The ratio of electric fields at r, 2r, and 3r at a distance r away from the charge q is 36 n/c is calculated to be 36:9:4.
Every point in space where a charge, in whatever form, is present can be thought of as having an electric field surrounding it. An alternative name for an electric field is the electric force per unit charge.
The relation between electric field intensity, charge and distance is known to be E = k Q/r².
where, E is the electric field
r is the distance
It is clear that E ∝ 1/r²
If the distance is 1/2r, E = 1/(2r)² = 1/4r² = E/4
If the distance is 1/3r, E = 1/(3r)² = 1/9r² = E/9
In this problem, E is given as 36 n/c, so the ratio is 36/4 = 9 and 36/9 = 4
Hence, the required ratio is 36:9:4.
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how many coulombs of positive charge are there in 1.54 kg of plutonium, given that its atomic mass is 244 and each plutonium atom has 94 protons?
Given that plutonium has an atomic mass of 244 and 94 protons per atom, there are 1.48108 C coulombs with positive charge present in 1.54 per kg plutonium.
What do the protons in atoms do?The particle possesses an electrical charge that is positive and opposite to the electron's. A single protons would weigh only 1.673? 10-27 kilograms if it were isolated, which is just a little bit less than a neutron.
What is the name for protons?Although protons were once thought of as elementary particles, the Standard Model of subatomic particles now recognizes them as composite particles made up of three valence quark, and they are grouped alongside neutrons as hadrons.
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If the charging collar has a positive charge, what will be the net charge on a droplet separating from the stream?
(a)Positive
(b)Negative
(c)Neutral
(d)The charge will depend on the type of cell
The net charge on a droplet separating from the stream will be (b) Negative.
How does the charge on a droplet affect its interaction with other charged objects?The charge on a droplet affects its interaction with other charged objects based on the principle of electrostatics, which states that like charges repel each other and opposite charges attract each other. A droplet that carries a positive charge will experience a repulsion force when it comes into contact with another positively charged object. On the other hand, a droplet that carries a negative charge will experience an attraction force when it comes into contact with a positively charged object. The strength of this interaction is dependent on the magnitude of the charges and the distance between the droplet and the other charged object.
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students analyze their data from a gravity experiment. they find that objects fall at a greater speed from a greater height than from a lower height. what can they conclude?(1 point)
An experiment using gravity lead students to the conclusion that gravity affects the speed of objects.
This is thanks to the experiment that they conducted, which showed that objects fall faster when released from a higher height than when released from a lower height. This indicates that gravity is accelerating the objects as they fall.
The rate of acceleration is proportional to the force of gravity, meaning that the more gravity that is present, the faster the objects will fall. This means that the higher the height, the greater the force of gravity and the faster the objects will fall.
Students can also conclude that the time taken for an object to fall is greater from a lower height than one from a higher height. This is because the higher the height, the greater the force of gravity, meaning that the objects reach their terminal velocity quicker. Terminal velocity is the maximum speed an object will reach, and this can be reached quicker from higher heights.
Overall, students can conclude that gravity affects the speed of objects as they fall and that the higher the height, the faster the objects will fall. This is due to the force of gravity increasing with height, meaning that the objects reach their terminal velocity quicker, leading to faster falls.
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Answer:
1. Mass is the measure of the amount of matter in an object.
2. The objects do not have the same size, shape, or mass, so any differences in drop times cannot be attributed to one variable.
3. Gravity is a force that attracts objects with mass toward each other.
4. by repeating the experiment several times
5. The longer an object falls, the more gravity increases its speed.
in the absence of air resistance, what launch angle of a projectile results in the longest range?
In the absence of air resistance, the launch angle of the projectile results in the longest range is found to be 45°.
What is the launch angle?The launch angle may be defined as the vertical angle at which the ball leaves a player's bat after being struck. Average Launch Angle (aLA) is calculated by dividing the sum of all Launch Angles by all Batted Ball Events.
