The hubble constant is about 70 km/s/mpc. you measure the redshift of four galaxies. the first has a redshift of 1500 km/s, the second has a redshift of 750 km/s, the third has a redshift of 5000 km/s and the fourth has a redshift of 2000 km/s. Andromeda is the closest galaxy.
A galaxy is made up of gravitationally bound clusters of stars, stellar debris, interstellar gas, dust, and dark matter. The word "galaxias" is a Greek word that means "milky" and alludes to the Milky Way galaxy, which is where the Solar System is located. Hubble constant, galaxies range in size from dwarfs, which have less than 100 million stars, to supergiants, which have more than 100 trillion stars. All of these stars orbit the galaxy's center of mass. Galaxies have an average of 100 million stars. Stars and nebulae make up a very small portion of the material of a typical galaxy; dark matter makes up the majority of the galaxy's mass. Typically, galaxy cores contain supermassive black holes. Galaxies can be characterized as elliptical, spiral, or irregular based on their visual shape. [6] Many of them are thought to have supermassive black holes in their cores. The main black hole of the Milky Way.
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an insulating sphere with a radius of 20 cm carries a uniform volume charge density of 1.5 x 10-6 c/m3. find the magnitude of the electric field at a point inside the sphere that lies 8.0 cm from the center.
The magnitude of the electric field at a point inside the sphere that lies 8.0 cm from the center is 4.5 × [tex]10^{3}[/tex]
Given
Radius = 20 cm
Electric field at a point inside the sphere that lies 8.0 cm from the center.
ρ = 1.5 x 10-6 c/m3
E (r) = ρr / 3εο = 1.5 × [tex]10^{-6}[/tex] × 8 × [tex]10^{-2}[/tex]/ 3 × 8.85 × [tex]10^{-12}[/tex] = 4.5 × [tex]10^{3}[/tex]
The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them, is known as an electric field (also referred to as an E-field[1]). [2] It also describes the physical field of a system of charged particles. [3] Electric charges and time-varying electric currents are the basis of electric fields. A manifestation of the electromagnetic field, one of the four fundamental interactions (sometimes known as forces) of nature, is electromagnetic fields, which also include electric and magnetic fields.
Electric fields play a significant role in many branches of physics and are used in electrical engineering. For instance, in atomic physics and chemistry, the electric field acts as the attracting force that holds the atomic nucleus and electrons together in atoms. Additionally, it is the driving force for atoms' chemical bonds.
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What is the change in internal energy in joules of a car if you put 13.5 gal of gasoline into its tank?
The change in internal energy of car will be 13.5 cal.
The internal energy of an ideal gas is a good approximation of a real system. In such a system, particles in an ideal gas appear as point objects that collide with each other in a perfectly elastic way. The actual behavior of monatomic gases (helium, argon, etc.) reflects this model.
For an ideal gas, the internal energy is proportional to the number of moles of gas and its temperature: U = cnT
Gibbs free energy is increasing as the curve of entropy.
The first law of thermodynamics states that the increase in internal energy is equal to the total heat input plus the work done by the environment. For isolated systems, it remains constant.
Q=u+w
u=Q-w
=13.5cal
since no reaction happened.
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There are 8 squares and 10 circles. What is the simplest ratio of squares to total shapes?.
The simplest ratio of squares to total shapes if we have 8 squares and 10 circles is 4:9.
What is Ratio?
A ratio is said to be is the simplest form or in the lowest term if two quantities of a ratio (i.e., antecedent and consequent) have no common factor (i.e. antecedent and consequent are co-prime) other than 1 (or their HCF is 1). The ratio must always be expressed in its simplest form or in its lowest terms.
Now,
There are 8 squares and 10 circles.
We have, total shapes = 8 + 10 = 18
Hence, The simplest ratio of squares to total shapes = 8 : 18 = 4 : 9
So, The simplest ratio of squares to total shapes is 4 : 9
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you take a spectrum of a faraway galaxy and find that its hydrogen alpha line peaks at 6782 angstroms. what is its recessional velocity?
The recessional velocity is 9,771,241 m/s.
