When identifying probabilities, the best estimate of p(-3.0<z<3.0) is 0.95. Because we can use the standard normal to find probabilities for a normal random variable with any mean and any standard deviation.
It is also simple to determine the likelihood that a standard normal random variable will fall between two values. The equation P(a<Z<b) = P(Z<b) - P(Z<a). For instance, let's say we're interested in the likelihood that a z-score will be both higher than -1.40 and lower than -1.20. If a random variable X has a pdf that is given by: If = 0, and = 1, we refer to it as a standard normal random variable. A random variable X is said to have a normal probability distribution with parameters and 2 if it does. We write X ∼ N(μ, σ2). for every normal random variable with mean and variance 2.
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complete question: When identifying probabilities, which is the best estimate of P(-3.0<Z<3.0) for the standard normal distribution? Use the Empirical Rule to determine your answer.
A 3000 kg truck moving rightward with a speed of 5 km/h collides head on with a 1000 kg car moving leftward with a speed of 10 km/h.
The momentum of the system after collison is 1.25 Km/hr.
What is the momentum?Momentum is a measure of an object's motion, defined as the product of its mass and velocity. In physics, it represents the tendency of an object to remain in motion or to change its motion, as a result of an external force.
We know that;
Momentum before collision = Momentum after collision
(3000 * 5) - (1000 * 10) = (3000 + 1000) v
v is the common velocity after collision
v = 15000 - 10000 = 4000v
v = 5000/4000
v = 1.25 Km/hr
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Missing parts;
A 3000 kg truck moving rightward with a speed of 5 km/h collides head on with a 1000 kg car moving leftward with a speed of 10 km/h. The two vehicles strike together after the collision. Determine the post-collision velocity of the car and truck.
a parallel plate capacitor has a plate area of 1m2. the plates are separated by 2 mm, and the space between them is filled with jelly with a dielectric constant of 5.6. how much electrical energy is stored when the potential difference between the plates is 6000 v?
The energy stored in the plates of the capacitor is 11.05 Joules.
The area between the plates of the capacitor is 1m² and the distance between the plates is 2mm(0.002m).
The capacitance will be given by,
C = KεA/d
Where,
K is the inserted dielectric constant,
ε is the permitivitty,
A is the area,
d is the distance of the plates.
Putting values,
C = 8.85 x 5.6 x 1/0.002
C = 24.780 nF.
Formula for energy stored in capacitor,
E = 1/2CV²
V is the potential difference,
Putting values,
E = 0.5 x 24.78 x 6000 x 6000 x 10⁻⁹⁹
E = 11.05 Joules.
So, the energy stored in the capacitors is 11.05 Joules.
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consider a strontium ion. there are four shells in this ion. how many electrons does it have in...
A strontium ion has four shells in this ion, so the number of electrons it have in is 36 electrons 29.
The chemical element strontium is a soft, silver-white, yellowish metallic element that is an alkaline earth metal and has a strong reactivity to chemicals. The most prevalent type of strontium found in dietary supplements is strontium chloride. Several distinct forms of strontium are employed in medicine.
Subatomic particles known as electrons have an intrinsic charge of magnitude -1. The size of an electron's charge is comparable to that of a proton, but its symbol is the opposite. The amount of electrons and protons in electrically neutral atoms and molecules should therefore be equivalent.
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Under what circumstances is the total magnetic flux through a closed surface positive?
a)if the surface encloses the north pole of a magnet, but not the south pole
b)if the surface encloses the south pole of a magnet, but not the north pole
c)if the surface encloses both the north and south poles of a magnet
d)more than one of the above
e)none of the above
Under none of the circumstances is the total magnetic flux through a closed surface positive.
Total magnetic surface through a closed surface will always be zero, according to Gauss's law.
Magnetic field lines form closed loops because there is no magnetic monopole.
Therefore, the quantity of field lines entering through the closed surface equals the quantity of field lines leaving. Magnetic flux that is linked to a closed surface is therefore always zero. If there is no source of the vector field in the volume encircled by the surface, the flux of a vector field through a closed surface is always zero.
