Your average velocity for the journey has been 94.57 km/h.
What is the average velocity of an object?The average velocity of an object is the ratio of total displacement to the total time of motion of an object.
V = ( total displacement ) / ( total time )
The total displacement of your journey is calculated as;
x = 485 km - 154 km
x = 331 km
The total time of the motion is calculated as;
t = 4:30 - 1:00 = 3:30 = 3.5 hours
v = x / t
v = ( 331 km ) / ( 3.5 hr )
v = 94.57 km/h
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Consider an object of mass 2 kg resting on the floor. The coefficient of static friction between the object and the floor is us& What force must be applied on the object to move it?
The maximal static friction force (F) between surfaces in contact prior to motion starting is divided by the normal force (N) to determine the coefficient of static friction. Solving yields a value of 1.08 m/s2.
Find coefficient of static friction ?
The maximal static friction force (F) between surfaces in contact prior to motion starting is divided by the normal force (N) to determine the coefficient of static friction.
Static friction's highest value is F s = _s mg.
where _s is the static friction coefficient
50kg is the box's weight in meters.
Gravitational acceleration is equal to 9.81 m/s2.
F s = 0.5×50×9.81 =245 N
The object must be in motion because the applied force exceeds the static friction's maximum value, F s.
As a result, kinetic friction rather than static friction must be considered.
by the equilibrium state
ma = F k m g
where F = 250 N, k = kinetic friction coefficient = 0.4, and m = 50 Kg
a = box's acceleration
50a = 250-0.4×50×9.81
Solving yields a value of 1.08 m/s2.
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The frequency of waves from a radio station is 15 megacycles per second. Calculate their wavelength. Please help!!
The wavelength of waves whose frequency of waves from a radio station is 15 megacycles per second is 20m
Given the frequency of radio waves (f) = 15 megacycles per second
The number of complete wave cycles that pass a location in a unit of time is the definition of frequency. The SI frequency unit is called a Hertz (Hz). A sinusoidal wave's frequency is defined as the total number of full oscillations that every wave constituent performs in a unit of time.
Let the wavelength = ∧
The speed of light waves (v) = 3 x 10^8m/s
We know that frequency = velocity/wavelength
Then f = v/∧ such that ∧ = v/f
∧ = 3 x 10^8/15 x 10^6 = 20m
Hence the wavelength of radio waves = 20m
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|| bio this scanning electron microscope image of a bacterium was produced using a beam of electrons accelerated through an 30 kv potential difference. what is the speed of the electrons?
According to the problem the speed of the electrons is 2.7 * 10^7 m/s.
What is electrons?Electrons are the smallest particles of matter and are part of an atom. They carry a negative charge and are found in the nucleus of an atom, orbiting around the nucleus in shells or energy levels. Electrons are important for chemical bonding, as they are the particles that form when atoms bond together. They also play a role in the transfer of energy, as they can move from one atom to another.
The speed of the electrons in the beam can be calculated using the equation v = √(2*E/m),
where E is the energy of the electrons (given by E = qV,
where q is the charge of the electron and V is the potential difference) and m is the mass of the electron.
Using the given values, we get v = √(2 * 1.6 * 10^-19 * 30 * 10^3 / 9.1 * 10^-31) = 2.7 * 10^7 m/s.
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if two magnets are placed on a table, which statement describes a situation with the most attraction between the two magnets
Answer:
Unlike charges attract
Explanation:
the force between unlike charges is strong,and the closer the charges are the stronger the electrostatic force between them
in taking your pulse, you count 76 heartbeats in 1 min m i n . part a what is the period of your heart oscillations?
Your heart beats with a Time period of 0.789 seconds.
Your heart beats 76 times per minute, or n.
One minute, or the 60s, is required to complete 76 heartbeats.
now, by figuring out the frequency
The speed of direction varies in current per second is known as frequency. It is denoted in hertz (Hz), and Hertz is the unit of measurement that is used internationally. One hertz is equal to one heartbeat per second.
f = n/t
The time is t, and the number of heartbeats is n.
f= 76/60
f= 1.2666 Hz
to determine the duration
The time period is the inverse of the frequency or one divided by frequency.
