The freight car which is being dumped into the metal scrap has the final velocity of 0.18 m/s.
In this problem, we use the principle of conservation of linear momentum.
Given that,
Mass of the freight car m₁ = 30,000 kg
Mass of the hopper m₂ = 110,000 kg
Velocity of the freight car u₁ = 0.85 m/s
Velocity of the hopper u₂ = 0
Let the velocity of the loaded freight car = v
We need to find out v.
m₁ u₁ + m₂ u₂ = ( m₁ + m₂) v
After putting the values into the equation above, we have,
30,000 × 0.85 + 110,000 × 0 = (30,000 + 110,000) v
140,000 v = 25500
v = 0.18 m/s
Thus, the required velocity of the loaded freight car is calculated to be 0.18 m/s.
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The average rate of erosion on the Moon is far less than on Earth because
A) the crust of the Moon is much denser than the Earth's crust.
B) the Moon is much younger than the Earth.
C) the Moon's magnetic field protects it from the solar wind better than ours does.
D) the Moon's mare long ago dried up, so there is no more wave erosion there.
E) the Moon lacks wind, water, and an atmosphere.
E) the Moon lacks wind, water, and an atmosphere. The average rate of erosion on the Moon is far less than on Earth because
What is atmosphere?
Atmosphere is the layer of gases surrounding the Earth, composed of nitrogen, oxygen, and other trace elements. It is held in place by the Earth's gravity and is responsible for the air we breathe, the weather we experience, and the climate of the planet.
The atmosphere is also important for providing protection from harmful ultraviolet radiation from the sun and reducing the temperature extremes on the Earth's surface.
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When building a device or structure, engineers must carefully consider how the materials they choose will change when heated or cooled. List four situations where thermal expansion and contraction could be a problem.
There are three infrastructure projects wherein thermal expansion & contraction may be a problem are constructing roads, towers, and sidewalks.
What does thermal expansion mean?The propensity of matter to alter structure, volume, or area in reaction to a temperature change is known as thermal expansion. The average molecular energy of a substance has a monotonic relationship with temperature. Heat makes molecules move more quickly & take up more space, which causes thermal expansion.
What is a good illustration of thermal expansion?The expansion of heated air is the most obvious example. Heat helps the air expand, making it lighter than the air around it. This causes the hot air to be forced (upward), which causes steam and smoke to rise, warm air balloons to float, and so on.
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We are warmed by condensation because water molecules in the air that strike our bodies
A. form an insulating layer on our bodies
B. gain kinetic energy as they change state
C. transfer some of their kinetic energy to us
Condensation warms us because airborne water molecules that impact our bodies give up some of their kinetic energy to us.
What is kinetic energy?
Kinetic energy is the energy of motion. It is the energy that a moving item possesses.It is typically measured in joules and is equal to the work done to accelerate the object from its rest state to its current state. Kinetic energy can be found by multiplying the mass of an object by its velocity squared, divided by two. The kinetic energy of an object increases as its velocity increases.Kinetic energy exists in both linear and rotational forms. Linear kinetic energy is the energy of an object moving in a straight line, while rotational kinetic energy is the energy an object has due to its spinning or rotating motion.
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Stern observed all of the following results EXCEPT _______ in his experiment. A. one of the recombinant phenotypes was associated with an X chromosome of normal length B-the number of car, B. male offspring was roughly equal to the number of car+, B male offspring C. the number of males was roughly equal to the number of females D. offspring with red, round eyes resulted from fertilization of eggs containing recombinant X chromosomes
The number of males was roughly equal to the number of females: Stern observed all of the following results EXCEPT _______ in his experiment.
What is experiment?
The Stern-Gerlach experiment (also known as the Stern-Gerlach experiment or the Stern-Gerlach magneto-optical experiment) was a landmark experiment in the early 20th century that demonstrated the inherent quantization of atomic-scale systems. It was conducted in 1922 by Otto Stern and Walther Gerlach in Germany.
The experiment showed that when a beam of silver atoms was passed through a non-uniform magnetic field, the beam split into two separate beams travelling in different directions. This showed that the silver atoms had two possible orientations of their magnetic dipole moment, which could only take on two discrete values. This phenomenon is now known as the Stern-Gerlach effect and is a fundamental part of quantum mechanics.