Step 1: The redshift of a faraway galaxy is determined by measuring the shift of its spectral lines compared to similar lines from nearby galaxies. The redshift is usually expressed as a ratio in terms of how much the wavelength of each line has shifted from its original value.
Step 2: The hydrogen alpha emission line has a known rest wavelength of 6562 angstroms. This means that the observed wavelength of 6782 angstroms is shifted from its rest wavelength by a factor of 1.03.
Step 3: The redshift of a galaxy can be converted into a recessional velocity in km/s by using the Hubble Law, which states that the recessional velocity of a galaxy is proportional to its redshift.
Step 4: To calculate the recessional velocity, the formula V = H0 x z is used, where V is the recessional velocity, H0 is the Hubble Constant, and z is the redshift.
Step 5: The Hubble Constant is currently estimated to be 70 km/s/Mpc, so using the formula, the recessional velocity of the faraway galaxy is 70 km/s/Mpc x 1.03 = 71.1 km/
Recessional velocity is the speed at which an object is moving away from an observer. This is typically measured in kilometers per second and is used to measure the expansion of the universe. It is calculated by measuring the wavelength shift of an object's light, which increases as the object moves away from the observer.
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a pair of narrow, parallel slits separated by 0.250 mm is illuminated by the green component from a mercury vapor lamp (l 5 546.1 nm). the interference pattern is observed on a screen 1.20 m from the plane of the parallel slits. calculate the distance (a) from the central maximum to the first bright region on either side
The length (a) of the first brilliant zone on either side of the central maxima is 2.62mm.
What does diffraction interference mean?Diffraction. Waves that emerge from two independent sources and produce distinct wave fronts are said to interfere. On the other hand, diffraction can be thought of as secondary waves that form from the many components of the same wave.
Why does an interference pattern occur?Thomas Young demonstrated how the interaction of two sources of light in the same medium results in an interference pattern. both prospective and retrospective meddling.
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a mass of 350 g connected to a light spring of force constant 24.2 n/m oscillates on a horizontal, frictionless track. the amplitude of the motion is 6.3 cm. calculate the total energy of the system. answer in units of j.
The total energy of the system is 0.01089 joules.
The mass of the object is, m = 0.35 kg
The spring constant is, k = 24.2 N/m
The amplitude of the motion is, A = 3 cm
The relationship of the total energy of the system is given by the following:
[tex]E_{T} = 1/2KA^{2}[/tex]
Substitute the values in the above relationship.
[tex]E_{T} = 1/2[(24.2 N/m (3cm * 1m/100cm)^{2} ][/tex]
= 0.01089 joules
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B is kept constant but the coil is rotated so that the magnetic field, B, is now in the plane of the coil. How will the magnetic flux through the coil change as the rotation occurs?
The magnetic flux decreases through the coil.
Due to a change in the angle between B and the coil's axis, the flux decreases.
Magnetic flux :
The magnetic field and the vector corresponding to the coil's area form a dot product, which determines the flux through the coil. The latter vector has a magnitude equal to the coil's area and a direction perpendicular to the plane in which the coil's area is located. The vector S is the vector representing the area of the coil, much like in the attached image. The flux will therefore be at its highest when the vector S points in the same direction as B, and at its lowest when their angles are perpendicular.
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this imposes another condition on the charge densities on the surfaces of the plates. how can this condition be expressed?
The requirement of the charge densities on the surfaces of the plates is that the charge on the plates must be of the same amount but in the opposite direction in order to complete this field. This condition requires that the charge on the plates be of the same amount but in the opposite direction.
What is an electric field?
It is a physical field that a charged particle occupies on another particle in its environment. In order to form this field, the charge on the plates must be the same amount but going in the opposite direction.
The parallel plate capacitor is the term given to the device that holds a charge. The charge concentrations on the plate surfaces will be under the following conditions:
The charges on the plates must be identical in size and directed in the opposite direction.
This enables the addition of fields to the inside of the plates and the removal of fields from the outside.
Therefore, in order to form this field, the charge on the plates must be the same amount but applied in the opposite direction.