T = 1/f
T = 1/ 1.266
T = 0.789s
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Your heart beats for 0.789 seconds each time.
The number of times your heart beats each minute is n.
76 heartbeats must occur in one minute, or the 60s.
Now, by determining the frequency
Frequency is the measure of how quickly a direction changes in current per second. It is expressed in hertz (Hz), the internationally accepted unit of measurement. Heartbeats per second are measured in hertz.
f = n/t
There are n heartbeats per second and time t.
f= 76/60
f= 1.2666 Hz
to establish the timeframe
The time period is equal to the frequency divided by one, or the inverse of the frequency.
T = 1/f
T = 1/ 1.266
T = 0.789s
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an ice floe has a rectangular shape with a surface area of 3 m2 and 1 m thick. what is the maximum mass of a polar bear can sit on the floor before sinking? (ice density 900 kg/m3, sea water density 1025 kg/m3)
The maximum mass of a polar bear can sit on the floor before sinking is 3075 kg.
What do you mean by mass?The mass of an object is constant and does not change with location, unlike weight which does change depending on the gravitational pull of the planet.
Mass can be determined by measuring the gravitational force on an object using a device called a balance or scale. The International System of Units (SI) unit of mass is the kilogram (kg)
The maximum mass of a polar bear that can sit on the ice floe before it sinks is determined by the buoyancy force. The buoyancy force is equal to the weight of the water that the ice floe displaces, which is equal to the volume of the ice floe multiplied by the density of seawater.
The volume of the ice floe is 3m2 * 1m = 3 m3.
The buoyancy force is 3m3 * 1025 kg/m3 = 3075 kg.
The mass of the polar bear that can sit on the ice floe before it sinks is equal to the buoyancy force. So the maximum mass of a polar bear that can sit on the ice floe before sinking is 3075 kg.
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suppose an arrow is shot upward on the moon with a velocity of 66 m/s, then its height in meters after seconds is given by . find the average velocity over the given time intervals.
Answer:
The height of the arrow in meters after t seconds is given by the equation h = -1.8t^2 + 66t.
The average velocity over a given time interval [t1, t2] is given by the formula:
(height at t2 - height at t1) / (t2 - t1)
To find the average velocity, we need to know the values of t1 and t2. Without this information, we can't calculate the average velocity. If you provide me with the values of t1 and t2, I can help you to calculate the average velocity.
It's also worth mentioning that the equation for the height of the arrow is considering that there is no air resistance on the moon, as well as the acceleration due to gravity on the moon is 1.6 m/s^2 (16.6% of Earth) which is the reason for the negative value of the coefficient of t^2.
A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 25. 1 m/s. A 1. 0-kg stone is thrown from the basket with an initial velocity of 12. 6 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 17. 6 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 25. 1 m/s. ?
The distance between the balloon and the rock can be found by using Pythagorean theorem: d = 198 .2 m
Find the solution ?The motion of the stone is the motion of a projectile, thrown with a horizontal speed of
vx = 15 .0 m/s
and with an initial vertical velocity of
= 20.0 m/s
where we have put a negative sign to indicate that the direction is downward.
h is the initial height
g = -9.81 m/s^2 is the acceleration due to gravity
The stone hits the ground after a time t = 6.00 s, so at this time the vertical position is zero:
y(6.00 s) = 0
Substituting into eq.(1), we can solve to find the initial height of the stone, h: = 296 .m
(b) 176.6 m
The balloon is moving downward with a constant vertical speed of
v x = -20.0 m/s
and substituting t = 6.0 s and h = 296.6 m, we find the height of the balloon when the rock hits the ground:
y(t) = 176.6 m
(c) 198.2 m
In order to find how far is the rock from the balloon when it hits the ground, we need to find the horizontal distance covered by the rock during the time of the fall.
