The time period of vibrations varies inversely as the square root of the force constant of the spring.
When released, the restoring force returns the ruler to a stable equilibrium position with zero net force. The deflection of the spring is zero when the object is at equilibrium. This means that the force on the object due to the spring is also zero.
Therefore, when the object is in the equilibrium position it reaches zero acceleration and maximum velocity. At equilibrium, the velocity is maximum and the acceleration is zero. Simple harmonic motion is characterized by this varying acceleration. This changing acceleration is always directed toward equilibrium and proportional to the displacement from equilibrium.
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What is Law of Conservation of Matter explain using an example?.
The law of conservation of matter and the law of conservation of energy essentially state that neither type of energy can be created nor destroyed, only transformed. The process by which grapes ferment to produce wine is an illustration of the law of conservation of matter. The amount of matter in the reactants in the bottle doesn't change, but its chemical form does.
It is a fundamental tenet of classical physics that matter cannot be created or destroyed in an isolated system; rather, it can only be changed from one form to another. This means that despite the apparent changes that are seen, no matter is lost during any chemical or physical change that may occur with any substance.
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A large pendulum with a 200-lb gold-plated bob 12 inches in diameter is on display in the lobby of the United Nations building. The pendulum has a length of 75 ft. It is used to show the rotation of the Earth-for this reason it is referred to as a Foucault pendulum.What is the least amount of time it takes for the bob to swing from a position of maximum displacement to the equilibrium position of the pendulum? (Assume that the acceleration due to gravity is g=9.81m/s2 at the UN building.)t=________s
The bob swings from a position of greatest displacement to the pendulum's equilibrium position in the least period of time possible is 2.4 seconds.
How does the time period change when the bob's displacement increases?As a result, the mass of the bob has no effect on the basic pendulum's time period. As a result, the pendulum's period is unaffected if the bob's mass rises.
when the mean position of a simple pendulum's bob is altered?A simple pendulum's bob is moved from its equilibrium position O to a position Q that is h heights above O, and then it is let go. assuming the bob's mass to be m and time period of oscillations to be 2 s, the tension in the string, when the bob passes through O
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Compared to an electron in the first electron shell of an atom an electron in the third shell.
They have more energy. One 1s orbital and two electrons are contained within the first shell. 8 electrons are located in the second shell, with 2 in a 2s orbital and 6 in three 2p orbitals.
What is a electron in an atom?The elementary electric charge of the electron is a negative one, making it a subatomic particle. Due to their lack of components or substructure, electrons, which are part of the lepton particle family's first generation, are typically regarded to be elementary particles.Electrons are fundamental to many physical processes, including gravity, electromagnetic interactions, weak interactions, electricity, magnetism, chemistry, and thermal conductivity.For neutrally charged species, the number of electrons in an atom is equal to the atomic number of an element. This indicates that an element has an equal amount of protons and electrons. Consequently, there are 8 electrons in oxygen.Three basic characteristics of an electron in an atom are charge, spin, and orbital angular momentum, the latter of which describes the electron's orbital motion around the nucleus.To learn more about electron refer :
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Light is emitted when an electron:
makes a transition to a lower energy level.
The electron in an atom is boosted to a higher orbit and excited. When the electron returns to its original state, it de-excites and emits a photon of light.
When the electron changes levels, it decreases energy and the atom emits photons. The photon is emitted with the electron moving from a higher energy level to a lower energy level.
The electron absorbs the energy and jumps to a higher energy level. In the reverse process, emission, the electron returns to the ground state by releasing the extra energy it absorbed. Recall that the electrons must occupy one of the energy levels.
The electrons in an atom exist in various energy levels. When an electron moves from a lower energy level to a higher energy level, energy is absorbed by the atom. When an electron moves from a higher to a lower energy level, energy is released.
When an electron falls from a higher energy to a lower energy level, it accelerates. We know accelerating charged particle radiates energy in the form of electromagnetic radiation.
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Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of d_1 and d_2, the repulsion and attraction should balance each other, resulting in no net force. For what ratio d_1/d_2 is there no net force on particle 0?
