Electric field and electric force are related quantities, but not the same thing.
The strength of the electric field is defined as the electrostatic force experienced by a small test charge [tex]q_{0}[/tex] placed at that point divided by the charge itself. The electric field is a vector quantity, and its direction is the same as the direction of the force on a positive test charge.
The strength of the Electric field at a point can also be checked by the density of electric field lines present at that point.
The S.I unit of the Electric field is Newton per columb.
The S.I unit of force is Newton.
[tex]F = E \ q_{0}[/tex]
F= electrostatic force
E= electric field
[tex]q_{0}[/tex] = test charge
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Part A
Drag words indicating what happens to the first blank and indicating the reason to the second blank.
The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward __________________________ because _______________________.
The overall force of gravity that draws the cloud inward increases because the cloud's density increases.
What is gravity?Gravity is a natural phenomenon by which all things with mass are brought toward one another. It is most commonly experienced as the weight of objects pulling them toward the Earth’s center. Gravity is the weakest of the four fundamental forces of nature, yet it is the most dominant force in determining the structure of the universe. It is the reason why planets, moons, and galaxies remain in their orbits. Gravity is also responsible for the formation of stars and planets, as well as the attraction between objects such as planets and moons. The gravity between two objects depends upon their mass and distance between them. Gravity is an important factor in the motion of all objects in the universe and is directly responsible for the tides, the motion of the planets and their motion around the sun.
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A person measures his or her heart rate by counting the number of beats in 30 s. If 33 ± 1 beats are counted in 30.0 ± 0.5 s, what is
the uncertainty in the heart rate in beats per minute?
The uncertainty in the heart rate in beats per minute is 2 minute by using the rules for propagation of uncertainty.
How to calculate uncertainty in the heart rate in beats per minute?
To find the heart rate in beats per minute, we need to divide the number of beats by the time in minutes. So, we have (33 ± 1 beats) / (0.5 min). To find the uncertainty in the heart rate, we need to find the propagation of uncertainty for this division.
Using the rules for propagation of uncertainty, we have:
(heart rate) = (33 ± 1 beats) / (0.5 min)
(heart rate) = 66 ± (1/0.5) beats/min
(heart rate) = 66 ± 2 beats/min
So the uncertainty in the heart rate is 2 beats per minute.
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find the distance that the earth travels in three days in its path around the sun. assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles. [note: the path of the earth around the sun is actually an ellipse with the sun at one focus (see section 11.2). this ellipse, however, has very small eccentricity, so it is nearly circular.] (round your answer to one decimal place.)
To find the distance that the Earth travels in three days in its path around the sun, we first need to find the circumference of the Earth's orbit. We can use the formula for the circumference of a circle, C = 2πr, where C is the circumference, π is approximately equal to 3.14, and r is the radius of the circle (93 million miles).
C = 2πr = 2 * 3.14 * 93 million miles = 584 million miles
Now that we know the circumference of the Earth's orbit, we can find the distance the Earth travels in three days by multiplying the circumference by the proportion of the orbit that the Earth travels in three days.
Three days is 3/365 of a year, so we can use the following formula:
Distance = (3/365) * C = (3/365) * 584 million miles = 40,931 miles
Therefore, the distance that the Earth travels in three days in its path around the sun is approximately 40,931 miles
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Question 4 (Mandatory) (1 point)
MS-PS1-2: Which is an example of a chemical reaction?
Examples of reactions could include burning sugar or steel wool, fat reacting with sodium hydroxide, and mixing zinc with hydrogen chloride.
Define chemical reaction?A chemical reaction is a process that transforms one set of chemical substances into another.A chemical reaction is a process that converts one or more substances, known as reactants, into one or more different substances, known as products.Chemical elements and compounds are both examples of substances.Chemical reactions involve the formation of new bonds between atoms in product particles and the breaking of chemical bonds between reactant molecules (particles). The number of atoms is the same before and after the chemical change, but the number of molecules is different.When chemical bonds between atoms form or break, chemical reactions occur.To learn more about chemical reaction refer to:
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What goes up must come down"-if you throw a baseball in the air, it will go upwards and then descend in a _____ curve.
Answer:
it will come down in a parabola curve
romeo (85.0 kg) entertains juliet (57.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from juliet, who is in the front of the boat. after the serenade, juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on romeo's cheek.
The 80 kg boat moves 0.694 meter towards the shore, if juliet moves towards the romeo.