The horizontal speed of the rock is
v x = 15.0 m/s
So the horizontal distance travelled in t = 6.00 s is
d x = 90 m
Considering also that the vertical height of the balloon after t=6.00 s is
d y = 176.6 m
The distance between the balloon and the rock can be found by using Pythagorean theorem:
d = 198 .2 m
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a heated gas expands and presses on a piston moving the piston. in this example, work is done: a) by the gas on the piston. b) on the gas by the heat source. c) by the piston on the gas. d) by the surroundings on the system.
Work is done: a) by the gas on the piston.
Pressure-volume work is work done by the expansion of a gas against a constant pressure, such as that provided by a moveable piston.The pressure-volume work (displacement work) is the work don on the gas or by the gas due to the acting gas pressure during a change in volume.If the initial and final state of a gas in a thermodynamic process are known, it is imperative to know the exact course of the state curve in the volume-pressure diagram in order to determine the pressure-volume work. This is because, depending on the path, there are different areas under the curves and thus different pressure-volume work.The pressure-volume work thus depends to a decisive extent on how the process proceeds exactly between the initial and final state. The pressure-volume work as a path-dependent quantity is a typical process variable.To know more about thermodynamics visit:
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why do cars accelerated up the slopes at the same speed but required different amounts of force
Answer:
The same way Newton’s apple fell from the tree and failed to “fall” back up. The steeper the slope the faster the pull of gravity will act. Assuming you are providing the exact same power to a car an upslope will slow the car and a down slope will speed the car. The greater the slope, the greater effect. Until you reach vertical, you should never operate a vehicle in such a manner.
Explanation:
5 g of ammonium nitrate was dissolved in 60 g of water in an insulated container. The temperature at the start of the reaction was 23.0°C and at the end it was 19.0°C. Use the equation below to calculate the energy absorbed by the reaction. (Hint: the mass of the solution changes when ammonium nitrate is added.)
Answer: The energy absorbed by the reaction from the water is 996 Joules.
Explanation:
Energy absorbed by the reaction or energy lost by the water to the reaction,Q.
Mass of the the reaction ,m = 60 g
Specific heat of water = c = 4.15 J\g ^oC
Change is temperature=
Negative sigh indicates that energy was given by the water to the reaction.
The energy absorbed by the reaction from the water is 996 Joules.
a 2.5-kw resistance heater in a water heater runs for 3 hours to raise the water temperature to the desired level. determine the amount of electric energy used in both kwh and kj.
To reach the appropriate water temperature, a 2.5 kilowatt resistance heater in a water heater runs for 3 hours. Therefore, the water heater consumes 7.5 kWh and 7500 kJ of electric energy.
The following formula may be used to calculate the quantity of electrical energy used in kWh and kJ:
Power (kW) x Time = Energy (kWh) (hours)
Energy (kJ) is equal to 1000 kWh of energy.
Considering that a 2.5 kW, 3-hour resistance heater:
2.5 kW times three hours is 7.5 kWh of energy.
Energy (kJ) equals 7.5 kWh times 1,000, or 7500 kJ.
Therefore, the water heater consumes 7.5 kWh and 7500 kJ of electric energy.
Remember that 1 kWh equals 1000 kJ, therefore multiplying the energy in kWh by 1000 yields the energy in kJ.
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10
Select the correct answer.
Which quantity is a vector quantity?
O A. displacement
OB. distance
O C.
O D. temperature
OE. volume
mass
Answer:
A. Displacement is a vector quantity.
Write a statement that explains how the internal and external structures you are discussing work together to support growth and reproduction.
(I WILL GIVE 90 POINTS IF YOU ANSWER THIS!)
Answer: plants have internal and external structures that support growth and reproduction Examples of internal structures are the xylem and phloem Examples of external structures are the roots and stems. All of these structures provide plants with nutrients and food
Explanation: BRAIN
The value of the electric field at a distance of 28.8 m from a point charge is 68.3 N/C and is directed radially in toward the charge.
