The projectile will be moving at a speed of 57.21 m/s when it reaches the top of its trajectory.
When a projectile is fired at a speed of 138 and an upward angle of 65 degrees, the speed at the top of the trajectory can be calculated. To solve this problem, you need to understand some basic physics concepts. Here's how you can solve this problem:
1. First, identify the given values and write them down:
Initial velocity (u) = 138 m/s
Angle of projection (θ) = 65 degrees
Acceleration due to gravity (g) = 9.81 m/s²
2. Now, break down the initial velocity into its horizontal and vertical components:
Initial velocity in the horizontal direction = u cos θ
Initial velocity in the vertical direction = u sin θ
3. Use the equation of motion to calculate the time taken by the projectile to reach the top of its trajectory:
u sin θ = gt/2
t = 2u sin θ/g
4. Use the time obtained in step 3 to calculate the velocity at the top of the trajectory:
v = u cos θ
Where,
v = final velocity
u = initial velocity
θ = angle of projection
5. Substitute the given values in the equation to get the final answer:
v = u cos θ
v = 138 cos 65
v = 57.21 m/s
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water flows through a pipe with a cross-sectional area of 0.002 m2 at a mass flow rate of 4 kg/s. the density of water is 1 000 kg/m3. determine its average velocity. multiple choice question. 20 m/s 200 m/s 0.02 m/s 2 m/s 0.2 m/s
Option D: 2 m/s is the average velocity of the water flowing through a pipe with a cross-sectional area of 0.002 m2 at a mass flow rate of 4 kg/s.
According to the question:
cross-sectional area of the pipe = 0.002m²
Mass flowrate = 4 kg/s
Density of water = 1000 kg/m³
We are asked to find, average velocity =?
Average velocity is the net or total displacement covered by a body in a given time. The mass flow rate divided by the pipe's cross-sectional area and density ratio is the formula for calculating a fluid's average velocity.
As a result, the water's average flow rate through the pipe is provided by:
v = m / (ρ × A)
where, v is the average velocity, m is the mass flow rate, ρ is the density of water, and A is the cross-sectional area of the pipe. Substituting the values in the above equation we get:
v = 4 / (1000 × 0.002)
v = 2m/s
Therefore, the average velocity of water flowing through a pipe of cross-sectional area of 0.002m² is 2m/s.
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Correct question is:
Water flows through a pipe with a cross-sectional area of 0.002 m2 at a mass flow rate of 4 kg/s. The density of water is 1 000 kg/m3. Determine its average velocity. Multiple choice question.
20 m/s
200 m/s
0.02 m/s
2 m/s
0.2 m/s
a mass-spring oscillating system undergoes shm with a period t. what is the period of the system if the amplitude is doubled?
The period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.
The period of a mass-spring oscillating system undergoing simple harmonic motion (SHM) is determined by the spring constant and mass of the system.
When the amplitude of the system is doubled, the period of the system remains the same, regardless of the amplitude. This means that the period of a mass-spring oscillating system undergoing SHM with a period t, when the amplitude is doubled, is still t.
To understand why the period remains the same, consider the equation for simple harmonic motion:
x(t) = A cos (2πft).
This equation describes the displacement of an object over time and is based on the principle that any system undergoing SHM oscillates about a fixed point at a constant frequency.
The frequency of the system is inversely proportional to the period, and is determined by the spring constant and mass of the system.
Increasing the amplitude of the system does not affect the frequency or period of the oscillations.
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use the impulse-momentum theorem to find how long a falling object takes to increase its speed from 4.23 m/s to 10.47 m/s?
The time it takes the object to fall through the change in speed using the impulse-momentum theorem is 0.62 seconds.
What is impilse-momentum theorem?
The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse exerted on it.
To calculate the time it takes the object to increase it speed using the impulse-momentum theorem, we use the formula below.
Formula:
Ft = m(v-u)Ft/m = (v-u)Recall that F/m = acceleration. Therefore,
at = v-ua = (v-u)/t.......................... Equation 1Where:
a = Acceleration due to gravityv = Final velocityu = Initial velocityt = TimeFrom the question,
Given:
v = 10.47 m/su = 4.23 m/sg = 9.8 m/s²Substitute these values into equation 1 and solve for t
9.8 = (10.27-4.23)/tt = (10.27-4.23)/9.8t = 6.04/9.8t = 0.62 secondsHence, the time it takes the object to fall is 0.62 seconds.