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Displacement is a measure of __________ in ________.
Displacement is a measure of the shortest distance between a starting point and an ending point in meters.
What is displacement?The displacement can be described as the change in the position of an object. The displacement can be described as the minimum length between the initial and the final point.
The displacement is the vector parameter that exhibits both distance and magnitude. Therefore, the measurement of the displacement of an object involves the direction.
Displacement can also be defined as the shortest distance between a starting point of an object and an ending point. Displacement can be measured as a straight line and the SI unit of the displacement is meters and the C.G.S. unit is centimeters.
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For an ideal gas in a sealed container, if you double the pressure and double the volume, while keeping everything else the same, what has happened to the temperature?
A. The temperature is one-quarter of its original value.
B. The temperature is now four times its original value.
C. The temperature is equal to its original value.
D. The temperature is now double its original value.
E. The temperature is now half its original value.
For an ideal gas in a sealed container, if pressure and volume are made double, then : B.) temperature is now four times its original value.
What happens when pressure and volume are doubled?Ideal gas is an hypothetical condition of gas state where molecules of the gas are spaced widely apart that is the inter molecular force of attraction is negligible. It obeys the equation,
PV = n RT
Here, P is the absolute pressure of the gas
V is Volume occupied by the gas
n is number of moles of gas
R is Gas constant
T is Absolute temperature of the gas
Ideal gas at two different states are given as:
((P1).(V1))/(T1) = ((P2).(V2))/(T2)
Given, P2 = 2*P1, V2 = 2*V1
So, ((P1).(V1))/(T1) = ((2*P1).(2*V1))/(T2)
1/T1 = 4/T2
T2 = 4 times of T1
Temperature of the gas becomes four times on doubling the absolute pressure and temperature of gas.
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mechanical energy is select one because the roller coaster select one energy due to friction and air resistance as it travels down the track.
Mechanical energy is: True, Mechanical energy is chosen because the roller coaster choose will have large potential energy.
Mechanical energy is the sum of capability strength and kinetic energy. it's far the power related to the motion and role of an object. as an instance, a shifting vehicle possesses mechanical power in the shape of kinetic power, a compressed spring possesses mechanical power in the shape of potential power.
There are two kinds of mechanical electricity – movement (kinetic power) and saved (ability power). you can learn more in our manual that explains capacity and kinetic energy. Mechanical conversion depends on the quantity of capability energy an object has and what kind of kinetic strength it is able to produce.
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you have a series circuit with a battery and two resistors, one of which is three times the other. how would the results be affected if you interchange the order of the resistors?
When the current is the same through all the resistors and the batteries of a circuit, you have resistors in series. Option B is correct.
What is series circuit?
In the series circuit, the amount of current flowing through any component in a series circuit is the same and the sum of the individual resistances equals the overall resistance of any series circuit.
The voltage in a series circuit, the supply voltage, is equal to the total of the individual voltage drops.
Components linked in series share a single “electrical route,” and each component receives the same current, which is equal to the network's current.
Therefore, when the current is the same through all the resistors and the batteries of a circuit, you have series circuit.
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A golf ball (m = 52.0g) is hit by a club that makes an angle of 50.1◦ with the horizontal. The ball lands 167 m away on a flat fairway. The acceleration of gravity is 9.8 m/s^2.
Answer:
DeeExplanation:
a hertzian antenna in free space is 10 cm long. it is fed by a current of 20 a at frequency of 50 mhz. find the electric and magnetic fields at far zone.
The electric and magnetic fields at far zones are 1.66 and 628.33 (...).
What are electric and magnetic fields?With the use of electricity and other types of artificial and natural illumination, invisible energy fields known as electric and magnetic fields (EMFs) and radiation are created.
The sole difference between the total energy (electrical plus magnetic) is that the B field energy rises as the E field energy falls. The magnetic component of the EM wave causes a current in the antenna when it is a coil, such as those employed in long/medium wavelengths.
