A physical field called an electric field surrounds electrically charged particles and attracts or repels all other charged particles nearby. The physical field of a system of charged particles can also be referred to as the electric field.
In a uniform electric field E, a particle with electric charge q moves in a straight line. The speed of the particle is u.
The electric force exerted in the charge is qE.
The electric field and the velocity of the particle are both in the x direction.
For a small speed u when compared to the speed of light c, the relativistic equation reduces to the classical acceleration:
a = qE / m
Now, as u approaches c, the acceleration will tend to zero, so that the object can or will never reach the speed of light.
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A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.200 A . The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30.0 turns/cm and carries a clockwise current of 15.0A . Find (a) the force on each side of the loop
The force on each side of the loop is [tex]2.26\times10^{-4}N[/tex] away from the centre .
Magnetic field at the centre of a solenoid of length 'L' having 'N' number of turns with a current 'I' is given by [tex]B=\frac{u_0NI}{L}[/tex] ...(1) where [tex]u_0[/tex] is the permittivity of free space whose value is [tex]4\pi \times10^{-7}Tm/A[/tex] .Force due to current carrying wire 'I' in a magnetic 'B' having length 'L' is given by [tex]F=BILsin\theta[/tex] ...(2) where θ is the angle between current and length of the wire .It is given that solenoid has 30.0 turns/cM which means we have given number of turns per unit length [tex]n=\frac{N}{L} =30\times10^{2}m[/tex] and carries a clockwise current of 15.0A .
Putting above values in equation (1) , we get
[tex]B=4\pi \times10^{-7}\times 30\times10^{2} \times15.0\\B=0.0565T[/tex]
The magnetic force exerted due to their magnetic field on the sides of the loop will be away from the center of loop and is given by equation (2) .
It is given that current in the loop is 0.200 A and length of the each side of the loop is 2.00 cm [tex]=2\times10^{_2}m[/tex] and plane of the loop perpendicular to the magnetic field of the solenoid.
Putting above values in equation (2) , we get
[tex]F=0.0565\times0.2\times2\times10^{-2}\times sin90\\F=2.26\times10^{-4}N[/tex]
Direction of force is found by Fleming' Left Hand rule which states that when the thumb, index finger and middle finger of the left hand are placed perpendicular to each other, the thumb points in the direction of the magnetic force, the index finger points in the direction of the magnetic field, and the middle finger points in the direction of the flow.
According to Fleming's left hand rule, the magnetic force exerted due to their magnetic field on the sides of the loop will be away from the center of loop and is given by equation (2) .
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Using 6. 0×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9. 8 m/s2 ? assume that the net force on the earth is the force of gravity she exerts on it.
The value of the acceleration of the earth toward it when it accelerates toward the earth with 9.8m/s² is a = 7.35×10-²³m/s².
What is acceleration?Acceleration is defined as the second derivative of displacement or the derivative of velocity:
a = d/dt(dS/dt) = dV/st.
It is the rate of change of velocity, it generates a constant change over time.
What are forces?Forces are the definition of Newton's second law, which is stated under the relation:
∑ Force = mass × acceleration.
In other words, force is the origin of motion since it generates acceleration in a system.
In this case we must complete the statement:
"A student with mass 45 kg jumps off a high diving board. Using 6. 0×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9. 8 m/s2 ? assume that the net force on the earth is the force of gravity she exerts on it."
We determine the Force of the student:
F = ma
F = 45kg * 9.8m/s².
F = 441N
Now we go to the acceleration of the earth:
a = F/m
a = 441N / 6×10²⁴ Kg
a = 7.35×10-²³m/s².
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velocity changes from 2m/s to 12m/s time taken is 5 seconds (with the guess method pleasee)
Answer:
a = 2 m/c²
Explanation:
Given:
V₁ = 2 m/s
V₂ = `12 m/s
t = 5 c
______________
a -?
Acceleration:
a = ( V₂ - V₁) / t
a = ( 12 - 2 ) / 5 = 10 / 5 = 2 m/c²
three scientists measure the standard meter bar kept at the international bureau of standards (the definition of a meter). their measurements are 1.01 m, 0.99 m, and 1.00 m. are their measurements accurate, precise, or both? group of answer choices accurate but not precise neither accurate nor precise precise by not accurate accurate and precise
The measurements by the different scientists were 1.01 m, 0.99 m and 1.00 m, which are not exactly same as the standard value of a meter. But all the three values are very much close to each other.
