Initially, the energies are:
[tex]U_{i}=-\frac{G M_{\varepsilon} m}{r_{e}} \\ =K_{i}=\frac{1}{2} m v_{0}^{2}[/tex]
At final point, the energies are:
[tex]U_{f}=-\frac{G M_{\varepsilon} m}{r_{e}+h} \\ K_{f}=\frac{1}{2} m(0)^{2}=0[/tex]
Using conservation law of energy,
[tex]-\frac{G M_{e} m}{r_{e}}+\frac{1}{2} m v_{0}^{2} &=-\frac{G M_{e} m}{r_{\varepsilon}+h} \\ -\frac{G M_{e}}{r_{e}}+\frac{v_{0}^{2}}{2} &=-\frac{G M_{e}}{r_{e}+h} \\ \frac{-2 G M_{e}+r_{e} v_{0}^{2}}{2 r_{e}} &=-\frac{G M_{e}}{r_{e}+h} \\ \frac{r_{e}+h}{G M_{e}} &=\frac{2 r_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}[/tex]
The equation is further simplified as:
[tex]r_{e}+h &=\left(\frac{2 r_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}\right) G M_{e} \\ h &=\frac{2 r_{e} G M_{e}}{2 G M_{e}-r_{e} v_{0}^{2}}-r_{e} \\ &=\frac{2 r_{e} G M_{e}-2 r_{e} G M_{e}+r_{e}^{2} v_{0}^{2}}{2 G M_{e}-r_{e} v_{0}^{2}} \\ & h=\frac{r_{e}^{2} v_{0}^{2}}{2 G M_{e}-r_{e} v_{0}^{2}}[/tex]
a projectile with two times the mass is placed into the launcher out with the same initial velocity would this change the range
Yes, the range would change. Since the mass of the projectile has doubled, its momentum has also doubled.
What is momentum?Momentum is the measure of an object's resistance to changes in its state of motion. It is a vector quantity, meaning it has both magnitude and direction. Momentum is calculated by multiplying the mass and velocity of an object. Momentum is conserved, meaning that the total momentum of a system remains constant, even if the individual momentum of each object within the system changes. In a collision between two objects, the total momentum before the collision is equal to the total momentum after the collision. Momentum is a powerful concept and has many applications in physics. For example, it is the basis for the laws of motion, the conservation of energy, and the study of planetary motion.
Since momentum is conserved, the projectile's velocity after launch will be reduced. This in turn will reduce the range of the projectile, as it will not be able to travel as far with a lower velocity as it would with a higher velocity.
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This range would increase 4 times.
What does the term "projectile motion" refer to?
The movement of an object that has been launched into the air is known as projectile motion. Only gravity is felt by the item after the initial force that launches it. Projectile and trajectory both refer to the same thing: an object.
The projectile's motion is divided into two parts: vertical motion and horizontal motion. Furthermore, since perpendicular components of motion are not reliant on one another, it is necessary to discuss each of these two components of motion independently.
Range of projectile is R=(vi²sin2∅)/g
So when the velocity is doubled, Range R will be
I.e R'= ((2Vi)²sin2∅)/g
R'=4(Vi²sin2∅)/g
R'=4R
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A vector is 14.4 m long and
points in a 133 degree
direction.
Find the y-component of the
vector.
Explanation:
To find the y-component of a vector that is 14.4 m long and points in a 133 degree direction, you can use the trigonometric functions sine and cosine.
The y-component of a vector is given by the product of the vector's length and the sine of the angle between the vector and the positive x-axis. The x-component of a vector is given by the product of the vector's length and the cosine of the angle between the vector and the positive x-axis.
You can find the y-component of the vector by using the formula:
y-component = vector length * sine(angle)
In this case, the vector length is 14.4 m, and the angle between the vector and the positive x-axis is 133 degrees. You can find the y-component of the vector by plugging these values into the formula:
y-component = 14.4 m * sine(133 degrees)
You can use a calculator or look up the value of sine(133 degrees) in a table to find the y-component of the vector. You will find that the y-component of the vector is approximately -11.9 m.
Note that the y-component of the vector is negative because the vector points in a direction that is below the positive x-axis. The x-component of the vector would be positive because the vector points in a direction that is to the right of the y-axis.
Use the trigonometric functions sine and cosine to determine the y-component of a vector that is 14.4 m long and points in a 133 degree direction.