Both antenna designs have the same distribution of electric and magnetic energy in the far field. Accelerating charges also create radiating fields in addition to the reactive field; stationary charges and charges travelling at constant speed do so. Reactive fields are created as a result of the continual charge drift caused by DC sources.
The complete calculation is attahced.
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at what temperature is the fahrenheit scale reading equal to (a) twice that of the celsius scale and (b) half that of the celsius scale?
At 320° Fahrenheit, which is equal to 160° Celsius, the temperature is precisely double what it is in Celsius.
24.6C is the temperature at which a reading on the Fahrenheit scale corresponds to half of a reading on the Celsius scale.
The unit of temperature on the Celsius scale—one of the two temperature scales used by the International System of Units (SI)—is the degree Celsius. The Kelvin scale is the other temperature scale. The symbol "degree Celsius" (°C) is used to indicate both a specific temperature on the Celsius scale and a measurement of the distance or range between two temperatures. It carries the name of Anders Celsius, a Swedish astronomer who invented a scale for measuring temperature in 1742 and was born in 1701–1744.
Centigrade, which derives from the Latin centum, which means "one hundred," and gradus, which means "steps," was the name of the measurement until 1948, when Anders Celsius was honoured with the new moniker. Most powerful countries utilise this scale.
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the density of the paper clip was greater than the density of water, so it should not have floated based on this idea alone. explain what properties of water allow the paperclip to float
A paper clip can certainly float on the water's surface, seemingly defying the rules of physics. The paper clip, which has a significantly higher density, can float on the water due to the strong surface tension.
The forces that hold liquid molecules together create the phenomenon known as surface tension.
A glass of water's surface molecules coheres more strongly with molecules that are directly related to them because they aren't surrounded by water molecules on all sides. It is less likely that a "skin" will develop on the water's surface the higher the cohesion between the water molecules as opposed to the water's attraction.
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A rocket burns fuel at a rate of 283 kg/s and
exhausts the gas at a relative speed of 8 km/s.
Find the thrust of the rocket.
Answer in units of MN.
Thrust force of the rocket is, T = 2.264 MN
Thus, the force required to move the rocket through the air is 2.264MN. This force is generated because of Newton's third law of motion.
What is thrust?
Thrust is the force which moves the rocket through the air, and through space. Thrust is generated by the application of Newton's third law of motion; "For every action there is an equal and opposite re-action. "
Calculation:The formula for calculating, thrust force of the rocket is T= vdm/dt
Where, T is the thrust of the rocket
v is th relative speed = 8km/s (given in question)
dm/dt is the mass flow rate = 283kg/s (given in question)
Substituting the values,
T = 8km/s × 1000m/1km × 283kg/s
= 2.264 (10^6N=2.264MN)
Therefore, main answer is that
Thrust force is, T = 2.264 MN
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How could one travel faster than the old speed limit without violating the new velocity limit.
Without violating the new speed limit rules, one can go faster than the old limit.
Because c=velocity includes displacement as it is a vector, one may move faster with a velocity meter than the traditional speed restriction. As a result, it will enable the passengers to go in a straight line without veering off the road, and it will assist them get there much quicker than the old approach without breaking the law.
As indicated above, following the displacement rather than the actual distance might let someone arrive at their goal considerably more quickly without violating the new velocity limit.
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two children sit on a seesaw such that a 300-n child is 2.00 m from the fulcrum. where should a second child of weight 375 n sit in order to balance the system if the support is at the center of the plank?
The second child should be at 1.6 m in order to balance the seesaw.
The equation of torque is given as,
τ = r * F sinθ
where, r is the distance from the fulcrum
F is the force
From the above equation, as the seesaw is in equilibrium, this means that left side is equal to right side, we can write
τ₁ = τ₂
r₁ * F₁ = r₂ * F₂
In order to calculate the amount of torque the right side is providing to the system, we need to find out the distance r₂ that the person on the right is sitting with respect to the fulcrum.
300 * 2 = 375 * r₂
r₂ = 600/375 = 1.6 m
Thus, the second child should sit at 1.6 m in order to balance the seesaw.