What is the charge? The Coulomb constant
is 8.98755 × 10⁹ Nm²/C².
Answer in units of C. Answer in units of
C.
To determine the charge, we can use the equation for the electric field due to a point charge:
E = k * q / r^2
Where E is the electric field, k is the Coulomb constant (8.98755 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the point charge.
We can rearrange this equation to solve for q:
q = E * r^2 / k
Plugging in the given values:
q = (68.3 N/C) * (28.8 m)^2 / (8.98755 x 10^9 Nm^2/C^2)
q = (68.3 N/C) * (826.24 m^2) / (8.98755 x 10^9 Nm^2/C^2)
q = (68.3 N/C) * (826.24 m^2/C^2)
q = (68.3 N/C) * (826.24 / 8.98755 x 10^9) C
q = (68.3 N/C) * (9.26 x 10^-9) C
q = 6.36 x 10^-7 C
The charge is approximately 6.36 x 10^-7 Coulombs.
does the glancing incident or near normal incidence result in a higher percentage of reflected light?
No, the glancing incident or near normal incidence does not result in a higher percentage of reflected light.
The percentage of reflected light is determined by the reflectivity of the surface and the angle of incidence. If the angle of incidence is closer to normal, then the reflected light will be more concentrated and will have a higher intensity, but the percentage of reflected light will remain the same.
The term "incidence" describes the emergence of new cases of illness or damage within a community within a predetermined time frame.
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can you draw a gaussian surface that offers a simple way to compute the electric field surrounding a charged dipole?
Yes No
When there is the proper symmetry, Gauss's law can be used to quickly determine the electric field.One of these scenarios is not the case of an electric dipole.
Can the electric field caused by an electric dipole be calculated using Gauss's law? When there is the proper symmetry, Gauss's law can be used to quickly determine the electric field.One of these scenarios is not the case of an electric dipole.The flux across any Gaussian surface surrounding an electric dipole should be zero as it encloses no net charge, and this is in fact the case.The net charge enclosed (qenc) divided by the permittivity of free space (qenc/0) determines the flux of the electric field E passing through any closed surface S (a Gaussian surface): =SEndA=qenc/0.The electric field caused by an electric dipole cannot be determined using the Gauss theorem since an electric dipole has equal and opposing charges, and since no electric field is present when the net charge of the system is zero, an electric dipole does not have an electric field surrounding it.
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the equator is characterized by relatively high or low atmospheric pressure aloft
The equator is characterized by relatively low atmospheric pressure aloft.
What is equator?The equator is a large circle that circles the planet Earth, being in a plane perpendicular to the axis of the planet and being equally spaced from geographic poles.
The geographic Equator, also known as the terrestrial Equator, is the imaginary line on the surface of the Earth from which latitude is calculated; it is the line at 0° latitude. It separates Earth into the Northern and Southern hemispheres.
Equatorial regions are hotter, which causes the air above to expand, lose density, and ascend. At this latitude, this results in a low pressure band.
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A compressor for a jackhammer expands the air in the hammer’s cylinder at a constant pressure of 8. 6 x 10^5 Pa. The increase in the cylinder’s volume is 4. 0^5 x 10^-4 m^3. During the process, 9. 5 J of energy is transferred out of the cylinder as heat.
A. What is the work done by the air
B. What is the change in the air’s internal energy
C. What type of ideal thermodynamic process does this approximate
The work done by the air is 88.06kJ, the change in the air’s internal energy is 357.8J and the type of ideal thermodynamic process is isobaric process.
Given the constant pressure of cylinder (P) = 8.6 x 10^5Pa.
The increase in the cylinder’s volume is (V) = 4.0^5 x 10^-4 m^3.
The energy transferred out of the cylinder as heat (Q) = 9.5J
(a) We know that work done (W) = -PexternalΔV
W = -8.6 x 10^5 x 4.0^5 x 10^-4 = -88.06kJ
Hence the work done is 88.06kJ.
(b) From first law of thermodynamics we know that change in internal energy is equal to heat released - work done.