What is Y component of vector?A vector's y-component is calculated by multiplying its length by the sine of the angle it makes with the positive x-axis. A vector's x-component is calculated by multiplying its length by the cosine of the angle it makes with the positive x-axis.
Utilizing the following formula, you can get the vector's y-component: y-component = sine * vector length (angle).
The vector length in this instance is 14.4 m, and the angle it makes with the positive x-axis is 133 degrees. the location of the y-component.
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a student is designing an experiment in which an object of unknown mass is pushed across a frictionless surface
The applied force must be larger than the frictional force for a body to move successfully.
What is friction?Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Friction always moves an object in a direction that is counter to the direction that it is traveling or attempting to move.
When a body is pushed, an exact quantity of frictional force is created, up until the point where Fs max = coefficient of friction * normal force.
After that, when fs max exceeds the frictional force, dynamic friction enters the picture, which is what causes the body to move.
The body begins to move after a force is applied that is more than the minimal need, or what we refer to as the Threshold (f applied > fs max).
In the case of a frictionless surface, the applied force will be perpendicular to the gravitational force that is being taken into account. Even the slightest acceleration must cause the body to move.
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a toy is tossed from the edge of a table. its path is shown; air resisitance is ignored. use the picture below to answer the following questions
As there is only one force acting on the ball i.e. gravitational force, the acceleration will be constant and downward. Also because ball moves in the direction of the acceleration, the velocity increases.
Acceleration - constant; velocity - increasing.
What is Acceleration?
Acceleration is the rate of change of velocity of an object over time. It can be positive, negative, or zero. Positive acceleration is when an object speeds up, negative acceleration is when an object slows down, and zero acceleration is when an object's velocity remains constant.
What is velocity?
Velocity is a measure of the speed and direction of an object's motion. It is typically measured in meters per second (m/s) or kilometers per hour (km/h). Velocity can also be expressed in other units, such as miles per hour (mph) or feet per second (ft/s). Velocity is related to a object's acceleration, as an object's acceleration is the rate of change in its velocity over time.
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Which one of the statements below describes the direction of thermal energy transfer in an isolated system? In an isolated system, for energy transfer to take place the entire system must remain at a constant temperature. In an isolated system, energy always transfers from a warmer region to a cooler region In an isolated system, energy always transfers from cooler region to a warmer region In an isolated system, no transfer of energy between regions of the system can take place. In an isolated system, energy cannot be transferred from a hotter region to a colder region.
The correct statement about the direction of transfer of energy in an isolated system is b) In an isolated system, energy always transfers from a warmer region to a cooler region .So, correct option is b.
An isolated system is a thermodynamic framework that can't trade either energy or matter beyond the framework. There are two manners by which this might happen: The framework might be so far off from another framework that it can't associate with them. The framework might be encased to such an extent that neither energy nor mass might enter or exit.
When temperature remains constant then energy transfer takes place between different components of system will be possible.Since temperature is different ,energy flow is favored from the warmer region to colder region because of difference in temperature.
Hence, correct option is b.
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(Complete question) is:
Which one of the statements below describes the direction of thermal energy transfer in an isolated system?
a)In an isolated system, for energy transfer to take place the entire system must remain at a constant temperature.
b)In an isolated system, energy always transfers from a warmer region to a cooler region
c)In an isolated system, energy always transfers from cooler region to a warmer region
d)In an isolated system, no transfer of energy between regions of the system can take place.
e)In an isolated system, energy cannot be transferred from a hotter region to a colder region.
You wish to chill your freshly brewed tea with the minimum amount of ice that will avoid watering it down too much. What is the minimum amount of ice you should add to2.70 kgof freshly brewed tea at91.98∘Cto cool it to6.19∘C? The ice is initially at a temperature of -51∘C. Heat capacity of water a 4190 Jikgik The specifio heat of ice=2010 J/kg/KLatent heat coeficient of fusion for ice=3.34×105 J/kg
To find the minimum amount of ice needed to cool the tea, you can use the formula:
Q = mcΔT + mL
where Q is the heat energy required, m is the mass of the ice, c is the specific heat capacity of ice, ΔT is the temperature change, and L is the latent heat of fusion.
The specific heat capacity of ice is 2010 J/kg°C. The latent heat of fusion of ice is 3.34 x 10^5 J/kg.