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You throw a ball vertically upward so that it leaves the ground with velocity 5. 68 m/s.
(a) What is its velocity when it reaches its maximum altitude? magnitude 0 Correct: Your answer is correct. M/s direction Incorrect: Your answer is incorrect.
(b) What is its acceleration at this point? magnitude -9. 8 Incorrect: Your answer is incorrect. The response you submitted has the wrong sign. M/s2 direction Incorrect: Your answer is incorrect.
(c) What is the velocity with which it returns to ground level? magnitude -5. 68 Incorrect: Your answer is incorrect. The response you submitted has the wrong sign. M/s direction Correct: Your answer is correct.
(d) What is its acceleration at this point? magnitude 9. 8 Correct: Your answer is correct. M/s2 direction Correct: Your answer is correct
The length of time needed to descend back to the earth's surface. Gravitational acceleration is equal to -9.8 m/s2. 2 s^2 s2
Explanation for the above answer:When anything is sent vertically upward, it slows down due to gravity. Up until it reaches a maximum height, where the velocity is zero, its speed is decreasing. After that, gravity accelerates it uniformly downward.
The three equations are as follows: v = u + at, v2 = u + 2as, and s = ut + 12at2.
What is the vertical velocity formula?With this knowledge, the vertical velocity formula, vf=vi+gt v f = v I + g t, can be used to calculate the object's terminal velocity. This equation is used by physicists to predict how any object will move on a vertical plane.
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2. A 1.0 kg roller coaster is at the top of a 25m hill, and has a velocity of 8 m/s.
a. Determine the velocity of the roller coaster when it is halfway down the hill, at height of 12.5 m. (Ignore Friction)
b. What is the velocity of the roller coaster at the bottom of the hill assuming a force due to friction of 3.0 N, and the length of the hill is 45.0 m.
SHOW ALL WORK!
The car's acceleration can be calculated as: a = v2/R = (18.0 m/s) 2/(12.0 m) = 27.0 m/s2. The conventional method can be used to determine net force: 13500 N is equal to Fnet = m•a = (500 kg)•(27.0 m/s2).
What happens to a roller coaster's speed as it climbs a hill?It may slow down or decelerate when traveling uphill or straight ahead. Roller coasters accelerate as they travel down hills due to the force of gravity dragging them downward.
How do roller coasters use math?Calculus and other fundamental mathematical concepts are used to calculate the maximum speed, the angles of ascent and descent, and the height necessary for the automobile to climb the next hill. The roller coaster's safety is further ensured by these calculations.
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1) compare the isochron map to the topographic map of the seafloor in the previous investigation. which seafloor features are associated with young crust what can you infer from this?
2) how does the age of the seafloor change as you move away from these features?
what can you conclude from this evidence?
From this evidence, you can conclude that the seafloor is not a static feature and is constantly being renewed through the movement of tectonic plates and the creation of new crust at mid-ocean ridges. The age of the seafloor can be used to help understand the history and dynamics of the Earth's crust and how it has evolved over time.
HOPE IT HELPS!A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous velocity?
A.Instantaneous velocity cannot be determined without additional information
B.At equilibrium, its instantaneous velocity is less than its maximum but not zero.
C.At equilibrium, its instantaneous velocity is at maximum
D.At equilibrium, its instantaneous velocity is zero.
At the instant when a mass is at its equilibrium position when undergoing simple harmonic motion, its instantaneous velocity is its maximum.
Therefore the answer is C. At equilibrium, its instantaneous velocity is at maximum
The simple harmonic motion is periodic motion that oscillates around an equilibrium position. At the equilibrium position, the net force on the mass is zero. Therefore, the mass is not accelerating, so its instantaneous acceleration is zero.
The motion is periodic, meaning it repeats itself at regular intervals of time. In the case of a mass on the end of a spring, the spring exerts a force on the mass that acts to bring it back to its equilibrium position. When the mass is at the equilibrium position, the spring force is zero, and the mass is not accelerating. Therefore, the acceleration is maximum at it ends and decreases to zero at equilibrium position.