The angle between an input ray and the fiber axis. If the end face of the fiber is perpendicular to the fiber axis, the launch angle is equal to the angle of incidence. The angle of a projectile's initial velocity is definitely calculated when measured from the horizontal direction. These angles are typically 90° or less.
Therefore, in the absence of air resistance, the launch angle of the projectile results in the longest range is found to be 45°.
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what is the acceleration of the dog sled??
Answer:
a=2m/s^2
Explanation:
F=ma => a=F/m=100/50=2m/s^2
Describe the motion of the object in the graph for the entire time. Explain how the motion changes, including direction and whether or not it is speeding up, slowing down or moving at a constant velocity.
The acceleration increases as the graph becomes more steep. A horizontal line indicates a constant speed of motion for the object. The object is slowing down when the line slopes downward.
What are the definition and examples of motion?Motion is the change in an object's location with relation to time. Motion can be heard in a book dropping off a table, water running from the faucet, rattling windows, etc. Even the air we breathe is in motion!
What is motion in science?Motion in physics is the shift in an object's location in relation to its environment over a specific period of time. Following phrases can be used to describe how a mass-containing object moves: Displacement. Distance. Speed.
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monochromatic light is beamed into a michelson interferometer. the movable mirror is displaced 0.301 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright 1608 times. determine the wavelength of the light.
A michelson interferometer receives beams of monochromatic light. The central spot in the interferometer pattern changes from brilliant to dark and back to bright 1608 times as a result of the movable mirror being moved by 0.301 mm. then the light's wavelength is 3.74.
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles.
This length is typically set in meters in wireless systems (m) Colors that are monochromatic are all variations of a single hue, including tints, hues, and tones. Lighter and darker shades of the primary color or hue will make up a monochromatic color scheme.
d=mλ / 2
so λ = 2d/m
= {2* 0.301 *10^(-3)}/1608
λ = 0.000602/1608
λ = 3.74
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the dwarf planet pluto has 1/500 the mass and 1/15 the radius of earth. what is the value of g (in m/s2) on the surface of pluto? use g
The value of g (gravity on the surface of Pluto is roughly [tex]0.632 m/s^2[/tex]
To find the value of g (speed increase because of gravity) on the surface of Pluto, we can utilize the condition:
[tex]g = GM/R^2,[/tex]
where G is the gravitational steady[tex](6.67 x 10^-11 m^3/kg s^2)[/tex], M is the mass of Pluto, and R is the radius of Pluto.
Since we realize that the mass of Pluto is 1/500 the mass of Earth and the radius of Pluto is 1/15 the range of Earth, we can utilize these qualities to work out g on Pluto.
To begin with, we'll find the mass of Pluto in kg by multiplying the mass of Earth [tex](5.972 x 10^{24} kg)[/tex] by 1/500:
[tex]M = 5.972 x 10^{24} kg * (1/500)[/tex] = [tex]1.1944 x 10^{22} kg[/tex][tex]1.1944 x 10^{22} kg[/tex]
Then, we'll find the radius of Pluto in meters by multiplying the radius of Earth (6,371 km) by 1/15:
R = 6,371 km * (1/15) = 424.73 km = 424,730 m
At long last, we can utilize these qualities to work out g on Pluto:
g = [tex](6.67 x 10^-11 m^3/kg s^2)[/tex] [tex]* (1.1944 x 10^{22} kg)/(424,730 m)^2[/tex]
[tex]g =[/tex] [tex]0.632 m/s^2[/tex]
So the acceleration due to gravity on the surface of Pluto is rough [tex]0.632 m/s^2[/tex], which is around 6.5% of the speed increase because of gravity on the earth.
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A hot air balloon is moving vertically upwards with a constant speed of 3.00 m/s. A sandbag is dropped from the balloon. It takes 5.00 seconds for the sandbag to fall to the ground. What was the height of the balloon when the sandbag was released?
The height of the balloon when the sandbag was released is 108m which is moving vertically upwards with a constant speed of 3.00 m/s.
Given the constant speed of hot air balloon (v) = 3m/s
Time taken by the sandbag to fall to the ground (t) = 5s
As the balloon is moving upwards and sandbag is falling downwards they both are in motion opposite to each other.
