The ratio of the orbital radii of the planets is 4:1.
The ratio of their periods is 8:1.
What is orbital radius and periods in circular motion?Planetary bodies circle the Sun according to Kepler's three laws. They explain how planets orbit the Sun in elliptical fashion, how they traverse the same amount of space in a given length of time regardless of where they are in their orbit, and how their orbital periods are related to the size of their orbits (its semi-major axis).
An object's orbital radius is the typical distance it travels around a bigger object. An illustration would be that the Sun and Earth are typically 150 million kilometres apart. The orbital radius is also this.
Let the mass of the planet be m and the mass of the star be M.
r = radius of ordit
v = speed
We know that
gravitational attraction = centripital force
GMm/r^2 = mv^2/r
[tex]v = \sqrt{GM/r}[/tex]
Hence
v ∝ 1/[tex]\sqrt{r}[/tex]
a) Here v₁/v₂ = v/2v = [tex]\sqrt{\frac{r2}{r1\\\ }[/tex]
squuaring both sides
1/4 = r2/r1
Thus r1/r2 = 4/1
Hence ratio of orbital radii is 4:1.
b) As per keplers law of planetary motion,
T^2 ∝ r^3
[tex]\frac{T_{v} ^{2} }{T_{2v} ^{2} } = \frac{r_{v} ^{3} }{r_{2v} ^{3} }[/tex]
[tex]\frac{r_{v} ^{3} }{r_{2v} ^{3} } = 4^{3} = 64[/tex]
[tex]\frac{T_{v} }{T_{2v}} = \sqrt{64} = 8[/tex]
Thus ratio of time periods is 8:1.
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When a sample of aluminum absorbed 9. 85 j of heat, its temperature increased from 23. 2oc to 30. 5oc. The mass of the sample was ___ g. (specific heat of al is 0. 90 j/g. Oc).
The mass of the sample = 1.50 g
From the question, we have
q= 9.86 J
C = 0.90 J/g-K
temperature ΔT = ( 30.5 ºC - 23.2 ºC ) = 7.3 ºC = 7.3 K
The heat (q) absorbed is,
q = m x C x ΔT
m= q/ (C x ΔT)
m = 9.86 J / ( 0.90 J/g-K ) x 7.3 K ) = 1.50 g
The mass of the sample = 1.50 g
Heat :
Heat is energy that is transmitted from one body to another when temperatures are different. Heat travels from the hotter body to the colder body when two bodies at differing temperatures come in contact. Heat is the result of the movement of kinetic energy within a material or an item, or from an energy source to a material or an object. Radiation, conduction, and convection are the three mechanisms through which such energy can be transferred.
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a spacecraft orbits an unknown planet at a distance of 5:2 107mfrom its center. the period of its orbit is 52 hours. what is the mass of the planet?
The mass of the planet is 2.37E²⁷kg.
What were the Kepler laws known as?The sun is at one focus in each of the planets' elliptical orbits, according to Kepler's First Law, also known as The Law of Ellipses. According to Kepler's Second Law, or The Law of Equal Areas in Equal Time, a planet's line of sight sweeps out equal areas in its orbital plane over equal periods of time.
According to Kepler's law,
m V² / R = G M m / R²
M = R V²/G (balancing forces)
V = 2πR/T (speed of craft)
M = 4 π²R³ / (G ×T²) (substituting for V)
M = 4 π²×52E²¹ / (6.67E¹¹×1.30E⁷)
M = 39.5 × 52 / (6.67×1.3) × 10²⁵ kg
M = 2.37E²⁷kg.
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How do I solve this equation
The kinetic energy of a electron that passes undeviated through perpendicular electric and magnetic field is 1.2 × 10⁻²⁶ kg.m².s⁻² .