The instantaneous velocity is zero at the end as it changes direction of motion, though the acceleration is decreasing from end position to equilibrium, velocity is increasing. The instant after equilibrium position, the acceleration is in opposite direction decreasing the velocity till it is zero at the end position.
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Select True or False: The mass of a nucleus is always less than the sum of the masses of the nucleons.
It is untrue to say that a nucleus's mass is always smaller than the total mass of its nucleons.
Why is nucleus mass lower than nucleon mass?The nucleons near the edge of their masses give binding energy to maintain the nucleons inside the nucleus.
Why is a nucleus' mass always smaller than the total?The protons and neutrons move in closer together to a distance of 10–14 m during the creation of a nucleus. The mass of the nucleons is sacrificed in order to spend the energy needed for the task.
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Why are dynamic flexibility tests not used as often as?
Dynamic flexibility tests are not used as often as static flexibility tests because dynamic flexibility tests involve more subjective measurements.
Static flexibility tests are more common in comparison to dynamic tests because static flexibility tests are easier to replicate. It is difficult to standardize motion-based tests such as dynamic flexibility tests between various subjects, while static flexibility tests are simple and easy to standardize it is because the metrics are fixed and not open to interpretation.
Since, dynamic flexibility tests are hard to perform because they measure the amount of stress on a muscle that is in motion. And it is difficult to assess this among multiple people and to get an accurate picture. That is why these tests are not used as often as static flexibility tests.
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Complete question
Why are dynamic flexibility tests not used as often as static flexibility tests?
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Which of the following is the law of action-reaction?
OA. Newton's first law
B. Newton's second lav
OC. Newton's third law
OD. Newton's fourth law
Answer:
OC.Newton's third law of motion which states that,"every action has equal and opposite reaction."
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Roller Coaster Physics Gizmo
With no friction, you can use the relationship between potential and kinetic energy to predict the speed of the car at the bottom of this hill from its starting height. To do this start by setting the kinetic and potential energy equations equal to one another. K= U
1/2mv^2 = mhm
a. Use algebra to solver for the speed. V=
b. With the no friction, does the final speed depend on the mass of the car?
c. With no friction, does the final speed depend on the steepness of the hill?
d. What is the final speed of the car if the height of the hill is 55 cm (. 55m)?
A) Using algebra, the required speed V=(2gh)1/2
B) With the no friction, the final speed does not depend on the mass of the car.
C) With no friction, the final speed does depend on the steepness of the hill.
D) The final speed of the car if the height of the hill is 55 cm is 3.569 m/s.
Given that there is no friction considered. Thus, the total energy of the system can be considered as conserved.
Thus, sum of kinetic and potential energy will be constant.
K = U
mu 2 = mgh ......................................(1)
m = mass of object
v = speed of object
g = acceleration due to gravity = 9.8 m/s2
h = height of object with respect to a reference position
Thus for an object at a height from ground, will have its potential energy converted to kinetic energy during it's descent.
(A) from (1)
mv2 = 2mgh
Thus, v2 = 2gh
v = (2gh)1/2
this, is the velocity of an object from conservation of energy.
(B) with no friction, the enrgy is taken to be conserved. from the answer of (A), we know,
v = (2gh)1/2.
clearly this equation doesn't depend on mass.
thus, final speed doesn't depend on the mass.
(C) Given height of hill , h = 65cm = 0.65 m
from (1), v = (2gh)1/2.
the potential energy of car at the hill top = mgh
this potential energy gets entirely converted to kinetic energy at the bottom of hill due to conservation of energy. Thus
v = (2 x 9.8 x 0.65)1/2
= 3.569 m/s
Thus, the final velocity of the car is 3.569 m/s
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Two small objects carry the same amount of charge, and the magnitude of the electric force exerted by one object on the other is 0.10 N when they are held 30 mm apart. If the force magnitude increases when the objects are released and free to move, are the objects of the same charge or opposite charge?
The objects must be of opposite charge because the electric force of attraction between them increases when they are released and free to move.
This means that the electric force must be a repulsive force that pushes the objects away from each other. Opposite charges attract and as charges repel, the objects must be of opposite charge for the electric force to increase when the objects are released and free to move.
Therefore when two small objects carry the same amount of charge, the magnitude of the electric force exerted by one object on the other is 0.10 N when they are held 30 mm apart. If the force magnitude increases when the objects are released and free to move, then we can say that they are opposite charges.
