the initial speed of the bullet as it was fired horizontally into the wooden block resting on a horizontal surface is 265m/s.
What is the law of conservation of momentum?A conservation law states that the total linear momentum of a closed system remains constant through time, regardless of other possible changes within the system.
Given, A 5.00g bullet is fired horizontally into a 1.20kg wooden block resting on a horizontal surface.
In our case,
Mass of bullet = 5 gram = 0.005 kg
Mass of wooden block = 1.2 kg
the initial velocity of block = 0
Kinetic friction = 0.20
First, we get the velocity of the Wood.
From Conservation of Energy:
1/2m v² = μ mgs
v = √(2 μgs)
Where v is the velocity of the block,
μ is the coefficient of kinetic friction,
s is the displacement of the bullet
g is the acceleration due to gravity (9.81)
v = √(2 *0.2*9.81 * 0.31)
v = 1.1 m/s
so, the velocity of the wooden block after the collision will be 1.10 m/s
Now, we determine the velocity of the bullet. Using Conservation of Momentum.
m₁v₁ + m₂v₂ = MV
0.005 *v + 0 = (1.20 + 0.005) * 1.1
v = 1.325/0.005
v = 265 m/s
Therefore, the initial speed of the bullet as it was fired horizontally into the wooden block resting on a horizontal surface is 265m/s.
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What are centripetal acceleration and centripetal force?derive their equations.
The acceleration in uniform circular motion is centripetal acceleration. a c =v 2 /r or a c =rω 2 where v is linear velocity, ⍵ is angular velocity, and r is radius of curvature. Then centripetal force formula of linear velocity is given by: F c =m v 2 /r.
A volume of gas starts at a pressure of 10 atmospheres (atm) and a temperature of 27°C. If the temperature is increased by 75°C and the volume of the gas remains constant, what is the new pressure?
Answer:
the new pressure is 11.64 atmospheres.
Explanation:
Assuming that the gas follows the ideal gas law, which states that PV = nRT (where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in kelvin), we can use the formula P1/T1 = P2/T2 to solve for the new pressure P2.
Converting the initial temperature of 27°C to kelvin, we get T1 = 27°C + 273.15 = 300.15 K. Increasing the temperature by 75°C gives us the new temperature T2 = 300.15 K + 75°C = 348.15 K.
Using the formula, we can solve for P2:
P1/T1 = P2/T2
10 atm/300.15 K = P2/348.15 K
Simplifying the equation, we get:
P2 = (10 atm * 348.15 K) / 300.15 K
P2 = 11.64 atm (rounded to two decimal places)
Therefore, the new pressure is 11.64 atmospheres.
rectangular plate is supported by three cables as shown. knowing that the tension in cable ac is 60 n, determine the weight of the plate.
The weight of the plate is equal to -(60 × LAC)/LAB - 60.
What is plate?Plate is a flat dish used for serving food. It is usually made of ceramic, glass, metal, or plastic, and is sometimes decorated with patterns or designs. Plates are usually round, but can also be rectangular, square, or oval. They are used for a variety of meals, from casual to formal.
Using the principle of static equilibrium, we can set up a system of equations to solve for the weight of the plate.
Equilibrium in the vertical direction:
Weight of the plate + Tension in cable AB + Tension in cable AC = 0
W + TAB + TAC = 0
Equilibrium in the horizontal direction:
Moment created by the tension in cable AB + Moment created by the tension in cable AC = 0
TAB × LAB + TAC × LAC = 0
Where W is the weight of the plate, TAB is the tension in cable AB, TAC is the tension in cable AC, LAB is the length of cable AB, and LAC is the length of cable AC.
We know that the tension in cable AC is 60 N, so we can substitute that into the equations above:
W + TAB + 60 = 0
TAB × LAB + 60 × LAC = 0
We can now solve for the weight of the plate by solving the system of equations.
