Answer:
(b) Yes, Rohan's act of using a bicycle instead of a car is environmentally friendly, as it reduces carbon emissions and promotes sustainable transportation. From him, we can learn the importance of making conscious choices that have a positive impact on the environment and our health. We can also learn that small actions, such as choosing to cycle instead of drive, can make a significant difference in reducing our carbon footprint and promoting a more sustainable future.
1. A fairground ride consists of a large vertical drum that spins so
fast that everyone inside it stays pinned against the wall when
the floor drops away. The diameter of the drum is 10 m. Assume
that the coefficient of static friction between the drum and the
rider's clothes is 0. 15. What is the angular velocity of the drum at this speed?
The angular velocity of the drum is approximately 0.558 radians per second.
To find the angular velocity of the drum, we can use the centripetal force equation:
F = ma = mrω^2
where F is the force of friction between the drum and the rider's clothes, m is the mass of the rider, r is the radius of the drum (which is half its diameter, or 5 m), and ω is the angular velocity of the drum.
We can rearrange this equation to solve for ω:
ω^2 = F / mr
The force of friction can be found using the coefficient of static friction and the normal force, which is the weight of the rider:
F = μN = μmg
where μ is the coefficient of static friction, m is the mass of the rider, and g is the acceleration due to gravity.
Putting it all together, we have:
ω^2 = (μmg) / mr
Plugging in the given values, we get:
ω^2 = (0.15)(mg) / (5m)
where g is approximately 9.81 m/s^2.
Simplifying:
ω^2 = 0.03g
ω = sqrt(0.03g)
ω = sqrt(0.03 x 9.81)
ω = 0.558 rad/s
Thus the value of angular velocity is 0.558 radians per second.
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when the mass of water that an iceberg displaces is equal to the mass of the iceberg, it floats. this is an example of: group of answer choices isostacy. gravity. tomography. upwelling.
The correct answer is isostasy. When the mass of water that an iceberg displaces is equal to the mass of the iceberg, it floats - This is known as isostasy.
Isostasy is the process whereby the mass of an object affects the gravitational forces and causes it to float. In this case, when the mass of an iceberg is equal to the mass of the water it displaces, the forces acting on the iceberg are balanced, and it will float.
Isostasy occurs when a body's mass is distributed in such a way that the gravitational forces acting upon it are equal in all directions.
In the case of an iceberg, when the mass of the iceberg is equal to the mass of the water it displaces, the downward force of the iceberg's weight and the upward force of the water's buoyancy balance each other out, and the iceberg floats.
This is thus an example of isostasy, a process by which the mass of an object affects the gravitational forces, causing it to float.
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To test the performance of its tires, a car travels along a perfectly flat (no banking) circular track of radius 179 m. The car increases its speed at uniform rate of
until the tires start to skid.
If the tires start to skid when the car reaches a speed of 29. 7 m/s, what is the coefficient of static friction between the tires and the road?
The acceleration of gravity is 9. 8 m/s^2
The coefficient of static friction between the tires and the road is approximately 0.252
The maximum speed that a car can travel without skidding is determined by the maximum force of static friction that the tires can exert on the road. The formula for this maximum force of static friction is:
f_s = m × g × μ_s
where f_s is the force of static friction, m is the mass of the car, g is the acceleration due to gravity (9.81 m/s^2), and μ_s is the coefficient of static friction between the tires and the road.
When the car reaches a speed of 20 m/s, it is moving in a circular path of radius 139 m. The centripetal force required to keep the car moving in this circular path is given by:
f_c = m × v^2 / r
where f_c is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the circular path.
At the point where the tires start to skid, the maximum force of static friction is equal to the centripetal force required to keep the car moving in the circular path:
f_s = f_c
Substituting the formulas for f_s and f_c and solving for μ_s, we get:
m × g × μ_s = m × v^2 / r
μ_s = v^2 / (g × r)
We are given that the car increases its speed at a uniform rate of 5.26 m/s^2. We can use the formula for uniform acceleration to find the time it takes for the car to reach a speed of 20 m/s:
v = u + a × t
20 = 0 + 5.26 × t
t = 20 / 5.26 = 3.8 s
Using this time, we can find the distance traveled by the car before the tires start to skid:
s = u × t + 1/2 × a × t^2
s = 0 + 1/2 × 5.26 × (3.8)^2
s = 36.6 m
Now we can substitute the given values into the formula for μ_s:
μ_s = v^2 / (g × r)
μ_s = (20)^2 / (9.81 × 139)
μ_s = 0.252
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since Which animal is a vertebrate?(1 point)
shrimp
octopus
crab
fish
The animal that is a vertebrate is a fish.