Let the initial speed of sandbag (u) = 3m/s
Acceleration due to gravity (a) = -9.8m/s^2
From equation of motion we have: s = ut + 1/2at^2
s = 3 x 5 + 1/2(-9.8)(5)^2
s = -108m
Hence the height of the balloon when the sandbag was released is 108m.
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Rank the colored waves in order of highest frequency to lowest frequency. highest frequency lowest frequency
Answer:
Explanation:
Highest → Lowest frequency
Violet→Indigo→Blue→Green→Yellow→Orange→Red
a 80-cm-thick layer of oil floats on a 140-cm-thick layer of water. what is the pressure at the bottom of the water layer?
The pressure at the bottom of the water layer is 1.22 x 10⁵ Pa
The fluid's weight divided by the surface area gives an estimate of the pressure that the fluid exerts on its surroundings. The density of the fluid can be calculated by multiplying its mass by the acceleration caused by gravity. In this case, we are given that:
Depth of oil (h oil) = 80 cm = 0.8 m
Depth of water (h water) = 140 cm = 1.4 m
Density of water (ρ water) = 1000 kg/m³
Density of oil (ρ oil) = 881 kg/m³
The Standard Atmospheric Pressure (P) = 101325 Pa = 1.01 x 10⁵ Pa
To calculate the pressure due to the weight of liquid, we can use this following formula:
P= ρ g h
Where:
P = pressure
ρ = density of liquid
g = acceleration due to gravity
H = depth of the liquid
To calculate the absolute pressure at the bottom of the water layer, we use:
P(absolute)= P x [ρ(water) × h(water)× g] + [ ρ(oil) × h(oil)× g]
P(absolute) = 1.01 x10⁵ + (1000 x 1.4 x 9.8) + (881 x 0.8 x 9.8)
P(absolute) = 1.01 x10⁵ + 0.21 x 10⁵
P(absolute) = 1.22 x 10⁵ Pa
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A force is required to keep a 5kg mass moving round a cycle of 3.5m at a speed of 7ms^-1. What is the speed of the force if tripled
The speed of the of the object if the force is tripled is 12.12 m/s.
What is the centripetal force?The centripetal force acting on an object moving in a circular path is calculated by applying the following formula as shown below.
F = mv² / r
where;
m is the mass of the objectv is the speedr is the radiusF = ( 5 x 7² ) / 3.5
F = 70 N
When the force is tripled, the new force becomes;
F' = 3 x 70 N
F' = 210 N
The new speed of the object is calculated as follows;
F = mv² / r
v² = Fr / m
v = √ ( Fr / m )
v = √ ( 210 x 3.5 / 5 )
v = 12.12 m/s
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by which element are gamma rays produced
Answer: Some elements like potassium, uranium, and thorium are naturally radioactive and give off gamma rays as they decay, but all elements can be excited by collisions with cosmic rays to produce gamma rays. The HEND and Neutron Spectrometers on GRS directly detect scattered neutrons, and the Gamma Sensor detects the gamma rays.
Explanation: searching
Light travels up through a pond of water of critical angle 49°. What happens at the surface if the angle of incidence is 30°?
The light will refract and pass through the water's surface at an angle of incidence greater than the critical angle if the angle of incidence is 30 degrees, leading to total internal reflection.
How does a substance's refractive index impact the angle of refraction?
A substance's refractive index is a measurement of how much light is bent as it passes through it. The angle of refraction increases with increasing refractive index. The angle of refraction increases as light travels from a medium with a lower refractive index, like air, to a medium with a higher refractive index, like water or glass. Because of this, as light enters the higher refractive zone, it bends more sharply. .
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Three oak blocks, ma = 4.0 kg, mB = 6.0 kg, and mc = 3.0 kg, are positioned next to each
other on a dry, horizontal oak surface. Use the data from Table 5.1 on page 148 to answer
these questions.
