This is because spray sunscreens contain fewer ingredients and preservatives than cream sunscreens.
What is sunscreen?
Sunscreen, also referred to as sunblock as well as sun cream, is a topical photoprotective product for the skin that primarily absorbs or, to a much lesser extent, reflects some ultraviolet (UV) radiation from the sun. This helps prevent sunburn and, more importantly, skin cancer. Lotions, sprays, hydrocolloids, foams, sticks, powders, as well as other topical products are all forms of sunscreen. Sunscreens are common additions to clothing, especially sunglasses, sunhats, and other types of photoprotective clothing (such as umbrellas). H.A. Milton Blake, an Australian chemist, created the first sunscreen in 1932 using a 10% concentration of the UV filter salol (phenyl salicylate).
Since they do not contain as many active ingredients, they are less likely to expire quickly. Additionally, because the sunscreen is in a spray form, it is less likely to be contaminated with bacteria or dirt, which can cause it to expire more quickly.
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suppose you observe a star-like object in the sky. how can you determine whether it is actually a star or a quasar?
Consider the light spectrum. The maximum Doppler shift for spectral lines from stars is a few hundred km/s. The lines of even the nearest quasars are significantly more redshifted.
Describe the spectrum of light.
The term "light spectrum" refers to the range of various wavelengths that a light source emits. Light is measured in nanometers (nm). Each nanometer corresponds to a wavelength of light or a band of light energy. Visible light is the portion of the spectrum between 380 and 780 nanometers (nm).
What kind of light spectrum does that entail?
The frequency of the light determines the hue of the light in the visible spectrum. A rainbow or the split light from a prism always has the same visible spectrum.
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A 50 kg ice skater moving at 6 m/s collides with a second stationary skater with mass 70 kg. The skaters cling together after the collision and move without friction. compute their speed after the collision.
Their speed after collision is 2.5.
What is the reason for this?
An ice skater with a mass of 50 kg is moving at a speed of 6m/s.
The ice skater with 50 kg mass collides with a second stationary skater whose mass is 70 kg.
These skaters cling together after the collision and they also move without friction.
Their speed after the collision would be as follows:
Formula: mv = mv
from above information, we know that
Mass of first skater is m= 50 kg
Speed of first skater v= 6m/s
Mass of second skater is m= 70 kg
Speed after collision v=?
mv = mv
50 x 6 = (50 + 70) v
v = 50 x 6 / 120 = 2.5
So therefore, their speed after collision would be 2.5.
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imagine that a tank is filled with water the height of the liquid column is 7 and the area is 1.5 square meters into the second power what's the force of gravity acting on the column of water
The force of gravity acting on the column of water is 1,02,900 N.
Given that, height of the liquid column is 7
Area = 1.5 m²
We know that, volume of water = 1.5* 7 = 10.5 m³
10.5 m³ when converted into litres can be written as 10,500 litres
Water mass = 10,500 litres * (1kg/litre) = 10,500 kg
Force of gravity on water is nothing but weight of the water
⇒ 10,500* 9.8 = 1,02,900 N
Pressure on the bottom of the tank = 1,02,900/1.5 = 68,600 N/m² = 68,600 pascal
Thus, the force of gravity acting on the column of water is calculated to be 1,02,900 N.
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the mass of earth is 5.972 * 1024 kg, and the radius of earth is 6,371 km. a 750 kg satellite orbits 35,800 km above earth in a perfectly circular orbit. if the gravitational force is acting as the centripetal force to keep the satellite in orbit, what is the tangential velocity of the satellite in its orbit?
The speed or the tangential velocity of the satellite to keep it in its orbit is 3,073.5 meters per second.
The gravitational force between two objects is given by:
F = GMm/r²
Where:
G = constant of gravity = 6.674 x 10⁻¹¹ N.m²/kg²
M, m = mass of each object
r = distance between objects
Parameters given in the problem:
M = 5.972 x 10²⁴ kg
m = 750 kg
r = 6371 + 35,800 = 42,171 km = 42,171,000 m
Hence,
F = 6.674 x 10⁻¹¹ x 5.972 x 10²⁴ x 750 / 42,171,000²
= 168.1 N
This is equal to centripetal force:
F = m . v² / r
168.1 = 750 . v² / 42,171,000
v² = 9,446,304
v = 3,073.5 m/s
Hence, the tangential velocity of the satellite to keep it in its orbit is 3,073.5 m/s
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calculate the angle, in degrees, for the fourth-order maximum (counting the center bright region) of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.