ΔU = Q - W where W is work and U is internal energy.
ΔU = -9.5 - 348.3 = -357.8J
(c) The type of ideal thermodynamic process this approximates is isobaric process. Under constant pressure, the isobaric process is a thermodynamic process. Even though the pressure is constant in this operation, the temperature, volume, and internal energy are not.
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The diagram below shows two processes, P and Q, in the carbon cycle. (1 point)
The picture shows a rectangular box labeled 'Carbon in atmosphere.' Below the box there is an arrow labeled P pointing downwards. Below the arrow P there is a rectangular box labeled 'Ocean.' There is an arrow pointing downwards, below the box labeled 'Ocean.' Below the arrow there is a rectangular box labeled 'Carbon in limestone.' An arrow labeled Q points from 'Carbon in limestone' towards 'Carbon in atmosphere.'
Which of these statements best describes the processes P and Q?
P shows diffusion and Q shows weathering.
P shows weathering and Q shows diffusion.
P represents combustion and Q represents decomposition.
P represents decomposition and Q represents combustion.
The process P shows diffusion and the process Q shows weathering.
What is carbon cycle?The carbon cycle is the ongoing process through which carbon atoms move back and forth between the atmosphere and the Earth. The carbon content of this closed ecosystem, which includes our planet and its atmosphere. The location of the carbon, whether it is on Earth or in the atmosphere, is continually changing.
The majority of the carbon on Earth is preserved in rocks and sediments, with the remainder found in the ocean, atmosphere, and living things.
Every time a creature dies, a volcano erupts, a fire breaks out, fossil fuels are burned, carbon is released back into the atmosphere.
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a cable is stretched between two posts 3.00 m apart. the speed of waves on this cable is 96.0 m/s , and the tension in the cable is 175 n . if a standing wave on this cable has five antinodes, what is the wavelength of the standing wave?
The wavelength of the standing wave will be 1.2 m if a cable is stretched between two posts 3.00 m apart. the speed of waves on this cable is 96.0 m/s, and the tension in the cable is 175 n. if a standing wave on this cable has five antinodes.
Length, l = 2 m
speed of waves, v = 96 m
Tension, T = 175 N
Antinodes, n = 5 means 5th harmonic
We know that,
l = nλ/2
or λ = 2l/n = 2x3/5 = 1.2 m
Therefore, the wavelength of the standing wave will be 1.2 m if a cable is stretched between two posts 3.00 m apart. the speed of waves on this cable is 96.0 m/s, and the tension in the cable is 175 n. if a standing wave on this cable has five antinodes.
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At 50 degrees Celsius the thermocouple measured an emf of 0. 00056V. Explain why this measurement is not midway between the emf values at 0 and at 100 degrees Celsius
Due to the non-linear relationship between the EMF and temperature differential, this measurement does not fall within the emf values at 0 and 100.
A thermocouple is a device that generates an electrical voltage when there is a difference in temperature between its two ends. The voltage generated by a thermocouple is known as the electromotive force (EMF) and it is a function of the temperature difference between the two ends. The relationship between the EMF and the temperature difference is not linear, it is described by a specific function called the Seebeck coefficient. The measurement of 0.00056V at 50 degrees Celsius does not represent the halfway point between the EMF values at 0 and 100 degrees Celsius because the relationship between the EMF and the temperature difference is not linear. The EMF generated by a thermocouple increases as the temperature difference increases, but at different rates for different thermocouple types. For example, at 0 degrees Celsius, the EMF generated by the thermocouple is zero, and at 100 degrees Celsius, the EMF generated by the thermocouple is a certain value. The EMF generated at 50 degrees Celsius is not halfway between these two values but it is a specific value determined by the feedbeck coefficient of the thermocouple material. Additionally, the measurement of 0.00056V at 50 degrees Celsius is also affected by the thermocouple's environment, such as the atmosphere, the heat radiation and the air currents.