Meter is a fundamental unit of length in the metric system and in the International Systems of Units (SI). It is denoted by m.
Therefore the measurements for the bar kept at the international bureau of standards taken by the three scientists were precise but not accurate.
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the coefficient of performance of a residential heat pump is 1.6. calculate the heating effect in kj/s this heat pump will produce when it consumes 2 kw of electrical power.
The heating effect in with the residential heat pump will be 3.2 KJ/s
Heat pump - mechanical device which convert heat from low temperature to high temperature reservoir with the use of external work.
Heating effect - it is the change of electrical energy which passes through the conductor into heat energy.
The rate of heat produced. [tex]Q_{H}[/tex] is calculated by
The coefficient of residential heat pump = 1.6
The consume of electric power = 2kw
The rate of heat produced.( [tex]Q_{H}[/tex]) =
The coefficient of performance × consume of electric power
[tex]Q_{H}[/tex] = 1.6 × 2
= 3.2 KJ/s
The heating effect in with the residential heat pump will be 3.2 KJ/s
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Answer please with working out
Answer:
(1) a) S=D/T
b)5m/s
c)3.33s
(2) a) 1.104m
Explanation:
(1) b) S=D/T
S=1500/300
S=5m/s
c) T= V-U/a
v=10
u= 2
a= 2.4
10-2=8/2.4=3.33s
(2) a) d=s×t
0.46×2.4=1.104m
A 2 kg block of cheese is in an elevator accelerating down at a rate of 1.5 m/s².
What is the normal force on the cheese?
which of these statements about density is true? group of answer choices the density of an object depends on the force of gravity. density does not depend on temperature. density is a physical property. larger objects are more dense.
The statement about density that is true is: density is a physical property
The density of an object is the relation that exist between the mass and the space that the object occupies. The general formula of the density is:
ρ = m/v
Where:
v= volumeρ= densitym= massFor example if we want to know which is the density of a body that has a mass of 100g and a volume of 150 cm³, applying the density formula we get:
ρ = 100 g/150 cm³
ρ = 0.666 g/cm³
What is density?It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.
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What is the mass of a rocket 5,000m above the Moon’s surface if 84kJ
of gravitational potential energy is stored? Assume g on the Moon =
1.63N/kg.
Considering the definition of potential energy, the mass of a rocket 5,000 m above the Moon’s surface is 10.31 kg.
Potential energyPotential energy is the energy that measures the ability of a system to do work based on its position. In other words, this is the energy that a body located at a certain height above the ground has.
Gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object to some reference point, the mass, and the strength of gravity. Then, the expression applied to the gravitational energy of the object is:
Ep= m×g×h
Where:
Ep is the potential energy in joules (J).m is the mass in kilograms (kg). h is the height in meters (m).g is the acceleration of the fall in m/s².Mass of the rocketIn this case, you know:
Ep= 84 kJ= 84,000 J (being 1 kJ= 1,000 J)m= ?h= 5,000 mg= 1.63 N/kg= 1.63 m/s²Replacing in the definition of gravitational potential energy:
84,000 J= m×1.63 m/s²×5,000 m
Solving:
84,000 J= m× 8,150 m/s²×m
84,000 J÷ (8,150 m/s²×m)= m
10.31 kg= m
Finally, the mass of a rocket 5,000 m above the Moon’s surface is 10.31 kg.
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Which two types of potential energies would be types of mechanical energies?
electrical and kinetic
nuclear and chemical
radiant and thermal
elastic and gravitational
The two types of potential energies which would be types of mechanical energies are elastic and gravitational.
The correct answer choice is option D
What is meant by potential energy?Potential energy means the energy a body possess in relation to its position. Other forms of energy include
Electrical energyKinetic energyChemical energySound energyNuclear energy Thermal energy Radiant energyKinetic energy is the energy a body possesses due to its motion.
So therefore, the two types of potential energies which would be types of mechanical energies are elastic and gravitational. The correct answer choice is option D
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Answer: it is d
Explanation: i took the unit test on edge
What is inertia and how does it relate to Newton's first law of motion?
Answer:
inertia is basically the fact that something will continue moving until something else stops it. take friction for example. If you roll a ball on the ground, it will eventually stop because of friction, you can kind of think of it like a gear wheel. and i guess it relates to newtons first law of motion because it is his first law?? i don't know how to answer that
Explanation:
How much kinetic energy does a 3.50kg block with a speed of 4.00m/s have?
Taking into account the definition of kinetic energy, the kinetic energy of a 3.50kg block with a speed of 4.00 m/s is 28 J.
