The constant acceleration of the green car which passes red color car is 2.81 m/s^2.
In this problem, the initial positions of the red and green cars are xr = 0 and xg = 220 m, respectively, and their initial velocities are vr = 20 km/h and vg = 0. When the red car has a velocity of 20 km/h, the cars pass each other at x = 44.5 m, and when the red car has a velocity of 40 km/h, they pass each other at x = 76.6 m.
We can use these two equations to solve for the acceleration of the green car. First, we convert the velocities from kilometers per hour to meters per second by dividing by 3.6. This gives us vr = 5.56 m/s and vg = 0 m/s.
Then, we can substitute these values into the equation for position and solve for the acceleration. When the red car has a velocity of 20 km/h, the equation becomes:
x = 0 + 5.56t + 1/2at^2
x = 44.5
Solving for a, we find that the acceleration of the green car is a = 2.61 m/s^2.
When the red car has a velocity of 40 km/h, the equation becomes:
x = 220 + 11.11t + 1/2at^2
x = 76.6
Solving for a, we find that the acceleration of the green car is a = 2.61 m/s^2.
When the red car has a velocity of 40 km/h, the equation becomes:
x = 220 + 11.11t + 1/2at^2
x = 76.6
Solving for a, we find that the acceleration of the green car is a = 3.02 m/s^2.
Since the acceleration is the same in both cases, we can take the average of these two values to find the constant acceleration of the green car. The average of 2.61 m/s^2 and 3.02 m/s^2 is 2.81 m/s^2.
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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.
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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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].
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.
if the absolute temperature of an object is tripled, the thermal power radiated by this object (assuming that its emissivity and size are not affected by the temperature change) will
If the absolute temperature of an object is tripled, the thermal power radiated by the object will increase by a factor of 3^4=81.
Increase by a factor of 9 i.e. (3^2). This is because the Stefan-Boltzmann law states that the power radiated by a black body (an object that absorbs all incoming electromagnetic radiation) is proportional to the fourth power of its temperature. Thus, if the temperature of an object is tripled, the thermal power it radiates will increase by a factor of 3^4=81. It's important to note that the emissivity and size of an object can affect the amount of thermal radiation it emits. The emissivity of an object is a measure of how efficiently it radiates energy, and a larger object will generally have a greater surface area, which means it will be able to radiate more energy.
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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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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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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 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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find the resistance between points a and b.
As per the given resistances, the equivalent resistance between points a and b will be equal to 14.43 Ω.
What is Resistance?When an electric current passes through a lightbulb or any other conductor, the conductor presents some resistance to the current.
This resistance is referred to as resistance value and is represented by the letter R. Since every substance has some electrical resistance, when current flows through a conductor, heat is released.
As per the given figure in the question,
Firstly, calculate the total resistance between points d and c,
R₂ = 35 + 56
R₂ = 91 Ω
Now,
R₁ = 22 Ω
R₂ = 91 Ω and,
R₃ = 78 Ω
All are connected in parallel,
[tex]\frac{1}{R_a_b}[/tex] = 1/22 + 1/91 + 1/78
= 5408/78078
[tex]R_a_b[/tex] = 14.43 Ω.
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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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A car can be brought to rest from a speed of 200m/s in a time of 2 seconds calculate average deceleration.
Answer:
The average deceleration of the car can be calculated using the formula for deceleration, which is given by the change in velocity divided by the time over which the change occurs. In this case, the initial velocity of the car is 200 m/s, the final velocity is 0 m/s, and the time over which the change occurs is 2 seconds. Therefore, the average deceleration can be calculated as follows:
Deceleration = (0 m/s - 200 m/s) / 2 s = -100 m/s^2
The negative sign indicates that the deceleration is in the opposite direction to the initial velocity of the car, which is what we would expect in this case, since the car is slowing down. Therefore, the average deceleration of the car is -100 m/s^2.
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.
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 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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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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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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in the following three arrangements each resistor has the same resistance r. rank the equivalent resistances of the arrangements in descending order (largest first).
C. Are B, C, and A in a series? Three layouts are shown, two in parallel and one in series. The resistance of each resistor is same. r. sort in declining order the analogous resistances of the layouts.
Which is better, a capacitor or a resistor?In resistors, electrical energy is transformed into heat that is subsequently dissipated. With negative and positive charges kept apart, capacitors are frequently employed to filter frequencies. Alternative current can be passed through capacitors while direct current is blocked.
Exactly why is everyone resistors used?Electrical resistance is provided by a resistor, a two-terminal electrical component. Resistors are mainly used to split voltages, impede transmission signals, reduce current flow, and bias active components in electronic circuits.
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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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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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Which velocity component is dependent on gravity?
Answer:
Explanation:
Vertical acceleration.
A neutron in a reactor makes an elastic headon collision with the nucleus of an atom initially at rest.
Assume: The mass of the atomic nucleus is
about 11.2 the mass of the neutron.
What fraction of the neutron’s kinetic energy is transferred to the atomic nucleus?
017 (part 2 of 2) 10.0 points
If the initial kinetic energy of the neutron is
6.58 × 10−13 J, find its final kinetic energy.
Answer in units of J.