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A massive tractor is rolling down a country road. In a perfectly inelastic collision, a small sports car runs into the tractor from behind. Which vehicle experiences a larger change in kinetic energy?.
Small sports car will experience a larger change in kinetic energy during inelastic collision.
In inelastic collision we know that loss of energy is possible. It means law of conservation of energy is not possible. An inelastic collision is an impact where there is a deficiency of motor energy. While force of the framework is moderated in an inelastic collision, motor energy isn't. This is on the grounds that some dynamic energy had been moved to something different. Nuclear power, sound energy, and material distortion are reasonable offenders.
Car has small mass as compared to a massive tractor. Due to its high mass car have greater speed as compared to massive tractor. During inelastic collision when a small mass car is collided with large massive tractor ,it transfers most of its energy to a massive tractor and lost that energy in form of heat.
Hence, a small sports car experience a larger change in kinetic energy.
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How do you find the image vertices for dilation with center 0 0 and scale factor 4?
Resolving scaling factor you find the image vertices for dilation with center 0 0
Magnification is defined as a number or conversion factor used to change the size of a shape without changing its shape. Used to increase or decrease the size of an object. If you know the dimensions of the original shape and the dimensions of the enlarged (scaled up or down) shape, you can calculate the scale factor.
For example, a rectangle is 5 units long and 2 units wide. If you scale this rectangle by a factor of two, the sides are 10 and 4 units, respectively. So you can use the scale factor to get the dimensions of the modified figure.
The coordinates of the image vertices can be calculated as follows:
For vertex A (-3, 1) then A' (4 × -3, 4 × 1) = A' (-12, 4)
For vertex B then (4, -3) then B' (4 × 4, 4 × -3) = B' (16, -12)
For vertex C (2, 3), C' ( 4 × 2, 4 × 3) = C' (8, 12)
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an fm radio transmitter has a power output of 170 kw and operates at a frequency of 105.5 mhz. how many photons per second does the transmitter emit?'
An FM radio transmitter has a power output of 170 kW and operates at a frequency of 105.5 MHz. The total number of photons emitted per second by the transmitter will be 0.229* 10³¹.
Given that, power of the transmitter p = 160 kW = 160* 10³ W
Frequency of the transmitter = 105.5 MHz = 105.5* 10⁶ Hz
Number of photons emitted per second is given by the formula,
N = p / h * v = 160* 10³/(6.6* 10⁻³⁴ * 105.5* 10⁶) = 160* 10³¹/(696.3) = 0.229* 10³¹
Thus, the total number of photons emitted by the transmitter will be 0.229* 10³¹.
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how do population of juvenile salmon alter respond to changes in salinity
Poorly Understood
The influence of salinity, temperature and physiological development on habitat choice by juvenile salmon is poorly understood.
Answer:
Below
Explanation:
It is likely that changes in salinity can affect the population of juvenile salmon in a number of ways. For example, if the salinity of the water increases, it can lead to increased stress on the fish and make it more difficult for them to survive.
This can lead to a decrease in the population of juvenile salmon. On the other hand, if the salinity decreases, it can make it easier for the fish to survive and potentially lead to an increase in the population.
It is important to note, however, that the exact response of the population to changes in salinity will depend on a variety of factors, such as the species of salmon, the specific environment in which they are living, and the magnitude of the change in salinity.
if two separate containers a and b have the same volume and temperature, but container a has more gaseous molecules than b, then container a will have: a) higher pressure b) lower pressure c) a greater universal gas constant d) a smaller universal gas constant
If two separate containers A and B have the same volume and temperature, but container A has more gaseous molecules than B, then the container A will have higher pressure than container B.
According to the approximations of ideal gas conditions, the pressure of a gas is directly proportional to the number of molecules of a gas at constant temperature and volume.
Having this in mind, at constant temperature and volume, container A has more gaseous molecules than B, then container A will have higher pressure than container B.
Below is the calculation for proof that shows which container has the higher pressure while keeping the volume and temperature the same.
So, V a = V b
n a* T a/ P a = n b* T b/ P b
Here, T a = T b
P a = n a/n b * P b
n a/n b > 1
P a/ P b > 1
P a > P b
Thus, the container A will have higher pressure than container B.