Hence there exist no solution for such angular position, in other words there is no fourth order maximum fringe.
What does a wavelength mean in plain English?The distance between the two consecutive peaks or troughs of a wave is known as its wavelength. It is calculated in the wave's direction.
The angular position of the bright fringes in the double slit interference is given by the following relation
[tex]m\lambda=d\sin\funcapply\left(\theta_m\right)[/tex]
Where,
m: Is the dazzling fringe's order, m.
[tex]\lambda :[/tex]580-nm (Is the wavelength of the incident light on the double slit.)
d: 0.100mm (Is the distance between the centers of the two slits.)
[tex]\theta_m:[/tex] is the angle at which the mth fringe is located.
[tex]\begin{aligned}\theta_4 & =\sin ^{-1}\left(\frac{4 \lambda}{d}\right) \\& =\sin ^{-1}\left(\frac{4 \times 580 \times 10^{-9}}{1.00 \times 10^{-4}}\right)\end{aligned}[/tex]
[tex]=\sin ^{-1}(0.02)\\=1.14[/tex]
Where, the sine function can never have a value greater than 1 , hence there exist no solution for such angular position
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what is the frequency of the second overtone if the fundamental frequency is 308 hz
A. 154hz
B. 924hz
C. 308hz
D 616hz
The frequency of the second overtone if the fundamental frequency is 308 Hz is equal to 1540 Hz.
What is overtone?An overtone can be described as any resonant frequency above the fundamental frequency of a sound. Overtones can be defined as all pitches higher than the lowest pitch within an individual sound. While the fundamental can be described as usually heard most prominently, overtones are present in any pitch except a true sine wave.
The lowest normal frequency is called the fundamental frequency, while the higher frequencies are known as overtones.
Given, the fundamental frequency, f₀ = 30 8 Hz
The relationship between the fundamental frequency and the second overtone is given by
f₂ = 5 f₀
f₂ = 5 × 308 = 1540 Hz
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a dulcimer string is supposed to vibrate at 247 hz. instead it is vibrating at 260 hz. ef picup part description answer save status a. determine the percent decrease in tension in the dulcimer string so that it vibrates at the correct frequency. (include units with answer) format check click here to check your answer 7.14 pts.100% 2% try penalty
The percentage decrease in the tension of the dulcimer string vibration is 99.09%.
Current vibration = 247 Hz
Required vibration = 260 Hz
We know that'
= V = vμ
= √ (T/μ)
Combining the two equations of two different vibrations'
= (T₁ / T₂) = (v₁/v₂)²
The percentage decrease is =
= [ 1 - (T₁ / T₂) ] X 100%
= [ 1 - (v₁/v₂)² ] X 100%
= [ 1 - (247/260)² ] X 100%
= [ 1 - 0.009025] X 100 %
= 99.09 %
The string with is supposed to vibrate at 260 Hz is vibrating at 247 Hz, thus the percentage decrease required to reduce the tension so that it vibrates at correct frequency is 99.09%.
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an object of mass m rests on a frictionless surface and is attached to a horizontal ideal spring with spring constant k . the system oscillates with amplitude a . the oscillation frequency of this system can be increased by
A horizontal ideal spring with a spring constant of k is linked to a mass m object that is at rest on a frictionless surface. By lowering m, the system's oscillation frequency can be raised.
What is an example of frequency?
The number of times that a specific data value occurs is its frequency. A data value's frequency is represented by the letter f. In the event that five students achieve The grade A was said to have a frequency of five, much like in science.
What does frequency serve to accomplish?
The frequency, a crucial factor in science and engineering, describes the temporal rate of change observed in oscillatory and periodic phenomena, including mechanical vibrations, audio signals (sound), radio waves, and light.
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which lighting method has a light source placed inside the surface of a partially reflective dome, with the camera focused on the object through a hole in the middle
Diffuse dome lighting method has a light source placed inside the surface of a partially reflective dome, with the camera focused on the object through a hole in the middle.
What is Diffuse dome lighting?
Machine vision dome lights, commonly referred to as "cloudy-day illumination," produce diffuse lighting. Reflected light offers gentle, shadow-free lighting that is non-directional and non-directional. At close working distances, this effect is ideal for scrutinizing highly specular, curving objects.