First, find the heat energy needed to cool the tea from 91.98°C to 6.19°C:
Q = 2.70 kg * 4190 J/kg°C * (91.98°C - 6.19°C) = 2.70 kg * 4190 J/kg°C * 85.79°C = 92959.58 J
Then, find the heat energy needed to melt the ice:
Q = mL = m * 3.34 x 10^5 J/kg = m * 3.34 x 10^5 J/kg
Then, add the heat energy needed to cool the tea to the heat energy needed to melt the ice:
Q = 92959.58 J + mL = 92959.58 J + 3.34 x 10^5 J/kg * m
Finally, rearrange the equation to solve for m:
m = (Q - 92959.58 J) / (3.34 x 10^5 J/kg)
Plugging in the given values, you get:
m = (92959.58 J - 92959.58 J) / (3.34 x 10^5 J/kg) = 0 kg
So the minimum amount of ice needed to cool the tea is 0 kg. This means that the tea is already at a temperature lower than the melting point of ice, so no ice is needed to cool it further. It's important to note that this calculation assumes that there is no heat loss to the surroundings and that the tea and ice are perfectly insulated. In practice, some heat will be lost to the surroundings and more ice may be needed to achieve the desired temperature.
A heavy stone and a light stone are released from rest in such a way that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small. Which of the following statements about these stones are correct? (There could be more than one correct choice)
a) The stones must have been released from the same height.
b) The stones both have the same kinetic energy just as they reach the ground.
c) The stones both have the same speed just as they reach the ground.
d) Just as it reaches the ground, the light stone is travelling faster than the heavy stone.
e) The initial height of the light stone is greater than the initial height of the heavy stone.
The stones needed to be dropped from the same height. The light stone is moving quicker than the hefty stone just as it touches the ground. The light stone is taller when it is first placed than the heavy stone is.
What exactly is meant by energy?Energy is the ability to carry out work. Potential, kinetic, thermal, electrical, chemical, nuclear, and other forms may all exist for it.
In Example, what is energy?There are numerous types of energy. Examples of these include: electromagnetic energy, chemical energy, nuclear or atomic energy, mechanical energy, gravitational energy, electrical energy, sound energy, and so on. Each form can be changed or transformed into the others.
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In an experiment, a student measured the volume of a substance while the mass was changed. The student measured up to five kilograms. The graph of the data is plotted below.
A volume versus mass graph is shown with mass on the vertical axes from 1 to 10 kilograms and volume on the horizontal axis from 1 to 5 milliliters. A line from the origin through all points and beyond.
Which of the following is an error the student made in creating an accurate graph?
The axes and graph are based only on measured values.
The axes are labeled with the incorrect variables.
The plotted points do not show all data collected.
The title has the incorrect order for the variables.
Answer:
Answer:
let the first point be a second be b third be c fourth be d and last point be e.
The point a and d are incorrect. because tye plotting of the is incorrect
Which velocity component is dependent on gravity?
Answer:
Explanation:
Vertical acceleration.
A 47.0 kg cheetah can run with a speed of 31.0 m/s. What is the cheetah's kinetic energy?
Answer:
22,583.5 J
Explanation:
KE = 1/2mv²
KE = 1/2(47 kg)(31.0 m/s)² = 22,583.5 J
Which of the following describes the independent variable?
It is called the respondent variable.
It is plotted on the vertical axis when graphed.
It refers to a quantity changed by the experimenter.
It is something that remains controlled during trials.
It refers to a quantity changed by the experimenter.
The independent variable is a variable that is manipulated or controlled by the experimenter in an experiment. It is the variable that is thought to affect the dependent variable, which is the variable being measured or observed in the experiment. The independent variable is plotted on the horizontal axis when graphed, and is often referred to as the predictor variable. The respondent variable is not a commonly used term in scientific research.
A block of mass 0.40 kg and density 2900 kg/m3 is completely submerged under the water in static equilibrium on top of a spring (k = 50.0 N/m) that is fixed to the bottom of the container as shown in the figure. How much is the spring compressed? (the density of water is 1000 kg/m3) cm40
A block of mass 0.40 kg and density 2900 kg/m3 is completely submerged under the water in static equilibrium on top of a spring (k = 50.0 N/m) that is fixed to the bottom of the container, the spring is compressed by 0.051 m.
To determine the amount that the spring is compressed, you will need to consider the mass of the block, the density of the block and the water, and the spring constant of the spring.
The weight of the block is equal to the mass of the block times the acceleration due to gravity.
The equation for the weight of the block can be written as:
W = m * g
where W is the weight of the block, m is the mass of the block (0.40 kg), and g is the acceleration due to gravity (9.8 m/s^2).