What are vertebrate animals?Vertebrates are animals that possess a backbone, also known as a vertebral column or spinal column. The backbone is composed of individual vertebrae, which protect the spinal cord and provide support for the body.
Vertebrates are a diverse group of animals and include fish, amphibians, reptiles, birds, and mammals. They are characterized by having a complex nervous system, a closed circulatory system, and a well-developed brain.
Vertebrates are also capable of a wide range of behaviors and have adapted to live in various habitats, from the depths of the ocean to the highest mountains.
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Determine the forces in all the members of the complex truss. State if the members are in tension or compression. Hint: substitute member ad with one placed between e and c
We can ascertain the forces in each component of the complex truss and whether they are in tension or compression by using the method of joints or method of sections.
To determine the forces in all the members of the complex truss, we can first substitute member AD with one placed between E and C. This will result in a simpler truss with fewer members and easier to analyze.
Once we have the simplified truss, we can apply the method of joints or method of sections to find the forces in each member. The method of joints involves analyzing the forces acting at each joint in the truss, while the method of sections involves cutting through the truss to create a section and analyzing the forces acting on that section.
After we have found the forces in the members, we can determine whether they are in tension or compression. A member is in tension if it is being stretched, while it is in compression if it is being compressed or shortened. This depends on whether the forces acting on the member are pulling it apart or pushing it together.
In general, a truss is designed so that all members are either in tension or compression, and none of them are in bending or shear. This is because trusses are designed to resist only axial loads, and not bending or shear loads.
Therefore, by using the method of joints or method of sections, we can determine the forces in all the members of the complex truss and whether they are in tension or compression.
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What term best describes the regular path of a spacecraft or other object around a planetary body?
a. Cycle
b. Orbit
c. Rotation
d. Spin
Answer:
Explanation:
b. orbit
 Two trumpet players are riding in separate convertibles which are moving in opposite directions at a speed of 30 m/s. They both strike a note with a frequency of 1024 Hz Calculate:
(A). The pitch heard coming from one vehicle by a listener of the other vehicle.
(B). The pitch heard coming from either vehicle by an observer stationed directly between both vehicles.
(C). The pitch heard by a listener in either vehicle if both vehicles turn around and move toward each other at the same speeds.
Solve fast please there is no time
25 km
please make me brainalist and keep smiling dude because I do don't have time I should help
Hypothesis of experiment of a focal length of a concave lens?
Variables?
The right choice is C) [tex]\frac{1}{v} +\frac{1}{u} =\frac{1}{f}[/tex] which is the equation that relates u and v
[tex]\frac{1}{u} = \frac{1}{f} - \frac{1}{v}[/tex]
The slant of this curve can be found by differentiation [tex]-\frac{1}{u^2} du = 0 + \frac{dv}{v^2} \\[/tex]
⇒ [tex]\frac{dv}{du} = - \frac{v^2}{u^2}[/tex]
[tex]\frac{dv}{du}[/tex] is the slant which is negative so either curve (c) or curve (a) is correct. Presently the incline relies on the worth of u and v for example it continues to change at each point according to the equation above. So figure (c) is the response.
A convex spherical mirror likewise has a focal point. Occurrence beams lined up with the optical pivot are reflected from the mirror and appear to begin from point F at focal length f behind the mirror. Subsequently, the focal point is virtual in light of the fact that no genuine beams really go through it; they just seem to start from it.
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the complete question is:
In an experiment to find the focal length of a concave mirror, a graph is drawn between the magnitudes of u and v. The graph looks like this:
refer to the attachment for the graph
A boat accelerates from 8.5 m/s west to 1.8 m/s west at a rate of 2.9 m/s^2 east. How far does it travel
The distance traveled while accelerating can be found by multiplying the average velocity by the time taken to accelerate
Complete question:
A boat accelerates from 8.5 m/s west to 1.8 m/s west at a rate of 2.9 m/s^2 east. How far does it travel while accelerating?