How is the kinetic energy calculated ?Given here is ,
q = 1.60218 × 10⁻¹⁹ C
m = 9.10939 × 10⁻³¹ kg
E = 0.18 kV/m = 180 V/m
B = 1.1 mT
where,
q is charge on electron
m is mass of electron
E is electric field
B is magnetic field
We know the kinetic energy of electron is calculated by
K.E = 1/2 (mv² )
∴ v = F / qB
∵ F = Eq
∴ F = 180 × 1.60218 × 10⁻¹⁹
∴ F = 288.3 × 10⁻¹⁹
∴ F = 2.8 × 10⁻¹⁷ N
Now,
v = F / qB
∴ v = (2.8 × 10⁻¹⁷ ) / (1.60218 × 10⁻¹⁹ ×1.1 )
∴ v = (2.8 × 10⁻¹⁷ ) / (1.7 × 10⁻¹⁹ )
∴ v = 1.64 × 10²
∴ v = 164 m.s
Now to calculate K.E,
K.E = 1/2 (mv² )
∴ K.E = 1/2 (9.10939 × 10⁻³¹ × 164²)
∴ K.E = 1/2 (9.10939 × 10⁻³¹ × 26896)
∴ K.E = 1/2 (245006.15 × 10⁻³¹ )
∴ K.E = 122503 × 10⁻³¹
∴ K.E = 1.2 × 10⁻²⁶
Hence , the kinetic energy of electron is 1.2 × 10⁻²⁶ kg.m².s⁻².
What is kinetic energy ?We must use force to accelerate an object. We must work in order to exert force. When an object is worked on, energy is transferred and the object moves at a new constant pace. The transferred energy is known as kinetic energy, and it is proportional to the mass and speed attained.In Physics, kinetic energy is defined as follows: The kinetic energy of an object is the amount of work it can do due to its mobility.Can learn more about kinetic energy from https://brainly.com/question/114210
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a spaceship, at rest in a certain reference frame s, is given a speed increment of 0.500c. it is then given a further 0.500c increment in this new frame, and this process is continued until its speed with respect to its original frame s exceeds 0.999c. how many increments does it require?
In order to give a spaceship at rest in a specific reference frame s a speed increment of 0.500c, seven increments are required. Then, in this new frame, it receives an additional 0.500c increment.
The speed of an object, also known as v in kinematics, is a scalar quantity that refers to the size of the change in that object's position over time or the size of the change in that object's position per unit of time. The distance travelled by an object in a certain period of time divided by the length of the period gives the object's average speed in that period.
The spacecraft moves at v1 = 0.5c after the initial increment.The equation becomes V2 = V+V1/1+V*V1/c after the second one. 2 V2 = 0.5c+0.50c/1+(0.50c)^2/c^ 2 = 0.80c
Likewise, V3 = 0.929c
V4 = 0.976c
V5 = 0.992c
V6 = 0.99c
V7 = 0.999c
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determine the magnitude of the flux in kg/s (no sign, just the magnitude) of air through the surface s. the density of air is 1.2 kg/m3. the velocity of the air is
the velocity of the air is94.25V kg/s
Calculation :
Assuming velocity of air through spherical shell = V m/s
then flux = ρ *π *[tex]a^{2}[/tex]*V kg/s
=1.2 *π *[tex]5^{2}[/tex]*V = 94.25V kg/s
Rate of change of distance. Rate of change of displacement. The velocity of a moving object can never be negative.
Velocity is the directional velocity of a moving object as an indicator of the observed rate of change of position from a given reference frame.
Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) versus change in time (Δt), given by the formula v = Δs/Δt.
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The correct answer is 94.25 kg/s
Flux can be stated as the rate of flow of a fluid, radiant energy, or particles across a given area.
The magnetic flux is the magnetic lines present in among two magnets or solenoid is mutual flux.
Velocity is the count of difference in displacement in a given time and it is a vector quantity which has both magnitude and direction.
The mass of a sample of a chemical compound divided by the quantity, or number of moles in the sample, measured in moles, is known as the molar mass of that compound.
Given
density = 1.2 kg/m³
The velocity of the air is 94.25V kg/s
Assuming velocity of air through spherical shell = V m/s
Then flux = ρ *π * a² * V kg/s = 94.25V kg/s
Therefore, the velocity given will be 94.25V kg/s
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four resistors are in parallel. if they are all the same (10 ohms each), what is the total equivalent resistance of the circuit?
the total equivalent resistance of the circuit if four resistors in parallel is 2.5ohm
Total resistance in a parallel circuit is less than any of the individual resistances: Rtotal = 1 / (1/R1 + 1/R2 + . . . 1/Rn)
Resistors are said to be connected together in parallel when both of their terminals are respectively connected to each terminal of the other resistor or resistors.