Using Gauss's law, the electric field's flux through a closed surface is equal to.
Therefore, the flux may be zero if the electric field is zero everywhere.
Charge inside the sealed surface must be zero in order for flux to be zero.
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two gamma photons are produced when a muon and an antimuon annihilate each other.what is the minimum frequency of the gamma radiation that could be produced
The minimum frequency of gamma radiation that produce, could be 2.55 × 10²² Hertz, If two gamma photons are produced when a muon and an antimuon annihilated each other.
The rest energy of the muon, = 106 Mev
We know 1 Mev = 1.6 × 10⁻¹³ Joules
So the total rest energy of the muon in joules = 106 × 1.6 × 10⁻¹³J
= 1.696 × 10⁻¹¹ Joules
We know Energy(E) = vh
Where v is the frequency and h is plank's constant = 6.62 × 10⁻³⁴ J/htz
1.696 × 10⁻¹¹ = v × (6.62 × 10⁻³⁴)
v = (1.696 × 10⁻¹¹)/(6.62 × 10⁻³⁴)
v = 2.55 × 10²² Htz
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what is the average power dissipated by a 100 ohm resistor when it is connected to an ac source with a peak value of 141 g
The average power which is dissipated by a 100 ohm resistor when connected to an AC source with a peak value of 141 g is 19.86 W.
What do you mean by resistor?
A resistor is an electrical component that is used to control the flow of electric current in a circuit. It is used to limit the amount of current that can pass through a circuit, to reduce the voltage in a circuit, and to create a desired amount of resistance to the flow of electric current. Resistors are typically made of metal, carbon, or other materials that allow electrons to flow through them at a certain resistance. They can be used in a variety of applications such as amplifiers, oscillators, and power supplies.
This can be calculated using the following formula:
P = V²/R
Where P is the power, V is the voltage, and R is the resistance.
V = 141 g
R = 100 ohms
P = (141 g)²/100 = 19.86 W
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all of the planets in the solar system orbit the sun, but in which plane do most of them orbit?
All the planets in the solar system orbit the sun in approximately the same plane.
Planetary orbits in a far-off solar system are in line with the rotation of the star. The orbits of all known planets in this distant solar system nearly all lay in the same plane and are in line with the rotation of the star. This solar system is quite similar to our own.
Because the planets formed from a disc of material that enveloped the Sun during the Solar System's formation, their orbits are coplanar. All of the planets originated in a plane because that disc of dust was a disc, all in one. Rings and disks are common in astronomy.
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Which moon phase come after a new moon and before a first quarter moon?
a place kicker must kick the football from a point 26 m horizontally away from the goal posts, at ground level, and clear a bar 3.00 m above the ground. the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0 degrees above the horizontal. (a) by how much does the ball clear (positive value) or fall short (negative value) of the cross bar? (this is vertical distance above or below the cross bar.) [8.5,9.5] m (b) when the ball gets to the horizontal location of the cross bar, find the vertical component of the ball's velocity and tell whether the ball is rising or falling. magnitude of vy is in the range [5,6] m/s
a) The ball so misses the crossbar by 8.63m. b) The ball clears the goal on its way down since the time when the ball reaches its highest point is earlier than when it will arrive at the goal.
An object's projection onto a plane is that object's orthogonal projection. A vector's projection on an orthogonal straight line to a plane is what causes it to be rejected from that plane. Each one is a vector. Whereas the second is orthogonal, the first is parallel to the plane.
From the vector's origin to its farthest x-coordinate, the horizontal component runs. The vector's greatest vertical point is where the vertical component starts at the x-axis and terminates.
a) First we have to find the time at which the ball reaches the goal using the particle under constant velocity model in the x direction:
[tex]X_f=X_i+V_{xi}t[/tex]
[tex]t=\frac{X_f-X_i}{V_{xi} }[/tex]
[tex]t=\frac{(26-0)}{20 Cos53}[/tex]
[tex]t=2.16sec[/tex]
Now we also find the height of the ball at this moment using the model of a particle moving at constant speed in the y direction.