Computation of DistanceThe average velocity is the difference between the initial and final velocities, divided by two. The time taken to accelerate is the difference between the initial and final velocities, divided by the rate of acceleration.
Given Data
Average velocity = (8.5 m/s - 1.8 m/s) / 2 = 3.35 m/sTime taken to accelerate = (8.5 m/s - 1.8 m/s) / 2.9 m/s^2 = 2.03 swe know that the expression for computing distance is given as
Distance traveled while accelerating = Average velocity * Time taken to accelerate
Substituting our data in the expression we have
Distance traveled while accelerating = 3.35 m/s * 2.03 s = 6.80 m
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A charge of 6. 00mc is placed at each corner of a square 0. 100m on a side. Determine the magnitude and direction of the force on each charge. (hint: only solve for one charge, you should notice that the magnitude is the same for all charges. )
3.24 x [tex]10^{-2}[/tex] N is the force acting on each charge.
We can use Coulomb's law to determine the magnitude and direction of the force on each charge. Coulomb's law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's assume that we are calculating the force on one of the charges located at a corner of the square. The distance between two adjacent charges is 0.1m, and the charge on each corner is 6.00mc, which is 6.00 x [tex]10^{-6}[/tex] C.
Using Coulomb's law, we can calculate the magnitude of the force on one charge as:
F = kq₁q₂/r²
where k is the Coulomb constant (9 x [tex]10^{9}[/tex] N m²/C²), q₁and q₂ are the charges, and r is the distance between the charges.
If we plug in the values, we get:
F = (9 x [tex]10^{9}[/tex] N m²/C²) * (6.00 x[tex]10^{-6}[/tex] C)² / (0.1m)²
F = 3.24 x [tex]10^{-2}[/tex] N
So the magnitude of the force on each charge is 3.24 x [tex]10^{-2}[/tex] N, and the direction of the force is towards the other charges located at the corners of the square. Since the charges are all the same, the direction of the force will be towards the center of the square.
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Auto companies frequently test the safety of automobiles by putting them through crash tests to
observe the integrity of the passenger compartment. If a 2000. -kg car is sent toward a cement wall
with a speed of 14 m/s and the impact brings it to a stop in 4. 00 X 10^-2 s, with what average
force is it brought to rest?
The average force acting on the car as it comes to a stop is [tex]7.00 \times 10^5 N.[/tex]
We can use the equation for average force, which is:
average force = change in momentum / time
To use this equation, we first need to find the change in momentum of the car. We can use the equation:
change in momentum = final momentum - initial momentum
The initial momentum of the car is:
p1 = m1 × v1
where m1 is the mass of the car (2000 kg) and v1 is the initial velocity (14 m/s).
p1 = (2000 kg)(14 m/s) = 28,000 kg × m/s
The final momentum of the car is zero, since it comes to a stop.
p2 = 0
So the change in momentum is:
Δp = p2 - p1 = -28,000 kg × m/s
Now we can substitute these values into the equation for average force:
average force = Δp / t
where t is the time it takes for the car to come to a stop[tex](4.00 \times 10^{-2} s).[/tex]
average force =[tex](-28,000 kg\times m/s) / (4.00 \times 10^{-2} s)[/tex]
average force =[tex]- 7.00 \times 10^5 N[/tex]
The negative sign indicates that the force is acting in the opposite direction to the motion of the car. We could also take the magnitude of the force, which would be:
|average force| = [tex]7.00 \times 10^5 N[/tex]
Therefore, the average force acting on the car as it comes to a stop is [tex]7.00 \times 10^5 N.[/tex]
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According to current understanding, how did the first generation of stars differ from stars born today?
According to current understanding, the first generation of stars differed from stars born today in their composition.
The first generation of stars, also known as Population III stars, were made up of mostly hydrogen and helium, with very little to no heavier elements.
This is because they formed from the gas and dust left over from the Big Bang, which was primarily hydrogen and helium.
In contrast, stars born today, also known as Population I stars, have a higher percentage of heavier elements, such as carbon, oxygen, and iron.