The mass of the romeo, m₁ = 85 kg
The mass of the juliet, m₂ = 57 kg
The mass of the boat, m₃ = 80 kg
Distance between romeo and juliet, = 2.70 m
If we take the juliet's initial position as a reference point, X₁ = 0
Centre of mass of the boat, X₂ = 2.7/2 = 1.35 m
Distance of romeo from reference point, X₃ = 2.7
Combined centre of gravity of the whole system,
Xₐ = (85×2.7 + 57×0 + 80×1.35)/(85+57+80)
Xₐ = 1.52
After juliet moves romeo, new center of gravity
Xₙ = ((85+57)×2.7 + 80×1.35)/(85+57+80)
Xₙ = 2.214 m
The distance moved by the boat, d = 2.214 - 1.52
d = 0.694 m
--The given question is incomplete, the complete question is:
"romeo (85.0 kg) entertains juliet (57.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from juliet, who is in the front of the boat. after the serenade, juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on romeo's cheek. How far does the 80 kg bus move towards the shore it is facing?"
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The Ejection Seat at Lake Biwa Amusement Park in Japan is an inverse bungee system. A seat with passengers of total mass 160 kg is connected to elastic cables on the sides. The seat is pulled down 12.0 m stretching the cables launch the passengers upward above their starting position at the ground. Assume that the cables are vertical
Part A
Determine the spring constant of the cable
According to the problem the spring constant of the cable is 130 N/m.
What is spring?Spring is a season of renewal and growth that occurs between winter and summer. It is the time of year when plants and animals come back to life and the days become longer and warmer.
The spring constant of the cable can be determined using Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from equilibrium. In this case, the displacement is 12.0 m, so the spring constant is given by:
k = F/x = (160 kg * 9.8 m/s2)/(12.0 m)
= 130 N/m
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some of the following circuits violate kvl/kcl and/or basic definitions of two-terminal elements given in section 1.3. for each one of the circuits, determine if it is correct or ill-specified. if it is ill-specified, explain the problem and indicate what will happen if the incorrect circuit has been built up in your real life?
This circuit is ill-specified. It violates KCL, as there is no path for current to flow from the + terminal of the battery, through the resistor, and back to the battery's - terminal. The circuit will not work as expected if it has been built up in real life.
What is violates KCL?Kirchhoff’s Current Law (KCL) states that the sum of all currents entering and leaving a node in an electrical circuit must be equal to zero. This means that the net current entering and leaving the node must be equal to zero. Violating KCL would occur when the sum of all the currents entering and leaving the node is not equal to zero, creating an imbalance in the circuit. This imbalance can lead to circuit malfunction, so it is important to ensure that KCL is not violated.
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According to Charle's law, the volume of the balloon in the freezer will be 35.30 cm³.
What is Charle's law?Charles law is an experimental gas law which provides description about the behavior of gases which tend to expand on heating.It states that, at constant pressure, the temperature is in direct proportion with the volume that is,V∝T or V₁/T₁=V₂/T₂.The relation between volume and temperature is linear as the temperature increases volume also increases.
The graph of volume versus temperature is a straight line passing through the origin.Substitution in formula gives V₂= 40×263/298=35.30 cm³.
Thus, the volume of the balloon in the freezer will be 35.30 cm³.
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if the 1.5-m-long cord ab can withstand a maximum force of 3500 n, determine the force in cord bc and the distance y so that the 200-kg crate can be supported. fbc
3500 N is the same amount of force in cord BC as it is in cord AB. The equation of equilibrium Fy=Fabsin(theta)=Fbccos(theta), where theta is the angle between the two cords, may be used to compute the distance y.
The idea of force equilibrium can be used. To balance the weight of the crate (200 kg * 9.8 m/s2 = 1960 N), the force in cord BC (F bc) must be equal to the force in cord AB (3500 N). The idea of mechanical advantage may also be used to determine the distance y, which in this example equals the weight-to-force ratio of the BC cord. As a result, y = (200 kg * 9.8 m/s2) / 3500 N = 0.564 m if we assume that y is the distance from the point of suspension to the container. As a result, the distance y is 0.564 m and the force in cord BC is 3500 N.
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A small fly of mass 0.30 g is caught in a spider's web. The web vibrates predominately with a frequency of 3.4 Hz.
-what is the value of the effective spring stiffness constant "k" for the web, in N/m?
-At what frequency would you expect the web to vibrate if an insect of mass 0.60g were trapped, in Hz?