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Invisible forces that are exerted between electric charges at a distance is evidence that each charge is surrounded by an electric.
1. Source
2. Field
3. Outlet
4. Plug
An electric field is an invisible field of force created by the attraction and repulsion of electric charges (the cause of electric flow) and is measured in volts per meter (V/m). With increasing distance from the field source, the electric field's intensity decreases.
Electrostatics Force :Electrostatic forces are attractive or repulsive forces between particles that have already been created by their respective electric charges. The electrical force between stationary charged substances is generally known as the electrostatic force.
An electric field is an area around a charged object where the electric force of the object acts on other charged objects. Electric fields weaken the further they are from the charge. The electric field is invisible.
You see, electrically charged particles like protons and electrons actually have invisible force fields around them.
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the united states has about 300 gw of coal-fired power plants that in total emit about 2 gt of co2/yr while generating about 2 million gwh/yr of electricity. what is the capacity factor (cf)?
The amount of CO2 emitted by coal-fired power stations reached a record high of 9.7 Gt, an increase of almost 6.6% from of the previous year.
What American coal-fired power station is the biggest?3564 MW at the Scherer plant. The Dr. Robert Schmidt Power Plant (Plant Schmidt), a 3564-megawatt (MW) coal-fired power plant near Juliette, Georgia, is called just after former CEO and chairman of its operator, Georgia Power.
The capacity factor formula is what?The formula for calculating the nameplate capacity (CF) is [(electricity have used in Thomas capacity in MWt)] 0.0317. This figure represents the proportion of full-load opening hours per year that are equal; for example, if the CF is 0.70, there are 6132 full-load working hours annually (8760 divided by 0.70).
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there is a hill which has parallel train tracks on it. the tracks run for 6 miles up the hillside. one train is at the top of the hill, moving down at 19mi/h . another train is on the other set of tracks, moving up the hill at 10mi/h . the first train accelerates at 10mi/h2 as it goes down the hill, but the second train does not accelerate or decelerate. how far up the hill are they when they pass?
With a speed over 1.8 km/h, a man is walking on train A from the direction that the train is moving away from. As seen from a train, this person speed is 1 ms.
How do you overcome a hill start?Choose first gear and depress the clutch. While slowly raising the clutch to the biting point, gradually depress the accelerator. When you are sure it is safe to move, release the handbrake and increase the clutch bite until the car begins to move.
How should I drive uphill?As you approach a bend while traveling uphill, slow down, change into a lower gear, and then accelerate. A crucial thing to keep in mind is that if a vehicle is approaching from above, you must be extremely vigilant. When driving downhill, you should once more slow down well before turn and let off the gas.
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As A Plant Grows, it gains mass Which of the following provides the most matter that a plant uses for its growth?
As a plant grows, what provides the most matter that a plant uses for its growth is carbon from the air.
The correct option is C.
What are the requirements for the growth of a plant?
The requirements for the growth of a plant are those things that a plant needs in order to grow.
In order to thrive, plants require nutrients such as carbon from air, water, light, warmth, and air. One of these criteria may prevent a plant from growing or possibly cause it to perish. For instance, a plant left in a dark environment may grow tall and spindly in search of light before deteriorating and dying.
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Complete question:
As A Plant Grows, it gains mass Which of the following provides the most matter that a plant uses for its growth?
Minerals and nutrients from the soil
Light from the sun
Carbon from the air
016 (part 1 of 2) 10.0 pointa objects with masses of 232 kg and 638 kg are separated by 0.342 m. a 60.6 kg mass is placed midway between them. 232 kg 538 kg 60.6 kg © - 0.342 m find the magnitude of the net gravitational force exerted by the two larger masses on the 60.6 kg mass. the value of the universal gravi tational constant is 6.672 × 10-11 n • m? /kg? answer in units of n. 017 (part 3 of 2) 10.0 points leaving the distance between the 232 kg and the 638 kg masses fixed, at what distance from the 538 kg mass (other than infinitely remote ones) does the 60.6 kg mass experience a net force of zero? answer in units of m
The magnitude of the net gravitational force exerted by the two larger masses on the 60.6 kg mass is 3.958e-9 N. The distance at which the 60.6 kg mass experiences a net force of zero is infinitely remote.