This is because they formed from gas and dust that has been enriched with heavier elements from previous generations of stars.
As stars age and die, they expel these heavier elements into the surrounding gas and dust, which then goes on to form new stars.
Therefore, the main difference between the first generation of stars and stars born today is their composition, with the first generation having a higher percentage of hydrogen and helium, and stars born today having a higher percentage of heavier elements.
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What is the term used to describe the maximum distance that a sound wave displaces air molecules from their original undisturbed position?
The term used to describe the maximum distance that a sound wave displaces air molecules from their original undisturbed position is called the amplitude
The term used to describe the maximum distance that a sound wave displaces air molecules from their original undisturbed position is called the amplitude of the sound wave. Amplitude refers to the magnitude of the wave's displacement and is typically measured in decibels (dB).
The higher the amplitude of a sound wave, the louder the sound will be perceived by our ears. The amplitude of a sound wave is determined by the amount of energy that the sound wave carries. A sound wave with a higher amplitude will have more energy and thus will displace air molecules more strongly than a sound wave with a lower amplitude.
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A uniform bar, of mass M, with seven evenly spaced holes is held by sliding the bar over a horizontal peg through one of the seven holes. The peg passes through hole C, and a cylinder hangs from a hook placed through hole B as shown above. The mass of the bar is equal to the mass of the cylinder, and the location of the center of mass of the bar is at the center of hole D. In this configuration, the bar-cylinder system remains motionless but is free to rotate around the peg in hole C. Frictional forces acting on the bar are negligible. In a clear, coherent paragraph-length response that may also contain equations, explain why the bar does not rotate in this configuration.
Please help!
The torques due to the weights of the bar and the cylinder are balanced, and the bar-cylinder system remains motionless and does not rotate around the peg in hole C.
What is COM?The bar-cylinder system does not rotate around the peg in hole C because it is in equilibrium. The torque on the system due to the weight of the cylinder hanging from hole B is balanced by the torque on the system due to the weight of the bar and its distribution around the center of mass at hole D. The center of mass is located such that the torques due to the weights of the bar and the cylinder are equal and opposite, and hence the net torque on the system is zero.
Mathematically, we can express this equilibrium condition as:
T_cylinder = T_bar
The torque due to the weight of the cylinder is given by:
T_cylinder = r_CB * F_cylinder
Similarly, the torque due to the weight of the bar is given by:
T_bar = r_CD * F_bar
where r_CD is the distance between the peg at hole C and the center of mass at hole D, and F_bar is the weight of the bar.
Since the mass of the bar is equal to the mass of the cylinder, we have:
F_cylinder = F_bar = Mg
where M is the mass of the bar and cylinder, and g is the acceleration due to gravity.
Substituting the above equations into the equilibrium condition, we get:
r_CB * Mg = r_CD * Mg
which simplifies to:
r_CB = r_CD
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A charge of 6.5 x 10-5 C is attracted by another charge with a force of 250 N when
they are separated by 0.15 m. Find the magnitude of the other charge.
8.65 X 105 C
9.62 × 10-2 C
6.15 x 10-6 C
O 9.62 x 10 c
Answer:
We can use Coulomb's law to solve this problem:
F = k * q1 * q2 / r^2
where F is the force between the two charges, k is Coulomb's constant (k = 9 x 10^9 N m^2 / C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
We know the force F, the distance r, and the magnitude of one of the charges q1. We can rearrange the equation to solve for the magnitude of the other charge q2:
q2 = F * r^2 / (k * q1)
Substituting the values we have:
q2 = (250 N) * (0.15 m)^2 / (9 x 10^9 N m^2 / C^2 * 6.5 x 10^-5 C)
Simplifying:
q2 = 8.65 x 10^5 C
Therefore, the magnitude of the other charge is 8.65 x 10^5 C.
Determine the total resistance for the current
The total flow of electricity from the source is equivalent to the sum of the currents through each path. To calculate the total impedance in a parallel circuit, use the method below : 1/Rt Equals 1/R1 + 1/R2 + 1/R3 +...
How do you find total resistance of a current?IT = VT/RT or I total = V total / R total or the total current = the total voltage / the total resistance.
Current still flows along the other routes even if one of the parallel ones is blocked.