[tex]Y_f=Y_i+V_{yi}t+\frac{1}{2}a_yt^2[/tex]
[tex]Y_f=[0+20*(sin53)*2.16]-[\frac{1}{2}*9.80*(2.16)^2][/tex]
[tex]Y_f=11.63m[/tex]
The ball so misses the crossbar by
[tex]11.63-3.00=8.63m[/tex]
b) As the ball reaches its greatest point in its flight, use the particle under constant acceleration model to calculate the time.
[tex]V_{yf}= V_{yi}-gt[/tex]
[tex]t=\frac{V_{yf}-V_{yi}}{g}[/tex]
[tex]t=\frac{(20*sin53)-0}{9.80}[/tex]
[tex]t=1.63 sec[/tex]
The ball clears the goal on the way down since this is earlier than when it will arrive at the goal.
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the maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period of oscillation is 2 s. if the mass is released with an initial displacement of 2 cm, find (a) the amplitude, (b) the initial velocity, (c) the maximum acceleration, and (d) the phase angle.
A: the amplitude is 3.18 cm ; B: the initial velocity is -9.55 cm/s ; C the maximum acceleration is -19.7 cm/s^2; and D: the phase angle is 0.201 rad.
a. The amplitude (A) of a simple harmonic oscillator is related to the maximum displacement from the equilibrium position. Given the maximum velocity (Vmax) and the frequency (f), the amplitude can be found using the formula:
A = (Vmax) / (2πf)
f = 1/T, where T is the period of oscillation
So, f = 1/2 s
A = (10 cm/s) / (2π * (1/2 s)) = 10 / π cm
A = 3.18 cm
b. The initial velocity (V0) of a simple harmonic oscillator can be found using the equation:
V0 = -Aωcos(θ), where ω is the angular frequency and θ is the phase angle
Since the mass was released with an initial displacement of 2 cm, θ can be found using the equation:
θ = arcsin(x0/A), where x0 is the initial displacement
x0 = 2 cm
θ = arcsin(2 cm / 3.18 cm) = 0.201 rad
V0 = -Aωcos(θ) = -(3.18 cm) (2π / 2 s) cos(0.201 rad)
V0 = -9.55 cm/s
c. The maximum acceleration (Amax) of a simple harmonic oscillator can be found using the equation:
Amax = -Aω^2 = -(2πf)^2 A
Amax = -(2π / 2 s)^2 (3.18 cm) = -19.7 cm/s^2
d. The phase angle (θ) of a simple harmonic oscillator can be found using the equation:
θ = arcsin(x0/A) = arcsin(2 cm / 3.18 cm) = 0.201 rad
The phase angle represents the phase difference between the position and velocity of the mass.
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two bodies attract each other electrically. do they both have to have a net charge? explain. answer the same question if the bodies repel one another.
Both bodies must be charged in order to repel each other, but they do not both have to be charged to attract each other.
The attractive force between two bodies is due to the electromagnetic force, which acts between charged particles. So, if one of the bodies is charged, it will experience an attractive force toward a neutral body. However, if both bodies are charged with the same type of charge (i.e., both positive or both negative), they will experience a repulsive force.
If two bodies repel each other, it means that they are both charged with the same type of charge (i.e., both positive or both negative). This is because like charges repel each other and opposite charges attract. So, in order for two bodies to repel each other, they must both be charged.
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GETTING STARTED: If something is "charged," what does that mean? If something is "neutral," what does that mean?
Charged means that an object has an unequal number of protons and electrons, thus giving it an electrical charge. Neutral means that the object has an equal number of protons and electrons, thus giving it no electrical charge.