Substituting the second equation into the first equation:
W + TAB + 60 = 0
W + (60 × LAC)/LAB + 60 = 0
W = -(60 × LAC)/LAB - 60
Therefore, the weight of the plate is equal to -(60 × LAC)/LAB - 60.
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show that, according to the distortion-energy criterion, the yield stress in plane strain is 1.15y, where y is the uniaxial yield stress of the material.
The value of Ey is greater than 1, it follows that:
σ = y * √(Ey / 1) > y
According to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
Yield Stress for Plane StrainThe distortion-energy criterion, also known as the Hill's criterion, states that the yield of a material occurs when the elastic distortion energy stored in the material is equal to the energy required to produce the yielding by plastic flow.
In plane strain conditions, the yield stress can be calculated as follows:
The elastic distortion energy stored in a material can be expressed as:U = 0.5 * σ_ij * ε_ij
Where U is the elastic distortion energy, σ_ij is the stress tensor and ε_ij is the strain tensor.
For uniaxial loading, the stress-strain relationship is given by:σ = Ey * ε
Where σ is the uniaxial stress, Ey is the Young's modulus and ε is the uniaxial strain.
Substituting the above expression for stress into the distortion energy equation, we get:U = 0.5 * Ey * ε^2
The energy required to produce the yielding by plastic flow can be expressed as:W = 0.5 * y * ε_p^2
Where W is the energy required for yielding, y is the uniaxial yield stress and ε_p is the plastic strain.
Equating the elastic distortion energy and the energy required for yielding, we get:0.5 * Ey * ε^2 = 0.5 * y * ε_p^2
Dividing both sides by 0.5 * ε^2, we get:Ey = y * ε_p^2 / ε^2
Substituting the definition of the uniaxial strain, we get:Ey = y * ε_p^2 / (ε/Ey)^2
Simplifying the above expression, we get:Ey = y * ε_p^2 * Ey^2 / ε^2
Finally, dividing both sides by Ey, we get:1 = y * ε_p^2 / ε^2
Rearranging, we get:ε^2 = y * ε_p^2 / 1
Taking the square root of both sides, we get:ε = √(y * ε_p^2 / 1)
Since ε = σ/Ey, substituting the uniaxial stress-strain relationship, we get:σ/Ey = √(y * ε_p^2 / 1)
Multiplying both sides by Ey, we get:σ = Ey * √(y * ε_p^2 / 1)
Finally, substituting the value of Ey, we get:σ = y * √(Ey / 1)
Since the value of Ey is greater than 1, it follows that:σ = y * √(Ey / 1) > y
Therefore, according to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
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What is the total displacement of person if he starts at home drives 2 kilometers due east and then turns around and drives 5 kilometers due west?
Include both magnitude and direction.
Answer:
3 West
Explanation:
Let east be the + direction.
2 - 5 = -3
Displacement = 3 West
Open the phase diagram for CO2 given in the introduction again. Use the phase diagram for CO2 in the interactive activity and determine which of the following statements are correct. CO2 is a gas under normal conditions of temperature and pressure.
All three phases of CO2 exist simultaneously at the triple point. When the pressure is 4 atm and the temperature is more than −56.7∘C, CO2 exists as a solid. When the pressure is 1 atm, there is no temperature at which the liquid phase of CO2 exists.
Movement across boundary line BO corresponds to a phase change.
CO2 forms a supercritical fluid at temperatures less than 31∘C.
The correct statements about the phase diagram for CO₂ from the given options are as follows:
All three phases of CO₂ exist simultaneously at the triple point.When the pressure is 1 atm, there is no temperature at which the liquid phase of CO₂ exists.CO₂ is a gas under normal conditions of temperature and pressure.Movement across boundary line BO corresponds to a phase change.The correct options are A, B, C, and D.
What is CO2's triple point?The parameters of temperature and pressure at which CO₂ is simultaneously present in all three physical states of matter are referred to as the triple point of CO₂.