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You're designing an external defibrillator that discharges a capacitor through the patient's body, providing a pulse that stops ventricular fibrillation. Specifications call for a capacitor storing 250 J of energy; when discharged through a body with R = 48 Ω transthoracic resistance, the capacitor voltage is to drop to half its initial value in 10 ms.
A) Determine the capacitance (to the nearest ) 10 μF).
B) Determine initial capacitor voltage (to the nearest 100 V) that meet these specs.
I need both correct answers to 2 significant figures.
a..... 1.04 x 10⁻⁴ Vi
b.... 9500 V
A) Determine the capacitance (to the nearest 10 μF).
First, we should identify the formula that we will use to solve the problem.
The formula that relates to capacitance is:
C = 2E / V². Where C is the capacitance in farads, E is the energy stored in joules, and V is the voltage across the capacitor in volts.
Converting the energy to joules, we have: E = 250J.
Now we know that the voltage needs to drop to half of its initial value in 10 ms. We can use the following formula to calculate the capacitance: C = R x t / ln(Vi / Vf) where R is the resistance in ohms, t is the time in seconds, Vi is the initial voltage, and Vf is the final voltage, which is half of the initial voltage.
B) Plugging in the given values, we get:
C = 48 x 0.01 / ln(Vi / (Vi / 2))Simplifying and solving for capacitance, we get:
C = 1.04 x 10⁻⁴ ViNow we can use the energy formula to solve for Vi:Vi = √(2E / C)
Plugging in the given values, we get:Vi = √(2 x 250 / 1.04 x 10⁻⁴)Simplifying and solving for Vi, we get:Vi = 9469 V
Therefore, the capacitance that meets these specifications is 100 μF and the initial capacitor voltage that meets these specifications is 9500 V, to the nearest 100 V.
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if a current of 5.5 a is used, what is the force generated per unit field strength on the 20.0 cm wide section of the loop? use units of newtons per tesla.
The force generated per unit field strength on a 20.0 cm wide section of the loop with a current of 5.5 A is: 0.001 newtons per tesla
The force generated per unit field strength on a 20.0 cm wide section of the loop with a current of 5.5 A is given by the formula F = (μI) / 2πr,
where μ is the permeability of free space, (4π x 10-7 N/A²)
I is current, and r is the radius of the loop.
In this case, the force is (4π x 10-7 x 5.5) / (2π x 0.1) = 0.001 N/T.
In other words, the force generated per unit field strength on a 20.0 cm wide section of the loop with a current of 5.5 A is 0.001 newtons per tesla.
The formula for the force generated per unit field strength on a loop is derived from the fact that the force is a result of the magnetic field generated by the current flowing in the loop.
The magnitude of the magnetic field generated is proportional to the current and inversely proportional to the radius of the loop. Since the force is a product of the current and the magnetic field, it is proportional to the square of the current and inversely proportional to the square of the radius of the loop.
In summary, the force generated per unit field strength on a 20.0 cm wide section of the loop with a current of 5.5 A is 0.001 newtons per tesla, given by the formula F = (μI) / 2πr, where μ is the permeability of free space (4π x 10-7 N/A²), I is current, and r is the radius of the loop.
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how to find the minimum thickness of a film such that reflected light undergo constructive interference
The minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.
The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),
where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
For example, if the order of interference is 3, the wavelength of the light is 600 nm, and the index of refraction is 1.4,
the minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.
Constructive interference of reflected light occurs when the phase difference between the two waves is equal to an integral multiple of 2π.
This can be determined using the formula Δφ = (2π*m)/(λ*n), where Δφ is the phase difference, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
To achieve constructive interference, the minimum thickness of the film can be determined by ensuring that the phase difference is equal to an integral multiple of 2π.
The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),
where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.
Constructive interference can be achieved by ensuring that the phase difference between the two waves is equal to an integral multiple of 2π.
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A skydiver of mass 95kg ,before opening his parachute, falls at t1 with V1= 11m/s and at t2 with t2 v2=27m/s; supposing friction is zero, find the distance covered between t1 and t2
The skydiver covered a distance of approximately 94.9 meters before opening his parachute between t1 and t2, assuming no air resistance or friction.
v = final velocity = v2 = 27 m/s
u = initial velocity = v1 = 11 m/s
a = acceleration = g = 9.8 m/[tex]s^2[/tex]
s = (v² - u²) / 2a
s = (27² - 11²) / (2 x 9.8) = 94.9 meters
Resistance measures an item's potential to impede the drift of electrical present-day through it. it's far measured in ohms (Ω). Resistance is decided by way of the bodily residences of an item, along with its dimensions, material, and temperature. while electric-powered present-day flows thru a conductor, it encounters resistance that slows down its float. This resistance is as a result of the collisions among electrons and the atoms inside the conductor.