Plugging in the values, you get:
W = 0.40 kg * 9.8 m/s^2
W = 3.92 N
The buoyant force acting on the block is equal to the weight of the water displaced by the block. The weight of the water displaced by the block is equal to the volume of the block times the density of the water times the acceleration due to gravity.
The equation for the buoyant force can be written as:
F_b = V * rho_w * g
where F_b is the buoyant force, V is the volume of the block, rho_w is the density of the water (1000 kg/m^3), and g is the acceleration due to gravity (9.8 m/s^2).
The volume of the block can be calculated using the density of the block and the mass of the block.
The equation for the volume of the block can be written as:
V = m/rho
where V is the volume of the block, m is the mass of the block (0.40 kg), and rho is the density of the block (2900 kg/m^3).
Plugging in the values, you get:
V = 0.40 kg / 2900 kg/m^3
V = 0.0014 m^3
Plugging this value into the equation for the buoyant force, you get:
F_b = 0.0014 m^3 * 1000 kg/m^3 * 9.8 m/s^2
F_b = 1.37 N
The net force acting on the block is equal to the weight of the block minus the buoyant force.
The equation for the net force can be written as:
F_net = W - F_b
where F_net is the net force, W is the weight of the block, and F_b is the buoyant force.
Plugging in the values, you get:
F_net = 3.92 N - 1.37 N
F_net = 2.55 N
The spring force is equal to the spring constant times the amount that the spring is compressed.
The equation for the spring force can be written as:
F_s = k * x
where F_s is the spring force, k is the spring constant (50.0 N/m), and x is the amount that the spring is compressed.
Solving for x, you get:
x = F_s / k
Plugging in the values, you get:
x = 2.55 N / 50.0 N/m
x = 0.051 m
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A ball has a mass of 2.0 kg. The ball approaches a wall at a speed of 3.0 m/s and rebounds at a
speed of 1.0m/s.
wall
What is the impulse on the wall?
A 4.0N
B 4.0NS
C 8.0N
D 8.0Ns
Answer:
D
Explanation:
Direction of motion is positive right side
P = mv
P = m (final - initial)
P = 2 ( -1 - 3)
P = 8 Ns
(negative sign ignored)
I hope my answer helps you.
The impulse on the wall with a mass of the ball is 2 kg and the initial speed of wass 3 m/s and the final velocity is 1 m/s is 8 Ns. Hence, option D is correct.
Impulse equals the product of net force and changes in time. Impulse is also equal to the change in momentum. It is also defined as the force applied to an object with a short duration of time. The unit of impulse is Newton. seconds(Ns).
From the given,
mass of the ball (m) = 2kg
The initial speed of the ball (u) = 3m/s
the final speed of the ball (v) = -1 m/s.
Impulse (I) = Momentum (p)
Momentum (p) = mΔv
= m(v-u)
= 2(-1-3)
= 2(-4)
= -8.
Thus, the impulse on the wall is 8Ns.
Hence, the correct option is D.
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Calculate the fringe separation for light of wavelength 680nm that falls on two slits 4 separated by 0.1 mm when the screen is placed 1.3 m away from the slits.
The fringe separation of the double-slit interference is 0.884 mm.
What is interference of lights?When two coherent light waves from separate sources collide, the energy distribution caused by the first wave is altered by the second. The term "interference of light" refers to this alteration in the distribution of light energy brought on by the superposition of two light waves.
Wavelength of light: λ = 680 nm = 680 × 10⁻⁹ m.
Separation between the two slits: d = 0.1 mm = 0.1 × 10⁻³ m.
Screen distance: D = 1.3 m.
Hence, the fringe separation: x = λD/d
= ( 680 × 10⁻⁹)×(1.3 )/(0.1 × 10⁻³ ) m
= 0.000884 m
= 0.884 mm.
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A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 10.0 s. We have taken counterclockwise rotation to be positive. How long is the time interval during which the speed of the wheel is increasing?
The time interval during which the speed of the wheel is increasing is 4 s.
What is angular acceleration?Angular acceleration is the term used to describe the temporal pace at which angular velocity varies. Radians per square second is used as the measurement unit.
At time t = 0, the angular velocity is ω₁ = - 6.00 rad/s.
At time t = 10.0 s, the angular velocity is ω₂ = +4.00 rad/s.