Express your answer in terms of any or all of the following variables: k, q0, q1, q2.
d1/d2 =
I need help with this please. I will rate expert. I only have one try left. I get that p1 has a weaker effect on p0 than p2 because it is further away. Here are the answers I tried:
When there is no net force on the particle 0, the value of d₁/d₂ is √(q₂/q₁).
The distance of the particle 0 from the particle 1 is d₁ and the distance of the particle o from the particle 2 is d₂.
The particle 0 is experiences attraction from particle 2 and repulsion from particle 1.
The charges on the particle 1 and particle 2 are q₁ and q₂ respectively.
So, to experience no net force, the electrostatic forces on the particle 0 from both the particles should be equal, so we can write,
F₁ = F₂
Kq₁q₂/d₁² = Kq₁q₂/d₂²
Now, rearranging the equation,
d₁/d₂ = √(q₂/q₁)
So, the ratio of the distances is given as √(q₂/q₁).
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A 1.0kg block is placed on a 6.0kg wedge as shown. The block slides down the wedge and then to the right on the frictionless surface. The wedge moves to the left (without friction).If the speed of the wedge when the block reaches the flat surface is 0.28ms , what is the height of the wedge?
The wedge moves to the left (without friction) If the speed of the wedge when the block reaches the flat surface is 0.28ms, the height of the wedge is 5m
A wedge is a simple machine that uses a small force P to lift a heavy weight W. To calculate the force required to push the wedge in or out, draw FBDs of the wedge and the object on top of it. = 0 to the wedge and the object, as well as the frictional equation for impending motion, F = S N. The desired angle of correction () and the actual tibial width () are used to calculate the actual wedge height (y) (x). Actual tibial width should be measured at 2.02.5 cm distal to the joint line and normalized based on magnification. Wedge Volume = Cross Sectional Area x Tank Breadth.
Distance needs to be calculated in meters
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How is risk of collision calculated?.
Taking compass bearings is one of the maximum important ways of figuring out the danger of collision. good visibility is wanted to use this technique and a series or quantity of bearings need to be taken.
On smaller vessels bearings may be taken the use of a hand-bearing compass, on large vessels, a bearing or azimuth ring is used.
As soon as you perceive a danger of collision, you should perceive an appropriate movement to avoid collision to make sure the vessels will pass at a safe distance. You should then take that action to avoid collision as quickly as it's miles appropriate to accomplish that. digital Bearing lines are used to take the bearing of goals. The EBL extends from its own delivery role to the circumference of the radar display. If the bearing remains steady with decreasing variety, the chance of collision exists.
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TRUE/FALSE. cross-sectional surveys can be used to establish baseline data prior to the initiation of longitudinal studies.
Answer: true
Explanation:
the drill used by most dentists today is powered by a small air-turbine that can operate at angular speeds of 350000 rpm. these drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. suppose a drill starts at rest and comes up to operating speed in 2.2 s . you may want to review (pages 305 - 307) .
The angular acceleration of the drill is 2651.5 rotation/s².
We need to know about angular acceleration to solve this problem. The angular acceleration can be defined as the change in angular speed per interval of time. It can be written as
α = dώ / dt
where α is angular acceleration, dώ is change in angular speed and dt is interval of time.
From the question above, the given parameters are
ώ = 350000 rpm
t = 2.2 s
Change the angular speed unit to rotation per second
ώ = 350000 rpm
ώ = 350000 / 60 rps
ώ = 5833.33 rps
Find the angular acceleration
α = dώ / dt
α = 5833.33 / 2.2
α = 2651.5 rotation/s²
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a container has the mass of 125g when a liquid is added the mass becomes 163g what is the mass of the liquid
The block moves up an incline with constant speed. What is the total work W. Total done on the block by all forces as the block moves a distance L = 3.40 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.
Since the block is moving at a constant speed there is no change in kinetic energy. Since work is the change in kinetic energy and there is no change, the net work on the block is zero.
There is no change in kinetic energy because the block is travelling at a steady pace. The net work on the block is 0 since work is the change in kinetic energy, and there is none.