Resistance can be laid low with changes inside the bodily properties of the conductor, such as duration, cross-sectional region, or temperature. an extended or narrower conductor may have higher resistance, even as a much broader conductor could have decreased resistance. understanding resistance is critical for designing and working electrical circuits. with the aid of controlling the resistance of a circuit, engineers can make sure that the appropriate amount of current flows to electricity the devices linked to it.
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a ball of mass is dropped. what is the formula for the impulse exerted on the ball from the instant it is dropped to an arbitrary time later?
The formula for the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:
Impulse = (Final momentum - Initial momentum)
What is impulse?Impulse is a vector quantity having both magnitude and direction, whereas momentum is a vector quantity, but the impulse is not equal to momentum. The impulse is the change in momentum.
If a ball of mass m is dropped from rest, then its initial momentum is zero.
The final momentum of the ball after falling for time t is:
Final momentum = mv
Where v is the velocity of the ball after falling for time t.
Therefore, the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:
Impulse = (mv - 0) = mv
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What would you expect the force to be if the distance was 30 meters? How did you come up with your answer?
The force would be 6 Newtons for a distance of 30 metres.
What connection exists between distance and force?A force is defined as any influence that results in a change in an object. Distance is the amount of distance that an object moves over time. A force is applied to an item, and the more force is applied, the farther the thing will move.
What is distance-based force?Action-at-a-distance forces are those that develop even when the two interacting objects are not in close proximity to one another but are nevertheless able to push or pull against one another despite this physical gap.
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An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?
Angular Momentum Kinetic Energy
(A) Increases Increases
(B) Increases Remains Constant
(C) Remains Constant Increases
(D) Remains Constant Remains Constant
(E) Decreases Remains Constant
An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled closer to the body, the angular momentum of the skater will remain constant while the kinetic energy of the skater increases. The correct option is C.
The angular momentum of the skater is given by
[tex]L = I\omega[/tex],
where I is the moment of inertia of the skater and ω is the angular velocity.
When the skater pulls their arms in, their moment of inertia decreases due to the decreased distance between their body and the axis of rotation.
According to the conservation of angular momentum, the product of the moment of inertia and angular velocity must remain constant. Therefore, if the moment of inertia decreases, the angular velocity must increase to keep the angular momentum constant.
The kinetic energy of the skater is given by
[tex]K = (1/2)I\omega^2[/tex]
As the moment of inertia decreases and the angular velocity increases, the kinetic energy of the skater also increases because it is proportional to the square of the angular velocity.
Therefore, the correct answer is: (C) Remains Constant Increases. The angular momentum remains constant, while the kinetic energy increases due to the increased angular velocity.
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a system releases 690 kj of heat and does 110 kj of work on the surroundings. part a what is the change in internal energy of the system?
A system releases 690 kj of heat and does 110 kj of work on the surroundings then part a what i the change in internal energy of the system -800 kJ.
The change in internal energy of the system can be calculated using the formula
ΔU = Q - W,
where ΔU is the change in internal energy, Q is the heat exchanged, and W is the work done.
In this case, the system releases 690 kJ of heat (Q = -690 kJ) and does 110 kJ of work on the surroundings (W = 110 kJ).
So, ΔU = -690 kJ - 110 kJ = -800 kJ.
The change in internal energy of the system is -800 kJ.
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a tired worker pushes a heavy (100-kg) crate that is resting on a thick pile carpet. the coefficients of static and kinetic friction are 0.6 and 0.4, respectively. the worker pushes with a force of 600 n. the frictional force exerted by the surface is
When a tired worker pushes a heavy (100-kg) crate that is resting on a thick pile carpet, the frictional force exerted by the surface on the crate is 588 N.
When a tired worker pushes a heavy (100-kg) crate that is resting on a thick pile carpet, the frictional force exerted by the surface can be calculated as follows:
The weight of the crate = m × g = 100 kg × 9.8 m/s² = 980 N
Force applied by the worker = F = 600 N
The force of friction acting on the crate is given by the following formula:
Ff = μF
Where, μ is the coefficient of friction, F is the normal force acting on the crate.