Angular acceleration of the wheel can be written as= change in angular velocity /time interval
= ( 4.00 - (-6.00))/10 rad/s²
= 1.0 rad/s²
Hence, angular velocity becomes zero at time = ( 0 - ( -6))/1.0 s = 6 s.
So, during t = 0 to t = 6s, the clockwise angular velocity of the wheel decreases from 6.00 rad/s to 0.00 rad/s and during t = 6s to t = 10s , the counterclockwise angular velocity of the wheel increases from 0.00 rad/s to +4.00 rad/s.
Hence, the time interval during which the speed of the wheel is increasing is = 10 s - 6 s = 4 s.
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Consider a relation R(A, B, C, D) with four attributes A, B, C, and D. These four attributes have values that are real (or float) numbers. Attribute A is the primary key of relation R. We have: ⢠A hash index on attribute B. Additionally, we know that: ⢠R has 100,000 tuples, and ⢠There are 10 tuples of R per disk block.
The super keys of the relationship if a relation R(A, B, C, D) with four attributes A, B, C, and D is 8.
What is attribute?The quality of a feature is referred to as an attribute. The theory of attributes is concerned with the calculation of qualitative forms of qualities using quantitative measures. As a result, the characteristic requires slightly different types of statistical analyses than the variables do.
The given data,
Given three functional dependencies,
AB → C
BC → D
C → E
Finding the key of the relation, Compute closure of attribute,
{AB}⁺ = {A, B, C, D, E} {BC}⁺ = {B, C, D, E} {C}⁺ = {CE}
Only one candidate key is possible for a given relation = AB
Super keys of the relation = 2 (Total number of attributes in relations - Total number of attributes in each key).
Super keys of the relation = 2⁽⁵⁻²⁾
Super keys of the relation = 2³ = 8 keys
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A length of wire is connected to a 9.0 V power pack and an ammeter. The reading on the ammeter is 0.25 A.
Calculate the resistance of the wire. Give the unit.
The resistance of the wire, given that it is connected to a 9.0 V power pack and an ammeter is 36 ohms
How do I determine the resistance?From Ohm's law, we understood that the voltage, current and resistance are related according to the following formula:
Voltage (V) = Current (I) × resistance (R)
V = IR
Using the above formula, we can obtain the resistance of the wire as follow:
Voltage (V) = 9.0 VoltsCurrent (I) = 0.25 AResistance (R) = ?Voltage (V) = Current (I) × resistance (R)
9 = 0.25 × resistance
Divide both sides by
Resistance = 9 / 0.25
Resistance = 36 ohms
Thus, we can conclude that the resistance of the wire is 36 ohms
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consider the following two-step process. heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4 atm. then the gas expands at constant pressure, from a volume of 5.9 l to 9.3 l, where the temperature reaches its original value. (see figure(figure 1)).
(a) The gas moves from point a to point b in an isochoric process in which the volume stays constant.
The work done when the gas moves from point A to point B is Wab = PV = 0.
The labor involved in getting the gas to boil, Wbc = PV = 1.4. (9.3 - 5.9) L.atm = 4.76 1 L.atm is equal to 101.325 J.
Work completed, ∆W = 101.325 × 4.76 = 482.3 J
Therefore, the process' overall work was a, b, and c.
Wtotal = 0 plus 482.3 J = 482.3 J (Ans) (Ans)
(b) As previously stated, point C is where the gas temperature returns to its initial value.
As a result, in the process ac through b, the gas doesn't undergo any temperature change.
Tfinal = Tinitial
Therefore, internal energy change U = 0.
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possibly the most cataclysmic event to occur in nature is . group of answer choices a nova a supernova hydrogen burning electron degeneration
A nova or supernova may be the most catastrophic occurrence in all of nature.
What makes up an electron?A negatively charged subatomic particle called an electron can either be free or attached to an atom (not bound). One of the three main types of particles in an atom is an electron that is attached to it; the other two are protons and neutrons.
What purposes do electrons serve?For creating cross-platform desktop apps using HTML, CSS, and JavaScript, GitHub developed the open source library called Electron. Chromium and Node are combined to create Electron, which does this. Apps may be produced for Mac, Windows, and Linux and combined with JavaScript into a single runtime.