When something is "charged," it signifies that electrical energy has accumulated inside it and that it is prepared to be put to use. This can apply to a person who is enthusiastic and full of energy, or it can refer to an electrical component like a battery or capacitor. On the other side, if something is "neutral," it indicates that it is not charged with any electricity or energy and cannot be utilised for any purpose. This may be used to describe an electrical instrument that is devoid of charge or has been discharged as well as a person who is disinterested or indifferent in a certain scenario.
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problem cf.17 a gas stream with stagnation pressure p0and stagnation density ⇢0discharges to an open atmosphere at pressure
A gas stream with a stagnation pressure (p0) and a stagnation density (0) discharges to an open environment at pressure (patm). The gas stream will expand when it discharges.
into the open environment in this situation, producing a reduction in pressure and density. The final pressure and density of the gas stream will be determined by a number of variables, including the beginning circumstances (p0 and 0) and ambient pressure (patm). Using the concept of continuity and the law of thermodynamics, the change in pressure and density may be estimated. According to the concept of continuity, the mass flow rate of a fluid must remain constant along a streamline. The law of thermodynamics describes the relationship between changes in energy, temperature, and entropy of a system.
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A student pushes a 40-n block across the floor for a distance of 10 m. how much work was done to move the block? responses a. 4 j b. 40 j c. 400 j d. 4,000 j
The work was done to move the block across the floor is 400 Joule.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
A spring balance can be used to calculate the Force. The Newton is the SI unit of force.
Force applied on the block: F = 40 N.
Displacement of the box = 10 m.
Hence, work done to move the block = Force × Displacement
= 40 × 10 joule
= 400 joule.
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what is fglass , the frequency of the light in the glass? express your answer in terms of some or all of the variables f , n , and l .
The frequency of light in glass is f.
The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Let the frequency of light in glass be, fₓ and the frequency of light in a vacuum is f.
The value of the refractive index is, n = c/v, where c is the speed of line in vacuum and v is the speed of light in glass. It's interesting to note that as light travels from air to glass, the frequency of the waves remains constant.
Therefore, the ratio for the frequency is,
fₓ/f = 1
The frequency of light in glass fglass = f.
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what is the wavelength of a 7.65 x 10-17 j wave?
The required wavelength of the wave when energy of the wave is specified is calculated to be 2.6 × 10⁻⁹ m.
The energy of the wave is given as 7.65 × 10⁻¹⁷ J.
The relation between energy, wavelength, speed of light is known as,
E = h c /λ
where,
h is planck's constant
c is speed of light
λ is wavelength
E is energy
The value of speed of light c = 3 × 10⁸ m/s
The value of Planck's constant h = 6.62 × 10⁻³⁴ m²kg/s
Putting all the known values into the above equation by making wavelength as subject, we have,
E = h c /λ
λ = h c /E = (6.62 × 10⁻³⁴)(3 × 10⁸)/(7.65 × 10⁻¹⁷) = 2.6 × 10⁻⁹ m
Thus, the wavelength is calculated to be 2.6 × 10⁻⁹ m.
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True or False? There is a point somewhere around a perfect electric dipole where the electric field is zero.
It is true. That point is called the "equipotential point" or "neutral point". It is the point where the electric field due to the two opposite charges of the dipole cancels out and the electric field is zero.
A perfect electric dipole refers to two charges of equal magnitude but opposite sign separated by a fixed distance. In the vicinity of a perfect electric dipole, there is a specific point where the electric field due to the two charges cancels out, resulting in a zero electric field. This point is known as the "equipotential point" or "neutral point". The equipotential point can be found along the line connecting the two charges, equidistant from each charge. The electric field at any other point around the dipole will be non-zero and will be directed away from one charge and towards the other charge. Understanding the electric field of a perfect electric dipole is important in several fields, including electrostatics, physical chemistry, and electrical engineering.
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when the bob of a simple pendulum is straight down during a cycle, the potential energy will be at maximum since its mass is traveling at a maximum velocity.
The given statement that the potential energy of a bob of simple pendulum will be maximum when it is straight down during a cycle, is false. Potential energy is minimum when bob of the pendulum is straight down.