At 5.2 atm, the triple point of CO₂ is -57 °C.At normal room temperature and atmospheric pressure, CO₂ is a gas.It is a significant greenhouse gas that is denser than air.Learn more about the triple point at: brainly.com/question/16945664
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A 117-lb student races up stairs with a vertical height of 5.7 m in 5.5 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity?
Work = (117 lbs) * (1 kg / 2.2046 lbs) * (9.81 m/s^2) * (5.7 m) = 296.8 J where 1 lb = 0.4536 kg. The time it takes for the student to climb the stairs he takes 5.5 seconds, so:
Power = work done / time taken = 296.8 J / 5.5 seconds ≈ 54 W So the power consumed by the student climbing the stairs is about 54 watts.
What is Acceleration?
Acceleration, the rate of change of velocity over time for both velocity and direction. A point or object moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated because it always changes direction even at constant velocity.
What is example acceleration?
If an object accelerates and moves in a positive direction, you have positive acceleration. The car accelerating in the first example is an example of positive acceleration. The car is moving forward and accelerating in the positive direction, so the acceleration is in the same direction as the car is moving.
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using the bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom.
The energy necessary to ionize a ground-state hydrogen atom using the Bohr model is approximately 2.18 x 10⁻¹⁸ J.
What is energy?
Energy is a physical quantity that describes the amount of work that can be done by a system or the amount of heat that can be transferred to or from a system. It is a scalar quantity and has units of joules (J) in the SI system of units. Energy can take many forms, including kinetic energy, potential energy, thermal energy, and electromagnetic energy.
The energy required to ionize a ground-state hydrogen atom can be determined using the Bohr model. According to the Bohr model, the energy of the electron in a hydrogen atom is quantized and can be calculated using the equation:
E = -(13.6 eV) / n²
where n is the principle quantum number. For the ground state (n = 1), the energy is -13.6 eV. To ionize the hydrogen atom, the electron must be removed from the atom, which requires an additional amount of energy equal to the ionization energy of the hydrogen atom.
The conversion factor from electron volts to joules is 1 eV = 1.6 x 10⁻¹⁹ J, so the ionization energy of a hydrogen atom in joules is:
E = -(13.6 eV) * (1.6 x 10⁻¹⁹ J/eV) = -2.18 x 10⁻¹⁸ J.
So, the energy necessary to ionize a ground-state hydrogen atom using the Bohr model is approximately 2.18 x 10⁻¹⁸ J.
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explain the similarities and differences between the observations that supported the geocentric models of the solar system and the phenomena described in the table.
Answer:
The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.
The velocity of a particle moving along the x-axis is given for
t > 0 by vx = (32.0t - 2.00t3) m/s,
where t is in s. What is the acceleration of the particle when (after
t = 0)
it achieves its maximum displacement in the positive x-direction?
The acceleration of the particle when it achieves its maximum displacement in the positive x-direction is -6.00[tex]m/s^2[/tex].
The acceleration of a particle is defined as the rate of change of its velocity with respect to time. In this case, the velocity of the particle is given by vx = 32.0t - 2.00t^3 m/s. To find the acceleration, we can differentiate this expression with respect to time:
ax = dvx/dt = 32.0 - 6.00[tex]t^2 m/s^2[/tex].
The particle achieves its maximum displacement in the positive x-direction when its velocity is zero, which occurs when vx = 0. Solving for t in the equation vx = 32.0t - 2.00[tex]t^3[/tex] = 0, we find that t = ±√(16/3) s. The particle achieves its maximum displacement in the positive x-direction, so we want the positive value of t, which is t = √(16/3) s. Plugging this value of t into the expression for ax, we find that the acceleration of the particle is ax = 32.0 - 6.00(16/3) = -6.00 [tex]m/s^2[/tex].
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A car takes off at a speed of 45 m/s. How far will the car travel in 77 seconds
The car will travel 3465 meter in 77 seconds s with this uniform speed.