R_total = R1 + R2 +... + Rn The sum of all individual resistances makes up the system's overall resistance. Take the example issue below as an
example. A resistor with a 100 ohm electrical resistance value is linked to a resistor with a 200 ohm electrical resistance value.
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Ronaldo or Messi? Who is better?
Answer:
In my opinion, Ronaldo
Explanation:
Ronaldo, who holds the record for most Champions League goals of all time, leads Messi by one on that trophy count. Messi, meanwhile, has a greater number of domestic cups and league titles.
What do you think?
Answer:
In my opinion, it's Christiano Ronaldo. But why is Ronaldo better than Messi?
Explanation:
Ronaldo is a more complete player.
His ability to jump and head balls was flawless. Ronaldo is such a complete player, emphasising his complete nature, that he is dangerous in every minute of the game. This is demonstrated by him being the first player in football history to score in every minute of a 90-minute game.
Describe three ways you can lower the intensity of sound from a speaker, at a rock concert. Refer to the equations learnt in lesson for two of them.
Reduce the volume: Reducing the volume is one of the simplest ways to lessen the sound intensity coming a speaker. As you move farther away from the source of the sound, the intensity of the sound also diminishes.
What level of volume is there at a rock concert?Nonetheless, regardless of the location, a rock concert can be quite loud. Decibel levels during rock concerts often range from 90 to 120 dB. This decibel level is alarming since it could endanger your ability to hear.
What causes a sound's strength to lessen?The intensity of the sound is proportional to the square of the distance from the source of the sound wave. The strength of a sound wave depends on whether it travels through a two-dimensional or three-dimensional medium to carry its energy.
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Determining the distance to stars can be challenging. The parallax method is one way of finding the distance to many stars around us. Your research team measures the parallax of two stars that have a distance of 5 degrees from each other in the night sky: The first star has a parallax of 0.11 arcsec, and the second has a parallax of 0.13 arcsec. How far apart are the two stars from each other? Express your answer in light-years
which of the following energy sources is not derived directly or indirectly from solar energy? responses biomass biomass geothermal geothermal hydroelectric hydroelectric wind
The energy source that is not derived directly or indirectly from solar energy is geothermal energy.
Geothermal energy is a type of energy that is generated from heat in the Earth's crust. This heat comes from the Earth's molten core, which is heated by nuclear reactions. Geothermal energy is generated in hot springs, geysers, and volcanoes, and is used to produce electricity by harnessing the energy of hot water and steam.Biomass energy is a renewable energy source that is derived from organic matter, such as wood, crops, and waste materials. Biomass is burned to produce energy, and is often used to power homes and businesses. Hydroelectric energy is generated by harnessing the power of water, which is usually done by building dams and using the energy of falling water to turn turbines. Wind energy is generated by harnessing the power of the wind, which is done by using wind turbines to capture the energy of the wind and turn it into electricity. All of these energy sources are derived directly or indirectly from solar energy, since the sun is responsible for heating the Earth's atmosphere and creating weather patterns that generate wind and precipitation.
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Please help me thank you
The equivalent resistance is 6R/11, the current flowing through the circuit is 55/6R, and the voltage across resistor R2 is 55/3 V when the three parallel resistors R1, R2, and R3 are joined in parallel across a 5V battery.
What is the unit of resistance?The unit of resistance is ohm (Ω), named after the German physicist Georg Simon Ohm. One ohm is defined as the amount of resistance that will allow one ampere of current to flow with one volt of applied potential difference.
To find the equivalent resistance (R_eq) of the three parallel resistors R1, R2, and R3, we can use the formula:
1/R_eq = 1/R1 + 1/R2 + 1/R3
Substituting R1 = R, R2 = 2R, and R3 = 3R, we get:
1/R_eq = 1/R + 1/2R + 1/3R
1/R_eq = (6/6R + 3/6R + 2/6R) / (1/6R)
1/R_eq = 11/6R
R_eq = 6R/11
To find the current (I) flowing through the circuit, we can use Ohm's Law, which states that:
I = V/R_eq
Substituting V = 5V and R_eq = 6R/11, we get:
I = 5 / (6R/11)
I = 55/6R
To find the voltage (V_R2) across resistor R2, we can use the formula:
V_R2 = I * R2
Substituting I = 55/6R and R2 = 2R, we get:
V_R2 = (55/6R) * (2R)
V_R2 = 55/3 V
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A kickball is struck with a 15.2 m/s velocity at a 63 degree angle. It lands on a rooftop 2.4 s later. How high is the roof?