The CCD stands for a Charge Coupled Device, which is a semiconductor element that converts images into digital signals.
Cameras are used by machine vision to collect visual data from the surroundings. It then prepares the data for usage in various applications by processing the photos using a mix of hardware and software. Specialized optics are frequently used in machine vision technologies to capture pictures.
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a long wire of finite resistance is connected to an ac generator. the wire is then wound into a coil of many loops and reconnected to the generator. is the current in the circuit with the coil greater than, less than, or the same as the current in the circuit with the uncoiled wire?
The current in the circuit with the coil is greater than the current in the circuit with the uncoiled wire
What is electric current?Electric current is the flow of electric charge in a circuit.
How to determine the current in the circuit?Since a long wire of finite resistance is connected to an ac generator, in this circuit, we know that the length of wire has a resistance and will draw a current from the generator.
Now, the wire is then wound into a coil of many loops and reconnected to the generator, the wire now has an inductance. In this circuit, the inductance of the wire causes it to draw extra current apart from that drawn by the resistance of the wire.
So, since it draws extra current, thus, the current in the circuit increases when the long finite wire is wound into a coil of many loops.
So, the current with the coil is greater than the current in the circuit with the uncoiled wire
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you are the science officer on a visit to a distant solar system. prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. you have previously determined that the planet orbits 8.6 × 1011 m from its star with a period of 402 earth days. once on the surface you find that the acceleration due to gravity is 63.6 m/s2. what are the mass of (a) the planet and (b) the star? (g
The mass of the star of the distant solar system is 82 * 10²² kg and the mass of the planet of the distant solar system is 8.58 * 10²⁵ kg
The planet stays in its orbit and moves in a centripetal motion due to the gravitational force of attraction between the planet and the star.
Fc = m v² / r
Fg = G M m / r²
Fc = Fg
m v² / r = G M m / r²
v² = G M / r
M = r v² / G
g = Acceleration due to gravity
G = Gravitational constant
M = Mass of star
r = Distance between both bodies
G = 6.67 * 10⁻¹¹ N m² / kg²
r = 8.6 * 10¹¹ m
T = 402 days = 3.47 * 10⁷ s
v = 2 π r / T
v = 2 * 3.14 * 8.6 * 10¹¹ / 3.47 * 10⁷
v = 15.56 * 10⁴ m / s
Ms = 8.6 * 10¹¹ * 15.56 * 10⁴ / ( 6.67 * 10⁻¹¹ )
Ms = 20.1 * 10²⁶ kg
F = G M m / r²
F = m g
Equating,
m g = G M m / r²
Mp = g r² / G
Mp = 63.6 * ( 1.8 * 10⁷ / 2 )² / 6.67 * 10⁻¹¹
Mp = 8.58 * 10²⁵ kg
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a hammer taps on the end of a 5.0-m-long metal bar at room temperature. a microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. the pulses are separated in time by 9.00 ms .
The time it takes for it to travel through the air is 5m / 343 m/s = 14.57 msec.
We know that it travels faster through the metal, so if the difference is 11, then tm = 11–14.57 ms
which means the speed through the metal is 5/0.00066 = 7575 m/s
But this is not a good answer, as the speed of sound in the air can vary over a large range. And the difference between 11 and 11.66 ms is small.
For example, the 343 number is at 20ºC. At 25ºC it is 346 m/s, which has a travel time of 11.55 ms, and when you subtract, you get 0.55 ms, or a speed of 7330 m/s. So it depends on the exact temperature, which you did not define.
Temperature is a measure of hot or cold expressed on one of several scales including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy spontaneously flows. Temperature is a measure of how hot or cold something is Specifically.
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a force of 20n is applied toa screwdriver to pry the lid off a paint can. the screwdriver applies 65n of force to the lids. what is the mechanical advantage of the screwdriver
The screwdriver being described above has a mechanical advantage of 65 N. Accordingly, this straightforward device would exert 65N of force on the can's lid for every 20N of force applied to the screwdriver.
How can you improve a screwdriver's mechanical advantage?A screwdriver's handle can have its torque increased by increasing the diameter of the handle. The force exerted by a person's hand on the handle must be farther away from the screwdriver's shaft in order to increase the torque that is applied to the screw by the tool.