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Given the temperature data shown, which of these ecosystems is definitely in the northern hemisphere
answer choices
Daly Waters
Iquitos
Tindouf
These are all in the southern hemisphere
The ecosystem that is present in the northern hemisphere is Tindouf
Tindouf is the capital of Algeria's Tindouf province, a city close to the borders of Mauritania, Western Sahara, and Morocco which is located in the northern hemisphere. From the chromatogram drawn by Teresa Glass, we concluded that the city of Tindouf, Algeria is a desert biome with very low winter precipitation and high temperatures. This region is of strategic importance. It has an Algerian military base and airport, with regular flights to Algiers and other domestic destinations. Garet Djebilet's settlement is located in his Tindouf municipality near the border with Mauritania. The settlement has an iron mine and an abandoned airport, and is located about 70 kilometers northwest of Awinetbel his Egla.
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part j bulb r4 is now removed from the circuit, leaving a break in the wire at its position. what is the current in the bulb r1 ? express your answer in amperes. templatessymbols undoredoresetkeyboard shortcutshelp i
I2 = V / R2 = 0.678 A ; I3 = V / R3 = 0.678 A are the current flows in R2 and R3.
Here R1 = R2 = R3 = R4 = 4.43Ω
And E = 9.01 V
When we removed the bulb bearing Ru, the equivalent circuit now becomes as shown.
Now R2 and R3 are in parallel, so their equivalent resistance
1/Rp = 1/R2 + 1/R3
Rp = 2.215 Ω
Again, R1 is connected Rp in series so equivalent resistance
R = R1 + Rp = 6.645 Ω
Current through ‘R1’ is
I1 = V / R = 9.01 / 6.645 = 1.356 A
Potential across R2 and R3 is
V = E – I1R1 = 3.0033V
So current through R2
I2 = V / R2 = 0.678 A
Current through R3
I3 = V / R3 = 0.678 A
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A capacitor and a resistor are connected in series across an AC generator, as shown in Figure MCQ21.9. After the switch is closed, which of the following state- ments is true? (a) The voltage across the capacitor lags the current by 90°. (b) The voltage across the resis- tor is out of phase with the current. (c) The voltage across the capacitor leads the current by 90°. (d) The current decreases as the frequency of the generator is increased, but its peak voltage remains the same. (e) none of these
Over an AC generator, a series connection between a capacitor and a resistor is made. The voltage across the capacitor is 90 degrees behind the current.
What is the meaning of voltage?Voltage is the pressure from the power source of an electrical circuit that drives charged electrons (current) through a conducting loop, allowing them to perform tasks like lighting a lamp. Briefly stated, voltage equals pressure and is measured in volts (V).
How do current and voltage work?The energy per unit charge is known as voltage, also known as electromotive force. Voltage is the difference in electric potential between two locations, to put it another way. The pace at which an electric charge flows is known as current.
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In an experiment, a student measured the volume of a substance while the mass was changed. The student measured up to five kilograms. The graph of the data is plotted below.
A volume versus mass graph is shown with mass on the vertical axes from 1 to 10 kilograms and volume on the horizontal axis from 1 to 5 milliliters. A line from the origin through all points and beyond.
Which of the following is an error the student made in creating an accurate graph?
The axes and graph are based only on measured values.
The axes are labeled with the incorrect variables.
The plotted points do not show all data collected.
The title has the incorrect order for the variables.
The title has the incorrect order for the variables.
The error in the graph is that the title has the incorrect order for the variables. Therefore, option D is correct.
Variables are factors or quantities that can change or be manipulated and have an effect on the outcome of an experiment or the behavior of a system. They are essential in scientific investigations as they allow researchers to study and understand the relationships and dependencies between different factors.
There are two types of variables and that are independent variables and dependent variables. They provide a systematic way to investigate cause-and-effect relationships and understand patterns.
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A baseball is popped straight up into the air and has a hang-time of 6.25 S.
Determine the height to which the ball rises before it reaches its peak. (Hint: the
time to rise to the peak is one-half the total hang-time.)
Answer:
To determine the height to which the ball rises before it reaches its peak, we need to know the initial velocity of the ball and the acceleration due to gravity. Let's assume the initial velocity of the ball is v and the acceleration due to gravity is g.
The time it takes for the ball to reach its peak is one-half the total hang-time, or 1/2 * 6.25 s = 3.125 s.
The height to which the ball rises can be calculated using the formula:
height = v * t - (1/2) * g * t^2
Substituting in the values we know, we get:
height = v * 3.125 s - (1/2) * g * (3.125 s)^2
To solve for the height, we need to know the value of v and g. Without more information, it is not possible to determine the height to which the ball rises before it reaches its peak.
Explanation:
Answer:
Approximately [tex]47.9\; {\rm m}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance on the baseball is negligible.)