(a) What horizontal force must be applied to accelerate the blocks at 1.4 m/s² [forward]. (Assume that the blocks are already moving at a constant velocity.)
(b) Calculate the force exerted by ma on mc.
(c) Calculate the force exerted by me on mA.
Friction Force Calculation.
(a) The horizontal force required to accelerate the blocks at 1.4 m/s² is the combined force of friction acting on the three blocks. To find this force, we need to know the coefficient of friction between the blocks and the surface.
According to Table 5.1, the coefficient of friction for oak on oak is 0.4. To find the force of friction, we use the equation: friction force = coefficient of friction * normal force.
The normal force is the force acting perpendicular to the surface and is equal to the combined weight of the three blocks, which is
ma + mb + mc = 4.0 kg + 6.0 kg + 3.0 kg = 13.0 kg. The force of friction is then: friction force = 0.4 * 13.0 kg * 9.8 m/s² = 52.24 N.
(b) To find the force exerted by ma on mc, we need to find the force of friction acting on ma and mc. The force of friction on ma is: friction force = coefficient of friction * normal force = 0.4 * 4.0 kg * 9.8 m/s² = 15.68 N.
The force of friction on mc is: friction force = coefficient of friction * normal force = 0.4 * 3.0 kg * 9.8 m/s² = 11.76 N.
The force exerted by ma on mc is the force of friction on ma + the force of friction on mc = 15.68 N + 11.76 N = 27.44 N
(c) To find the force exerted by mc on ma, we can use the same method as above. The force of friction on mc is: friction force = coefficient of friction * normal force = 0.4 * 3.0 kg * 9.8 m/s² = 11.76 N.
The force of friction on ma is: friction force = coefficient of friction * normal force = 0.4 * 4.0 kg * 9.8 m/s² = 15.68 N.
The force exerted by mc on ma is the force of friction on mc + the force of friction on ma = 11.76 N + 15.68 N = 27.44 N
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you are given three wishes, but there's a catch: one of them won't come true for the rest of your life, and you don't get to pick which one it is. what do you wish for?
For myself and my loved ones, I would wish for good health, happiness, and success so that even if my wish did not come true, I would still have the things that matter most in life.
To interact with individuals from all over the world and fully appreciate all cultures, I would first wish for the capacity to comprehend and speak all languages with ease. This would significantly improve my capacity for international travel and communication. My second desire is for unrestricted riches and resources so that I might support charity causes, assist people in need, and have a constructive effect on society. To enjoy my money and resources and carry on having a beneficial influence on the world, a long and healthy life is my third and last wish.
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a baseball bat collides with a 0.145 kg baseball moving with an initial velocity of 35 m/s to the left. if the collision lasts 0.005 seconds and the final velocity of the ball is 25 m/s to the right, what was the force of the bat on the ball?
According to Newton's third law of motion, the ball imparts an equal and opposite force on the bat. i.e 290 N
Given that,
The mass of the ball = .145 kg
initial velocity of 35 m/s
collision lasts 0.005 seconds
final velocity of the ball is 25 m/s
We have momentum = mass x velocity.
a) Initial momentum = 0.145*35 = 5.075 kg-m/s
b) Final momentum = 0.145*25 = 3.625 kg-m/s
c) Change in momentum = 5.075 - 3.625 = 1.45 kg-m/s
Impulse = Force x time = change in momentum
F = change in momentum/time = 1.45/0.005 = 290 N
d) By Newton's third law of motion, the ball imparts an
equal and opposite force on the bat.
therefore, Force = 290 N.
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darcel runs the simulation for the large version of each object. what can he say in general about the energies of the objects in the simulation as they roll down the incline? (select all that apply.)
The total energy of the system remains constant and is equal to the gravitational potential energy of the object at the top of the incline.
What is gravitational potential energy?Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. This energy is determined by the objects mass, height and the strength of the gravitational field. Gravitational potential energy increases as the object moves higher from the ground and its mass increases. Gravitational potential energy can be converted into kinetic energy when an object falls or moves down a slope.
The total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.