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Energy can neither be created nor destroyed. Why?
Answer:
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside
How are static and passive stretching similar?
Static stretching and passive stretching are very similar in that they both involve moving the limbs into and holding the stretch posture.
Static stretching involves the individual holding their own limbs in place, while passive stretching involves a partner assisting with the movement and holding of limbs. When you stretch to your limit and hold that position, you are engaging in a form of stretching known as static stretching. Passive stretching, on the other hand, is also a form of static stretching; however, during this technique, you remain relaxed and do not actively participate in increasing your range of motion.
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Normal
Question
Question 22
A projectile is launched into space where there is very little friction. According to Newton's law of inertia, the projectile willmost likely continue to travel in a straight line and?
The projectile will probably keep moving in a straight line and at a constant speed as long as no unbalanced forces are acting on it, according to Newton's law of inertia.
What is law of inertia?The law of inertia, also known as Newton's first law, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by a net external force. In simple words, an object will remain in the same state of motion unless acted upon by an external force. This law explains why it is difficult to start an object moving and easy to keep it moving once it is in motion. This law applies to all objects and is a fundamental principle of physics. It also helps to understand the concept of force, motion and energy in physics.To learn more about law of inertia refer:
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Particles q1 = -8.99 uC, q2 = +5.16 uC, and q3 = -89.9 uC are in a line. Particles q1 and q2 are separated by 0.220m and particles q2 and q3 are separated by 0.330m. What is the net force on particle q1?
Answer: -39200.45 Nm^2/C^2 This is rough work
Explanation:
So, the net force will be felt on particle [tex]\sf{q_1}[/tex] approximately 15.39 N to the right.
IntroductionHi! Here I will explain the net force of three charges that interacts. Remember that this question can be solved using Coulomb's Law. Coulomb's Law states that the interaction force between two interacted charges will be proportional to the magnitude of the charges that have specific interaction but inversely proportional to the square of the value of the distance between each other. So, with this concept, we can calculate the magnitude of coulomb force with this equation:
[tex] \boxed{\sf{\bold{F = k \cdot \frac{q_1 \cdot q_2}{(r_{12})^2}}}} [/tex]
Formula UsedOn this condition, the net force will be felt only by the first charge, so we must define the position of the first charge as a fixed one. So, we can calculate the magnitude of coulomb force concerning the first charge with this equation:
[tex] \boxed{\sf{\bold{\sum F_{q1} = k \cdot (\frac{q_1 \cdot q_2}{(r_{12})^2} + \frac{q_1 \cdot q_3}{(r_{13})^2})}}} [/tex]
With the following condition:
[tex] \sf{\sum F_{q1}}[/tex] = the net force will be felt by the first charge (N)k = constant of coulomb ≈ [tex] \sf{9 \times 10^{9}}[/tex] N.m²/C².[tex] \sf{q_1}[/tex] = first charge (C)[tex] \sf{q_2}[/tex] = second charge (C)[tex] \sf{q_3}[/tex] = third charge (C)[tex] \sf{r_{12}}[/tex] = the distance between first and second charge (m)[tex] \sf{r_{13}}[/tex] = the distance between first and third charge (m)Problem SolvingWe know that:[tex] \sf{q_1}[/tex]= first charge = -8.99 [tex] \sf{\mu C}[/tex] = [tex] \sf{-8.99 \times 10^{-6}}[/tex] C.[tex] \sf{q_2}[/tex]= second charge = +5.16 [tex] \sf{\mu C}[/tex] = [tex] \sf{+5.16 \times 10^{-6}}[/tex] C.[tex] \sf{q_3}[/tex]= third charge = -89.9 [tex] \sf{\mu C}[/tex] = [tex] \sf{-8.99 \times 10^{-5}}[/tex] C.[tex] \sf{r_{12}}[/tex] = the distance between first and second charge = 0.220 m = [tex] \sf{2.2 \times 10^{-1}}[/tex] m.[tex] \sf{r_{13}}[/tex] = the distance between first and third charge = 0.220 + 0.550 m = [tex] \sf{5.5 \times 10^{-1}}[/tex] m.What was asked?[tex] \sf{\sum F_{q1}}[/tex] = the net force will be felt by the first charge = ... NStep by Step:[See the attached image to know how to solve this problem]
Conclusion:So, the net force will be felt on particle [tex]\sf{q_1}[/tex] approximately 15.39 N to the right.