Definition of kinetic energyKinetic energy is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
In other words, kinetic energy is defined as the amount of work necessary to accelerate a body of a certain mass and in a position of rest, until it reaches a certain speed.
Kinetic energy is represented by the following expression:
Ec = 1/2×m×v²
where:
Ec is kinetic energy, which is measured in Joules (J). m is mass measured in kilograms (kg).v is velocity measured in meters over seconds (m/s).Kinetic energy in this caseIn this case, you know:
m= 3.50 kgv= 4 m/sReplacing in the definition of kinetic energy:
Ec = 1/2× 3.50 kg× (4 m/s)²
Solving:
Ec= 28 J
Finally, the kinetic energy of a 3.50kg block with a speed of 4.00 m/s is 28 J.
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Positively charged particles of radiation emitted from the decay of radioactive substances are known as.
Positively charged particles of radiation emitted from the decay of radioactive substances are known as alpha particles.
What is an alpha particle?A helium nucleus that some radioactive compounds release that was once thought to be a ray. Ionized alpha particles are made up of two protons, neutrons ( no charge), and no electrons.
Two protons and two neutrons from the atom's nucleus combine to form the positive charge alpha particles (α). The most toxic radioactive materials, such as uranium, radium, and polonium, decay to produce alpha particles.
A ray-like emission of a helium nucleus from some radioactive materials.
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Using 6. 0×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9. 8 m/s2 ? assume that the net force on the earth is the force of gravity she exerts on it.
The value of the acceleration of the earth toward it when it accelerates toward the earth with 9.8m/s² is a = 7.35×10-²³m/s².
What is acceleration?Acceleration in theoretical terms refers to the derivative of the velocity function, it is the rate of change of this variable, and the physical magnitude of the motion that gives rise to the change of position.
What are forces?Forces are the definition of Newton's second law, which is stated under the relation:
∑ Force = mass × acceleration.
In other words, force is the origin of motion since it generates acceleration in a system.
In this case we must complete the statement:
"A student with mass 45 kg jumps off a high diving board. Using 6. 0×1024 kg for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9. 8 m/s2 ? assume that the net force on the earth is the force of gravity she exerts on it."
We determine the Force of the student:
F = ma
F = 45kg * 9.8m/s².
F = 441N
Now we go to the acceleration of the earth:
a = F/m
a = 441N / 6×10²⁴ Kg
a = 7.35×10-²³m/s².
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Rank the wavelengths of the following quantum particles from the largest to the smallest. If any have equal wavelengths, display the equality in your ranking. (a) a photon with energy 3eV(b) an electron with kinetic energy 3eV(c) a proton with kinetic energy 3eV(d) a photon with energy 0.3eV(e) an electron with momentum 3eV/c
The wavelengths of the following quantum particles from the largest to the smallest is (d) > (a) = (e) > (b) > (c)
De Broglie proposed that because light has both wave and particle properties, matter exhibits both wave and particle properties. This property has been explained as the dual behavior of matter. From his observations, de Broglie derived the relationship between the wavelength and momentum of matter. This relationship is known as de Broglie's relationship.De Broglie's relationship is given by [tex]\lambda=\frac{h}{mv}[/tex] .
This can be written as [tex]\lambda=\frac{h}{p}[/tex] .....(1) where λ is known as de Broglie wavelength and p is momentum , h = Plank’s constant .
As we know that mass of proton is greater than electron and photon .
(a)For photon , the momentum is given by [tex]p=\frac{E}{c}[/tex] ...(2) where c is the speed is the speed of light .
Putting E = 3eV in equation (2) , we get
[tex]p=\frac{3\times 1.6\times10^-^1^9}{3\times 10^8} \\p=1.6\times10^-^2^7Js/m[/tex]
Putting this value of p in equation (1) , we get
[tex]\lambda=\frac{6.62\times10^{-34}}{1.6\times10^{-27}}\\\lambda=4.13\times10^{-7}[/tex]
(b) As we know that kinetic energy is given by
[tex]K.E=\frac{1}{2} mv^2\\\\2K.E = mv^2\\2K.E\times m = m^2v^2\\2K.E\times m = (mv)^2\\2K.E\times m = p^2\\\\\sqrt{2K.E\times m }=p[/tex] ...(3)
Where mass of electron is [tex]9.1\times10^-^3^1 kg[/tex] .