Answer:
the height of the rooftop is approximately 16.4 meters or about 54 feet high.
Explanation:
To solve this problem, we need to use the kinematic equations of motion. We will assume that air resistance is negligible and that the acceleration due to gravity is -9.8 m/s^2.
First, we will use the initial velocity and angle of the kickball to find its horizontal and vertical components of velocity.
The horizontal component of velocity (Vx) can be found using the equation:
Vx = V * cos(theta)
where V is the initial velocity and theta is the angle of the kickball.
Vx = 15.2 m/s * cos(63 degrees)
Vx = 6.62 m/s
The vertical component of velocity (Vy) can be found using the equation:
Vy = V * sin(theta)
Vy = 15.2 m/s * sin(63 degrees)
Vy = 13.7 m/s
Next, we can use the vertical component of velocity to find the maximum height (h) reached by the kickball. We can use the following kinematic equation:
h = Vy^2 / (2 * g)
where g is the acceleration due to gravity.
h = (13.7 m/s)^2 / (2 * 9.8 m/s^2)
h = 9.47 meters
So, the maximum height reached by the kickball is 9.47 meters.
Finally, we can use the time it takes for the kickball to land on the rooftop to find the height (d) of the rooftop. We can use another kinematic equation:
d = Vy * t + 0.5 * g * t^2
where t is the time it takes for the kickball to land on the rooftop.
d = 13.7 m/s * 2.4 s + 0.5 * (-9.8 m/s^2) * (2.4 s)^2
d = 16.4 meters
Therefore, the height of the rooftop is approximately 16.4 meters or about 54 feet high.
if two objects that have charges of +8 C and -4 C touch each other and are then separated what will be the charge on each object
Answer:
30q1
Explanation:
Uniformly charged spheres are “touching”. 4. What must be the distance between point charge q1 = 26.0µC and point charge q2 = −47.0µC
Find the work done by a force F = 4i − 3j + 2k that moves an object from the point (3, 2, -1) to the point (2, -1, 4) along a straight line. The distance is measured in meters and the force in newtons.
Answer:
15 N
Explanation:
work done by the force in vector form is given by the equation,
[tex]W = \vec{F}.\delta \vec{r}[/tex]
where . represents the dot product.
in the given question,
[tex]F = 4i - 3j + 2k[/tex]
and
[tex]\delta \vec{r} = (2 - 3)i + (-1 - 2)j + (4 - (-1))k[/tex]
[tex]\delta \vec{r} = -i - 3j + 5k[/tex]
on doing the dot product we get
[tex]W = -4 + 9 + 10\\W = 15[/tex]
Hopefully this answer helped you.
Which uses direct current?
A) A toaster oven thingy (look at pic)
B) A flashlight (look at pic)
C) A microwave (look at pic)
D) A vacuum (look at pic)
The correct answer is Option- B: A flashlight uses direct current (DC).
Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams.
Electric current flows in two ways as an alternating current (AC) or direct current (DC). The main difference between AC and DC lies in the direction in which the electrons flow. In DC, the electrons flow steadily in a single direction, while electrons keep switching directions, going forward and then backwards in AC.Thus,The correct answer is Option- B: flashlight.
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How long will it take a runner to complete a marathon race of 42. 2 km if that runner can maintain an average speed of 4. 1 m/s?
It would take the runner approximately 10,268.29 seconds (or about 2 hours, 51 minutes, and 8 seconds) to complete a marathon race of 42.2 km, maintaining an average speed of 4.1 m/s.
We can use the formula:
time = distance ÷ speed
to calculate the time it would take the runner to complete a marathon race of 42.2 km, given an average speed of 4.1 m/s.
First, we need to convert the distance to meters, as the speed is given in meters per second:
42.2 km = 42,200 m
Now, we can substitute the values into the formula:
time = distance ÷ speed
time = 42,200 m ÷ 4.1 m/s
time ≈ 10,268.29 s
Thus the time that the runner would take is 10,268.29 seconds to complete a marathon race.