The mechanical advantage and force that a screw can exert for a given applied force increase as the distance between its threads decreases. However, since most real screws have high levels of friction, the mechanical advantage they provide is less than that predicted by the previous equation.
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The mohorovicic discontinuity is the _______. A. Division between the lithosphere and asthenosphere b. Boundary between solid and molten rock c. Transition from granitic to basaltic crust d. Boundary where crust gives way to mantle please select the best answer from the choices provided a b c d.
The mohorovicic discontinuity is the Boundary where the crust gives way to the mantle
What is Mohorovicic discontinuity ?
The line separating the Earth's crust and mantle is known as the Moho discontinuity. Because it was found by a Croatian scientist named Andreaja Mohorovicic, it retains that name. Within the (lithospheric) plate, this boundary denotes a change in seismic wave velocity from the crust to the uppermost mantle. The surface that separates the earth's crust from its mantle, located roughly 24 to 30 miles (40 to 50 km) below the continents and 6-7 miles (10 to 12 km) below the ocean floor.
According to the above definition
We get to know that
The mohorovicic discontinuity is the Boundary where the crust gives way to the mantle
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which type or types of motion is particle motion in surface waves?
In surface waves, circular motion refers to particle motion. The particles that make up the majority of the medium are present in both transverse and longitudinal waves.
And travel both perpendicularly to the direction of the transported energy and parallel to it. Surface waves have particle motion that is neither longitudinal wave nor transverse waves. Motion is the phenomenon whereby an item shifts in relation to time. Motion is quantitatively characterized in terms of the body's change in position with respect to the observer's frame of reference as well as the velocity, acceleration, and speed of the body. Each material particle vibrates in a longitudinal wave about its usual rest position.
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a metal sphere of radius 15 cm has a net charge of 7.0 10-8 c. (a) what is the electric field at the sphere's surface?
Answer:
Electric field on the surface of the ball 28 kV/m
Explanation:
Given:
R = 15 cm = 0.15 m
q = 7.0·10⁻⁸ C
________________
E - ?
Electric field on the surface of the ball:
E = k·q / R²
E = 9·10⁹·7.0·10⁻⁸ / (0.15)² ≈ 28 000 V/m or E = 28 kV/m
a girl is skipping stones across a lake. one of the stones accidentally ricochets off a toy boat that is initially at rest in the water (see the drawing). the 0.072-kg stone strikes the boat at a velocity of 13 m/s, 15° below due east, and ricochets off at a velocity of 11 m/s, 12° above due east. after being struck by the stone, the boat's velocity is 2.1 m/s, due east. what is the mass of the boat? assume the water offers no resistance to the boat's motion.
The precept of the conservation of momentum dictates that because the stone enters the water and pushes a number of the water downwards, the stone is compelled upwards.
There are 3 unique axes in any delivery, known as longitudinal, transverse, and vertical axes. The movements around them are called the roll, pitch, and yaw respectively.in order for the boat to move, the force of the wind pushes at the sail and reasons the boat to move.
Start something shifting, deliver impetus to something, as in A press convention set the brand new assignment in motion. it is also put as set the wheels in motion, as in permit's set the wheels in motion for the brand new library wing. This idiom dates from approximately 1800.
The answer is C, the force is a result of the interaction between the oars and the water the boat is visiting. that is the force that actions the boat forward.
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1. A 50 kg carton slides at 4 m/s across an icy surface.
The sliding carton skids onto a rough surface and
stops in 3 seconds. Calculate the force of friction it
encounters.
Answer:
A carton of mass 50-kg slides across an icy surface at a speed of 4 m/s. Conclusion : The momentum of a carton of given mass moving with a particular velocity is 200 kg−m/s .
does the pa-28 have an alternate static source? if so, how is it activated and what actions are necessary to acquire the most accurate reading?
Optional equipment includes an alternate static source.