I tried using the equation f=1/2pi*sqrt(k/m) but am not getting it right. Help greatly appreciated!!!!
The effective spring stiffness constant "k" for the web will be 0.139 N/m and frequency will be 2.83 Hz.
Frequency is defined as the rate of changes in current direction per second. It is given in hertz (Hz), an internationally recognised unit of measurement. One cycle per second is equal to one hertz. Cycles per second are represented by the unit hertz (Hz). A cycle is the technical term for a whole alternating current or voltage pulse.
(a) m = 0.30 g = 0.30 x 10^-3 kg
f = 3.4 Hz
Spring frequency can be calculated using the formula below
f = [tex]\frac{1}{2pi} \sqrt{\frac{k}{m} }[/tex]
so solving,
Where, k be the spring constant
k = 0.139 N/m
(b)
k = 0.139 N/m
Let the frequency be f.
f = [tex]\frac{1}{2pi} \sqrt{\frac{k}{m} }[/tex]
f = 2.83 Hz
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a spring is stretched by 35 cm and attached to a 500 g air-track glider, which is then released. the spring does 0.30 j of work on the glider as it returns to its equilibrium length. What is the value of the spring constant?
The value of the spring constant for the spring stretched by 35 cm is 0.000244 J/cm.
To calculate the spring constant, the equation
Work = Force x Distance. The work of the spring (0.30 J) is known, as well as the distance the spring is stretched (35 cm). Therefore, the force is calculated by dividing the work by the distance is 0.0086 erg.
Force = - spring constant x Distance
The force is then divided by the distance the spring is stretched back to its equilibrium position (35 cm) to find the spring constant. The spring constant is the amount of force required to stretch the spring 1 cm. In this example, the spring constant is 0.000244 J/cm.
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Answer these questions please
Atomic theory development, a new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's.
What progress has been made in the atom model?
According to John Dalton, atoms—which he pictured as little solid balls—are the smallest units of matter. The following concepts were part of Dalton's model: it is impossible to simplify an atom. Every element has the same number of atoms.Atomic theory development, A new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's. The orbits of the electrons surrounding the nucleus, according to his theory, are circular and concentric. The term "planetary model" refers to this model, which is based on the solar system.Atomic theory development, a new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's.To learn more about atom model refer to:
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Identify the following ways in which a good psychologist views new and surprising conclusions of research studies.
The ways in which a good psychologist views new and surprising conclusions of research studies are critical thinking and amiable skepticism.
A quality known as amiable scepticism combines openness to ideas and scientific findings with a wariness that arises when the concept is not supported by sound logic or evidence. You need to be a critical thinker if you want to be receptive to friendly scepticism.
The topic of critical thinking is complicated, and there are many multiple interpretations of what it means to analyse or evaluate verifiable facts in a reasonable, sceptical, and objective manner. The capacity to assess data and be conscious of prejudices or preconceptions, including your own, is referred to as critical thinking.
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with what tension must a rope with length 3.00 m and mass 0.100 kg be stretched for transverse waves of frequency 42.0 hz to have a wavelength of 0.710 m ? activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type t
The equation of a transverse wave traveling on a rope is given by y=10sinπ(0. 01x−2. 000t) where y and x are in cm and t in seconds.
What is transverse waves?
A transverse wave is a wave in which particles move perpendicular to the direction of the wave propagation.A transverse wave is a type of progressive wave. The direction of propagation of a transverse wave is always perpendicular to its direction of vibration. Few specific types of transverse waves can travel through a vacuum. An electromagnetic wave or light wave is an example of a transverse.Hence a transverse wave of this nature is called a shear wave. Since fluids cannot resist shear forces while at rest, propagation of transverse waves inside the bulk of fluids is not possible. In seismology, shear waves are also called secondary waves or S-waves.
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1000N and pa = 10 ^8 .then find area
Pressure in pa = (total force) x (area)
10⁸ pa = (1000 N) x (area)
Divide each side of the equation by 1000N.
10⁸ pa/1000N = area
area = 10⁵ square meters
which of the following is an example of kinetic energy? view available hint(s)for part a which of the following is an example of kinetic energy? the energy held in bonds between atoms wind rotating a turbine a book on the top shelf of a closet a rock on top of a hill
A windmill turning An illustration of kinetic energy is the following.
What exactly is an energy in science?The ability to "achieve work," or the capability to exert a force strong enough to move an item, is how energy is defined. Despite the ambiguity in the definition, the idea is actually pretty simple: electricity simply refers to the force that propels objects. The two different categories of energy are potential and kinetic.