What is speed?Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
Uniform speed of the car = 45 m/s
Time interval of motion of the car = 77 seconds.
Hence, total distance travelled by the car = speed of the car × time interval
= 45 m/s × 77 seconds
= 3465 meter.
Therefore, the car will travel 3465 meter in 77 seconds with this uniform speed.
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given planet mass, radius, object mass, and height how to find gravitational force acting on the object
The gravitational force (F) acting on an object can be calculated using the formula:
What is gravitational force?
Gravitational force is the force of attraction between two masses that results from the interaction of their gravitational fields. This force is proportional to the product of their masses and inversely proportional to the square of the distance between them.
[tex]\mathbf{F = G \times (m_1 \times m_2) / r^2}[/tex]
Where:
G is the gravitational constant (approximately equal to 6.67 x 10⁻¹¹ N m² / kg²)m1 is the mass of the planetm2 is the mass of the objectr is the distance between the centre of the planet and the center of the objectTo find the gravitational force, you need to know the mass of the planet and the object, as well as the radius of the planet and the height of the object above the planet's surface. The distance between the center of the planet and the center of the object can be calculated as:
r = R + h
Where:
R is the radius of the planeth is the height of the object above the planet's surfaceSo, substituting r into the formula for the gravitational force, you get:[tex]\mathbf{F = G \times (m_1 \times m_2) / (R+h)^2}[/tex]
Now you can substitute in the values for the mass, radius, and height to find the gravitational force.
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Let H(z) be the transfer function of a linear-phase FIR filter with real coefficients. The filter is known to have zeros in the following locations: Z1 = 1, Z2 = 2e^(-j0.41), Z3 = -j
(1) What is the smallest possible length (M) of this FIR filter? What are all possible zeros corresponding to your length-M FIR filter? (2) Which FIR filter type (I, II, III, IV) is your filter? ? (3) Please show the magnitude plot of frequency response of this FIR filter.
1) The smallest possible length (M) of the FIR filter is 4. The zeros for this length-4 FIR filter are: Z1 = 1, Z2 = 2e^(-j0.41), Z3 = -j, Z4 = -1.
What is FIR filter?A FIR filter (finite impulse response filter) is a type of filter used in signal processing. It is a linear, time-invariant, discrete-time filter whose impulse response (output in response to an impulse input) is of finite duration. This means that the output of the filter is only dependent on the current and previous inputs. FIR filters are used in many applications such as audio processing, telecommunications, and control systems.
2) The type of this FIR filter is Type III since its zeros are located on the unit circle.
3) The magnitude plot of the frequency response of this FIR filter is shown below. It is a linear-phase filter with real coefficients, so the frequency response should be symmetric around the Nyquist frequency.
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(c) An experiment was carried out in the laboratory to obtain the acceleration due to gravity 'g' as Shown in Fig. 1. The observations recorded were entered in the Table 1 as shown below. Table 1 S/N 1 2 3 4 5 L (cm) 100.00 90.00 70.00 50.00 40.00
No of Oscillation. 50 50 50 50 50
Mean time (s) 102.00 85.50 64.50
T (s) 1.92 1.47 T'(s)
The acceleration due to gravity can be obtained from the experiment.
How do you obtain the acceleration due to gravity experimentally?We know that when we talk about the acceleration due to gravity what we mean is that we want to know the magnitude of the gravitational pull in a given area and this can be known when we look at the data that we have from the oscillation experiment.
As such gravity is the force that causes the oscillation of the material to stop and such the magnitude can be determined from the experiment.
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Joshua is attracted toward Earth by a 500-N gravitational force. The Earth is attracted toward Joshua with a force of1. 250 N.
2. 500 N.
3. 1000 N.
4. 0 N.
Joshua is attracted toward Earth by a 500-N gravitational force. The Earth is attracted toward Joshua with a force of 500 N (2)
The gravitational attraction that exists between an individual and the earth is directly proportional to the mass of the individual and inversely proportional to the square of the radius of the planet (distance from the person to the center of earth). Your weight is the number that represents the gravitational attraction between you and the Earth.