.kinetic energy. is the ONE of the energy. that an object has as a result of motion. It is defined as the effort necessary to move a mass-based body from rest to the given velocity. In the absence of a change in speed, the body retains the kinetic energy it acquired during acceleration. Kinetic energy is the energy that is present in a moving object. You strolling down the street, molecules moving in space, and the planet rotating around the sun all have kinetic energy. The relationship between an object's kinetic energy and mass and square of its velocity is direct. A particle, an object, or a collection of particles can move because of kinetic energy, which is the force that drives motion.
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Compare the probabilities for an oscillating particle in its ground state to be found in a small interval of width dx at the center of the well and at the classical turning points.
Pturning points
----------------------
Pcenter=?
I don't even know where to begin. Show work please.
the probabilities for an oscillating particle in its ground state to be found in a small interval of width dx at the center of the well and at the classical turning points is as the Pturning points is e times smaller than Pcenter.
The probability of finding the particle in a small interval of width dx around the point x (at the center of the well) is---
P (x) = |(x)|²dx
P (x) = (mωo/hπ)½ e^[(-mωo/h) *x²] dx
Putting in the values of x=0 and x=+_xo , we can compare the probabilities of the particle being in the center and of it being at the turning point, respectively
P (x=0) =(mωo/hπ)½ dx.........at center
P (x=+_xo) =(mωo/hπ)½ e-¹ dx.........at turning points
From this, we can see that the probability for the particle to be found at the turning point s is e times smaller than at the center.
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calculate the amount of charge incoloumbs that flows through an electric heater in 20 mins when the ucrrent is 8 amps
Q is the energy in coloumbs that passes through with an current heater in 20 minutes at an 8 amp current.
What's current?Charge moves across a point on the a circuit at a rate known as current. When numerous coulombs of charge pass over a wire's cross section in a circuit, a large current is the result. if the wire is tightly packed with charge carriers.
What is the current recipe?The electric current equation is I=V/R, and it can be used to determine electric current. This equation, which is based on Ohm's Law, is also referred to as the "current equation." The variables "I" and "V" stand for current, voltage, and resistance, respectively.
Briefing:I=8Amph,
T=1hr=3600sec,
Charge flow Q=it
=8*3600
Q=28800C
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A student is conducting an experiment to analyze the mechanical energy of a block-spring system. The student places a block of mass 2kg on a horizontal surface and attaches the block to a horizontal spring of negligible mass and spring constant 100N/m, as shown in the figure. There is negligible friction between the block and the horizontal surface. The other end of the spring is attached to a wall. The block-spring system is initially at the spring's equilibrium position.
The student wants to collect data of the block-spring system that can be used to determine the work done on the spring by the block when the spring is compressed. Which of the following includes only the measuring devices that the student will need in order to collect the data?
Force probe and meterstick
Out of the given options, the measuring devices that the student will need in order to collect the data to determine the work done on the spring by the block are Force probe and meterstick.
W = F d cos θ
W = Work done
F = Force
d = Distance
θ = Angle between force and displacement vector
Here θ = 0°. So,
W = F d
The force applied on the block can be measured using a force probe. The force sensors essentially measure the deformation of an elastic support subject to the force. The distance that the block moves can be measured using a meter stick.
Therefore, in order to collect the data the student will need Force probe and meterstick.
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in which situation should you use high beams? in the fog or heavy snow when you're alone on a poorly lit road within 500 feet of an approaching vehicle within 300 feet behind a vehicle submit answer
Only use high beam lights in low traffic areas or on highways, especially if there are no other vehicles within 200 metres of them. High beam lights provide brilliant illumination.
In which of the following situations are high beams necessary?High beam headlights should be used when it is too dark to see the road ahead well enough to drive safely. Even the most seasoned drivers may find nighttime low visibility unnerving.
Which situations need the use of low beams?Low beams are the perfect choice if you don't want to blind other motorists while driving in traffic with your blazing high beams. Driving in heavy rain, snow, or fog requires the use of your low beam lights.
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what height does a frictionless playground slide need so that a 35 kg child reaches the bottom at a speed of 6.3 m/s ?
The height of the frictionless playground slide is 2.155 meters
What is kinetic and potential energy ?An object possesses kinetic energy when it is in motion. A force needs to be applied if we want to accelerate an object. We must use effort to apply a force. The object will be moving at a new constant speed once the operation is finished and energy has been transferred to it.