Notes: The normal force is equal and opposite to the weight of the crate. i.e., N = 980 N1. The frictional force exerted by the surface on the crate is the static frictional force initially. Hence, we use the coefficient of static friction for our calculation.
2. If the force applied by the worker is not enough to overcome the static frictional force, then the crate will not move and the frictional force will remain static friction.
3. Once the crate starts moving, the static friction will convert to kinetic friction. Hence, we will use the coefficient of kinetic friction if the force applied by the worker is greater than the force of static friction. Initially, the force applied by the worker is less than the force of static friction, hence the frictional force exerted on the crate will be the static frictional force.
Frictional force = Ff = μN
The normal force acting on the crate = Weight of the crate = 980 N
Frictional force =
Ff = μN
= 0.6 × 980 N
= 588 N
Therefore, the frictional force exerted by the surface on the crate is 588 N.
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We were just introduced to electricity in physics and I have some questions:
1. Since electrons can be transferred from our hair to the balloon, can electrons also be transferred from the balloon to our hair? (Do questions always say whether an object is positive or negative charge)
2. Do electrons stay in place since balloons are rubber insulators?
3. What point do neutrons serve? Are they just there?
4. Are objects in constant exchange of energy with one another? Whenever they come in contact they exchange electrons until equal?
1 - Since electrοns can be transferred frοm οur hair tο the ballοοn , electrοns cannοt be transferred frοm ballοοn tο οur hair because. This is an illustratiοn οf charging by cοnductiοn.
2 - Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.
3 - Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.
What is charging by cοnductiοn?A charged οbject must cοme intο cοntact with a neutral οbject tο cοnduct electricity. As a result, when twο charged cοnductοrs cοme intο cοntact, the charge is split between the twο cοnductοrs, charging the uncharged cοnductοr.
When twο neutral οbjects are rubbed against οne anοther, electrοns are transferred. The οbject that has a strοnger affinity fοr electrοns will take electrοns frοm the οther οbject, and the twο becοme charged in οppοsitiοn. In this instance, the electrοns frοm the hair are taken up by the ballοοn , which nοw has an excess οf electrοns and a negative charge cοmpared tο the hair's current electrοn shοrtage and pοsitive charge.
2- Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.
3- Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.
4-Insulating materials may becοme electrically charged when they cοme intο cοntact with οne anοther. Negatively charged electrοns can "rub οff" οne material and "rub οn" tο anοther. After bοth things have the same quantity οf οppοsite charges, the substance that gets electrοns becοmes negatively charged, and the material that lοses electrοns becοmes pοsitively charged.
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two stationary point charges q1 and q2 are shown in the figure along with a sketch of some field linesrepresenting the electric field produced by them. what can you deduce from the sketch?
From the sketch, we can deduce that the two charges q1 and q2 are of opposite signs, as field lines start at the positive charge q1 and end at the negative charge q2. The field lines also indicate that the magnitude of the electric field produced by q1 is larger than that of q2.
Additionally, the field lines show that the electric field lines near the charges are denser, indicating a stronger electric field intensity near the charges. The direction of the electric field points from q1 to q2, which is consistent with the direction of the force that a positive test charge would experience if placed in the field. The field lines also show that the electric field is radial, i.e., the field lines point directly away from or towards each charge in a straight line, which is a characteristic of the electric field produced by a point charge. Finally, the density of the field lines decreases with distance from the charges, indicating that the electric field strength decreases with distance from the charges, following an inverse-square law.Learn more about electric field at: https://brainly.com/question/14372859
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a 10.0-mf capacitor is fully charged across a 12.0-v bat- tery. the capacitor is then disconnected from the battery and connected across an initially uncharged capacitor with capacitance c. the resulting voltage across each capacitor is 3.00 v. what is the value of c?
The value of uncharged capacitor in series with a 10.0-microfarad capacitor, given that each capacitor has a voltage of 3.00 volts, can be calculated using the formula for equivalent capacitance in series and formula for charge on a capacitor. The value of c is approximately 4.00 microfarads.
To determine the value of c, which is [tex]1/Ceq = 1/C1 + 1/C2[/tex] . Initially, the 10.0-microfarad capacitor has a charge of [tex]Q = CV = (10.0 * 10^{-6 }F) * 12.0 V = 1.20 * 10^{-4} C[/tex].