When you contact with the Earth, however, the momentum you gain is equivalent to the momentum the Earth obtains. Additionally, according to the traditional point of view, the force with which you are attracted to the Earth is equivalent to the force with which the Earth is attracted to you. Even if your gravity isn't particularly strong, it nonetheless manages to pull a vast amount of mass from the Earth.
Therefore, the Earth is attracted toward Joshua is equal to Joshua attracted towards Earth = 500 N
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A rider is training a horse. Horse moves 60 metres towards right in 3 seconds. Then it turns back and travels 30 metres in 2 seconds. Find its average velocity?
The average velocity of the horse, given that moves 60 m to the right and 30 m backward is 18 m/s
How do I determin the average velocity?Average velocity is defined as:
Average velocity = Total displacement / total time
With the above formula, we can obtain the average velocity. Details below:
Displacement to the right = 60 metersDisplacement to the left = 30 metersTotal displacement = 60 + 30 = 90 metersTime to the right = 3 secondsTime to the left = 2 secondsTotal time = 3 + 2 = 5 secondsAverage velocity =?Average velocity = Total displacement / total time
Average velocity = 90 / 5
Average velocity = 18 m/s
Thus, we can conclude that the average velocity is 18 m/s
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A 1105 kg automobile is pulied by a horizontal towline with a net force of 818 N. What is the acceleration of the auto? (Neglect friction, Enter your answen
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The acceleration of the auto is 0.74 m/s².
What is the acceleration of the automobile?
The acceleration of the automobile is calculated by applying Newton's second law of motion as shown below;
F = ma
where;
m is the mass of the automobilea is the acceleration of the automobileThe applied force of the automobile is given as 818 N and the mass of the automobile is given as 1105 kg.
a = F / m
a = ( 818 N ) / ( 1105 kg )
a = 0.74 m/s²
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Analyze the word to determine its Greek prefix. Then use your understanding of the prefix meaning to choose the
correct meaning of the word.
analgesic
a medicine to increase hearing ability
a medicine to remove pain
a mixture of paint and linseed oil
The meaning of the word, " analgesic " is B. a medicine to remove pain.
What is an analgesic ?Any substance used to relieve pain is referred to as an analgesic drug, also known as an analgesic, analgaesic, pain reliever, or painkiller.
Analgesics, commonly known as painkillers, are drugs that treat a variety of pains, such as headaches, injuries, and arthritis. Both opioid analgesics and anti-inflammatory analgesics alter how the brain interprets pain. Some analgesics, such as stronger OTC medicines, combination analgesics, and all opioids, must be purchased with a prescription.
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A cart loaded with bricks has a total mass of 9.4 kg and is pulled at constant speed by
a rope. The rope is inclined at 23.8 degrees above the horizontal and the cart moves 16.3 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.7 . The acceleration of gravity is 9.8 m/s^2. How much work is done on the cart by the rope? Answer in units of kJ.
Four lightweight balls A, B, C, and D are suspended by threads. Ball A has been touched by a plastic rod that was rubbed with wool. When the balls are brought close together, without touching, the following observations are made: Balls B, C, and D are attracted to ball A. Balls B and D have no effect on each other. Ball B is attracted to ball C.
The observations in this scenario can be explained in terms of electrostatic principles and charge behavior in the presence of an external electric field.
How do calculate the balls are brought close together, without touching?This is an example of an electrostatic interaction involving charge. Rubbing a plastic rod with wool electrified it and acquired an excess negative charge. This left an excess positive charge on the wool.
When the negatively charged sphere A approaches another sphere, it repels the electrons in the sphere, leaving an overall positive charge. Therefore, balls B, C, and D are attracted to ball A. Sphere B and sphere D are both positively charged, so they repel each other and do not affect each other.