Learn More:Basic explanation about Coulomb's Law https://brainly.com/question/26892767How to count net force of three charged particles that placed at each of three corners of an equilateral triangle https://brainly.com/question/13437206jordan wants to see if earthworms prefer rough or smooth terrain to crawl through. What will be his independent variable
The independent variable in this investigation is the type of surface which is changing whereas, the dependent variable is the mobility of earth worm.
What is independent variable?In a experiment or investigation, there are two types of variables which are dependent and independent variable. Dependent variable are those which are dependent on other variables and are changing with respect to other variables.
Independent variables are those not dependent on any other variables and we can change the independent variable to study the change in dependent variable.
Here, the one we studying is the mobility of earth worm which is the dependent variable and the type of surface rough or smooth is the independent variable.
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an object of mass m experiences a gravitational acceleration from a planet of mass M. If the objects mass is doiubled
The force of gravity between two objects is equal to their respective masses multiplied by two. If one of the items triples in mass, the gravitational pull between them will also triple.
The force of gravity between two objects is multiplied by two when their masses are each doubled, and so on. Since an object's kinetic energy is exactly proportional to its mass, it will double along with the object's mass. The force of gravity between two objects is equal to their respective masses multiplied by two. If one of the items triples in mass, the gravitational pull between them will also triple.
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What is the work applied to a 1000kg car when it is pushed 1000m up along a 10- degree incline at a constant velocity. Assume the coefficient of friction between the car and the ramp is 0.30.
The required work applied to a 1000 kg car when it is pushed 1000 m up along a 10- degree incline at a constant velocity is calculated to be 4.6 × 10⁶ J.
Given that,
Mass m = 1000 kg
Displacement d = Δx = 1000 m
Angle of inclination θ = 10°
Coefficient of friction μ = 0.3
The equation for work done is known to be,
W = F × d
We must divide the force of gravity into its component parts and examine the side acting in the x-direction in order to calculate the force of gravity in that direction.
F gx direction = F g sinθ = mg sinθ
The force of friction is directly related to μ times the normal force. The normal force in this situation is equivalent to the y component of the force of gravity.
F gy direction = F g cosθ = mg cosθ
We know force of friction, Ff = μ FN
FN = F gy direction
Ff = μ mg cosθ
We know that our force applied must balance both of these forces,
F applied = mg sinθ + μ mg cosθ
As, W = F × d = (mg sinθ + μ mg cosθ) d = ( 1000× 9.8 sin10° + 0.3 × 1000× 9.8 cos10°) 1000 = (9800 sin10° + 2940 cos10°) 1000 = (0.17 × 9800 + 0.985 × 2940) 1000 = (1666 + 2895.9) 1000 = 4561.9 × 10³ J = 4.6 × 10⁶ J
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A quarterback runs 5 yards backwards and then 15 yards forward.
What is the quarterback's distance traveled?
What is the quarterback's displacement?
The quarterback also touches the ball on almost every offensive play, and is almost always the offensive player that throws forward passes.
What is the quarterback's?The quarterback (sometimes abbreviated "QB") is a position in gridiron football, also referred to as the "signal caller" Quarterbacks typically line up directly behind the offensive line and are part of the offensive platoon.
In contemporary American football, the quarterback is typically regarded as the offensive coordinator and is frequently in charge of calling the play in the huddle. The quarterback almost always delivers forward passes for the offence and touches the ball on practically every offensive play.
A sack occurs when the quarterback is beaten behind the line of scrimmage. In contemporary American football, the starting quarterback is typically the offensive coordinator, and his or her accomplishments or shortcomings can have a big impact on the team's performance.
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The offensive player who delivers forward passes almost always is the quarterback, who touches the ball on almost every offensive play as well.
The quarterback's, what is it?In gridiron football, the quarterback, sometimes known as the "signal caller," is one of the positions. As a member of the offensive platoon, quarterbacks often line up directly behind the offensive line.