When it is connected in series with uncharged capacitor with capacitance c, charge is shared between the two capacitors. The charge on 10.0-microfarad capacitor is also equal to the charge on uncharged capacitor, which is given by [tex]Q = (3.00 V) * C[/tex] .
Equating the two expressions for Q and solving for c, we get [tex]C = Q/3.00[/tex] [tex]V = (1.20 * 10^{-4 C}) / (3.00 V) = 4.00 * 10^{-5 F}[/tex]. Therefore, value of c is approximately 4.00 microfarads.
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the intensity of the sound of a television commercial is 10 times greater than the intensity of the television program it follows. by how many decibels does the loudness increase?
The television commercial loudness increases by 10 decibels.
Increase in the Intensity of soundThe decibel (dB) scale is a logarithmic measure of sound intensity. The intensity of a sound is measured in watts per square meter and the decibel scale is a way to express the relative loudness of a sound, compared to a reference level.
A 10 dB increase in intensity is a 10-fold increase in sound power. This means that a sound with an intensity of 10 watts per square meter is 10 times louder than a sound with an intensity of 1 watt per square meter.
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A 23.3 kg boy is moving along a circular path with the constant speed of 2.7 m/s. What is the magnitude of the centripetal force acting on the boy if the radius of the circle is 12.9 m. Note : Calculate the answer to 3 (three) significant figures by presenting it in normal ( decimal) form. Don't forget to include the unit.
The centripetal force for the given question would be 16.3 N.
Explanation:
The magnitude of the centripetal force acting on a 23.3 kg boy moving along a circular path with a constant speed of 2.7 m/s and the radius of the circle is 12.9 m is 16.3 N (newton).
What is centripetal force?
Centripetal force is the net force acting on an object moving in a circular path toward the center of the circle. It always points towards the center of the circle, hence the name "center-seeking force".
What is the formula for centripetal force?
The formula for centripetal force is Fc = (mv²)/r, where Fc is the centripetal force, m is mass, v is velocity or speed and r is the radius of the circular path.
In the given question: Mass, m = 23.3 kgVelocity, v = 2.7 m/s, Radius, r = 12.9. To calculate centripetal force,
F = (m x v^2)/r
Putting the given values in the above formula: F = (23.3 kg x (2.7 m/s)^2)/12.9 m= 16.3 N (newton)
Therefore, the magnitude of the centripetal force acting on the boy is 16.3 N (newton).
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Two aircraft are flying toward each other at the same speed. They each emit a 800 HZ whine. what speed (km/hr) must each aircraft have an order that pitch they both hear is 2 times the emitted frequency. Hint: the speed of sound is 343m/s
Each aircraft must be moving at a speed of 85.75 km/hr towards each other to hear a pitch that is 2 times the emitted frequency.
What is frequency ?
Frequency is a physical quantity that describes the number of occurrences of a repeating event per unit of time. It is often measured in Hertz (Hz), which represents the number of cycles or vibrations per second.
In the context of waves, such as sound waves or electromagnetic waves, frequency refers to the number of complete cycles of the wave that occur in one second. A high frequency wave has more cycles per second than a low frequency wave.
Frequency is also an important concept in physics, particularly in the study of oscillations and waves. It is used to describe the behavior of systems that oscillate or vibrate, such as a simple pendulum or a guitar string. In these cases, the frequency of the oscillation is related to the natural frequency of the system, which is determined by its mass, stiffness, and other properties.
When two aircraft are moving towards each other, the sound waves from each aircraft are compressed, leading to a higher pitch than the emitted frequency. The pitch heard by the pilots of the aircraft can be calculated using the following formula:
Pitch heard = Emitted frequency * (Speed of sound + Speed of observer) / (Speed of sound - Speed of source)
Since the two aircraft are flying towards each other at the same speed, we can assume that the speed of one aircraft is x km/hr, and the speed of the other aircraft is also x km/hr. Therefore, the relative speed between the two aircraft is 2x km/hr.
Substituting the values given in the formula, we get:
2 * Emitted frequency = Emitted frequency * (343 + 2x) / (343 - x)
Simplifying this equation, we get:
686 - 2x = 343 + 2x
4x = 343
x = 85.75 km/hr
Therefore, each aircraft must be moving at a speed of 85.75 km/hr towards each other to hear a pitch that is 2 times the emitted frequency.