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The difference between meteoroids and meteor
Answer:
Meteoroids are objects in space that range in size from dust grains to small asteroids. Think of them as “space rocks." When meteoroids enter Earth's atmosphere (or that of another planet, like Mars) at high speed and burn up, the fireballs or “shooting stars” are called meteors.
Explanation:
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5. A block with mass m = 250 g is compressing a spring with a spring constant k = 60 N/m a distance of d = 16.0 cm from its equilibrium position. If the mass let go, how high above its initial position does the mass rise?
Answer:
The potential energy stored in the spring when it is compressed by a distance of 16.0 cm can be calculated using the formula:
U = (1/2) k x^2
where U is the potential energy, k is the spring constant, and x is the displacement from equilibrium position.
Plugging in the given values, we get:
U = (1/2) * 60 N/m * (0.16 m)^2
U = 0.768 J
When the mass is released, the potential energy stored in the spring is converted to kinetic energy of the mass as it moves upward. At the highest point, all of the kinetic energy is converted back to potential energy. The total mechanical energy of the system (spring + block) is conserved, so we can equate the potential energy at the highest point to the initial potential energy stored in the spring:
mgh = U
where m is the mass of the block, g is the acceleration due to gravity (9.81 m/s^2), h is the maximum height reached by the block.
Plugging in the values, we get:
(0.250 kg) * (9.81 m/s^2) * h = 0.768 J
Solving for h, we get:
h = 0.768 J / (0.250 kg * 9.81 m/s^2) ≈ 0.312 m
Therefore, the block rises to a maximum height of approximately 0.312 m above its initial position.
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Very far from earth (at R=infinity), a spacecraft has run out of fuel and its kinetic energy is zero. If only the gravitational force of the earth were to act on it (i. E. , neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. The mass of the earth is Me and its radius is Re. Neglect air resistance throughout this problem, since the spacecraft is primarily moving through the near vacuum of space.
a. Find the speed Se of the spacecraft when it crashes into the earth.
Express the speed in terms of Me, Re, and the universal gravitational constant G.
b. Now find the spacecraft’s speed when its distance from the center of the earth is R=αRe, where α >=1. Express the speed in terms of Se and α.
a. The speed Se of the spacecraft when it crashes into the earth is approximately 11.2 km/s.
b. The spacecraft's speed when its distance from the center of the earth is R = αRe is Se / √(α).
a. To find the speed Se of the spacecraft when it crashes into the earth, we can use the law of conservation of energy. At R = infinity, the spacecraft has zero kinetic energy and potential energy, so its total mechanical energy is zero. As it falls towards the earth, the potential energy decreases while the kinetic energy increases. At the moment of impact, all of the potential energy has been converted to kinetic energy.
Using the law of conservation of energy, we have:
[tex]0 = 1/2 mv^2 - GM_em/r[/tex]
where m is the mass of the spacecraft, v is its speed at impact, G is the universal gravitational constant, and r is the distance from the center of the earth to the spacecraft at impact.
We can rearrange this equation to solve for v:
[tex]v = \sqrt{(2GM_e/r)}[/tex]
Substituting the values for G, M_e, and r, we get:
[tex]v = \sqrt{(2 \times 6.6743 \times 10^{-11} m^3/kg s^2 \times 5.97 \times 10^{24} kg / 6.38 \times 10^6 m)}[/tex]
[tex]v = 11.2 km/s[/tex]
Therefore, the speed Se of the spacecraft when it crashes into the earth is approximately 11.2 km/s.
b. To find the spacecraft's speed when its distance from the center of the earth is R = αRe, we can use conservation of energy again. The spacecraft still has zero kinetic energy and potential energy at R = infinity, so we can use the same equation as before:
[tex]0 = 1/2 mv^2 - GM_em/r[/tex]
But now r = αRe, so we can solve for v in terms of Se and α:
v = √(2GM_e/αRe)
Substituting the value of [tex]GM_e[/tex] from before and simplifying, we get:
v = Se / √(α)
Therefore, the spacecraft's speed when its distance from the center of the earth is R = αRe is Se / √(α).
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