungs.
The conducting zone is part of the respiratory system. It serves as a route for incoming and outgoing air and filtering debris and pathogens from the incoming air.In order to compensate for the reduction in gas exchange in the respiratory system, ventilation will increaseThe volume of air that is inhaled that does not take part in the gas exchange is dead space. Because it either remains in the conducting airways or reaches alveoli that are not perfused or poorly perfused.
Dead space volume is air in the conducting airways that does not participate in gas exchange between the alveoli and blood.
Hence,
Dead space is the name of the air in the conducting zone that is not available for gas exchange.
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A car generator turns at 400 rpm (revolutions per minute) when the engine is idling. It has a rectangular coil with 300 turns of dimensions 5.00 cm by 5.22 cm that rotates in an adjustable magnetic field. What is the field strength needed to produce a 24.0 V peak emf
The field strength needed to produce a 24.0 V peak emf is 0.73T.
To find the answer, we need to know about the expression of emf.
What's the expression of peak emf produced in a rotating rectangular loops?
The peak emf produced in a rotating loops= N×B×A×wN= no. of turns of the loop, B= magnetic field, A= area of loop and w= angular frequencySo, B = emf/(N×A×w)What's the magnetic field applied to the loop, when rectangular coil with 300 turns of dimensions 5.00 cm by 5.22 cm rotates at 400 rpm produce a 24.0 V peak emf?N= 300, A= 5cm × 5.22cm = 0.05m × 0.0522m = 0.00261 m²Emf= 24V, w= 2π×400 rpm= 2π×(400rps/60) = 42 rad/sNow, B= 24/(300×0.00261×42)B= 24/(300×0.00261×42) = 0.73T
Thus, we can conclude that the magnetic field is 0.73T.
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PLEASE HELP QUICK! Why does thermal energy increase on a roller coaster? Especially when it goes up the second hill?
The light ray is now incident on a glass-air interface, with an angle of incidence in the glass of 45 degrees. What is the angle of light ray emerging from the glass into air
The ray will not emerge into the air medium from glass medium.
To find the answer, we need to know about the critical angle.
What's critical angle of glass?Critical angle of a medium can be determined from the relation as sinФ = 1/n, n = refractive index of that medium.As glass has refractive index of 1.5, so Critical angle = sin⁻¹(1/1.5) = 42 °Why does the light incident at 45° inside a glass not emerge to the air medium?As we got the critical angle of glass is 42°, so the light incident at 45° which is greater than 42° will reflect back into the glass medium instead of emergence into the air medium.Thus, we can conclude that the light will not emerge into air medium.
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How many watts of power are needed to exert a force of 30 n over a distance of 100 m for 1 minute?
Power require in Watts is 50 watts
Given:
Force = 30 N
Distance = 100m
Time for which force applied = 1 min = 60 sec
To Find:
Power
Solution: A watt is a unit of power. It is the amount of energy an item needs to function; the rate at which energy is consumed. One watt is equivalent to electricity flowing at a rate of one joule (unit of energy) per second
P = W/t
where W is work done by force and t is the time for which force is applied
W = F x d
W = 30 x 100 = 3000
P = 3000/60 = 50 watts
So Power require in Watts is 50 watts
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Two 1-d waves of amplitude a and period t and constant phase 0 are superposed. If wave 1 travels 13. 5 wavelengths farther than wave 2, will the interference be:________
Two 1-d waves of amplitude a and period t and constant phase 0 are superposed. If wave 1 travels 13. 5 wavelengths farther than wave 2, the interference is 3/2π.
Interference of light is the phenomena of multiple light waves interfering with each other under certain circumstances, causing the mixed amplitudes of the waves to both boom or lower.one of the exceptional examples of interference is demonstrated by the light contemplated from a film of oil floating on water.
The phenomenon of addition or superposition of mild waves which produces an increase in intensity at some factors and a decrease in depth at a few other points are known as interference of light.
The intensities of light at exceptional factors of the medium are distinctive. At a few factors of the medium, depth is most and at a few different points intensity is maximum ( about 0) This phenomenon is called the interference of mild waves, the interference is known as negative interference.
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5.1 What is the nucleus composed of ?
Answer:
5.1 The DNA double helix is the most recognizable nucleic acid structure, but these are ribozymes.
Which statement about income is not true?
A. Income should increase over your career.
B. Income is part of a budget.
C. Income can come from multiple sources.
D. Income only includes salary.
Answer: d) income only includes salary
Explanation:
i just took a test for economics and personal finance and got it correct
The statement that "Income only includes salary " is not true.
Income is the money that an individual or organization receives in return for their services or goods.
Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
For the majority of people, their total earnings include their wages and salaries, investment returns, pension payments, and other receipts.
For businesses, income refers to the money made from selling goods and services as well as any interest or dividends paid on the company's cash holdings and reserves.
So, the amount of money, property, and other value transfers received over a predetermined period in return for goods or services is often referred to as "income."