Potential energy is a form of stored energy that is dependent on the arrangement of a system's components. When stretched or squeezed, a spring has higher potential energy. When lifted above the ground, a steel ball has more potential energy than when it is brought to rest on the ground.
Kinetic energy = Potential energy
K. E = 0.5m v² ; P.E = mgh
0.5mv² = mgh
Dividing both sides by m, we get ;
gh = 0.5v²
h = [(0.5v²) ÷ g]
h = (0.5 × 6.5²) ÷ 9.8
height = 2.155 m
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archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. suppose a chunk of copper with a mass of 467.5 g in air is found to have an apparent mass of 431.4 g when completely submerged in an unknown liquid. (a) what mass (in g) of fluid does the copper displace? webassign will check your answer for the correct number of significant figures. g (b) what is the volume of copper (in cm3), using its density as given in this table? webassign will check your answer for the correct number of significant figures. cm3 (c) calculate the fluid's density and identify it. water
Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. If a chunk of copper with a mass of 467.5 g in air is found to have an apparent mass of 431.4 g when completely submerged in an unknown liquid. (a) The mass (in g) of fluid does the copper displace will be36.1 g (b) The volume of copper (in cm3), using its density will be 51.944 [tex]cm^{3}[/tex] (c) The fluid's density will comes out to be 0.694 g/[tex]cm^{3}[/tex].
Given,
The mass of the copper chunk, M = 467.5 g
Apparent mass of the copper chunk, m = 431.4 g
According to the Archimedes' principle
(a) The mass of fluid does the copper displaces = M - m
= 467.5 g - 431.4 g
=36.1 g
(b) To calculate the density of the copper chunk we must know its density, which is 9 g/[tex]cm^{3}[/tex],
So, volume of the copper = Mass (M)/density
= 467.5/9
= 51.944 [tex]cm^{3}[/tex]
(c) The density of the fluid will be the mass of the fluid divided by the volume, which can be represented as;
Density = Mass/ volume
= 36.1/51.944
= 0.694 g/[tex]cm^{3}[/tex]
Hence, the mass of fluid does the copper displaces will be 36.1 g, volume of the copper chunk will be 51.944 [tex]cm^{3}[/tex] and density of the fluid will be 0.694 g/[tex]cm^{3}[/tex].
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draw a phasor diagram, showing v1 , v2 , and vs . state the phase relationships between each pair of these phasors.
The least interference when (A1 - A2)2 is the phase difference between adjacent slits.
What do you understand the term phasor?A phasor is a complex number that represents a sinusoidal function in physics and engineering whose amplitude, angular frequency, & beginning phase are all time-invariant. Phasors are revolving vectors with an angular rate similar to a angular frequency of a oscillations and a length equal to a peak value of the oscillations. When illustrating the phase relationship between the two or more oscillations, they are useful. They can be used to add or eliminate oscillations.
What's a phasor diagram?Phasor diagrams show an oscillating quantity as a rotating vector in phase space with an angular velocity equal to the original trigonometric function's angular frequency. The value of the quantity at a given moment can be determined by projecting the phasor onto an axis at that time.
Briefing:Let A1 represent the first wave's amplitude and A2 represent the second wave's amplitude.
Let the resultant amplitude be A. Using the interference formula, we obtain,
A= (A1)²+(A2)²+ 2×A₁× A₂ (cos theta)
When theta = 180 degrees = π radian, cos π= -1
When we plug the cos theta value into the equation, we get,
A= (A1)² +(A2)² - 2×A1×A2
A= ( A1 -A2)²
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What are the 10 conjunctive adverbs?.
Accordingly, also, additionally, similarly, likewise, therefore, specifically, yet, although, still, then, additionally, incidentally, next, subsequently, unquestionably, unquestionably, yet, nevertheless, therefore.
Conjunctive words: What are they?Words that link other words or word groupings together are called conjunctions. Words, phrases, and sentences of equal significance are joined by a coordinating conjunction. There are three basic coordinating conjunctions: and, or, and but.
Which words that are conjunctions are some examples?The term used to join words, phrases, and clauses is called a conjunction. Conjunctions come in many shapes and sizes in English, but some of the more popular ones include and, or, but, because, for, if, and when.