Ball B is attracted to ball C because it has the opposite charge. Ball C is attracted to ball A, but ball B is not attracted to ball A. This is because both are negatively charged and therefore repel each other.
Therefore, the observations in this scenario can be explained by the electrostatic principle and the behavior of charges in the presence of an external electric field.
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You encounter a moving walkway taht is 85m long and has a speed of 1.9m/s relatice to the ground. How long will it take you to cover the 85m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.4 m/s relative to the walkway
It will take you 24.6 sec to cover the 85m length of the walkway.
What does the word "speed" mean?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.
V = 85m / 68s. = 1.25m/s Walking on ground.
t = d / V = 85m / (2.2+1.25)m/s = 24.6s.
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Two rivers have the same volume of water flow over time but fall from different heights to power hydroelectric turbines. Which river would provide the most power? Explain why you chose that answer, describing the water's kinetic energy, potential energy and the law of conservation of energy.
The higher the water fall, the more the HEP produced.
What does the height of the water fall have to do with the HEP?The height of a waterfall is directly related to the potential energy of the water and the amount of hydroelectric power (HEP) that can be generated from it. Hydroelectric power is generated by harnessing the energy of falling water to generate electricity. The height of the waterfall determines the potential energy of the water, which is then converted into kinetic energy as the water falls and drives a turbine.
The higher the waterfall, the more potential energy the water has, and the more kinetic energy it can generate as it falls. This means that a taller waterfall has the potential to generate more hydroelectric power than a shorter waterfall.
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Determine the number of cubic feet of air per minute required to cool a room having a sensible heat gain of 4500 btu per hour to a temperature of 78 F dry bulb, if the air enters the room at a temperature of 63 F and the outside temperature is 93F
It is given that, the heat gained is 4500 btu per hour. The temperature difference here is 30 F and the specific heat of air is 0.24 btu/lb°F. Then the cubic feet of air per minute is 138.8 CFM.
What is sensible heat transfer ?The sensible heat transfer in a system can be calculated using the equation below:
q = CFM × 1.08 ×ΔT
q = CFM x 0.075 lb/ft3 x 60 min/hour x 0.24 btu/lb°F x ∆T
where, 0.24 btu/lb°F is the specific heat of the dry air.
Given that q = 4500 btu/hour.
temperature difference = 93 F - 63 F.
Then 4500 btu/hr = CFM × 1.08 × 30 F
CFM of air = 4500 btu/hr /(1.08 × 30 F ) = 138.8 CFM.
There for the number of cubic feat of air per minute is 138.8.
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a mass attached to the end of a spring is set in motion. the mass is observed to oscillate up and down, completing 12 complete cycles every 3.00 s.
The frequency of such mass oscillation approximately 4 Hz, and its period is 0.5 seconds.
A frequency is defined.The quantity of pulses that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in less than a second, the frequencies is 2 per second. The periodicity is 100 times per hour if it consumes 1/100 of an hour.
Describe the frequency formula.The frequency equation is written as f = /, where is the waveform speed and is the wavelengths of the wave. f = /2, where is the resonant velocity, is the frequency formula described in terms of angular velocity.
12 complete cycle = 3 sec.
1 complete cycle = 3/12
= 1/4 sec.
mass oscillation, T = 1/2 sec.
= 0.5 sec.
f = 12/3
= 4 Hz
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An Atwood machine is constructed using two
wheels (with the masses concentrated at the
rims). The left wheel has a mass of 2 kg and
radius 23.1 cm. The right wheel has a mass of
2.1 kg and radius 30.77 cm. The hanging mass
on the left is 2 kg and on the right 1.69 kg.
Answer:ruedas (con las masas concentradas en las llantas). La rueda izquierda tiene una masa de 2 kg y un radio de 23,1 cm. La rueda derecha tiene una masa de 2,1 kg y un radio de 30,77 cm. La masa colgante de la izquierda es de 2 kg y la de la derecha de 1,69 kg.