That's why income does not include only salary.
Hence Statement (D) about the income is not true.
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What relation can you state about the acceleration of the charge and it mass? Describe the mathematical relation, such as "directly proportional ", or "inversely proportional
Relation can you state about the acceleration of the charge and it mass is they are inversely proportional .
According to the question
Newton's second law :
Newton's second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it.
F = m * a
a = [tex]\frac{F}{m}[/tex]
Relation can you state about the acceleration of the charge and it mass is
According to Newton's second law of motion, acceleration is inversely proportional to the mass when the force is a constant.
The acceleration is directly proportional to the force when the mass remains constant.
Hence, Relation can you state about the acceleration of the charge and it mass is they are inversely proportional .
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The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. How is the plastic affected?.
When the north-pole end of a bar magnet is held near a stationary positively charged piece of plastic, it remains unaffected.
What is a bar magnet?
A bar magnet is made of ferromagnetic substance that produces
magnetic field.
What are the properties of a bar magnet?
Magnets attract ferromagnetic materials like iron, cobalt and nickel.Like poles repel each other and unlike poles attract each other.The strength of both poles is always the same.When a magnetic material is kept in contact with a bar magnet it acquires the magnetic property.Some materials like gold, silver and water get repelled by magnets.Since plastic is not a ferromagnetic material or any other material like gold and silver ,they remain unaffected in the presence of magnetic field.
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An airplane traveling at speed, 180 m/s, emits sound at a frequency of 2 000 Hz. What is the change in frequency (in Hz) heard by a stationary listener as the plane approaching and passing by
Answer:
As the plane moves toward the listener, the apparent frequency of the plane would be [tex]4250\; {\rm Hz}[/tex] ([tex]2250\; {\rm Hz}[/tex] higher than the frequency at the source.)
As the plane moves away from the listener, the apparent frequency of the plane would be approximately [tex]1308\; {\rm Hz}[/tex] (approximately [tex]692\; {\rm Hz}[/tex] lower than the frequency at the source.)
Assumption: the speed of sound in the air is [tex]340\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
Crests of this sound wave travel toward the listener at a constant [tex]v = 340\; {\rm m\cdot s^{-1}}[/tex]. Since there is a pause of [tex]t = 1 / f = (1/2000)\; {\rm s}[/tex] between every two consecutive crests of this sound wave, the distance between each pair of consecutive crests would be:
[tex]\begin{aligned}\lambda &= \frac{v}{f} \\ &= \frac{340\; {\rm m \cdot s^{-1}}}{2000\; {\rm s^{-1}}} \\ &= 0.17\; {\rm m} \end{aligned}[/tex].
Hence, if the aircraft wasn't moving, the first crest would have a head start of [tex]\lambda = 0.17\; {\rm m}[/tex] relative to the second one. This head start would ensure that the first crest arrive [tex]t = \lambda / v = 0.17\; {\rm m} / (340\; {\rm m \cdot s^{-1}}) = (1/2000)\; {\rm s}[/tex] earlier than the second crest.
However, at a speed of [tex]v_{\text{s}} = 180\; {\rm m\cdot s^{-1}}[/tex], the aircraft would have travelled an additional [tex]v_\text{s}\, t = 180\; {\rm m\cdot s^{-1}} \times (1/2000)\; {\rm s} = 0.09\; {\rm m}[/tex] within that [tex]t = (1 / 2000)\; {\rm s}[/tex].
If the aircraft was travelling towards the listener, the head start of the first crest over the next one would be reduced to [tex]\lambda - v_\text{s}\, t =[/tex][tex]0.17\; {\rm m} - 0.09\; {\rm m} = 0.08\; {\rm m}[/tex]. The first crest would arrive earlier than the second one by [tex](\lambda - v_{\text{s}}\, t) / (v) = (0.08\; {\rm m}) / (340\; {\rm m\cdot s^{-1}}) \approx 0.000235\; {\rm s}[/tex].In contrast, if the aircraft was travelling away from the listener, the head start of the first crest over the next one would be increased to [tex]\lambda + v_\text{s}\, t = 0.17\; {\rm m} + 0.09\; {\rm m} = 0.26\; {\rm m}[/tex]. The first crest would arrive earlier than the second one by [tex](\lambda + v_{\text{s}}\, t) / (v) = (0.26\; {\rm m}) / (340\; {\rm m\cdot s^{-1}}) \approx 0.000765\; {\rm s}[/tex].In other words, if the aircraft was moving towards the listener, the period of the sound would appear to the listener to be approximately [tex]0.000235\; {\rm s}[/tex]. in contrast, if the aircraft was moving away from the listener, the period of the sound would appear to the listener as approximately [tex]0.000765\; {\rm s}[/tex].