From 1/R=1/r1 +1/r2+ 1/rn for resistors in parallel you will find that 4ohm resistors in parallel are equivalent to 2 ohms.in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 + .The total resistance of a parallel circuit is NOT equal to the sum of the resistors (like in a series circuit).
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when cassini, a saturn-orbiting spacecraft, made its first flybys of enceladus in 2005, what unusual discovery did it make, and what did this imply?
Cassini recorded the water geysers at the south polar region which suggests that the particles of Saturn's E ring are provided by Enceladus.
What makes Enceladus so special?According to research, Enceladus likely possesses hydrothermal vents that pour hot, mineral-rich water into its ocean in addition to having most of the chemical components required for life. Enceladus, which is about the same width as Arizona, has the solar system's whitest, most reflective surface.When the spacecraft Cassini did its first flyby of Enceladus, the sixth largest moon of the planet Saturn, it discovered that the magnetic field of Saturn was deflected nearby signifying the presence of an atmosphere which might be thin but still significant. Cassini also recorded the water geysers at the south polar region which suggests that the particles of Saturn's E ring are provided by Enceladus.
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A loop is placed in a region where the magnetic field is changing. At t = 0 s the magnetic field is 1 t directed into the page. Over a period of 2 s the field changes uniformly to 1 t directed out of the page.
A circular loop carrying current has no magnetic field at its center.
What is the magnetic field's direction at the loop's center?The magnetic field inside the loop will either be oriented along the axis or counter clockwise depending on the direction of the current. A current-carrying circular loop will have its magnetic field oriented along its axis at its center.
What changes in the magnetic field occur as the loop's radius grows?With an increase in the circular loop's radius, the magnetic field intensity drops. As more electric current flows through the circular wire loop, the magnetic field becomes more intense.
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A 725 kg car that is moving with 14 m/s hit a truck of mass 2750 kg moving at 17 m/s in the opposite direction.
What is the velocity of the car after impact if the car and truck lock together?
PLEASE HELP ASAP
Answer:
16.4 m/s
Explanation:
725*14+2750*17=
10150+46750=56900
56900=(725+2750)*v ==> v, velocity, is what we're solving for
56900=3475v
56900/3475=3475v/3475
v=16.374 m/s
v=16.4 m/s
the computations based upon the quantum mechanics model take longer and are more rigorous.
The computations based upon the quantum mechanics model take longer and are more rigorous is true.
Why is quantum mechanics so complicated?
The most difficult area of physics is regarded as quantum mechanics. Systems with quantum behavior do not behave according to the usual laws; they are difficult to see and feel, they can have contentious properties; they can exist in multiple states simultaneously; and others,
Therefore, the mathematical terms that provide a thorough explanation of quantum mechanics are known as quantum mechanical mathematical formulations. This mathematical formalism primarily makes use of linear spaces called Hilbert spaces, a subset of functional analysis.
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The complete question:
The computations based upon the quantum mechanics model take longer and are more rigorous. ( true or false.)
the circuit is protected by a ground fault interrupter in the plug. the water in the tank is grounded. the two bare wires correspond to the two pins on the ground fault interrupter plug. if the __________ wire is touched to the water, the ground fault interrupter will disconnect the circuit.
If the hot wire is touched to the water, the ground fault interrupter will disconnect the circuit.
GFI or GFCI This device protected from collecting the electric shocks arise from the faults in the electric devices that are used at home. It would be work by comparing the current on the input side that shows the hot side to the current on the outside side that shows the neutral side of the circuit.
In the case when hot wire give 120 VAC current source while on the other hand the neutral wire gives the return path that are given by the hot wire
Therefore, if the hot wire is touched to the water, the ground fault interrupter will disconnect the circuit.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: The circuit is protected by a ground fault interrupter in the plug. The water in the tank is grounded. The two bare wires correspond to the two pins on the ground fault interrupter plug. If the __________ wire is touched to the water, the ground fault interrupter will disconnect the circuit. Select the best answer from the choices provided. Neutral, Hot, Ground]
The computations based upon the quantum mechanics model take longer and are more rigorous. True or false?