Simple energy definitionThe most basic definition of energy is the capacity for work. Energy causes things to move and change. It's everywhere and comes in a variety of shapes. Energy is needed while cooking food.
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for the charge distribution provided, indicate the region (a to e) along the horizontal axis where a point exists at which the net electric field is zero. (figure 2)
At point C along the horizontal axis, the net electric field is zero.
Electrically charged particles are surrounded by a physical phenomenon termed an electric field that either attracts or repels all other adjacent charged particles. The physical field surrounding a system of charged particles can also be referred to. Electric charges and time-varying electric currents make up electric fields.Both electric and magnetic fields are manifestations of the electromagnetic field, one of the four fundamental interactions (sometimes known as forces) of nature.
1. In the region B along the horizontal axis , a point exists at which the net electric field is zero.
2. Nowhere in any region along the horizontal axis the net electric field is zero.
3. In the region A along the horizontal axis , a point exists at which the net electric field is zero.
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the drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 3230 n/c. determine the electric potential difference the following points.
These locations, where the potential difference between Vab and Vcb is 0 and 258v, respectively, have a uniform electric field with a magnitude of 3230 n/c.
The potential difference, also referred to as voltage, is equal to the amount of current multiplied by the resistance. One Joule of energy is consumed by a charge when it moves between two points in a circuit at a potential difference of one Volt. respectively, have a uniform electric field with a magnitude of 3230 n/c. An electric field is a type of physical field that exists around electrically charged particles and which influences the behaviour of all other charged particles nearby (or E-field).
whereas Vcb = E/d = 3230*0.08 = 258v, Vba = E/d = 0
Vba = E/d = 0
Vcb = E/d = 3230*0.08 = 258v
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men went to the moon by means of a shell shot from a large cannon sunk in the ground. part a what muzzle speed must the cannon have in order for the shell to reach the moon? express your answer to two significant digits and include the appropriate units. activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type vshell vshell
The smallest speed at which a moving object, like a rocket, can fly outward into space and escape the gravitational field of a celestial body, such the earth.
How is escape velocity calculated?The smallest speed at which a moving object, like a rocket, can fly outward into space and escape the gravitational field of a celestial body, such the earth.Escape Earth's speed is 2 X 9.8 X 6.4 X 106 m/s or V = (gR) M/s is equal to 11200 M/s, or 11.2 km/s or 7 mph. Consequently, if an object is launched upward from the surface of the earth at a speed of 11.2 km/s, it will be able to escape, or move past the influence of the earth's gravitational field.Egress speed, When anything decelerates faster than gravity weakens, it never returns because gravity weakens more quickly than it does. With the speed of Earth's escape, the object will continue to move away from the planet forever.To learn more about escape velocity refer to:
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a small metal ball is given a negative charge, then brought near (i.e., within a few millimeters) to end a of the rod. what happens to end a of the rod when the ball approaches it closely this first time? select the expected behavior.
Weak attraction between the sphere and the rod is caused by end A of the rod inducing a positive charge (and correspondingly, end B acquires a negative induced charge).
This suggests that a charge may have moved from A to B. In an insulator, charge flow is restricted, hence the induced charges are frequently insignificant. because a pliable metal ball is charged negatively. Charged matter experiences a force when exposed to an electromagnetic field because of the physical nature of electric charge. Electrical charges can be positive or negative (commonly carried by protons and electrons respectively). Matter experiences a force when retained in an electromagnetic field due to the physical property of electric charge.
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Vacillate the change in the. Kinetic energy KE of the bottle when the mass is increased use the formula KE=1/2 mv2 where m is the mass and v is the speed
When the mass is 0.125 kg, the kinetic energy is 1 J
When the mass is 0.250 kg, the kinetic energy is 2 J.
When the mass is 0.375 kg, the kinetic energy is 3 J.
When the mass is 0.500 kg, the kinetic energy is 4 J.
What is the kinetic energy of the bottle?
The kinetic energy of the bottle is the energy possessed by the bottle due to its mass and motion.
K.E = ¹/₂mv²
where;
m is the mass of the bottlev is the speed of the bottleWhen the mass is 0.125 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.125 kg x ( 4 m/s )²
K.E = 1 J
When the mass is 0.250 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.25 kg x ( 4 m/s )²
K.E = 2 J
When the mass is 0.375 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.375 kg x ( 4 m/s )²
K.E = 3 J
When the mass is 0.500 kg, the kinetic energy is calculated as;
K.E = ¹/₂ x 0.5 kg x ( 4 m/s )²
K.E = 4 J
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How do measured values of weather and climate differ?