Potential energy is the energy which is possessed by the object due to position relative to other object. Gravitational potential energy of an object is due to its position with respect to the ground. It is formulated as p = mgh.
Kinetic energy is the energy which is possessed by the object due to the virtue of its motion. It is formulated as: K = 0.5mv²
So when the bob of a simple pendulum is straight down during a cycle, its having the maximum velocity. Thus the kinetic energy will be maximum and not the potential energy. Hence the given statement is false.
--The given question is incomplete, the complete question is:
"Is it true or false that when the bob of a simple pendulum is straight down during a cycle, the potential energy will be at maximum since its mass is traveling at a maximum velocity."--
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as a result of a glancing collision with a surface, the velocity of a 0.2 kg mass changes from 9 m/s directed downward, to 8 m/s directed 60 degrees below the horizontal. what is the magnitude of the change in momentum of the mass?
The magnitude of the change in momentum is 0.346 kg m/s.
What is magnitude?
Magnitude is defined as the maximum extent of size and the direction of an object.
We can calculated the magnitude of the change in momentum by using this formal:
Δp = m * Δv
where Δp is the change in momentum
M is the mass
Δv is the change in velocity.
The initial velocity is 9 m/s directed downward and the final velocity is 8 m/s directed 60 degrees below the horizontal.
The change in velocity can be found using vector subtraction:
Δv = v_f - v_i = 8 m/s directed 60 degrees below the horizontal - 9 m/s directed downward
Calculating the magnitude of Δv:
Δv = sqrt(8^2 + 9^2 - 2 * 8 * 9 * cos(60))
Δv ≈ 1.73 m/s
Finally, calculating the change in momentum:
Δp = m * Δv = 0.2 kg * 1.73 m/s = 0.346 kg m/s
The magnitude of the change in momentum is 0.346 kg m/s.
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complete the following sentence, then explain why you wrote what you did. "becoming aware that i am a person living during the anthropocene makes me feel
"Becoming aware that I am a person living during the anthropocene makes me feel concerned about the impact that humans are having on the planet and the future of our species."
I wrote this sentence because the Anthropocene is a term used to describe the current geological age, characterized by human activities having a significant impact on the Earth's ecosystems and geology. The awareness of living in this time period can evoke feelings of concern for the future of the planet and humanity, as the negative consequences of human activities are becoming increasingly evident. "becoming aware that I am a person living during the anthropocene makes me feel concerned about the impact that humans are having on the planet and the future of our species." I wrote this sentence because the Anthropocene is a term used to describe the current geological age.
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identify which bases pair together. the stars (*) indicate important atoms in each structure. how did you determine your answer?
To determine which bases pair together, you need to look at the chemical structures of the nucleic acid bases.
Each of the four nucleic acid bases (adenine, guanine, cytosine, and thymine) has a specific chemical structure. The stars (*) indicate important atoms in each structure, such as nitrogen atoms, which are involved in the formation of hydrogen bonds that link the two bases together.
To determine which bases pair together, you need to look at the number and type of nitrogen atoms in each base. Adenine and thymine have two nitrogen atoms and are complementary, meaning they form hydrogen bonds and pair together. Guanine and cytosine also have two nitrogen atoms and are complementary, so they form hydrogen bonds and pair together.
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what is the magnitude of the net electric field at the center of the square due to the four charges in terms of q and a ?
The net electric field at the center of the square due to the four charges is 4kq√2/a²
According to the Coulomb's law, the magnitude of the electric field caused by a point charge q is:
E = k q/r²
Where:
k = Coulomb constant
r = distance from the point charge.
In this problem,
r = a/√2
The electric field caused by a single positive charge is:
Ep = k q/(a/√2)² = 2kq/a²
The x-components from the two positive charges cancel out, hence, the resultant electric field is only in y-axis.