The mathematical formalisms that provide a thorough explanation of quantum mechanics are known as quantum mechanical mathematical formulations. This mathematical formalism primarily makes use of linear spaces called Hilbert spaces, a subset of functional analysis.
What are the key features of the quantum mechanical model?
According to a mathematical function known as a wavefunction, which is sometimes abbreviated as, the quantum mechanical model of atoms represents the three-dimensional position of the electron in a probabilistic manner. Oscillations are another name for atomic wavefunctions.
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What is the frequency of 2 waves per second?
The frequency of 2 waves per second is 0.5Hertz.Frequency is measured in Hertz.
Frequency implies the amount of cycles in a particular unit of time. The legitimization for why the sky is blue or anything contains assortment can be successfully figured out by it. Besides, it can similarly get a handle on why the voice of specific individuals is significant while for others it isn't significant. Similarly, Frequency plays a significant impact on the notes of a piano or different instruments.
This number of occasions is irrefutably a crucial property of a wave. The waves include people reliably. Besides, light is an electromagnetic wave and the fan is a sound wave. A wave is clearly a vibration and conveys energy with it. For the most part basic, the amount of waves passing by each second insinuates the repeat of the wave. Additionally, its assessment occurs in Hertz (Hz).
We know a formula
Frequency=1/Time period
=>v=1/T
Putting the values, we get
=>v=1/2
=>v=0.5/sec or
v=0.5Hz.
Hence, frequency of wave is 0.5Hz.
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one end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 127 hz . the other end passes over a pulley and supports a mass of 1.50 kg. the linear mass density of the rope is 0.0550 kg/m . part a what is the speed of a transverse wave on the rope?
The speed of a transverse wave on the rope is 16.359 m/s
The tension in the rope will be equal to the weight of the hanging mass:
T = mg = (1.5 kg)(9.81 m/s)
T = 14.72 N
Now, the speed of the transverse wave on the rope is given by the following formula:
V = [tex]\sqrt{T/μ}[/tex]
where,
v = speed = ?
μ = linear mass density = 0.0550kg/m
Therefore,
V = [tex]\sqrt{14.72/0.0550}[/tex]
V = 16.359 m/s
A wave that oscillates perpendicular to the direction of the wave's advance is said to be transverse. Comparatively, a longitudinal wave moves in the direction of its oscillations. Transverse waves include those in the water.
A straightforward illustration may be seen in the waves that can be made on a horizontal length of string by anchoring one end and moving the other end up and down. The waves made on a drum's membrane are another illustration. The directions in which the waves travel are parallel to the membrane plane, yet the membrane's individual points move up and down in directions that are perpendicular to that plane. Another example of a transverse wave with oscillations that are not periodic is light.
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You place a 500 g block of an unknown subtance in an insulated container filled 2 kg of water. the block has an initial temperature of 50 degrees c. the water is initially at 20 degrees c. if the equilibrium temperature of the block and water is 25 degrees c, what is the specific heat of the block? the specific heat of water is 4186 j/kg k.
The specific heat of the block is 3349J/kg C if a 500 g block of an unknown substance in an insulated container.
We know very well that if a system is in equilibrium state, it means that Heat loss = Heat gained
Also, Quantity of heat gained or released is given by = mcΔ∅
where m is defined as mass of substance
c is defined as the specific heat capacity
and Δ∅ is defined as the change in temperature
Therefore, applying the above formula by assuming heat lost by water will be heat gained by the block.
=>m₁×c₁×(∅₂-∅₁) = m₂×c₂×(∅₁-∅₃)
where, we have m₂ as mass of water = 2kg
c₂ as specific heat capacity of water = 4186J/kg C
∅₃ as initial temperature of water = 20°C
Also, we have m₁ is defined as the mass of block = 500g = 0.5kg
c₁ is defined as the specific heat capacity of unknown substance
∅₂ is defined as block initial temperature = 50°C
∅₁ is defined as equilibrium temperature of block and water after mix= 25°C
Therefore, on putting the above quantities on above formula, we get
=>0.5×c₁×(50-25) = 2 x 4186×(25-20)
=>0.5×c₁×25=41860
=> c₁×12.5=41860
=>c₁=41860/12.5
=>c₁ = 3348.8J/kg C≅ 3349J/kg C
Hence, specific heat of the block is 3349J/kg C.