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A 710 kg k g car drives at a constant speed of 23 m/s m / s. It is subject to a drag force of 500 n n.
A 710 kg k g car drives at a constant speed of 23 m/s and is subject to a drag force of 500 N. The required power to drive the car on the ground is 11.5 kW
Power is defined as the amount of work done per unit time.
P = W/Δt
Where:
W = work done
Δt = time period
Since W = F . s
Hence,
P = F . s/Δt = F . v
Where:
F = force acted on the object
s = distance
v = velocity
Parameters given in the problem:
F = 500 N
v = 23 m/s
Hence, the required power is:
P = (500) (23 ) = 11,500 Watt = 11.5 kW
Your question is incomplete, but most probably your question was:
A 710kg car drives at a constant speed of 23m/s . It is subject to a drag force of 500 N. What power is required from the car's engine to drive the car on level ground?
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what is the de broglie wavelength (in m) of the 1.00 tev protons accelerated in the fermilab tevatron accelerator? these high-energy protons are needed to probe elementary particles.
The de Broglie wavelength is 1.24 × 10⁻¹⁸ m.
What is de Broglie equation?
Specifically, the wave character of the electron is described by the de Broglie equation, which is an equation used to describe the wave aspects of matter. De Broglie proposed that particles can display characteristics of waves using the formula λ= h/mv, where λ is the wavelength, h is Planck's constant, and m is the mass of a particle travelling at a velocity of v.
Given,
K = 1.0 TeV
The energy of particle moving with a high speed is
=E² = p²c² + (m₀c²)²
Where,
p = momentum of the particle
m₀ = rest mass
∴ Momentum of the particle=
p²c² = E² - (m₀c²)² = p²
So, the de Broglie wavelength for the given particle,
λ = [tex]\frac{h}{p}[/tex] = [tex]\frac{hc}{\sqrt{E^{2}-(m_{0}c^{2})^{2}} }[/tex]
Now, the total energy of the particle is
= E = K + [tex]m_{0}[/tex]c²
Where,
K = Kinetic energy of the particle
λ[tex]_{p}[/tex] = [tex]\frac{hc}{\sqrt{E^{2}- (m_{0}c^{2})^{2}} }[/tex]
= [tex]\frac{hc}{\sqrt{(K + m_{0}c^{2})^{2} - (m_{0}c^{2})^{2}} }[/tex]
= [tex]\frac{hc}{\sqrt{K^{2} + 2Km_{0}c^{2} + (m_{0}c^{2})^{2} - (m_{0}c^{2})^{2}} }[/tex]
= [tex]\frac{hc}{\sqrt{K^{2} + 2Km_{0}c^{2}} }[/tex]
= [tex]\frac{4.1357 X 10^{-15}eVs X 3 X 10^{8}ms^{-1}}{\sqrt{(1.0 X 10^{12})^{2} + 2 X 1.0 X 10^{12} X 938.28 X 10^{6}eV^{2}} }[/tex]
= 1.24 × 10⁻¹⁸ m
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which of these stars will take the shortest time to go from the earliest protostar stage to the main sequence?
The stars are ten times the mass of our sun will take the shortest time to progress from the earliest protostar stage to the main sequence.
What is a star?A star is simply a luminous body that is typically, frequently, and most of the time found in the night sky. A star, like the sun, is an incandescent body with a fixed point of rotation. Stars are massive celestial bodies composed primarily of hydrogen and helium that generate light and heat from the churning nuclear forges inside their cores.The following are some of the star's characteristics:
A star is enormous.A celestial body is a star.Radiation causes a star to shine.Gravity holds a star together.A star also produce Its own lightIt also generates its own heat energy.Finally, it is clear from the preceding explanation that stars are luminous and massive bodies.The complete question:
"Which of these stars will take the shortest time to go from the earliest protostar stage to the main sequence?
a. the star which has the same mass as our sun.
b. the star ten times the mass of our sun.
c. the star six times the mass of our sun.
d. none of the above."