What is alternate static source?When the alternate static source is used, the instrument indications should differ as follows: The altimeter will show a higher altitude than the actual altitude, and the airspeed will show a higher speed than the actual airspeed.The airspeed will be higher than the actual speed. The altimeter will show a marginally higher altitude.Whenever the primary source of static air pressure is unavailable, use the alternate static air source.The most important rule to remember when using an alternate static air source is to always consult the owner's manual, POH, or AFM for information and limitations.The alternate static air source is simple to test. Activate the system with the appropriate control and monitor the VSI and altimeter for changes. As the lower static air pressure enters the system, the VSI will rise briefly and the altimeter will rise a few feet.To learn more about alternate static source refer to :
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a single-turn square loop of side $l$ is centered on the axis of a long solenoid. in addition, the plane of the square loop is perpendicular to the axis of the solenoid. the solenoid has 1370 turns per meter and a diameter of 7.70 cm, and carries a current of 3.11 a. calculate the magnetic flux through the loop when $l$
The statement predicts magnetic flux toward being 37.82*10⁻⁷ Wb, 131.73*10⁻⁷ Wb and 131.73*10⁻⁷ Wb
What does an automobile solenoid do?It typically sits between the engine and the ignition module of your car. When the automobile key is turned, solenoids (also known as start solenoids or starter relay) operate by combining big electric pulses from your vehicle's charge with smaller electrical impulses from ignition system.
Briefing:(a). Flux is given by
Ф= BACosФ
μ₀ηIL² cos0
= 4*π*10⁻⁷*1370*3.11*0.0275²
= 37.82*10⁻⁷ Wb
(b). Here diameter and length are equal
Ф = BACosФ
= μ₀ηI(π(L/2)²)cos 0
= 4*π*10⁻⁷*1370*3.11*3.14*(0.028)²
= 131.73*10⁻⁷ Wb
(c). Here as length is greater than diameter the flux will be same as flux on solenoid
Ф = 131.73*10⁻⁷ Wb
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The complete question is-
A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1370 turns per meter and a diameter of 7.70 cm, and carries a current of 5.11 A.
Part A: Find the magnetic flux through the loop when L= 2.75 cm .
Part B: Find the magnetic flux through the loop when L= 5.60 cm .
Part C: Find the magnetic flux through the loop when L= 13.5 cm .
During soccer practice one of your teammates sprains her ankle. You take an instant cold pack from the first aid kit to use on her ankle. It is not at all cold when you take it out. The instructions on the cold pack tell you to punch the pack so that you break open a sake of chemicals inside it. When you do that, you notice that the cold pack rapidly becomes quite cold. What happened?.
When you punch the pack of ice, you notice that cold pack rapidly becomes quite cold. This is because, chemical reaction took place absorbing thermal energy from the pack.
What is the absorption of thermal energy?Chemical reactions that absorb energy are called endothermic. In an endothermic reactions, more energy is absorbed when the bonds in the reactants are broken than it is released when new bonds are formed.
The process in making the cold pack is the physical act of dissolving. When ammonium nitrate is dissolved in water, that process is endothermic and thus producing the cold pack. All the reaction absorb energy, for example thermal energy from heat for its activation.
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a bucket full of sand has a mass of 30 kg (including the bucket and the sand). the bucket is to be lifted to the top of a building 15 meters tall by a rope of negligible weight. however, the bucket has a hole in it, and leaks 0.1 kgs of sand each meter it is lifted. find the work done lifting the bucket to the top of the building.
The Total work done lifting the bucket to the top of the building is 405 kg m
What is work?
Work in physics is the energy that is transmitted to or from a object when a force is applied along a displacement. In its simplest form, it equals the goods of the force's magnitude and the distance travelled for a constant force directed in the same direction as the motion. When a force is applied, it is said to have a component that points inside the direction of a displacement of the application point.
The work done lifting the bucket to the top of the building can be calculated by multiplying the force of the weight of the bucket by the distance it is moved. In this case, the force is equal to the mass of the bucket and sand, which is 30 kg, and the distance is 15 m. So, the work done is:
Work = Force x Distance
= 30 kg x 15 m
= 450 kg m
However, as the bucket is leaking sand, the mass of the bucket and sand is decreasing as it is being lifted. The mass of the bucket and sand at the top of the building will be less than 30 kg and the amount of work done will be less than 450 kg m.