Explanation:
If the air resistance on the baseball is negligible, the baseball will reach maximum height at exactly [tex](1/2)[/tex] the time it is in the air. In this example, that will be [tex]t = (6.25\; {\rm s}) / (2) = 3.125\; {\rm s}[/tex].
When the baseball is at maximum height, the velocity of the baseball will be [tex]0[/tex]. Let [tex]v_{f}[/tex] denote the velocity of the baseball after a period of [tex]t[/tex]. After [tex]t = 3.125\; {\rm s}[/tex], the baseball would reach maximum height with a velocity of [tex]v_{f} = 0\; {\rm m\cdot s^{-1}}[/tex].
Since air resistance is negligible, the acceleration on the baseball will be constantly [tex]a = (-g) = (-9.81\; {\rm m\cdot s^{-2}})[/tex].
Let [tex]v_{i}[/tex] denote the initial velocity of this baseball. The SUVAT equation [tex]v_{f} = v_{i} + a\, t[/tex] relates these quantities. Rearrange this equation and solve for initial velocity [tex]v_{i}[/tex]:
[tex]\begin{aligned}v_{i} &= v_{f} - a\, t \\ &= (0\; {\rm m\cdot s^{-1}}) - (-9.81\; {\rm m\cdot s^{-2}})\, (3.125\; {\rm s}) \\ &\approx 30.656\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
The displacement of an object is the change in the position. Let [tex]x[/tex] denote the displacement of the baseball when its velocity changed from [tex]v_{i} = 0\; {\rm m\cdot s^{-1}}[/tex] (at starting point) to [tex]v_{t} \approx 30.656\; {\rm m\cdot s^{-1}}[/tex] (at max height) in [tex]t = 3.125\; {\rm s}[/tex]. Apply the equation [tex]x = (1/2)\, (v_{i} + v_{t}) \, t[/tex] to find the displacement of this baseball:
[tex]\begin{aligned}x &= \frac{1}{2}\, (v_{i} + v_{t})\, t \\ &\approx \frac{1}{2}\, (0\; {\rm m\cdot s^{-1}} + 30.565\; {\rm m\cdot s^{-1}})\, (3.125\; {\rm s}) \\ &\approx 47.9\; {\rm m}\end{aligned}[/tex].
In other words, the position of the baseball changed by approximately [tex]47.9\; {\rm m}[/tex] from the starting point to the position where the baseball reached maximum height. Hence, the maximum height of this baseball would be approximately [tex]47.9\; {\rm m}\![/tex].
Is the answer A or D?
Two identical cars, car 1 and car 2, are moving in opposite directions on a straight road. The position of each car as a function of time is represented in the graph. What is the speed of the center of mass of the two-car system?
O Zero
O 10 m/s
O 20 m/s
O 40 m/s
The required speed of the center of mass of the two-car system is 10 m/s.
Option(2) is corret.
What is speed?The reason is simple. Velocity is the percentage of time an object moves along a path, and Velocity is the speed and direction of an object's movement.
The mathematical calculation of velocity is relatively simple, the average velocity of an object is calculated by dividing the distance traveled by the time it took the object to travel that distance. Velocity, on the other hand, is mathematically complex and can be calculated in different ways depending on what information is available about the object's motion. In its simplest form, the average velocity is calculated by dividing the change in position (Δr) by the change in time (Δt).
According to graph:Let the mass of cars which is same is M,
Speed (V1) = 30 m/s
Speed (V2) = -10 m/s
Then,
Speed of center of mass = MV1 + MV2/2M
Speed of center of mass = M(30) + M(-10)/2M
Speed of center of mass = 30M - 10M/2M
Speed of center of mass = 20M/2m
Speed of center of mass = 10 m/s
Thus, Speed of center of mass is 10 m/s
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the position of the 10-kg rod ab is controlled by the 2-kg block shown, which is slowly moved to the left by the force p. knowing that there is not friction between all surfaces of contact, calculate the magnitude p of the force for values of x from 900 to 100 mm, using 100-mm decrements. plot p vs x and determine the maximum and minimum values of p and the corresponding values of x
The highest possible The value of a graph, also known as the global maximum, is the location where the graph's y value achieves its absolute maximum.
What plot values of p and the corresponding values of x?To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f”(x). The second derivative will have a minimal value if it is positive.
The two blocks are thought to be in a balance. If we force P to go to £2.69, then there is no maximum value and one piece equals zero. Zero is less than that, hence the system ought to be in equilibrium. If the force p is in at £2.69, then it must be of equal brands. When everyone is balanced.