Putting K.E = 3eV in equation (3) , we get
[tex]\sqrt{2K.E\times m }=p\\p=\sqrt{2\times3\times1.6\times10^{-19} \times 9.31\times10^{-31} }\\p=\sqrt{89.376\times10^{-50}} \\p=9.45\times10^{-25}Js/m[/tex]
Putting this value of p in equation (1) , we get
[tex]\lambda=\frac{6.62\times10^{-34}}{9.45\times10^{-25}}\\\lambda=0.7005\times10^{-9}[/tex]
(c) Putting [tex]m=1.67\times10^{-27}kg[/tex] and K.E = 3eV in equation (3) , we get
[tex]\sqrt{2K.E\times m }=p\\p=\sqrt{2\times3\times1.6\times10^{-19} \times 1.67\times10^{-27} }\\p=\sqrt{16.032\times10^{-46}} \\p=4.003\times10^{-23}Js/m[/tex]
Putting this value of p in equation (1) , we get
[tex]\lambda=\frac{6.62\times10^{-34}}{4.003\times10^{-23}}\\\lambda=1.65\times10^{-11}[/tex]
(d) Putting E = 0.3eV in equation (2) , we get
[tex]p=\frac{0.3\times 1.6\times10^-^1^9}{3\times 10^8} \\p=1.6\times10^-^2^8Js/m[/tex]
Putting this value of p in equation (1) , we get
[tex]\lambda=\frac{6.62\times10^{-34}}{1.6\times10^{-28}}\\\lambda=4.13\times10^{-6}[/tex]
(e) Putting [tex]p=3eV/c[/tex] in equation (1) , we get
[tex]\lambda=\frac{6.62\times10^{-34}\\\times3\times10^8}{3\times1.6\times10^{-19}}\\\lambda=4.13\times10^{-7}[/tex]
On comparing the wavelength order should be (d) > (a) = (e) > (b) > (c) .
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The subatomic particles that are least massive and most massive respectively are the.
The subatomic particles that are least massive and most massive are the electron and neutron respectively.
Subatomic particles are defined as the elementary particles which make the fundamental constituents of all matter. The subatomic particles constitute the negatively charged electrons, the positively charged protons, and the neutral neutrons which do not have any charge on them.
Protons and neutrons on the other hand are made up of other elementary particles namely quarks. Subatomic particles have emerged a lot in the coming days with the construction of particle accelerators.
The electron is the least massive subatomic particle. It carries a negative charge of 1.602176634 × 10^−19 coulomb which is about 0.000548 amu.
Neutron is the heaviest subatomic particle having a mass of about 1.008 amu.
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13. Two identical metallic spheres A and B, each carry- ing a charge q, repel each other with a force F. A third metallic sphere C of the same size, but un- charged, is successively made to touch the spheres A and B, and then removed away. What is the force of repulsion between A and B? (Ans. 3F/8) 4.
Answer:
Who knows the answer please I need the answer
who is Isacc.Newton??
Answer:
Sir Isaac Newton contributed significantly to the field of science over his lifetime. He invented calculus (opens in new tab) and provided a clear understanding of optics. But his most significant work had to do with forces, and specifically with the development of a universal law of gravitation and his laws of motion
Explanation:
A genius with dark secrets. Isaac Newton changed the way we understand the Universe. Revered in his own lifetime, he discovered the laws of gravity and motion and invented calculus. He helped to shape our rational world view.
A 100kg box is on an incline of 60 degrees. What is the perpendicular force
Answer:
490N
Explanation:
the formula to use for perpendicular force is:
[tex]Fg=mg(cos\theta)[/tex]now we plug in:
*for g, it can be 9.8 m/s^2 or 10 m/s^2 depending on your teacher
[tex]Fg=(100)(9.8)(cos60)[/tex]
then you get:
[tex]Fg=490N[/tex]
which truth did isaac newton’s investigations of gravity explain? jupiter has more moons than earth. jupiter has more moons than earth. the sun is more massive than earth. the sun is more massive than earth. gravity acts on all objects in the universe. gravity acts on all objects in the universe. earth is not the center of the universe. earth is not the center of the universe.
Newton's investigations of gravity explain the truth that Jupiter has more moons than Earth.
The fact that Jupiter has more moons than Earth was first discovered by Galileo Galilei in 1610, and it was later confirmed by Newton. In addition to having more moons, it is also thought that Jupiter may be home to some of the most powerful magnetic fields in the solar system.
What was explained by Isaac Newton's law of gravity?Every particle in the cosmos attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.