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q7. a rod is free to slide on a frictionless sheet of ice. one end of the rod is lifted by a string. what would be the angle of the string to maintain the rod at rest? (acute angle, right angle, obtuse angle) explain your choice.
If a rod is free to slide on a frictionless sheet of ice and one end is lifted by a string, the angle of the string would be a right angle in order to maintain the rod at rest.
This is because in order for an object to be at rest, the forces acting on it must be balanced. In this case, the only forces acting on the rod are the force of gravity pulling the rod down and the force of the string pulling the rod up. If the string is at a right angle to the rod, the forces will be balanced and the rod will remain at rest.
If the string were at an acute angle (less than 90 degrees), the force of the string would not be strong enough to balance the force of gravity, and the rod would slide down. If the string were at an obtuse angle (greater than 90 degrees), the force of the string would be too strong and the rod would be pulled off the sheet of ice.
Therefore, the angle of the string must be a right angle in order to maintain the rod at rest on the frictionless sheet of ice.
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Calculate the angular momentum of a olid uniform phere with a radiu of 0. 115 m and a ma of 15. 0 kg if it i rotating at 5. 70 rad/ about an axi through it center
The angular momentum of a solid uniform sphere of radius 0.115 m and mass 15.0 kg if it rotates about an axis at its center at 5.70 rad/s
A uniform solid sphere of radius (r) = 0.115m
Mass of sphere (m)= 15kg
Rotation speed = 5.70 rad/s about an axis at its center
To find the angular momentum about its axis L =IW
I = moment of inertia = 2/5mr^2
W= speed of rotation
L= (2/5)*15*0.115*0.115*5.70
L = 0.452295kgm2/s
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a 60-lb uniform thin panel is placed in a truck with end a resting on a rough horizontal surface and end b supported by a smooth vertical surface. knowing that the panel remains in the position shown, determine (a) the maximum allowable acceleration of the truck, (b) the corresponding minimum required coefficient of static friction at end a.
The maximum allowable acceleration of the truck is 0.544, the corresponding minimum required coefficient of static friction at end is 34.64.
What is acceleration?
Acceleration describes the speed and direction changes in velocity over time. Acceleration refers to the change in speed or direction of an item or point traveling straight forward. Due to the constant change in direction, motion on a circle accelerates even while the speed is constant.
What is static friction force?
Static friction occurs when an object is subjected to a force that is opposed by the frictional force; as a result, the object is kept at rest until the static friction force is removed. When there is kinetic friction, an object is not allowed to move.
Free body diagram
When the acceleration of the truck is maximum there is no contact between the parallels and the waves therefore, the reaction force at point "B" will be zero.
Mₐ= (ma) d
= (w* 2.5 cos 60°) = (ma 2.5 sin 60°)
=( 60*2.5 cos 60°)= (60/32.2 *a*2.5 sin 60°)
a= 15.89 ft/ s²
Equation of equilibrium in y- direction
Fy=0, Nₐ=w=60lb
Equation of equilibrium in x direction
Fₓ= max
F= mₐ (60/32.2*18.59)
f= 34.64
and as frictional force in μN
34.64= μ*60
μ= 0.544
Therefore, the maximum allowable acceleration of the truck is 0.544, the corresponding minimum required coefficient of static friction at end is 34.64.
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The illustration below shows three toy ducks floating on water, moving up and down as a wave travels to the right with a velocity of 3 m/s.Which of the following is the frequency of the wave?A. 0.75 Hz
B. 1.33 Hz
C. 1.5 Hz
D. 6.0 Hz
The illustration below shows three toy ducks floating on water, moving up and down as a wave travel to the right with a velocity of 3 m/s, the wave frequency is 0.75Hz
Wave frequency is the number of waves that travel through a fixed location in a specific amount of time. The hertz (Hz) is the SI unit for wave frequency, with 1 hertz equaling 1 wave passing a fixed point in 1 second. A greater wave has much more energy than a lower-frequency wave that has the same amplitude. Because higher frequency waves have closer crests, they have shorter wavelengths.
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The capacitors in each circuit are fully charged before the switch is closed. Rank, from longest to shortest, the length of time the bulbs (resistors) stay lit in each circuit.