The quarterback is frequently in charge of calling the play in the huddle and is generally considered as the offensive coordinator in modern American football. In almost every offensive play, the quarterback touches the ball and almost always completes forward throws for the offense.
The quarterback is tackled behind the line of scrimmage, which results in a sack. Currently, the starting quarterback in American football is Usually, the offensive coordinator, and his or her successes or failures, can have a significant effect on the team's performance.
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Which of the following is NOT considered crucial for life to exist on some world?
A. Liquid water
B. At atmosphere
C. Source of nutrients
D. Source of energy that can be used by life
Answer
Atmosphere is not required in some world
Suppose two dinosaurs with masses of 80. 0 kg and 120. 0 kg sat on the middle and the far end, respectively, of a tree branch. The dinosaurs produced a net counterclockwise torque of 9,400N•m about the end of the branch that was attached to the tree. What was the length of the branch?
The dinosaurs produced a net counterclockwise torque of 9,400Nm about the end of the branch that was attached to the tree. The length of the branch is 4.7m.
τ = Σr × F = rmg
where g is the acceleration caused by gravity, m is the mass, and r is the distance.
Torque has a direct relationship with -
1.the object's mass, in m
2. The mass's separation, r, from the location where the torque is being calculated.
Therefore, the torque will change whether we increase or reduce them.
Therefore, increasing mass will result in an increase in torque, but since we must retain the same torque, we must reduce mass's distance from the location of the torque.
As a result, the mass should be moved closer to the location of the torque.
Total Mass = (80 + 120)kg
= 200kg
Torque = 9400N
τ = Σr × F = rmg
τ = 200 × r × 10
9400 = 200 × r × 10
r = 9400 / 2000
r = 4.7m
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The net electric force acting on each of the three objects below is sketched as a green arrow. For example, if the green arrow points to the left the object feels a net electric force pushing it to the left. If there is no green arrow, the object feels no net electric force. Use this information to assign an electric charge to each object. That is, decide whether each object has a positive electric charge, a negative electric charge, or is neutral.
Electric force is the attraction or repelling force that exists between any two charged objects. Newton's laws of motion, which apply to all forces, describe how a force acts and what it does to the target body.
Electric force is produced by what?Mutual interactions between two charges produce electrical forces. When there are three or more charges present, the cumulative effects of each charge's interactions with the other charges produce the electric force acting on a single charge.
Electric force: how powerful is it?2.40 x 1043 times more powerful than the gravitational force is the electric force between these electrons. Or, to put it another way, gravity is only about a trillion trillion trillion trillion times as strong as electricity.
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Item 2 Sea stars, sea urchins, sand dollars, and brittle stars are all members of the same group. What is the common name of the group to which they all belong
Sea stars, brittle stars, as well as feather stars are a few examples of echinoderms. Despite their apparent differences, echinoderms share two key identifying traits that make them all identifiable.
What is the reputation of echinoderms?Echinoderms are effective scavengers of decomposing material on the seafloor and feed on a range of microscopic organisms, which helps control their population. Sea urchins can destroy tropical sea-grass beds when they are present in great numbers, harming the creatures that live there astrophysics
Why do they go by the name echinoderms?Because of their spiny skin, Echinodermata are so termed (from the Greek "echinos" for "spiny" and "dermo's" for "skin"). There are around 7,000 described extant species in this phylum. Only marine species can be classified as Echinodermata.
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To report the position of an object, first choose a reference point. Then, describe the of the object with respect to the reference point. Next, measure the from the reference point to the object.
We will understand the given concept through an example
The rat serves as your point of reference if you mentioned that the rabbit was to the left of it. You are expressing its position when you specify the distance and direction. The present separation and direction of an object from a reference point is its position.
When something moves with relation to a reference frame, like when a passenger gets off an airline or a lecturer gets up to leave, the object's position changes.the right in relation to a whiteboard. Displacement describes this shift in location.Every location helps you to achieve various location positions.Your position is defined by how you describe your place. The separation in the first illustration is one meter. The reference point helps to locate each and every point.To know more about reference point here
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The populations of the great apes in Africa are recovering and on the rise.