E+ = 2Ep . cos45⁰
= 2 x 2kq/a² x √2/2
= 2kq√2/a²
The magnitude and the direction of electric field caused by the two negative charges are the same. The x-components cancel out and the resultant is only due to y-components.
E- = 2Ep . cos45⁰
= 2 x 2kq/a² x √2/2
= 2kq√2/a²
Therefore, the total field at the center of the square is:
E = E+ + E-
= 2kq√2/a² + 2kq√2/a² = 4kq√2/a²
The picture in your question is missing. Most likely it was like on the attached picture.
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a plastic ball of mass 0.2 kg moves at 0.6 m/s, east. it collides with a 0.1 kg ball moving at 0.8 m/s, west. after the collision, the velocity of the 0.1 kg ball is 0.6 m/s, east. what is the velocity of the 0.2 kg ball after the collision? what type of collision is this (elastic, inelastic)? how do you know? ans: 0.1 m/s, west
The velocity is 0.1 m/s, west. This is an inelastic collision.
The velocity of the 0.2 kg ball after the collision is 0.1 m/s, west. This is an inelastic collision, meaning that some energy is lost in the form of heat, sound or other forms of internal energy. You can determine this because the velocities of both balls have changed, and the final kinetic energy is different from the initial kinetic energy. A collision is an event in which two or more objects come into contact and interact with each other for a short period of time. During a collision, the objects exchange momentum and energy, causing changes in their velocity, direction, or other physical properties. Collisions can be classified into two types: elastic and inelastic. In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the kinetic energy is converted into other forms of energy such as heat or sound. The type of collision is determined by the relative magnitudes of the initial and final kinetic energies of the system.
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On the planet Venus, a Venusian picks up a stone and drops it into a deep hole. If it falls 3 m in 1 second, how far will it fall in 2 seconds? You can neglect Venusian air resistance.
Under the effect of the planet's acceleration from gravity, a stone put on Venus will fall 35.48 m in 2 seconds.
The following formula can be used to determine the distance that an object falls while being pulled by gravity:
d = 1/2 * g * t^2
where g is the gravitational acceleration, t is the passing of time, and d is the distance fallen. On Venus, the acceleration brought on by gravity is equivalent to 8.87 m/s2.
The distance fell at t = 2 seconds would be as follows:
d = 1/2 * 8.87 m/s * (2 s), which is 1/2 * 8.87 m/s * (4 s), or 8.87 * 4 = 35.48 m.
The stone will therefore travel 35.48 metres on Venus in 2 seconds.Acceleration is the rate at which an object's velocity changes over time. It has metres per second squared (m/s2) as its SI unit of measurement and is a vector quantity. Different things, such forces acting on an item or modifications in the speed or direction of motion, can lead to acceleration.
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a proton is very far from the wire. what is the ratio ff/fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?
The ratio of the electric force on the proton (Ff/Fi) after the segment is shrunk to the force before the segment was shrunk is determined by the geometry of the wire.
When the segment is shrunk, the electric force on the proton decreases, as the proton is further from the wire. The ratio of the electric force on the proton after the wire is shrunk to the force before the wire was shrunk is given by the equation Ff/Fi = (l1/l2)^2, where l1 is the length of the wire before shrinking and l2 is the length of the wire after shrinking.
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the indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively. what type of light is produced by the incandescent light bulb?
The incandescent light bulb emits thermal radiation in the form of visible light, which has a refractive index close to 1, as air does.
The incandescent light bulb produces thermal radiation, which is a type of electromagnetic radiation that is produced by the heat of an object. When the filament in an incandescent light bulb is heated by an electric current, it emits light due to the heat energy being converted into electromagnetic radiation. The refractive index of a material is a measure of how much a wave of light slows down when it passes through the material. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The refractive index of air is close to 1, which means that light travels at close to its maximum speed in air. The refractive index of glass is between 1 and 2, meaning that light travels slower in glass than it does in a vacuum or air. The refractive index of the solution is between 1 and 1.5, meaning that light travels slower in the solution than it does in air, but faster than it does in glass. Based on the given refractive indices of air, glass, and the solution, it can be concluded that the incandescent light bulb emits thermal radiation in the form of visible light, which has a refractive index close to 1, as air does. This is why light from the incandescent bulb travels at close to its maximum speed through air.