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an n-type piece of silicon experiences an electric field equal to 0.1v/m. (a) calculate the velocity of electrons and holes in this material
In an n-type piece of silicon, the electric field causes the electrons to accelerate due to the attractive force between the negatively charged electrons and the positively charged electric field. This acceleration causes the electrons to reach a velocity of V = E/μ, where E is the electric field (0.1V/m) and μ is the mobility of electrons in silicon (1350 cm2/V⋅s). Therefore, the velocity of electrons in this material would be equal to 0.1V/m/1350cm2/V⋅s = 0.0741 cm/s.
The holes, on the other hand, experience a repulsive force due to the positive electric field. This causes the holes to decelerate, with a velocity of V = -E/μ. Therefore, the velocity of holes in this material would be equal to -0.1V/m/1350cm2/V⋅s = -0.0741 cm/s.
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I have no clue what im doing..
If work = 100J and time = 20 seconds, what is power
Answer:
5 J/s or 5 watt
Explanation:
Given,
Work (W) = 100 J
Time (t) = 20 s
To find : Power (P)
Formula :
P = W/t
P = 100/20
P = 5 J/s
P = 5 watt
Note : -
J/s and watt are units are power.
when rotating the platform, the hanging mass should be removed from the platform. question 2 options: true false
The given statement, while the platform is rotating, the hanging mass remains attached to the test mass and is not removed from the platform is true, if the purpose of the experiment or test is to determine the effect of the hanging mass on the rotation or stability of the platform.
In this case, the hanging mass must remain attached to the test mass during the rotation to observe the behavior of the system under the specified conditions. If the purpose of the experiment or test is to study the effect of the hanging mass on the platform's rotation or stability, the hanging mass must remain attached to the test mass during the rotation. This is because the presence of the hanging mass affects the overall weight and center of gravity of the system. Removing the hanging mass would alter the system's behavior and prevent accurate observations of the phenomenon under investigation. Therefore, if the experiment requires the hanging mass to be present, it must remain attached to the test mass while the platform is rotating.
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--The complete question is, While the platform is rotating, the hanging mass remains attached to the test mass and is not removed from the platform. State true/false.--
a value of mass is given as 14.6 g to 15.2 g. a value of volume is given as 2.4 to 2.8 m3. state the density using reasonable outer limits.
The density using reasonable outer limits is the density of an object can be determined by dividing its mass (measured in grams, g) by its volume (measured in cubic metres, m3). To calculate the density using the given values of mass and volume, we can use the following formula: Density = Mass/Volume.
Therefore, the density of the given object can be calculated using the outer limits of mass and volume, which are 14.6 g to 15.2 g and 2.4 m3 to 2.8 m3, respectively. The calculated density of the given object is in the range of 5.75 g/m3 to 5.45 g/m3.
To calculate the density, the mass and volume of the object must be known. Mass is a measure of how much matter an object has, and is calculated in grams (g). Volume, on the other hand, is a measure of the amount of space an object takes up, and is calculated in cubic metres (m3).
When these two values are known, the density can be calculated using the formula: Density = Mass/Volume. In this case, the given values of mass and volume are 14.6 g to 15.2 g and 2.4 m3 to 2.8 m3, respectively. By substituting these values into the formula, the density of the object can be calculated as follows:
Density = Mass/Volume
Density = 14.6 g/2.4 m3 = 5.75 g/m3
Density = 15.2 g/2.8 m3 = 5.45 g/m3
Therefore, the density of the given object is in the range of 5.75 g/m3 to 5.45 g/m3.
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(a) when a 9.00-v battery is connected to the plates of a capacitor, it stores a charge of 27.0 mc. what is the value of the capacitance? (b) if the same capacitor is connected to a 12.0-v battery, what charge is stored?
The formula for calculating capacitance is as follows:
C = Q/V
Where,
C = capacitance (Farads)
Q = charge (Coulombs)
V = voltage (Volts)
As given,
Q = 27.0 μC
V = 9.00 V
Substituting the given values in the above equation
C = 27.0 μC/9.00 V = 3.00 μF
Therefore, the value of capacitance is 3.00 μF.
The formula for calculating charge stored is as follows:
Q = CV
Where,
Q = charge (Coulombs)
C = capacitance (Farads)
V = voltage (Volts)
As given,
C = 3.00 μF
V = 12.0 V
Substituting the given values in the above equation,
Q = (3.00 × 10⁻⁶ F) × 12.0 V = 36.0 μC
Therefore, the charge stored is 36.0 μC.
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at what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?
The first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm is approximately 6.2°.
The angle of the first-order maximum refers to the angle at which the brightest interference pattern appears on a screen placed behind two closely spaced slits when illuminated with the blue light of 450-nm wavelength.