Measured values of weather and climate differ from one another because the weather is a short-term change in the atmosphere whereas climate is the environmental condition over a long period in a specific area.
How do measure values of weather and climate differ?The part of weather and climate are those quantities or properties that are steady regularly. The six main elements are weather and climate: temperatures, atmospheric pressure, wind, humidity, drizzle, and cloudiness. Different land can have different climates.
Weather is called the day-to-day information of atmospheric changes in a specific area at a specific time. Climate is the statistical details on the average weather condition of a specific land for more than 30 years. 2. The weather of a place involves the short-term atmospheric condition.
So we can conclude that The difference allying weather and climate is a measure of time.
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A racecar starting from rest acclerates uniformly at a rate of 4.9 meters per second2.What is the car's speed after it has traveled 200 meters
The speed of the car after 200 meters is v = 44.3 m/s (3 sf).
What is speed?The rate at which an object's position changes in any direction is referred to as speed. The ratio of distance travelled to travel time is used to calculate speed. Speed and Velocity both refer to how quickly something moves along a path. Speed measures how quickly something moves along a path.
In other words, velocity is a vector and speed is a scalar value. The rate at which a distance changes over time is referred to as speed. The base unit of distance plus the base unit of time are combined to form the SI unit of speed. Distance times speed metre second equals time. m/s is the SI unit for speed.
u = 0
a = 4.9
s = 200
v² = 0²+2*4.9*200
v = √(2*4.9*200)
v = √1960
v = 44.3 m/s (3 sf)
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if 34.5 g of copper reacts with 70.2 g of silver nitrate, according to the following reaction, what is the maximum number of grams of silver that can be produced?\
44.55g of silver can be produced by reacting 34.5 g of copper with 70.2 g of silver nitrate by following the chemical reaction in the given condition.
First, we balanced the equation
1Cu + 2AgNO3 → 1Cu(NO3)2 + Ag
Then, we find the moles of each reagent
molCu = 34.5g/(63.55*9/mol) = 0.543 mol
molAgNO3 = 70.2/(63.55*9/mol) = 0.423 mol
Now, we find the limiting reagent from the quantities of product that can be formed from each reagent
molAgNO3 = 0.543 molCu.2molAgNO3/1molCu= 1.086 mol
molCu = 0.413molAgNO3.1molCu/2molAgNo3 = 0.206mol
1,086 moles of AgNO3 is necessary for each mole of Cu since we have 0.413 moles of Ag(NO3), the nitrate is the limiting reagent
the value of the limiting reagent determines the amount of product that is generated
∴ 0,413 mol of Ag can be produced
Ag = 0.423mol.107.87*g/mol = 44.55 g = 44,55g
Ag≈ 44.6 g
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Suppose you hold a small ball in contact with, and directly over, the center of a large ball. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. To show the extreme case, ignore air resistance and suppose the large ball makes an elastic collision with the floor and then rebounds to make an elastic collision with the still-descending small ball. Just before the collision between the two balls, the large ball is moving upward with velocity v
→
and the small ball has velocity -v
→
. (Do you see why?) Assume the large ball has a much greater mass than the small ball.
A. What is the velocity of the small ball immediately after its collision with the large ball?
B. From the answer to part A, what is the ratio of the small ball's rebound distance to the distance it fell before the collision?
We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved. Both before and after the impact, the relative velocity is of equal magnitude.
After a collision, how can you determine an object's velocity?If you know the other values of an object's properties, you may determine its momentum or velocity using the momentum equation p = m•v.Despite not being able to move the huge ball very far, the small ball's momentum and velocity will be transferred to it. State the third law of motion of Newton.We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved. Both before and after the impact, the relative velocity is of equal magnitude.We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved.To learn more about relative velocities refer to:
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using conservation of energy, derive an expression for the velocity of the cart when it is at the top of the neptune sphere in terms of r, r and physical constants as needed.
We can derive the required expression by using the conservation of energy law with the help of potential energy concept. The velocity will be v = √(2gh + 2Fdcos(θ)/m)
The conservation of energy can be used to derive an expression for the velocity of a cart when it is at the top of a Neptune sphere. The total mechanical energy of the cart at the top of the sphere is equal to the initial potential energy of the cart at the bottom of the sphere plus the work done by non-conservative forces, such as friction and air resistance.