To calculate the work done lifting the bucket to the top of the building, we need to calculate the mass of the bucket and sand at the top of the building. We can do this by subtracting the amount of sand lost from the initial mass of the bucket and sand. As the bucket leaks 0.1 kg of sand each meter it is lifted, the mass of the bucket and sand at the top of the building can be calculated as:
Mass at top of building = 30 kg - 0.1 kg x 15 m
= 27 kg
Now, we can calculate the work done lifting the bucket to the top of the building by multiplying the force of the weight of the bucket and sand at the top of the building by the distance it is moved. In this case, the force is equal to the mass of the bucket and sand at the top of the building, which is 27 kg, and the distance is 15 m. So, the work done is:
Work = Force x Distance
= 27 kg x 15 m
= 405 kg m
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if it is known that the toggle clamp is a machine, what assumptions can be made about it? check all that apply. (you must provide an answer before moving to the next part.)
A toggle clamp is a tool that you use to firmly secure components or pieces in place, frequently but not always as part of a production process.
What is toggle clamp?A toggle clamp is a device that you employ, often but not exclusively as part of a production process, to firmly place components or parts in place. A toggle clamp's main characteristics are its rapid action and ability to be easily turned on and off by an operator.
Toggle clamps also lock in place firmly. Because of this, toggle clamps are frequently employed in production lines where components need to be held firmly and quickly removed during routine manufacturing procedures.
Toggle clamps come in six primary categories: vertical toggle clamps, horizontal toggle clamps, plunger toggle clamps (also known as push action toggle clamps), hook action toggle clamps, plier action toggle clamps, and cam action toggle clamps.
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A 1. 00 l sample of a gas has a mass of 1. 92 g at stp. What is the molar mass of the gas?.
The molar mass of the gas is
43.008 g/mol
Avogadro stated that "Equal volumes of all gases at the same temperature and pressure contain the same number of molecules". Hence at standard temperature and pressure 1 mole of a gas occupies 22.4 liters of volume.
1 mol = 22.4 liters
Given a gas with 1 L and mass of 1.92 g at STP
Number of moles = 1 L / (22.4 L/mol) = 0.0446 mol
The molar mass = mass of gas / number of moles
molar mass = 1.92 g / 0.0446 mol
molar mass = 43.008 g/mol
Hence, molar mass of the gas is
43.008 g/mol
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what is the speed of visible light waves when traveling through a vacuum? about 3 cross 10^8 m/s about 350 m/s about 1 cross 10^8 m/s light waves cannot travel through a vacuum. about 2 cross 10^8 m/s
The speed of visible light waves when travelling through a vacuum is about 3 X 10⁸ m/s.
What is electromagnetic waves?
In terms of science, electromagnetic radiation is made up of electromagnetic field waves that travel over space while carrying radiant electromagnetic energy. It consists of X-rays, gamma rays, microwaves, infrared, light, and radio waves. These waves are all a component of the electromagnetic spectrum.
The speed of electromagnetic waves, which includes visible light, radio light and x-rays is 3 X 10⁸ m/s. This is same as that of the speed of visible light in the presence of air.
The speed of light is depicted using the letter 'c', and it a universal constant value. It is a physical constant and important in many areas of physics.
The speed of light in water is 2.25 X 10⁸ m/s and that in glass is 2 X 10⁸ m/s. The speed varies with respect to the medium.
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what is the escape speed on a spherical asteroid whose radius is 823 km and whose gravitational acceleration at th surface is 1.38 m/s^2.
A spherical asteroid with a radius of 823 km has an escape speed of 4 103 m/s.
Explain about the gravitational acceleration?Gravitational acceleration is the acceleration that an object experiences as a result of the gravitational force acting on it. Its symbol is "g," and its unit is m/s2. Gravitational acceleration is a vector quantity, having a magnitude and a direction.
(a) The given values are
[tex]$$r=500 \mathrm{~km}$$[/tex]
[tex]$$\Rightarrow a=3.0 \mathrm{~ms}^{-2}$$[/tex]
[tex]$$\Rightarrow v=1000 \mathrm{~ms}^{-1}$$[/tex]
[tex]$$\Rightarrow h=1000 \mathrm{~km}$$[/tex]
We know that the formula for gravitational acceleration is given as
[tex]$$a_g=\frac{G M}{r^2}$$[/tex]
And the formula for the escape velocity is given by
[tex]$$v=\sqrt{\frac{2 G M}{r}}$$[/tex]
Substituting for gravitational acceleration in the above formula we get
[tex]& \Rightarrow v=\sqrt{\frac{2 a_g r^2}{r}} \\[/tex]
[tex]& \Rightarrow v=\sqrt{2 a_g r}[/tex]
Substituting the given values for the radius and gravitational acceleration.