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Complete Question:
Darcel runs the simulation for the large version of each object. What can he say in general about the energies of the objects in the simulation as they roll down the incline? (Select all that apply.)
"The total energy of the system remains constant and is equal to the gravitational potential energy of the object at the top of the incline.""The total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.""The translational kinetic energy is always greater than the rotational kinetic energy.""The potential energy of the system remains constant, and is equal to the total energy."
when you boil a pot of liquid water, the water turns to steam and rises in the air. this is an example of
Water vapour, or the gaseous state of water, results from the vibration of the water molecules when it is heated. Some of these water molecules escape into the air as steam as a result. It is called evaporation because of this.
What sort of transformation takes place when water boils and turns into steam?
A shift in temperature causes a physical change in water as it boils and transforms into steam.
What kind of energy is transferred to moving water in a boiling pot?
Thermal energy can be seen in the boiling of water on a stove. When a substance's atoms and molecules vibrate more quickly as a result of a rise in temperature, thermal energy is created.
What does evaporation mean?
A liquid transforms into a gas during evaporation. It is simple to picture when puddles of rain "vanish" on a hot day or when wet clothing dries in the sun. In these instances, the liquid water is evaporating into a gas known as water vapor rather than really dissipating.
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The conversion of a liquid into a gas is known as evaporation.The global water cycle includes it as one of its three key stages.
Does liquid water transform to steam when it is boiled and ascend to the surface of the air? The conversion of a liquid into a gas is known as evaporation.The global water cycle includes it as one of its three key stages.When water is heated, its molecules vibrate, some of which escape into the air, converting to water vapor, or the gaseous state of water.Therefore, we refer to it as e VAPORation.The process by which matter transitions from the gaseous to the liquid phase in its physical condition is known as condensation.Condensation, for instance, happens when airborne water vapour, which is in the gaseous state, interacts with a colder surface to transform into liquid water.To learn more about evaporation refer
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a student has an unlabeled magnet and a piece of iron. these items are identical in appearance. how can she use a bar magnet to determine which item is which?
A bar magnet will pull unmagnetized iron toward it. A current loop is comparable to an atom. When placed in a bar magnet's magnetic field, a piece of iron, which has magnetic properties, aligns into two poles.
It is the north pole if the north pole reports the side in front of it, and vice versa if the south pole reports the south pole. When placed in a bar magnet's magnetic field, a piece of iron, which has magnetic properties, aligns into two poles.
An atom possesses charges that are in motion, which results in current. The rotational orbits of the atoms allow them to function as an analogous current loop. But despite the absence of current, iron is drawn to magnetic.
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what is the overall displacement δx of the particle?
Answer: I am not sure about this but here you go
he overall displacement of the particle, δx, is equal to the final position of the particle minus its initial position. Since the initial and final velocities of the particle are given, the displacement can be calculated using the equation δx = vft - vit, where vf is the final velocity, vi is the initial velocity, and t is the time interval. In this case, δx = 18.0 m/s11.5 s - 29.0 m/s11.5 s = -131 m. Therefore, the overall displacement of the particle is -131 m.
The initial and final velocities of a particle are shown in the figure below. Find the particle's average acceleration if the change in velocity takes place in a 11.5 s interval. (Let vi = 29.0 m/s and vf = 18.0 m/s.)
Answer:
To calculate the average acceleration of the particle, we use the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. In this case, a = (18.0 m/s - 29.0 m/s)/11.5 s = -2.3 m/s2. Therefore, the average acceleration of the particle is -2.3 m/s2.
what is the possible cause of an engine running rich at full throttle if it is equipped with a float type carburetor
Clogged main air bleed is the possible cause of an engine running rich at full throttle if it is equipped with a float type carburetor .
Bleed air is mostly used in civil aircraft to feed the environmental control system with air, which maintains pressure in the cabin. Bleed air is also utilised to prevent ice from forming on important sections of the aircraft, including the wing leading edges. the throttle valve of a carburetor with a float design.