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what is the voltage at which one (1) capacitor stores the same amount of energy as four (4) capacitors, each charged to volts?
At 40 volts voltage a 3 μF capacitor will store the same amount of energy as four 3 μF capacitor do, when each charges to 20 volts.
Capacitance of the capacitor, C = 3 μF = 3 × 10⁻⁶ F
Voltage of four capacitors, V₂ = 20 volts
Let the voltage of the first capacitor, = V₁
We know the energy stored by the capacitor is formulated as, E = 0.5 CV²
0.5 CV₁² = 4 × 0.5 CV₂²
V₁² = 4 V₂²
V₁² = 4 × 20²
V₁² = 1600
V₁ = √1600
V₁ = 40 volts
--The given question is incomplete, the complete question is:
"what is the voltage at which one 3 μF capacitor stores the same amount of energy as four 3 μF capacitors, each charged 20 to volts?"--
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as you play the moon orbit video, notice how the arrows representing the sun's rays are at first spread apart but become parallel as the video zooms in on the moon's orbit. why do the sun's rays become parallel at the end of the video?
They actually don't become parallel at the end of the video.
Only a very small portion of the Sun's radiation reaches Earth and the Moon.
Because the distance between the Sun and the Moon's orbit is so small in comparison, all of the rays that reach the orbit basically come from the same direction.
The video is not accurate; Instead of being parallel, the Sun's rays actually converge on the Moon from all directions.
As they move away from the Sun, rays that started out going in different directions from the Sun turn toward Earth.
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9. Show that the equation for the gravitational potential energy E
GMm is dimensionally
R
correct given that the units for the gravitational constant G are N.m².kg2, M and m are masses of
interacting objects and R is their separation distance.
- is dimensionally homogeneous.
The equation of gravitational energy is E = [tex]\frac{GMm}{R}[/tex] and it is dimensionally correct.
What is Dimension ?The minimal set of coordinates required to specify any point within a mathematical space is the dimension of that space. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line.
A unit of measurement is a specific magnitude of a quantity that has been established and recognized by law or convention and is used as a benchmark for measuring other quantities of the same sort. A multiple of the unit of measurement can be used to express any other quantity of that type. A length is an example of a physical quantity.
The formula for Gravitational Energy is
E = [tex]\frac{GMm}{R}[/tex]
unit of G = N m² kg⁻²
unit of M and m = kg
unit of R = m
Unit of Gravitational Energy = N. m
[tex]\frac{GMm}{R}[/tex] = [tex]\frac{Nm\x^{2}*kg\x^{-2} * kg * kg }{m} = N. m[/tex]
The equation of gravitational energy is E = [tex]\frac{GMm}{R}[/tex] and it is dimensionally correct.
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what is the minimum height h the car should be released so that it goes around the loop safely? assume friction is negligible.
The minimum height from which the car should be released so that it goes around the loop safely neglecting friction is 5r/2.
N and mg are the two forces acting downward at the top of the loop.
ΣFr = N + mg = mv²/r → N = mv²/r - mg.
Minimum speed is given by N=0 → v² = gr.
Multiply by ½ m to get: ½ mgr = ½ mv².
At the summit, the kinetic energy is at its lowest—1/2 mgr.
The potential energy zero level is represented by the loop's bottom.
Ui + Ki = Uf + Kf.
Ki = 0, Ui = mgh, while Kf = ½ mgr, Uf = mg(2r).
Energy conservation: mgh = ½ mgr + mg(2r)
Finally, h = 2r + r/2 = 5r/2.
A mass that is released from a lower point than h = 5r/2 will exit the loop. A mass that is discharged from above will have a normal force that is greater than zero at the top and will circle the loop.
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