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10 kg of liquid water is in a container maintained at atmospheric pressure, 101325 pa. The water is initially at 373. 15 k, the boiling point at that pressure. The latent heat of water -> water vapor is 2230 j/g. The molecular weight of water is 18 g. 103 j of heat is added to the water.
Water is transformed into vapour at m is 0.0462 g. Be aware that even at lower temperatures, some water molecules will leave the water's surface since they have high kinetic energy.
What exactly is water vaporization heat?At 100 °C, where water boils, the heat of vaporization for water is around 540 cal/g. Be aware that even at lower temperatures, some water molecules will leave the water's surface since they have high kinetic energy.
Water has a mass of 10 kg, a pressure of 101325 Pa, a temperature of 373.15 K, and a latent heat of vapourization of 2230 J.g-1. This water has received 103 J of heat energy.
Now, applying solely the latent heat principle to the heat equation: (since water already at boiling point at atmospheric temperature).
Q = m. The amount of water that becomes vapour is L 103 = m * 2230 m = 0.0462 g.
The complete question is,
A container containing 10 kg of liquid water is kept at 101325 Pa atmospheric pressure. At that pressure, the water is originally at its boiling point of 373.15 K. Water to water vapor has a latent heat of 2230 J/g. Water has a molecular weight of 18 g. The water receives 103 J of heat. 1) How much water evaporates into vapor? mass(vapor)=
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A block weighing 100. newtons is positioned on an incline that makes an angle of 30.° with the horizontal. The magnitude of the friction force between the block and the incline is 10. newtons. A force of 120. newtons is applied by pulling on a rope that makes an angle of 30.° with the incline, as shown.
Draw a free-body diagram, and provide appropriate labels for each of the forces. (Optional)
Calculate the component of the block’s weight parallel to the incline.
Calculate the magnitude and direction of the component of the tension that is useful in moving the block up the incline.
Calculate the magnitude and direction of the block’s acceleration.
(a) The perpendicular component of the block's weight is 86.6 N.
(b) The parallel component of the block's weight is 50 N.
(c) The magnitude and direction of the tension needed to move the block is 103.9 N upwards.
(d) The magnitude and direction of the block's acceleration is 4.3 m/s² upwards.
What is the components of the block's weight?The perpendicular and parallel component of the blocks weight is calculated as follows;
The perpendicular component of the block's weight is calculated as follows;
W (n) = W cosθ
where;
W is the weight of the blockθ is the angle of inclination of the blockW (n) = 100 x cos(30)
W (n) = 86.6 N
The parallel component of the block's weight is calculated as follows;
W (p) = W sinθ
W (p) = 100 x sin (30)
W (p) = 50 N
The magnitude of the tension needed to move the block is calculated as follows;
T = F cosθ
where;
F is the applied forceθ is the angle of inclinationT = 120 x cos(30)
T = 103.9 N upwards
The acceleration of the block is calculated as follows;
T - Ff - W (p) = ma
where;
Ff is force of frictiona is accelerationm is the massm = W /g
m = 100 N / 9.8 m/s² = 10.2 kg
T - Ff - W (p) = ma
103.9 - 10 - 50 = 10.2a
43.9 = 10.2a
a = 43.9 / 10.2
a = 4.3 m/s² upwards
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the structure of a solid can be determined by diffraction of radiation in which region of the electromagnetic radiation spectrum?
Atoms' surrounding electron clouds can serve as diffraction gratings and x-ray scattering sites. This makes it possible to determine the structure of molecules as well as the solid-state structure (i.e., the lattice types and unit cell dimensions).
The principles of diffraction are based on Bragg's Law:
nλ=2dsinθ
n is the diffraction order, which is typically 1.
lambda is the radiation's wavelength of incidence
d is the distance between the lattice planes, where
is the angle between the incident radiation and the scattering plane.
Powder x-ray diffraction (PXRD), which gives the cell constants for the solid's unit cell, is used when the material is a powder.
The intensity of the diffraction peaks is utilised to determine all atom locations when the sample is a single crystal, which provides bond lengths and bond angles.
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