The angle is determined by the equation:
theta_m = (m*lambda)/d
where m is the order, lambda is the wavelength, and d is the slit separation.
theta_m = (1*450E-9 m)/0.0500 mm
theta_m = 6.2°
Thus, the first-order maximum for double slits of 0.0500 mm at 450 nm λ blue light is around 6.2°.
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A boy on a 1.9 kg skateboard initially at rest
tosses a(n) 8.0 kg jug of water in the forward
direction.
If the jug has a speed of 2.7 m/s relative to
the ground and the boy and skateboard move
in the opposite direction at 0.65 m/s, find the
boy’s mass.
Answer in units of kg.
Answer:
Approximately [tex]31.3\; {\rm kg}[/tex]. (Assuming the friction between the skateboard and the ground is negligible.)
Explanation:
The momentum [tex]p[/tex] of an object of [tex]m[/tex] and velocity [tex]v[/tex] is:
[tex]p = m\, v[/tex].
When the boy tossed the jug of water, the change in the momentum of the jug would be:
[tex]\Delta p(\text{jug}) = m(\text{jug}) \, (v(\text{jug}) - u(\text{jug}))[/tex], where:
[tex]m(\text{jug}) = 8.0\; {\rm kg}[/tex] is the mass of the jug;[tex]v(\text{jug}) = 2.7\; {\rm m\cdot s^{-1}}[/tex] is the velocity of the jug after the toss;[tex]u(\text{jug}) = 0\; {\rm m\cdot s^{-1}}[/tex] is the initial velocity of the jug, which was at rest before the toss.Hence:
[tex]\begin{aligned}\Delta p(\text{jug}) &= m(\text{jug}) \, (v(\text{jug}) - u(\text{jug})) \\ &= (8.0)\, (2.7 - 0)\; {\rm kg\cdot m\cdot s^{-1}} \\ &= 21.6\; {\rm kg\cdot m\cdot s^{-1}}\end{aligned}[/tex].
Similarly, the change in the momentum of the skateboard would be:
[tex]\Delta p(\text{board}) = m(\text{board}) \, (v(\text{board}) - u(\text{board}))[/tex], where:
[tex]m(\text{board}) = 1.9\; {\rm kg}[/tex] is the mass of the board;[tex]v(\text{board}) =(-0.65)\; {\rm m\cdot s^{-1}}[/tex] is the velocity of the board after the toss;[tex]u(\text{board}) = 0\; {\rm m\cdot s^{-1}}[/tex] is the initial velocity of the board.Note that the velocity of the board [tex]v(\text{board})\![/tex] after the toss is opposite to that of the jug. The sign of [tex]v(\text{board})[/tex] would be opposite to that of [tex]v(\text{jug})[/tex]. Since [tex]v(\text{jug})\![/tex] is positive, the value of [tex]v(\text{board})\!\![/tex] should be negative.
[tex]\begin{aligned}\Delta p(\text{board}) &= m(\text{board}) \, (v(\text{board}) - u(\text{board})) \\ &= (1.9)\, ((-0.65)- 0)\; {\rm kg\cdot m\cdot s^{-1}} \\ &= (-1.235)\; {\rm kg\cdot m\cdot s^{-1}}\end{aligned}[/tex].
Let [tex]m(\text{boy})[/tex] denote the mass of the boy. The velocity of the boy was initially [tex]u(\text{boy}) = 0\; {\rm m\cdot s^{-1}}[/tex] and would become [tex]v(\text{boy}) =(-0.65)\; {\rm m\cdot s^{-1}}[/tex] after the toss. The change in the velocity of the boy would be:
[tex]\Delta p(\text{boy}) = m(\text{boy}) \, (v(\text{boy}) - u(\text{boy}))[/tex].
Under the assumptions, the total changes in the momentum of this system (the boy, the skateboard, and the jug) should be [tex]0[/tex]. Thus:
[tex]\Delta p(\text{boy}) + \Delta p(\text{boy}) + \Delta p(\text{jug}) = 0[/tex].
Rearrange and solve for the mass of the boy:
[tex]\Delta p(\text{boy}) = -\Delta p(\text{jug}) - \Delta p(\text{board})[/tex].