This improves fuel vaporisation and discharge management, especially at low engine speeds. In the carburetor barrel, close to one end of the venturi, is where the throttle, or butterfly valve, is situated. By adjusting the airflow to the engine, it offers a way to control engine speed or power production. The float needle valve is worn or otherwise not seated if a float-type carburetor spills fuel while the engine is turned off.
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If an engine has a float type carburetor, a clogged main air bleed could be the reason why it runs rich when the throttle is fully opened.
Bleed air is mostly utilized in civil airplanes to supply air to the environmental control system, which maintains cabin pressure. Bleed air is also used to stop ice from accumulating on critical areas of the aircraft, such as the wing leading edges. a carburetor's throttle valve with a float arrangement.
This facilitates better fuel vaporization and discharge control, particularly at low engine speeds. The butterfly valve, also known as the throttle, is located inside the carburetor barrel, close to one end of the venturi. It provides a technique to regulate engine speed or power output by changing the airflow to the engine. If a float-type carburetor leaks fuel when the engine is off, the float needle valve is worn or otherwise not seated.
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What is the net work done on a 0.430kg football as, starting from rest, it is thrown at
12.7m/s?
a. Wnet = 0
b. Wnet = 34.7J
c. Wnet = 69.4J
d. Wnet = 2.73J
The work that is done by the ball is 2.73J.
What is the net force?We have to note that the net force has to do with the force that we can obtain from the Newton's law. We have to note that from the use of the Newton's law that we are going to have that;
F = ma
F = force
m = mass
a = acceleration
Assuming the time to be 1s
a = 12.7 - 0/1
a = 12.7m/s^2
Then the work that is done is obtained by the use of the formula stated above as follows;
F = 0.430kg * 12.7m/s^2
F = 2.73J
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If all 152 million discarded phones in America were recycled, how many pounds of each mineral would be recovered?
Gold- _____pounds
Silver- ____ pounds
palladium- ______ pounds
Copper- _____ pounds
7,600
3,040,000
3,040
83,600
Please help asap!! Thank youuuuuu!
Gold 7,600 pounds, Silver 83,600 pounds, palladium 3,040 pounds and
Copper 3,040,000 pounds.
What is meant by pounds?
The name of a unit of currency is pound. Both presently and in the past, it was employed in many different nations.The Roman era on the continent of Europe is where the British pound first appeared. From the Latin word "poundus," which means "weight," comes its name. The elaborate L in Libra is where the £ sign originated. The pound, which represented one pound of silver weight, was a monetary unit in Anglo-Saxon England as early as 775 AD.The two units are equal because one lb is another term for one pound. 1 pound equals 1 lb. Actually, "lb" is an acronym for "pound."To learn more about pounds refer to
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What is the speed of a car that goes 150 km in 45 minutes. What is its velocity is it is traveling south?
The speed of the car is 200 km/hour.
The velocity of the car is 200 km/hour in south direction.
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.
Distance travelled is = 150 km.
Time taken is = 45 minute = 0.75 hour.
Hence, the speed of the car is = 150/0.75 km/hour = 200 km/hour.
As the car is traveling south, the velocity of the car is 200 km/hour in south direction.
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the ability to do activities for more than a few minutes is
"Endurance" is the capacity to perform tasks for longer than a few minutes. Endurance, which typically refers to aerobic capacity, is the capacity to maintain an activity for prolonged periods of time.
Define the term Endurance and its features?Endurance, which typically refers to aerobic capacity, is the capacity to maintain an activity for prolonged periods of time.
The ability to withstand muscular fatigue and the capacity to sustain a particular type of contraction are the best definitions of local muscle endurance, which is often expressed in terms of repetitions. Muscular endurance depends on aerobic metabolism, just like aerobic endurance.The capacity of a muscle or a muscle group to sustain repeated contractions against such a force over a prolonged period of time is known as muscular endurance.The more repetitions you could perform, the stronger your muscle endurance was.
Increased metabolism as a result of being able to perform active activities for longerreduced exhaustion while exercisedecent posturefewer accidentsless likelihood of back issues because trunk muscles have become more resilient.improved athletic performanceimproved training methods for a variety of workoutsTo know more about the Endurance, here
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define speed in your own words. why does a car speedometer only have positive values, even though you can move in reverse?