The initial potential energy of the cart can be calculated using the equation:
U = mgh
where U is the potential energy, m is the mass of the cart, g is the acceleration due to gravity, and h is the height of the sphere.
The work done by non-conservative forces can be calculated using the equation:
W = Fdcos(θ)
where W is the work done, F is the force acting on the cart, d is the distance traveled by the cart, and θ is the angle between the force and the displacement.
At the top of the sphere, the kinetic energy of the cart, which is given by (1/2)mv^2 where m is the mass of the cart and v is the velocity, is equal to the initial potential energy plus the work done by non-conservative forces.
Therefore, we can write the following equation:
(1/2)mv^2 = mgh + Fdcos(θ)
Solving for v, we get
v = √(2gh + 2Fdcos(θ)/m)
In this expression v is the velocity of the cart when it is at the top of the Neptune sphere in terms of r, r and physical constants as needed. To find the value of velocity we need to know the values of the variables such as mass, height of the sphere, distance traveled, force acting on it and θ, and the acceleration due to gravity.
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A proton is released from rest inside a region of constant, uniform electric field 1 pointing due north.
29.8 s after it is released, the electric field instantaneously changes to a constant, uniform electric field 2 pointing due south. 7.65 s after the field changes, the proton has returned to its starting point. What is the ratio of the magnitude of 2 to the magnitude of 1? You may neglect the effects of gravity on the proton
Answer:
The ratio of the magnitude of 2 to the magnitude of 1 is 1:1
Explanation:
The proton is released in an electric field pointing due north and, 29.8 seconds later, the field changes to a constant, uniform electric field pointing due south. 7.65 seconds after the field changes, the proton has returned to its starting point.
The proton was initially at rest and the electric field caused it to accelerate. The proton's acceleration is directly proportional to the electric field and inversely proportional to its mass.
The proton is acted on by two fields with opposite direction, which means that the net acceleration is zero. Therefore, the ratio of the magnitude of electric field 2 to the magnitude of electric field 1 is 1:1
The ratio of the magnitude of 2 to the magnitude of 1 is 1:1
) find the amplitude, period, and horizontal shift. (assume the absolute value of the horizontal shift is less than the period.)
By applying trigonometry function graph theory, it can be concluded that the amplitude is 2, the period is π, the horizontal shift is 0, and the equation that represents the graph is y = 2 cos (2x)
A trigonometry function is a function whose graph repeats continuously over a certain period. The trigonometry function graph consists of hills and valleys that repeat continuously over a certain period.
There are some terms regarding a trigonometry function graph:
Amplitude is the farthest deviation of a point on a trigonometric function graph from its horizontal line (eg the x-axis).Period is the distance the trigonometric function graph repeats from the initial reference point to the first repetition point.Horizontal shift is a shift to the left or right of the sin graph so that it is the same as the cosine graph and vice versa.Now we look at our trigonometric function graph.
Since the farthest deviation of the graph is in points (0,2), (π/2,-2), and (π,2), thus the amplitude of the graph is 2. We denote it as a = 2.
The graph repeats from the initial reference point to the first repetition point after π, thus the period of the graph is π.
The value of k can be obtained from this:
2π/k = period
k = 2π/period
= 2π/π
= 2
The horizontal shift is 0, which means there's no shifting on the cosine graph.
Now we input the value of a, k and b into the equation:
y = a cos (k (x - b))
= 2 cos (2 (x - 0))
= 2 cos (2x)
Thus the amplitude is 2, the period is π, the horizontal shift is 0, and the equation that represents the graph is y = 2 cos (2x)
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suppose that you drive the 9.7 km from your university to home in 25.5 min. (note: average speed is distance traveled divided by time of travel.) your average speed in km/h is
The average speed of the travel from university to home is calculated to be 22.82 km/hr.
Average speed is known to be described as the total distance travelled by an object in particular time interval.
Given that,
Distance travelled = 9.7 km
Time taken for travel = 25.5 min
We know, 1 hour = 60 min
Converting minutes to hours, we have, 25.5/60 = 0.425 hr
The relation between distance, speed and time is known to be, distance = speed × time
Making speed as subject, we have,
Speed = Distance/time = 9.7/0.425 = 22.82 km/hr
The required average speed of the travel from university to home is calculated to be 22.82 km/hr.
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