(picture)
The idea here is to simplify circuit analysis by using resistors and capacitors. Using the time constant for every circuit, rank the circuits from longest to shortest. The circuit's time constant is ranked as follows: C > A = E > B > DC > A = E > B > D.
A capacitor is a device that stores electrical energy in an electric field by building up electric charges on two nearby surfaces that are isolated from one another. It has two terminals and is a passive electronic part.
Capacitance is the name for a capacitor's effect. While there is some capacitance between any two electrical conductors that are close to one another in a circuit, a capacitor is a component made to increase capacitance. Condenser is still used in a few compound names for the capacitor, like condenser microphone. Capacitors are made from a wide range of materials and come in a wide variety of shapes, sizes, and designs. They all have at least two electrical conductors, known as plates, separated by an insulating layer (dielectric).
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if you see a lightning bolt in the distance and 15 seconds elapse before you hear the corresponding thunder, how far away was the lightning bolt?
The distance of the lightning bolt from the point is 850m
What is speed of sound in air?The speed of sound is defined as the distance through which a sound wave’s point, such as a compression travels per unit of time. The speed of sound remains the same for all frequencies in a given medium under the same physical conditions.
We can use echo formula to calculate the distance at which the sound in air travels. it is given by v= 2x/t
where v is the speed of sound in air which is 340m/s and x is the distance traveled and t is the time.
therefore,
340= 2x/5
2x= 1700
x= 1700/2
x= 850m.
Therefore the distance of the lightning bolt to the point of staying is 850m.
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A was of sticky clay of mass m is hurled horizontally at a wooden block of mass M initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides a distance d before coming to rest. If the coefficient of friction between the block and the surface is μ. what was the speed of the clay immediately before impact?
If the coefficient of friction between the block and the surface is μ. what was the speed of the clay immediately before impact:
solution:-
1st conservation of momentum
(m1 * v1i) + (m2 * v2i) = (m1 +m2) * vf
v2i = 0 m/s because the wooden block is at rest
(m1 * v1i) + (m2 * 0) = (m1 +m2) * vf
(m1 * v1i) = (m1 +m2) * vf
Equation #1
vf = (m1 * v1i) ÷ (m1 +m2)
vf is the velocity of the clay and block as they slide a distance d before coming to rest.
2nd conservation of energy.
The work of friction will reduce the kinetic energy of the clay and block to 0 Joules as the clay and block slide across the horizontal surface.
Initial Kinetic energy of the clay and block = ½ * (m1 +m2) * vf^2
Work of friction = µ * (m1 +m2) * g * d
Final KE = 0
Initial Kinetic energy of the clay and block – Work of friction = 0
[½ * (m1 +m2) * vf^2] – [µ * (m1 +m2) * g * d] = 0
[½ * (m1 +m2) * vf^2] = [ µ * (m1 +m2) * g * d]
Divide both sides by (m1 +m2)
[½ * vf^2] = [ µ * g * d]
vf^2 = [2 * µ * g * d]
Equation #2
vf = [2 * µ * g * d]^0.5
Equation #1
vf = (m1 * v1i) ÷ (m1 +m2)
set Equation #1 = Equation #2
(m1 * v1i) ÷ (m1 +m2) = [2 * µ * g * d]^0.5
Multiply both sides by (m1 +m2)
(m1 * v1i) = (m1 +m2) * [2 * µ * g * d]^0.5
Divide both sides by m1
v1i = (m1 +m2)/m1 * [2 * µ * g * d]^0.5
Speed is the gap traveled in step with unit of time.
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a vehicle with headlights separated by 1.80 m approaches an observer holding an infrared detector sensitive to radiation of wavelength 885 nm. what aperture diameter is required in the detector if the two headlights are to be resolved at a distance of 20.0 km?
The aperture diameter required in the detector if the two headlights are to be resolved at a distance of 20.0 km is 1.2 cm.