[tex]\begin{aligned} m(\text{boy}) &= \frac{-\Delta p(\text{jug}) - \Delta p(\text{board})}{v(\text{boy}) - u(\text{boy})} \\ &= \frac{-(21.6) - (-1.235)}{(-0.65) - 0}\; {\rm kg} \\ &\approx 31.3\; {\rm kg}\end{aligned}[/tex].
To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50m apart, as indicated in the figure . If the left scale reads 290 N, and the right scale reads 112 N. What is the student's mass and find the distance from the student's head to her center of mass.
The location of her centre of mass, a physics student lies on a lightweight plank supported by two scales 2.50m apart, as indicated in the figure. If the left scale reads 290 N and the right scale reads 112 N The student's mass is approximately 41 kg, and the distance from her head to her centre of mass is approximately 0.696 m.
To determine the student's mass, we can sum up the readings from both scales, which are measures of force (Newtons) and then convert it to mass using the gravitational acceleration (g = 9.81 m/s²).
Step 1: Calculate the total force acting on the plank:
Total Force = Force_left_scale + Force_right_scale
Total Force = 290 N + 112 N
Total Force = 402 N
Step 2: Convert the total force to mass using gravitational acceleration:
Mass = Total Force / g
Mass = 402 N / 9.81 m/s²
Mass ≈ 41 kg
Now, to find the distance from the student's head to her centre of mass, we'll use the principle of torque equilibrium.
Step 3: Set up the torque equation:
Torque_left_scale = Torque_right_scale
Force_left_scale × Distance_left_scale = Force_right_scale × Distance_right_scale
Let x be the distance from the student's head to her centre of mass. Then, the distance from the left scale to the centre of mass is x, and the distance from the right scale to the centre of mass is (2.50 - x).
Step 4: Plug in the known values and solve for x:
290 N × x = 112 N × (2.50 - x)
Step 5: Simplify the equation and solve for x:
290x = 112(2.50) - 112x
290x + 112x = 112(2.50)
402x = 280
x ≈ 0.696 m
The student's mass is approximately 41 kg, and the distance from her head to her centre of mass is approximately 0.696 m.
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Why is momentum not conserved in real life situations
Momentum is not always conserved in real-life situations because external forces can act on a system and change its momentum.
For example, when two cars collide, friction and air resistance can cause the momentum of the system to change. Similarly, when a ball is thrown in the air, gravity and air resistance act on it and cause its momentum to change. Other factors such as deformation, energy loss, and imperfect collisions can also cause momentum to be lost or gained. Therefore, while momentum is a useful concept in physics, it is important to consider the impact of external factors when analyzing real-world situations.
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if you hold a 1.85 kg k g package by a light vertical string, what will be the tension in this string when the elevator accelerates as in the previous part?
The tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. When the elevator accelerates, the force of acceleration on the package will be equal and opposite to the tension in the string, causing the tension to increase.
The equation for tension in a string is:
Tension = Mass x Acceleration
Therefore, in this case, the tension in the string is equal to 1.85 kg x Acceleration.
If we assume that the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.
To sum up, the tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. If the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.
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pry on the power steering reservoir to adjust the tension of the power steering belt. true or false?
The statement "pry on the power steering reservoir to adjust the tension of the power steering belt" is: false.
The tension of the power steering belt is adjusted by adjusting the position of the power steering pump. There is a tension adjustment bolt on the power steering pump that is used to adjust the tension of the power steering belt. The adjustment bolt should be turned clockwise or counterclockwise to adjust the tension of the belt.
A belt tension gauge may be used to ensure that the belt is properly tensioned. A pry bar should not be used on the power steering reservoir to adjust the tension of the power steering belt. This could cause damage to the reservoir or other components of the power steering system. The reservoir should be inspected for damage or leaks, but it should not be used to adjust the tension of the belt.
In summary, the tension of the power steering belt should be adjusted by adjusting the position of the power steering pump, not by prying on the power steering reservoir.
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logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. what is the average density of a uniform-diameter log that floats with 20.0% of its length above water?
Uneven-diameter logs that float with 20.0% of their length above water have an average density of 0.8g/cm3. The density is the proportion of weight to capacity.
An item it's far less compact that liquid may be supported up liquid water, and hence it floats. More dense objects can sink when submerged in water. Less dense logs float whereas more thick logs sink. A body can change its condition of rest or motion by the application of force
Instead of obliquely reading from either the side, read the scale stick straight from of the end of both the log. → The diameter of a log is only ever calculated within the bark. Employ a log measuring rod to determine the log's small end's "diameter from within bark," also known as "d.i.b."
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