Explanation:
A hockey player hits a hockey puck sitting at rest and applies an average force of 440.0 N to the 0.15 kg
hockey puck for a time of 0.01 seconds. How fast does the puck go after the hit in m/s?
Answer:
29.333
Explanation:
This is a standard F=ma problem which then uses kinematics.
The 440 newtons is the force applied to the puck, the mass is the mass obviously. F+ma turns into A=F/m, A=440/.15 which equals 2933.333.
Vf=Vi+aT.
Vi=0, A=2933.333, T=.01
Vf = 29.333
A stationary mass explodes in to two parts of masses 2kg and 1kg if the smaller mass has a kinetic energy of 400J. What is the kinetic energy of the larger mass?in physics
200J is the correct answer
What is Kinetic Energy ?
Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity and is proportional to the object's mass and the square of its velocity. The equation for kinetic energy is given by:
KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
Kinetic energy is a measure of an object's ability to do work, as it can be transferred to other objects through collisions or other interactions. The total energy of a system is conserved, so an increase in an object's kinetic energy corresponds to a decrease in another form of energy, such as potential energy.
K.E=400J=1/2x1xV^{2}
V=\sqrt{800}
Applying conservation of momentum
maVa+ mbVb=0 ; Va=\sqrt{200}
Therefore ; K.E of larger mass = 1/2x2x200 = 200 J
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An ideal gas is compressed at constant pressure to one-half its initial volume. If the pressure of the gas is 120 kPa, and 760 J of work is done on it, find the initial volume of the gas.
The work done on the gas can be calculated using the equation: W = -PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. so the initial volume of gas is [tex]12.67 m^{3}[/tex]
For the given conditions, the work done is 760 J, the pressure is 120 kPa, and the change in volume is -1/2 the initial volume, so:
760 = -120 kPa * (V_initial / 2)
Expanding the right side of the equation:
760 = -60 kPa * V_initial
Dividing both sides by -60 kPa:
V_initial = [tex]760 / (-60 kPa) = 12.67 m^3[/tex]
So the initial volume of the gas is [tex]12.67 m^3.[/tex]
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while big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation.
While big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation. The statement is true.
Big-Theta notation is used to measure the average-case complexity of an algorithm. It provides an upper and lower bound on the growth rate of the algorithm, expressing it as the tightest asymptotic bound.
This means that the running time of an algorithm expressed in big-Theta notation lies within a constant factor of the actual running time. For example, if the running time of an algorithm is O(n²) and Θ(n²), it means that the algorithm's running time grows proportional to n², but with a constant factor that is not necessarily equal to 1.
Thus, big-Theta notation provides a more accurate representation of the algorithm's running time compared to big-O notation which only provides an upper bound.
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Your question seems incomplete, but I suppose the question was:
"While big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation. True or false."
A sinusoidal wave of frequency 710 Hz has a speed of 360 m/s. (a) How far apart are two points that differ in phase by π/2 rad? (b) What is the phase difference between two displacements at a certain point at times 4.00 ms apart?
the answer is (a) The corresponding length is 127 mm and (b) the phase difference is 4[tex]\pi[/tex] rad.
Using v = fλ,
we find the length of one cycle of the wave is
λ = 360 / 710
= 0.508 m
λ = 508 mm.
From f = 1 / T,
we find the time for one cycle of oscillation is
T = 1 / 710 = 0.002 × [tex]10^{-3}[/tex] s
T = 2.00 ms.
(a) A cycle is equivalent to 2[tex]\pi[/tex] radians, so that [tex]\pi[/tex]/2 rad corresponds to one-fourth of a cycle.
The corresponding length, therefore, is [tex]\pi[/tex]/4 = 508 / 4 = 127 mm.
(b) The interval 4.00 ms is double of T and thus corresponds to double of one cycle, or double of 2[tex]\pi[/tex] rad.
Thus, the phase difference is 2 × 2[tex]\pi[/tex]= 4[tex]\pi[/tex] rad.
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