Speed is defined as the rate of change of distance over time. It has the dimension of distance x time. The SI unit of speed is a combination of the base unit of distance and the base unit of time. The SI unit for speed is meters per second.
Speed is the speed at which an object's position changes, measured in meters per second. For example, if an object starts at the origin and moves 3 meters in 3 seconds, its speed is 1 meter/second. A car's speedometer only has positive numbers, but it can run backwards. This is because it measures speed based on the distance the car travels, not the direction the car is heading.
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An Atwood's machine consists of blocks of masses m1 = 13.0 kg and m2 = 17.0 kg
attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 8.60 kg and radius r = 0.200 m. The block of mass m2 is allowed to drop, and the cord turns the pulley without slipping.
(a) Why must the tension T2 be greater than the tension T1?
(b) What is the acceleration of the system, assuming the pulley axis is frictionless? (Give the magnitude of a
c) find the tensions
T1 =
T2 =
(a) The tension T2 must be greater than the tension T1 because it is pointing downwards, supporting both masses.
(b) The acceleration of the system is 9.74 m/s².
(c) The tension in T₁ is -0.78 N and T₂ is 1.02 N.
What are the tension in the cord?
There are two tensions in the cord and their magnitude is obtained from the following equation.
T₁ = m₁a - m₁g
T₁ = m₁ (a - g )
T₂ = m₂g - m₂a
T₂ = m₂ (g - a )
The resultant tension in the cord is determined as;
( T₂ - T₁)R = Iα
where;
R is the radius of the pulleyI is the moment of inertia of the pulleyα is the angular acceleration of the system( T₂ - T₁)R = I(aR)
where;
a is the tangential accelerationT₂ - T₁ = Ia
m₂g - m₂a - ( m₁a - m₁g ) = Ia
m₂g - m₂a - m₁a + m₁g = Ia
- m₂a - m₁a + m₂g + m₁g = Ia
a(m₂ + m₁) + Ia = m₂g + m₁g
a (m₂ + m₁ + I ) = m₂g + m₁g
a = ( m₂g + m₁g ) / ( m₂ + m₁ + I )
I = ¹/₂MR²
I = ¹/₂ x 8.6 x 0.2²
I = 0.172 kgm²
a = ( 17 x 9.8 + 13 x 9.8 ) / ( 17 + 13 + 0.172 )
a = 9.74 m/s²
The tension in the cords is calculated as;
T₁ = m₁ (a - g )
T₁ = 13 (9.74 - 9.8 )
T₁ = -0.78 N
T₂ = 17 (9.8 - 9.74 )
T₂ = 1.02 N
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A charge q= 2. 00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C). Calculate the flux of the net electric field through a Gaussian sphere of radiuscentered at the origin. (ε0= 8. 85 × 10-12C2/N. M^2)
a. 2. 26 × 10^5 N · m^2/C
b. 5. 52 × 10^5 N · m^2/C
c. 1. 13 × 105 N · m^2/C
d. Zero
Hence, The net electric field flux is 2. 26* 10^ 5 N m2/C.
What is electric field?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. It also refers to the physical field of a charged particle system. The electric field can be thought of as an electric property associated with any point in space where a charge exists in any form. The electric force per unit charge is another way to describe an electric field. The formula for the electric field is E = F /Q. Volts per metre (V/m) is the SI unit for the electric field. This unit is the same as Newton's per coulomb. These are derived units in which Newton is a unit of force and Coulomb is a unit of charge.
Here,
Charge, Q=2.00 uC
Electric field E = 100 N/C i
Radius R = 10.0 cm
We need to find the flux. It can be calculate using Gauss's law
The flux of the net electric field,
flux=Q/E0
=2*10^-6/8.85*10^-12
=2.26*10^5 Nm²/C
Hence, The flux of the net electric field is 2. 26 × 10^5 N · m^2/C.
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