What is the value of the universal gravitational constant?The universal gravitational constant, denoted as G, is a physical constant that is used to describe the strength of the gravitational force between two objects. Its value is approximately 6.672 x 10^-11 Nm^2/kg^2. This constant is used in the equation for the force of gravity, which is F = G(m1m2)/r^2, where m1 and m2 are the masses of the two objects, and r is the distance between them. The constant is considered to be a fundamental constant of nature and is used in many fields of physics, including cosmology and celestial mechanics.
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what is the angular separation (in radians) between the central maximum and the first-order maximum?
The angular separation between the central maximum and the first-order maximum is equal to 1.22 radians.
This is the angle between the two points on the wavefront that have the same intensity of the wave, and is determined by the wavelength of the wave and the distance between the two points.
The angular separation is an important factor in understanding the behavior of a wave, as it affects the intensity of the wave at different points.
Additionally, the angular separation between two points on the wavefront can provide insight into the wavelength of the wave, as longer wavelengths yield larger angular separations.
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determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to
The additional mass should be distributed as 2.75g, 0.25g, and 3 gm at vertices V1, V2, and V3 respectively, to move the center of mass of the plate at (2, 2).
The center of mass (x, y) of a triangular plate with vertices V1=(0,1), V2=(8,1), and V3=(2,4) can be calculated by taking the average of the x and y coordinates of the vertices.
x = (0 + 8 + 2)/3 = 10/3
Similarly y = 6/3 = 2
So, the center of mass of the plate is (4, 2).
New center of the mass is (2, 2)
w1 + w2 + w3 = 6 g ....eqn(1)
Mass of the plate, m = 3 g
To distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2,2), we need to determine the masses w1, w2, and w3 that need to be added at each vertex.
The formula for finding the center of mass of a system of point masses is:
x = (w1 × x1 + w2 × x2 + w3 × x3 + m × 10/3)/(m + w1 + w2 + w3)
y = (w1 × y1 + w2 × y2 + w3 × y3 + m × 2)/(m + w1 + w2 + w3)
2 = (w1 × 0 + w2 × 8 + w3 × 2 + 3 × 10/3)/(3 + 6)
18 = 8w2 + 2w3 + 10
8 = 8w2 + 2w3....eqn(2)
Similarly
2 = (w1 × 1 + w2 × 1 + w3 × 4 + 3 × 2)/(3+6)
18-6 = w1 + w2 + 4w3
12 = w1 + w2 + 4w3 ...... eqn(3)
On solving three equations
6 = w1 + w2 + w3
8 = 8w2 + 2w3
12 = w1 + w2 + 4w3
We get
w1 = 2.75 g
w2 = 0.25 g
w3 = 3 g
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--The given question is incomplete, the complete question is:
"A thin triangular plate of uniform density and thickness has vertices V1=(0,1), V2=(8,1), and V3=(2,4), and the mass of the plate is 3 g.
Determine how to distribute an additional mass of 6g at the three vertices of the place to move the balance point of the plate to (2,2). Hint: Let w1,w2,w3 denote the masses added to the three vertices so that w1+w2+w3= 6."--
how to calculate velocity given displacement is 0 m, time interval is 35s, but the vector is going down
The velocity will be 0 m/s. We calculated it as shown below.
It is the directional speed of a moving object, as measured by a specific unit of time and viewed from a particular vantage point, that is called velocity. Vectorial velocity describes the displacement that an object or particle experiences with respect to time. It is accepted that the metre per second (m/s) is the unit of magnitude of velocity (also called speed). As well as meters per second (m/s), centimeters per second can also be used to express magnitude.
Velocity = [tex]\frac{Displacement}{Time}[/tex]
= 0/ 35
= 0 m/s
So , The velocity will be 0 m/s.
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