Therefore:
When the aircraft moves toward the listener, the listener would hear a frequency of [tex]f = 1 / t \approx 1 / 0.000235\; {\rm s} = 4250\; {\rm Hz}[/tex].When the aircraft moves away from the listener, the listener would hear a frequency of approximately [tex]f = 1 / t \approx 1 / 0.000765\; {\rm s} \approx 1307\; {\rm Hz}[/tex].What is the radial distance between the 500 v equipotential surface and the 1000 v surface?.
Answer: the radial distance between the 500-v equipotential surface and the 1000 v surface will be 8.91*106 times the charge Q.
Explanation: To find the answer, we have to know more about the equipotential surfaces.
What are equipotential surfaces?An equipotential surface is the locus of all points which have the same potential due to the charge distribution.Any surface in an electric field, at every point of which, the direction of electric field is normal to the surface can be regarded as equipotential.We have the equation for electric potential as,[tex]V=\frac{Qk}{r}[/tex] , where k is equal to 1/(4π∈₀) =[tex]8.99*10^9[/tex] .
equation for radial distance will be,[tex]r_d=r_1-r_2[/tex]
How to solve the problem?For the first surface, we can write the equation of potential as,[tex]500V=\frac{Qk}{r_1} \\thus, r_1=\frac{Qk}{500V}= (1.79*10^7 *Q) m[/tex]
For the second surface, we can write the equation of potential as,[tex]1000V=\frac{Qk}{r_2}\\ r_2= \frac{Qk}{1000V} =(8.99*10^6*Q) m[/tex]
Thus, the radial distance will be,[tex]r_d=1.79*10^7Q-8.99*10^6Q=(8.91*10^6*Q)m[/tex]
Thus, we can conclude that, the radial distance between the equipotential surface of 500V and 1000V will be,8.91*106 times the charge Q.
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A 0.10-m 3 0.20-m 3 0.30-m block is suspended from a wire and is completely under water. What buoyant force acts on the block
The buoyant force acting on the block is 58.8 N.
Calculation:The dimensions of the block are given as 0.10 m, 0.20 m and 0.30 m.
The volume of the block will be = 0.10 × 0.20 × 0.30 m³
= 0.006 m³
We know that,
W = mg .....(1)
where,
W = weight of the block
m = mass of the block
g = acceleration due to gravity = 9.8 m/s²
We also know that mass is proportional to density and volume
m = ρ.V .....(2)
Substituting the equation (2) in (1)
W = ρ.V.g .....(3)
Density of water, ρ = 1000 kg/m³
Force is the net weight acting on the block
F = W = ρ.V.g
F = 1000 × 0.006 × 9.8
F = 58.8 N
Therefore, the buoyant force acting on the block is 58.8 N.
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I need to know how to solve: finding magnitudes of forces related to a sum of three vectors
The solution is (v, u) = (- 585.709, 593,034). Please notice that the value of v only means that the direction of the real vector is antiparallel to the supposed one.
What are the magnitudes of two vectors to get the zero vector by vector sum?
According to the definition of vector sum and vectors in rectangular form, we must solve the following vector equation:
(0, 0) = 205 · (cos 23°, - sin 23°) + v · (- cos 75°, sin 75°) + u · (- cos 55°, - sin 55°)
(0, 0) = (188.703, 80.100) + v · (- 0.259, 0.966) + u · (- 0.574, 0.819)
(- 188.703, - 80.100) = v · (- 0.259, 0.966) + u · (- 0.574, 0.819)
Then, we must solve the following system of linear equations:
- 0.259 · v - 0.574 · u = - 188.703
0.966 · v + 0.819 · u = - 80.100
The solution is (v, u) = (- 585.709, 593,034). Please notice that the value of v only means that the direction of the real vector is antiparallel to the supposed one.
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A 1-oz bullet is traveling with a velocity of 1400 ft/s when it impacts and becomes embedded in a 5-lb wooden block. The block can move vertically without friction. Determine (a) the velocity of the bullet and block immediately after the impact, (b) the horizontal and vertical components of the impulse exerted by the block on the bullet.
After impact velocity = 14.968 ft/s
Weight and mass of Bullet and wooden block:
Bullet: w = 1oz = 1/16 lb m = 0.001941 lb
wooden block : W = 5lb M = 0.15528 lb
velocity of block and bullet immediately after impact:
Σmv1 + ΣImp = mv2
Resolving vertical component
( m× v₀cos30⁰) + 0 = ( m+M) v'
v' = ( m× v₀cos30⁰)/ (m+M)
v' = 14.968 ft/s
Horizontal and vertical component of the impulse exerted by block on the bullet:
Here we will apply the principle of impulse and momentum.
Horizontal component:
-mv₀ cos30⁰ + RxΔt =0
RxΔt = mv₀sin30⁰
= 0.001941 × 1400sin30⁰
RxΔt = 1.3587 lb.s
Vertical component:
-mv₀cos30⁰ + RyΔt = -mv'
RyΔt = m( v₀cos30⁰-v')
RyΔt = 0.001941(1400cos30⁰ - 14.968)
= 2.32 lb.s
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