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while the astronaut is near the black hole for what it seems to her like an hour, how much time passes on the spaceship?
For a black hole observer, one hour is equivalent to 100,000,000 years on Earth.
In contrast to time distant from a black hole, time moves more slowly as you approach closer to one. (According to Einstein's theory, this effect is produced by any big body, including the Earth. Because of how weak Earth's gravity is, the impact of time slowing has been seen and verified by sensitive devices. For instance, if you lived on the summit of Mount Everest, you would age one billionth of a second faster than you do at sea level.) The tremendous slowing of time is seen close to a black hole. Time is stopped from the perspective of an observer outside the black hole. The border of the hole, for instance, would seem to be frozen in time while an item fell into it.
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Compare the magnitude and range of gravity with the magnitude and range of electromagnetic force.
The magnitude and range of gravity depends on he mass of the objects and their distance. The electromagnetic force of an electromagnetic component depends on the number turnings of the electromagnetic field and the current flowing through it.
What is gravity?Gravity or gravitational force is the force exerted by an object by which it attracts other objects into its centre of mass. Earth gravitationally pull every objects into its centre and we exeriance as our weight.
The gravitational force between two objects is always dependant on the mass of the objects and the distance between them. Gravity is directly proportional to the mass and inversely proportional to the distance.
The electromagnetic force is associated with both electric field and magnetic field and is proportional to the field strengths. It is dependent n the current carried and the turnings of coil by which magnetic field induction is created.
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The Doppler Effect has applications in robotics.
A) False
B) True
in a certain process, the energy of the system decreases by 250 kj . the process involves 480 kj of work done on the system. find the amount of heat q transferred in this process.
Therefore, in this process, 230 kJ of heat was transferred.
Find the amount of heat q transferred in this process? This process follows the first law of thermodynamics, which states that energy can be converted from one form to another, but it cannot be created or destroyed.The amount of heat transferred in this process can be calculated by using the equation: Q = W + Ewhere Q is the amount of heat transferred, W is the work done on the system, and E is the change in energy of the system.In this process, W is 480 kJ and E is -250 kJ. Using the equation above, we get:Q = 480 kJ + (-250 kJ)Q = 230 kJTherefore, in this process, 230 kJ of heat was transferred.This equation applies to any type of process involving a change in energy, and can be used to calculate the amount of heat transferred when given the amount of work done on the system and the change in energy of the system.To learn more about the first law of thermodynamics refer to:
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Galaxies
A. are not known for certain to exist.
B. contain many millions of stars, and some contain a billion or more.
C. are too far away to photograph clearly.
D. have very little, if any, mass.
a 16m long string is stretched to a tension of 60n. the string is plucked, and the resulting wave travels at 40m/s. what is the mass of the string?
The string is plucked, and the resulting wave travels at 40m/s. mass of the string 0.6 kg.
Given
velocity(v)=40m/s.
length of string(l)=16m.
Tension in string(T)=60N
formula to calculate velocity in a string:
v=root(T/m/l)
putting the value of given data and calculating we get,
mass of string as 0.6kg
Tension:
In physics, stress is described as tension transmitted axially by a cord, rope, chain, or similar object, or through the ends of a rod, truss member, or similar three-dimensional object. Stresses can also be described as pairs of acting and reaction forces acting at each end of the element.
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One type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.700 s for a 0.0225 kg mass?
The force constant of the spring is 1.81 N/m.
When all other forces acting on the mass in a damped mass-spring system are grouped together into one term denoted by F(t). The spring constant is the type of force that is required to stretch the string.
Using the relation;
T = 2π√m/k
T = period = 0.700 s
m = mass in kilograms = 0.0225-kg
k = spring constant = ?
Making k the subject of the formula;
k = 4π²m/T²
k = 4 × (3.14)² × 0.0225/(0.700 )²
k = 1.81 N/m
Therefore, the force constant of a spring needed to produce a period of 0.700 s for a 0.0225 kg mass is 1.81 N/m.