Please select the best answer from the choices provided
T
F
Answer:
False
Explanation
Poaching, habitat loss and diseases are contributing to the death of animals there, example: Gorilla
Answer:
false
Explanation:
How much current flows through the bottom wire in the figure(Figure 1) ?
Express your answer to two significant figures and include the appropriate units.
The current through the bottom of the wire is 0.415 A and the negative sign of the current indicates that current flows from left to right from the bottom wire.
The current through various parts of the circuit is as shown in figure.
Here we have to calculate the current I_5.
Applying Kirchoff's loop rule on each of the loops in the circuit, Consider the left triangle, for it, we have
[tex]$$\begin{aligned}& \left(I_1\right) 6 \Omega+\left(I_3\right) 12 \Omega-9 \mathrm{~V}=0 \\& \Rightarrow 6 I_1+12 I_3=9 \\& \Rightarrow I_1=\frac{9}{6}-\frac{12}{6} I_3 \\& \Rightarrow I_1=1.5-2 I_3-----(1)\end{aligned}$$[/tex]
For the centre of the triangle, we have
[tex]$$\begin{aligned}& \left(I_4\right) 24 \Omega-\left(I_3\right) 12 \Omega=0 \\& \Rightarrow I_4=\frac{12}{24} I_3 \\& \Rightarrow I_4=\frac{I_3}{2}-----(2)\end{aligned}$$[/tex]
And for the right triangle, we have
[tex]$$\begin{aligned}& \left(I_2\right) 10 \Omega+\left(I_4\right) 24 \Omega-15 \mathrm{~V}=0 \\& \Rightarrow I_2=\frac{15}{10}-\frac{24}{10} I_4 \\& \Rightarrow I_2=1.5-2.4 I_4------(3)\end{aligned}$$[/tex]
The junction rule applied at the left corner gives
I_1 =I_3+I_5
=I_5 =I_1-I_3
=1.5-2 I_3-(I_3)=1.5-3 I_3--------(4)
And applying the junction rule at the right corner,
I_4 =I_2+I_5
I_5 =I_4-I_2
=I_4-(1.5-2.4 I_4)=3.4 I_4-1.5-------(5)
Using equation (2) [tex]$I_4=\frac{I_3}{2}$[/tex], equation (5) can be written as
[tex]$$\begin{aligned}I_5 & =3.4\left(\frac{I_3}{2}\right)-1.5 \\\end{aligned}$$[/tex]==1.7 I_3-1.5
Solving equations (4) and (6), we have
1.5-3 I_3=1.7 I_3-1.5
(1.5+1.5)=(1.7+3.0) I_3
3.0=4.7 I_3
[tex]\Rightarrow I_3=\frac{3.0}{4.7} \mathrm{~A}[/tex]
Hence the current in the bottom wire is given by
[tex]I_5 & =1.7\left(\frac{3.0}{4.7}\right)-1.5 \\[/tex] =1.085-1.5 =-0.415 A
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A particle travels at a constant speed of 19.0 m / s in a circular path of radius 954.9 cm. How many turns (revolutions) does the particle make in 1 minute
The 10/π ms² turns (revolutions) the particle make in 1 minute.
What is revolution ?Whereas rotation involves travelling around the axis, occurs when one body moves around another. As an illustration, the Moon orbits the Earth, and the Earth revolves around the Sun.
What is particle ?Paul Dirac and other researchers found that the concept could be applied to electrons and everything else in addition to photons, the unit of light called a quanta: Particles are thought to be excitations of quantum fields that are present throughout space, according to quantum field theory.
When the particle completes half revolution change in velocity
Δv=[5−(−5)]m/s=10m/s
Time taken to complete the half revolution is
t = πr/ v
= π *5 / 5
= πs
Thus, average acceleration = Δv / t
= 10/π ms²
Therefore, the 10/π ms² urns (revolutions) does the particle make in 1 minute.
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cinder block is sitting on a platform 20 m high. It weighs 79 N. The block has
energy. Calculate it.
Answer: 1580 J
Explanation:
Energy is in the form of gravitational potential energy. (GPE)
GPE = mgh , where m is the mass of the block, h is the height and g is the gravitational constant of 9.81 ms-2.
Hence,
Total energy = mass x gravitational constant x height
= Weight x height (since W = mg)
= 79 x 20 J
= 1580 J