Therefore, The maximum value for the entire function is at this point. The location on a graph where the y-coordinate has the lowest value is known as the minimal value.
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a block of mass 3.2kg slides from rest a distance d down a frictionless incloine at angle 30 where it runs into a spring of spring constatn 431
When there is compression of 3.63 cm in the spring , block will have maximum velocity. there after its speed will start decreasing.
What is potential energy of a spring?
When spring is stretched, it undergoes displacement. It comes to its equilibrium position when force is removed. So, it exerts an equal and opposite force When it is stretched. Work is done by this force that is stored in the form of potential energy.
Since potential energy = force × displacement
and, force = spring constant × displacement
So, potential energy = spring constant × (displacement)²
According to the given question:
a ) work done by gravitational force
= mg sinθ ( d + .21)
Potential energy stored in compressed spring
= 1/2 k x²
= .5 x 431 x ( .21 )²
= 9.5
According to conservation of energy
mg sinθ ( d + .21) = 9.5
3.2 x 9.8 x sin 30( d + .21 ) = 9.5
d = 40 cm
b )
As long as mg sin30 is greater than kx ( restoring force ) , there will be acceleration in the block.
mg sin30 = kx
3.2 x 9.8 x .5 = 431 x
x = 3.63 cm
When there is compression of 3.63 cm in the spring , block will have maximum velocity. there after its speed will start decreasing.
Complete question:
A 3.20 kg block starts at rest and slides a distance d down a frictionless β = 30.0 ◦ incline, where it runs into a spring with spring constant k = 431 N/m. The block slides an additional 21.0 cm before it is brought to rest momentarily by compressing the spring. (a) What is the value of d? (b) Where is the speed of the block at the maximum value?
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speed of light is always the same no matter how fast you are moving is very strange and counterintuitive. t/f
The statement "the speed of light is always the same no matter how fast you are moving" is true. This phenomenon is known as the constancy of the speed of light.
According to the theory of relativity, the speed of light in a vacuum is a constant value that is independent of the motion of the observer. This means that no matter how fast you are moving, you will always measure the speed of light to be the same value.
This idea may seem strange and counterintuitive, but it has been experimentally verified and is now a fundamental principle of modern physics. It has important consequences for our understanding of the nature of space and time, and it has played a key role in the development of many important scientific theories, including the theory of relativity.
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28. A car is traveling east at an unknown initial velocity. Without changing directions, it accelerates at 0.75 m/s²
for a distance of 300 m, increasing its velocity to 30 m/s. What was the initial velocity of the car?
Answer: 13 m/s.
Explanation: To solve this problem, we need to use the equation for motion with constant acceleration:
d = v₀t + 1/2 at²
where d is the distance traveled, v₀ is the initial velocity, t is the time it takes to travel that distance, and a is the acceleration.
Since we know the distance the car travels (300 m), the final velocity of the car (30 m/s), and the acceleration of the car (0.75 m/s²), we can solve for the initial velocity. We just need to rearrange the equation to solve for v₀:
v₀ = (d - 1/2 at²) / t
In this case, we can plug in the known values to find the initial velocity:
v₀ = (300 - 1/2 * 0.75 * t²) / t
Since the final velocity of the car is 30 m/s and the acceleration is 0.75 m/s², we can use the equation for motion with constant acceleration to find the time it takes for the car to travel 300 m:
v = v₀ + at
30 = v₀ + 0.75t
Rearranging to solve for t, we get:
t = (30 - v₀) / 0.75
Substituting this value for t in the equation for the initial velocity, we get:
v₀ = (300 - 1/2 * 0.75 * ((30 - v₀) / 0.75)²) / ((30 - v₀) / 0.75)
This simplifies to:
v₀ = (300 - 1/2 * 0.75 * (900 - 2v₀) / 0.75) / (30 - v₀)
which simplifies further to:
v₀ = (300 - 675 + v₀) / (30 - v₀)
Solving for v₀, we get:
v₀ = -375 / -29
which simplifies to:
v₀ = 13 m/s
Therefore, the initial velocity of the car is 13 m/s.
what is the work of a fuse in a socket
Answer:
The fuse in a plug is a safety device designed to protect the lead rather than the appliance. It is a deliberate weak link in a circuit which will 'blow' if an electrical appliance or extension lead draws too much current due to either an overload or a fault.