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water flows with a speed of 3.50 m/s through a garden hose with a diameter of 20.0 mm. what is the volume flow rate, q ? meters
The volume flow rate of water flows with a speed of 3.50 m/s through a garden hose with a diameter of 20.0 mm is 1.099 × 10⁻³ m³s⁻¹.
Given:
Speed, s = 3.5 m/s
Diameter, d =20 mm
Volume flow rate—also referred to as volumetric flow rate or flow rate—is a key idea in fluid dynamics that quantifies the volume of fluid that passes through a particular site in a given amount of time. It measures the amount of fluid that moves across a specific cross-sectional area in a given amount of time.
The rate of flow is given by:
Q = As
Q = π(d/2)² × 3.5
Q = 3.14× 10⁻⁴ × 3.5
Q = 1.099 × 10⁻³ m³s⁻¹
Hence, the volume flow rate of water flows with a speed of 3.50 m/s through a garden hose with a diameter of 20.0 mm is 1.099 × 10⁻³ m³s⁻¹.
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what is the wavelength (in m) of an electron accelerated through a 21.4 kv potential, as in a tv tube? for the purpose of this exercise assume the electron is non-relativistic.
An electron accelerated over a 21.4 kV potential, such as in a TV tube, has a wavelength of about 5.3 103.
What is an electron's wavelength (measured in metres) when it is propelled through a 21.4 kV potential, such as in a television tube?When an electron is driven through a potential, V, its wavelength,, may be calculated using the formula = h/2mV, where h is Planck's constant. The wavelength of an electron accelerated via a 21.4 kV potential can be computed using the formula: = 6.626 x 10-34 Js / 2. (9.11 x 10-31 kg) (21.4 x 103 V)
λ = 1.19 x 10-10 m
The above expression can be used to determine the electron's wavelength because it is assumed that the electron behaves non-relativistically. The end result is a wavelength of 119 pm, or 1.19 x 10-10 m. (picometers). This wavelength is extremely tiny, measuring roughly 1/500th the size of a hydrogen atom.
The size of the image on the screen depends on the wavelength of an electron in a TV tube.
The resolution of the image increases with decreasing wavelength. The wavelength gets smaller and the image gets clearer as the voltage increases.
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what is the total displacement of a student who walks 100 meters north and then turns around and walks 30 meters south?
The total displacement of a student is -30 m/s.
100 meters north, 30 meters south
Δd1 = -100 (- ve indicates direction)
Δd2 = 70
Total displacement = d1 + d2 = -100 + 70 = -30 m/s
The final distance from the beginning location, or total displacement, is represented by a vector sum. A person moving toward the back of an airplane or a professor moving to the right in relation to a whiteboard are two examples of how an object can move relative to a reference frame and change position. Displacement is a term used to describe this shift in location. Displacement refers to a movement or displacement of an object. Displacement refers to a movement or displacement of an object. Displacement refers to the shift in position along a straight line, whereas position is the numerical value of x along a space where an item might be. Because displacement specifies direction, it is a vector and can be either positive or negative.
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the de broglie equation relates the wavelength and the kinetic energy of particles. what is the mass of a particle with a speed of 2.34 × 106 m/s with a de broglie wavelength of 2.25 × 10-9 m?
Mass is [tex]1.26*10^{-81} kg[/tex]
What is kinetic energy?
The energy an item has as a result of motion is known as kinetic energy. A force must be applied to an item in order to accelerate it. We must put forth effort in order to apply a force. After the job is finished, energy is transferred to the item, which then moves at a new, constant speed.
As per de broglie equation,
λ = h/p
where h is plank's constant and p is momentum
as, p = mv
therfore,
λ = h/mv
m = h/vλ
mass = [tex]1.26*10^{-81} kg[/tex]
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An airplane starts from rest and accelerates on a runway at 5 m/s^2 for 7 seconds. How far down the runway is the plane after 7 seconds?
The runaway is far down for 122.5 m from the plane after 7 seconds.
What do you mean by equation of motion?Equations of motion relate the displacement of an object to its velocity, acceleration and time.