Thus, the equation for universal gravity has the following structure:
[tex]{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}}{\displaystyle[/tex]
where r is the distance between the centers of the two objects' masses, m1 and m2 are their respective masses, G is the gravitational constant, and F is the gravitational force acting between them.
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The correct answer is; Gravity acts on all objects in the universe.
The answer above is incorrect…
when driving downhill, gravity will cause you to go slower and decrease your stopping distance. a. true b. false
False.While driving downhill, the gravity will cause you to go faster and increase your stopping distance.
What is stopping distance?Brakes are suddenly applied while the body is travelling at a given speed. You would have observed that after travelling a given distance, the body stops entirely. The stopping distance is that distance.
The distance travelled between the moment the body decides to stop a moving vehicle and the moment the vehicle comes to a complete stop is known as the stopping distance. The stopping distance, indicated by the letter d, is dependent on a number of variables, including as the road's surface and the driver's reflexes.
Stopping Distance formula is given by,
[tex]d=\frac{v^{2} }{2ug}[/tex]
Where,
d = stopping distance (m)
v = velocity (m/s)
μ = friction coefficient
g = the gravitational acceleration
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A wire 2.80m in length carries a current of 5.00A in a region where a uniform magnetic field has a magnitude of 0.390T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (b) 90.0° .
The force on the wire will be
F = 5.46 Newton.
We have a current carrying wire in a uniform magnetic field.
We have to determine the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is 60.0°.
What is the magnitude of force acting on a current (I) carrying wire of length (L) placed in a Magnetic field (B)?The force on the current carrying wire will be -
F = IBL sinθ
According to the question, we have -
L = 2.80 m
I = 5 A
B = 0.39 T
Therefore -
F = IBL sinθ
F = 5 x 0.39 x 2.80 x sin(90)
F = 5.46 x sin(90)
F = 5.46 Newton
Hence, the force on the wire will be
F = 5.46 Newton
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The magnitude of the magnetic force on the wire 5.46 N.
To find the magnetic force, the values given are:
Length A = 2.80m
Current I = 5 A
Magnetic field B = 0.390 T
Angle = 90° .
What is meant by magnetic force?
The attraction or repulsion that arises between electrically charged particles because of their motion is called Magnetic force.Magnetic force is the basic force which is responsible for such effects as the action of electric motors and the attraction of magnets.A force experienced through the magnetic field with some moving charges is perpendicular to its own velocity.The formula to find the magnetic force,F =iBLsinθ Newton
Substituting the values given,
Magnetic force,
F = 5 A × 0.390 T × 2.80 m × Sin 90°
= 5 A × 0.390 T × 2.80 m × 1
F = 5.46 N.
The magnitude of the magnetic force on the wire 5.46 N.
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Please someone help me.
is the block of wood at rest or in motion?
refer to the figure below draw the forces acting on the block of wood use the gas as the origin of the forces.
thank you very much for answering this.
Answer:
1) The block of wood is at rest.
2) Weight and Normal Reaction (see attached diagram).
Explanation:
Assumptions
The block of wood is a particle (a body whose mass acts at a point, so its dimensions don't matter).There are no other external forces involved.Question 1
"At rest" or "resting" means that the object isn't moving.
Therefore, the block of wood is at rest.
Question 2
Forces that are acting on the block of wood:
Weight (W): Due to the particle's mass, m, and the acceleration due to gravity, g: W = mgSee attached diagram.
The rest energy of an electron is 0.511MeV. The rest energy of a proton is 938MeV. Assume both particles have kinetic energies of 2.00MeV. Find the speed of(d) Repeat the calculations in parts (a) through (c) assuming both particles have kinetic energies of 2000MeV
Answer:
The speed of the electron is 0.98c, given that the rest energy of an electron is 0.511MeV and the rest energy of a proton is 938MeV, with both particles having kinetic energies of 2.00MeV.
Explanation:
A particle's total energy and the rest energy follow the laws of physics and the theory of relativity. The energy of any particle is equal to mass times the speed of the light-squared relatively.
Where; E=γ.〖mc〗^2
γ is the ratio of total energy to rest energy of the particle.
m_0 is known as the rest mass of the particle.