[tex]$$\Rightarrow v=\sqrt{2(3.0)\left(500 \times 10^3\right)}$$[/tex]
[tex]& \therefore v=1.732 \times 10^3 \mathrm{~ms}^{-1}[/tex]
The complete question is,
(a) What is the escape speed on a spherical asteroid whose radius is 5 (lind whose gravitational acceleration at the surface is 3.0 [tex]\mathrm{~ms}^{-2}$[/tex]
(b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of[tex]$1000 \mathrm{~ms}^{-1}$[/tex]
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Nuclear decay occurs according to first-order kinetics. Argon-37 decays with a rate constant of 0. 0198 days–1. After 98. 3 days, a sample has a mass of 2. 14 g. What was the original mass of the sample?.
The original mass of the sample was 14.79 grams.
We know that rate of reaction of first order reactions is given by: [tex]kt = 2.303* log(R'/R)[/tex]
where k = rate of reaction = 0.0198
t = time = 98.3 days
R = final mass = 2.14 grams
Putting these values in above equation we get R' = 14.79 grams.
i.e. The original mass of the sample was 14.79 grams.
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a 4 lb b ball is traveling around a circle of radius r1 = 3 feet quickly v1 = 6 ft/s. if the attached rope is pulled down the hole with constant speed vr = 2 ft/s
Answer:
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Explanation:
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Part A:Two football players run at each other. One has a mass of 75 kg and is moving at 6 m/s.
The second has a mass of 100 kg and is moving at 8 m/s. Calculate the momentum of each
football player.
Part B:The two football players collide. What is the total momentum of the football players?
Part C:What is the velocity of the football players after the collision?
A: The momentum of the first player be 450 kg.m/s.
The momentum of the second player be 800 kg.m/s.
B: The total momentum of the football players be 1250 kg.m/s.
C: The velocity of the football players after the collision be 7.14 m/s.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Given that:
One has a mass of 75 kg and is moving at 6 m/s.
The second has a mass of 100 kg and is moving at 8 m/s
So, momentum of the first player = mass * velocity
= 75×6 kg.m/s
= 450 kg.m/s.
The momentum of the second player = mass * velocity
= 100×8 kg.m/s
= 800 kg.m/s.
If the two football players collide, the total momentum of the football players be = 450 kg.m/s + 800 kg.m/s = 1250 kg.m/s.
The velocity of the football players after the collision be = total momentum/total mass = 1250 kg.m/s./(75+100)kg = 7.14 m/s.
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A tradesman sharpens a knife by pushing it against the rim of a grindstone. The 45 cmcm diameter stone is spinning at 200 rpmrpm and has a mass of 25 kgkg . The coefficient of kinetic friction between the knife and the stone is 0.20.If the stone loses 10% of its speed in 10 ss of grinding, what is the force with which the man presses the knife against the stone?N = ?
The force with which the man presses the knife against the stone is 2.96 N.
Given that,
Diameter of the stone d = 45 cm = 0.45 m
Radius r = 45/2 cm = 22.5 cm = 0.225 m
Initial angular velocity ω₀ = 200 rpm = 200* 2π/6 rad/s = 20.94 rad/s
Final angular velocity ωf = (1 - 0.1)* 200 rpm = 180 rpm = 180* 2π/6 rad/s = 18.85 rad/s
Mass of the stone m = 25 kg
Coefficient of kinetic friction μ*k = 0.2
Time t = 10 s
Part a:
By using the equation of motion with uniform angular acceleration we will find out the angular acceleration of grindstone:
ω* f = ω₀ + α*t
⇒ α = ( ω* f - ω₀) / t = (18.85 rad/s - 20.94 rad/s)/ (10s) = -0.21 rad/s²
Negative sign shows that the wheel is decelerating.
Part b:
Consider the rim of grindstone as a solid disk, therefore the moment of inertia
I = 0.5*m*r² = 0.5*25* (0.225)²
We know that, Torque = Force* perpendicular distance
τ = (μ*k*F)*r ----(1)
Also:
τ = I* α = 0.5*25* 0.225²* 0.21 = 0.133 N-m
F = 0.133/(0.2*0.225) = 2.96 N
Thus, the force with which the man presses the knife against the stone is 2.96N.
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