For motion with a constant acceleration (a), from an initial velocity (u), to a final velocity (v), the equations are given as follows:
Velocity, v = u + at
Displacement with positive acceleration, [tex]s=ut+\frac{1}{2}at^{2}[/tex]
Displacement knowing initial and final velocities, [tex]s=\frac{1}{2}(u+v)t[/tex]
Velocity squared, [tex]v^{2} =u^{2} +2as[/tex]
where,
t is the time over which the acceleration occurs
s is the displacement of the object from its initial position.
Calculation:Acceleration (a) = 5 m/s^2
Time (t) = 7 seconds
Initial velocity is zero i.e., u = 0
Therefore, the distance travelled (s) can be given by the following Equation of motion:
[tex]s=ut+\frac{1}{2}at^{2}[/tex]
[tex]s= 0\times7+\frac{1}{2}\times5\times7^{2}[/tex]
[tex]s=122.5 m[/tex]
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a uniform sphere made of modeling clay has radius r and moment of inertia i1 for rotation about a diameter. it is flattened to a disk with the same radius r. part a in terms of i1, what is the moment of inertia of the disk for rotation about an axis that is at the center of the disk and perpendicular to its flat surface?
The moment of inertia will increase after transformation from a uniform sphere to a disk. Moment of inertia is represented by I.
We know that for a uniform sphere, moment of inertia is given by the expression =(2/5)mr² =0.4mr² where m is the mass of the sphere and r is the radius of the sphere.
Now, when a sphere is converted to disk, then its volume remains same as it is given that radius of disk and radius of sphere is same after conversion.
So, only factor is moment of inertia, we know that moment of inertia of disk is given by the formula=(1/2)mr² = (0.5)mr² where m is the mass of the disk and r is the radius of the disk.
We can see that on conversion of sphere into disk, moment of inertia increases from 0.4 to 0.5.
Hence, moment of inertia increases.
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a simple harmonic oscillator consists of a block of mass attached to a spring of spring constant what are the amplitudes
Apmlitutde for the system will be [tex]A = A_{o}e^{\frac{-bt}{2m} }[/tex].
What is amplitude in a spring mass system?Simply said, a spring-mass system is a spring system with a block hanging or fastened to the free end of the spring. The period of any item moving in a simple harmonic motion may often be determined using the spring-mass system. There are several other uses for the spring-mass system. For instance, the spring-mass system may be used to replicate foot skin deformation and the action of human tendons using computer images.
In a closed environment, a spring with mass m and spring constant k exhibits a straightforward harmonic motion.
T = 2π √m/k
It is obvious from the aforementioned equation that neither gravitational acceleration nor amplitude affect the oscillation's period. Furthermore, the period of oscillation cannot be changed by a constant force. While this is happening, the length of time directly relates to the mass of the body that is attached to the spring. If you connect a hefty object to it, it will oscillate more slowly.
Apmlitutde for the system will be [tex]A = A_{o}e^{\frac{-bt}{2m} }[/tex].
Where, A = Amplitude of oscillation
b = Decay constant
m = mass
t = time
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A tone i thrown traight up. After three econd it reache the dropping point again. Find out how high it wa yeterday
H=132.3m and U=29.4ms−1 are height and velocity respectively.
What is motion?
Motion is a change in position of an object over time. It occurs when an object moves from one point to another. Motion can be described in terms of displacement, distance, speed, velocity, and acceleration. Motion can also be described using Newton's laws of motion which state that an object in motion will remain in motion unless acted upon by an external force. Motion also describes the motion of particles in a fluid or gas, as well as the motion of waves in a medium. Motion is an essential part of the physical world and is essential for understanding the fundamental laws of nature.
Motion in a straight line
Let,
u = Initial velocity of stone
H = Maximum height attained by the stone
v = final velocity at maximum height = 0
t = time taken to attain maximum height = 3s
a=−g= acceleration due to gravity
a. We know that,
V=u+at
0=u−g×3
U=3g=3×9.8ms−2
U=29.4ms−1
b. From the equations of motion, we know that,
S=ut+ ½ a t2
H=29.4×3+½ * 9.8 *32
H=88.2+44.1
H=132.3m
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