Rest energy can be written as: E_0=〖m_0 c〗^2
γ=K/E_0 +1 (1)
γ=1/(√1-v^2/c^2) (2)
Putting the values of the electron energy into equation (1):
γ=2.00MeV/0.511MeV+1
γ= 3.91 + 1
γ=4.91
From equation (2),
γ=1/(√1-v^2/c^2)
Squaring both sides of the equation,
γ^2=1/(1-v^2/c^2)
1/γ^2 =1-v^2/c^2
v^2/c^2 =1-1/γ^2
v/c=√1-1/γ^2
Making v subject of the formula,
v=√1-1/γ^2 ×c (3)
Inserting the values into Equation 3,
v=√1-1/〖4.91〗^2 ×c
v=√1-1/24.11×c
v=√0.959×c
v=0.98×c
v=0.98c
Therefore, the speed of the electron is 0.98c.
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list 5 example where pivot is present
The five examples where pivot can be seen include the following: 1. Nut Cracker · 2. Seesaw · 3. Scissors · 4. Plier · 5. Stapler
What is a pivot?A pivot is the fulcrum of a simple machine that serves as a point in the machine that allows for easy movement when force of load or effort is being applied at either ends.
The pivot can eithe be located at the either ends of the simple machine or at the middle of the simple machine.
Typical examples of machines that has pivot include the following:
Nut Cracker,Seesaw,Scissors,Plier, and Stapler.From the examples listed above, the pivot of nutcracker and stapler are located at its end while the pivot of seesaw, scissors and pliers are located at the middle.
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Help me to answer this..
Click the picture to see the full question.
Explanation:
Newton second law of motion
The furniture was designed to go a top speed of 87.0mph. How far would this sofa travel to the mall 1.00 hour away?
The sofa with a top speed of 87 mph would travel a distance of 43.5 miles to the mall 1 hour away.
Considering the sofa accelerates constantly throughout the motion,
s = ( u + v ) t / 2
s = Distance
u = Initial velocity
v = Final velocity
t = Time
v = 87 mph
t = 1 hr
u = 0
s = ( u + v ) t / 2
s = ( 0 + 87 ) 1 / 2
s = 43.5 mi
This is an equation of motion.
Therefore, the sofa would travel a distance of 43.5 miles
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Owen and Dina are at rest in frame S' , which is moving at 0.600 c with respect to frame S . They play a game of catch while Ed , at rest in frame S , watches the action (Fig. P39.75). Owen throws the ball to Dina at 0.800 c (according to Owen), and their separation (measured in S' ) is equal to 1.80 × 10¹²m .(a) According to Dina, how fast is the ball moving?
The speed of the ball with respect to Dina is 0.800c.
A frame of reference is a set of reference points—geometric points whose positions are known mathematically and physically—that define the origin, orientation, and scale of an abstract coordinate system.
If a body does not continuously adjust its position in relation to its environment throughout the course of time, it is said to be at rest.
In frame S', Dina and Owen are at rest.
The speed of the ball with respect to Owen, u =0.800c
The speed of the frame S' with respect to frame S, v = 0.600c
Distance between Dina and Owen, L(p) = 1.8 × 10¹² m
Speed of light, c = 3 × 10⁸ m/s
Therefore, the speed of the ball according to Dina is 0.800c. As Dina and Owen are in the same frame.
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An amusement park designer wants his swing to have a centripetal
acceleration of 21 m/s2. If the velocity of the swing is 13 m/s, how long
should the chain on the swing be?
The chain on the swing should be 8.0 m long .
Centripetal Acceleration ( a ) = v ² / r ........... Eq. 1
It is given that ,
a = 21 m / s ²
v = 13 m / s
Now , using the values of ' a ' and ' v ' i.e. 21 m / s ² & 13 m / s respectively in Eq. 1
a = v ² / r
21 = ( 13 ) ² / r
21 = ( 13 x 13 ) / r
r = ( 13 x 13 ) / 21
r = 8.047 m
⇒ r = 8.0 m ( rounded off to nearest tenth )
Hence , the chain on the swing should be 8.0 m long .
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a spring is compressed by 1 cm when a force of 5.0N is applied. what is the potential energy stored in the spring when it is compressed by 10.cm
The potential energy stored in the spring is 0.025 J.
What is potential energy stored in a spring?This is the energy stored in a spring when its is stretched or compressed through a certain length.
To calculate the potential energy stored in a spring, we use the formula below.
Formula:
E = Fe/2............... Equation 1Where:
E = Potential energy of the springF = Force applied to the springe = Extension or CompressionFrom the question,
Given:
F = 5 Ne = 1 cm = 0.01 mSubstitute these values into equation 1
E = 5×0.01/2E = 0.025 JHence, the potential energy stored in the spring is 0.025 J.
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