When a vehicle approaches with separated headlights S = 1.80 m and resolved at a distance of r = 20.0 km = 2 × 10⁴ m. The angle for the headlights is
S = θr
θ = S ÷ r
θ = 1.8 ÷ (2 × 10⁴)
θ = 9 × 10⁻⁵ radians
The Rayleigh criterion for the diffraction limit is the formula to calculate the aperture and limited angle with the radiation wavelength = λ = 885 nm = 885 × 10⁻⁹ m
θ = 1.22 × (λ ÷ D)
θD = 1.22 × λ
9 × 10⁻⁵ × D = 1.22 × 885 × 10⁻⁹
D = 1.0797 × 10⁻⁶ ÷ (9 × 10⁻⁵)
D = 0.012 m
D = 1.2 cm
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calculate the recoil velocity in the horizontal direction, in meters per second, of a 0.95-kg plunger that directly interacts with a 0.0205-kg bullet fired at 615 m/s from the gun. take the firing direction to be the positive direction.
The recoil velocity in the horizontal direction of the plunger is 13.27 m/s
What is recoil in physics?Recoil is the backward force or momentum produced by an object such as a gun while discharging at a very high rate of velocity.
This can be understood by the famous Newton’s third law of motion in physics.
What are Newton's laws of motion?The three fundamental laws of classical mechanics known as Newton's laws of motion describe how an object's motion and the forces acting on it interact.
Newton's first law states that unless a net external force acts on an object, it will either remain at rest or continue moving at a constant speed.
According to the second law, an object's force is determined by multiplying its mass by its acceleration.
The third law of motion by Newton states that equal but diametrically opposed forces always act in pairs. There is an equal but opposite reaction to every action, to put it another way.
Given Data:mass of bullet, m1=0.0205kg
velocity of bullet before firing, u1=0 m/s
velocity of bullet after firing, v1=615 m/s
mass of plunger,m2=0.95kg
velocity of gun before firing,u2=0 m/s
Let velocity of gun after firing be, v2
From law of conservation of momentum,
m1u1+ m2u2= m1v1+ m2v2
m1×0+ m2×0=0.0205×615 + 0.95×v2
⟹0=12.60+0.95v2
⟹ v2=−13.27 m/s
This means gun moves in opposite direction to bullet, which is called recoil.
Thus, recoil velocity of plunger is equal to
13.27 m/s
Here, the negative(- ve) sign shows that plunger moves in the opposite direction of bullet.
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What would be the orbital speed and period of a satellite in orbit 1.22 ✕ 10^8 m above the Earth?
The orbital speed and orbital period of a satellite are 1765 m/s and 4.56 ×10⁵s.
What is orbital speed?The orbital speed can be described as the speed at which it orbits around either the barycenter or its speed relative to the center of mass of the most massive body.
Given the distance of the satellite from Earth's surface = 1.22 ×10⁸ m
The distance of the satellite from the center of the earth:
r = 1.22 ×10⁸ m + 6.38 ×10⁶
r = 1.284 ×10⁸ m
The orbital speed of the satellite : [tex]V = \sqrt{\frac{GM}{r} }[/tex]
The mass of the earth, [tex]M = 6 \times 10^{24} Kg[/tex]
[tex]V=\sqrt{\frac{6\times 10^{24}\times 6.67 \times 10^{-11}}{1.284 \times 10^{8}} }[/tex]
V = 1765 m/s
The orbital period of the satellite:
[tex]T =\frac{2\pi r}{V}[/tex]
[tex]T=\frac{2\times 3.14\times 1.284 \times 10^8}{1765}[/tex]
T = 4.56 ×10⁵ s
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suppose that hiring one, two, three, or four workers at a glass factory generates total outputs of 200, 350, 450, or 500 fancy glasses, respectively. the marginal product of the fourth worker is fancy glasses.
If hiring one, two, three, or four workers at a glass factory generates total outputs of 200, 350, 450, or 500 fancy glasses, respectively. The marginal product of the fourth worker is 50 fancy glasses
Marginal product = ( Qn - Qn-1 ) / ( Ln - Ln-1 )
Qn = Output at n
Qn-1 = Output at n - 1
Ln = Number of workers at n
Ln-1 = Number of workers at n - 1
For the fourth worker,
Qn = 500
Qn-1 = 450
Ln = 4
Ln-1 = 3
Marginal product = ( 500 - 450 ) / ( 4 - 3 )
Marginal product = 50 / 1
Marginal product = 50
Therefore, the marginal product of the fourth worker is 50 fancy glasses
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