Answer:
The energy of the system and total momentum are both conserved in an elastic head-on collision. The atomic nucleus receives 1.87 percent of the neutron's kinetic energy and final kinetic energy is 12.3×10-13J.
Explanation:
In elastic head-on collision, the energy of the system and total momentum is conserved.
For the neutron,
m - mass, - initial velocity, - final velocity
For the atom,
M- mass , - initial velocity, - final velocity
Conserved momentum on the head-on collision
mv_i=mv_f+MV_f
v_i-v_f=MmV_f
v_i-v_f=14.9V_f.........(I)
The kinetic energy
v_i^2-v_f^2=14.9V_f^2............(II)
From equation (I) and (II)
(v_i-v_f)/(v_i^2-v_f^2 )=(12v_f^2)/(12v_f^2 )
v_i+v_f=V_f.........(III)
Solve equation (I) and (III) for
v_i=7.9v_f
Now, the fraction of the neutron's kinetic energy transferred to the atomic nucleus,
(1/2 MV_f^2)/(1/2 mv_i^2 )=14.9/7.95=1.87
K2=1.87×6.58×10-13J=12.3×10-13J
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Select the correct answer.
A Kelvin (K) is a unit of measurement in the International System of Units. Which quantity is measured in Kelvin?
Group of answer choices
length
electric current
mass
temperature
weight
Answer: Temperature
Explanation:
The viscous drag (f) between two layers of liquid with surface area of contact (A) in a region of velocity gradient (dv/dx) is given by F=ETA A(dv/dx) where ETA is the co efficient of viscosity of the liquid. what is the dimension of ETA. Hence, write the unit of ETA in terms of the basic unit of S.I
The unit of ETA in terms of the basic units of the SI system is:
ETA = [kg] * [s]⁻¹* [m]⁻¹= kg * s / m
What is the viscous drag about?The dimension of the coefficient of viscosity (ETA) can be determined by using the dimensions of the other variables in the equation:
F = ETA * A * (dv/dx)
The dimension of force (F) is [M] * [L] * [T]⁻², the dimension of surface area (A) is [L]⁻², and the dimension of velocity gradient (dv/dx) is [L] * [T]⁻¹.
Since the equation must be dimensionally consistent, we can set up the following equation:
[M] * [L] * [T]⁻²= ETA * [L]² * [L] * [T]⁻¹
Solving for the dimension of ETA, we get:
ETA = [M] * [T]⁻¹ * [L]⁻¹
Therefore, the basic unit of mass in the International System of Units (SI) is the kilogram (kg), the basic unit of time is the second (s), and the basic unit of length is the meter (m). Therefore, the unit of ETA in terms of the basic units of the SI system is:
ETA = [kg] * [s]⁻¹* [m]⁻¹= kg * s / m
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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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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.
A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop?
The magnitude of the force that must be applied to the wedge must be equal to the weight of the block, or force = mg.
If the block is to remain at a constant height above the tabletop, then the net force acting on it must be zero. The only force acting on the block is the normal force, which is the force exerted by the wedge on the block. Since the block is not accelerating, the normal force must be equal and opposite to the gravitational force acting on the block. This means that the magnitude of the normal force must be equal to the weight of the block, which is mg, where g is the acceleration due to gravity.
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A mild steel ring of 30 cm mean circumference has a cross-sectional area of 6 cm2 and has a winding of 500 turns on it. The ring is cut through at a point so as to provide an airgap of 1 mm in the magnetic circuit. It is found that a current of 4 A in the winding, produces a flux density of 1 T in the air-gap. Find (i) the relative permeability of the mild steel and (ii) inductance of the winding
Inductance of the winding is 69.
What is Inductance?The way a wire coil reacts to changes in electric current through the coil is an example of inductance. The inductance L, which results from Faraday's law, can be expressed in terms of the emf produced to oppose a specific change in current:
Inductors generate a self-induced emf within themselves as a result of their changing magnetic field.
In an electrical circuit, when the emf is induced in the same circuit in which the current is changing this effect is called Self-induction, (L) but it is sometimes commonly called back-emf as its polarity is in the opposite direction to the applied voltage.
Therefore, Inductance of the winding is 69.
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consider a two-stage turbine operating at steady state with reheat at constant pressure between the stages. show that the maximum work is developed when the pressure ratio is the same across each stage. use a cold air-standard analysis, assuming the inlet state and the exit pressure are specified, each expansion process is isentropic, and the temperature at the inlet to each turbine stage is the same. kinetic and potential energy effects can be ignored.
The maximum work is developed when the pressure ratio is the same across each stage as Pi/P2 = P1/Pi
Describe work.
When an object is moved over a distance by an external force, at least some of that force must be applied in the direction of the displacement. That is called work. Work is a measure of energy transfer.
The definition of energy is the capacity for work. The work produced is consistent. There are many different types of energy, including kinetic and potential energy.
The turbine work ,w =(h 1−h a)(h b −h 2 )
=cp [(T 1−Ta)+(T b−T 2 )]
As the temperature at the inlet at each stage is same: T 1=T b
So
turbine work ,w = cp [(T 1−Ta)+(T b−T 2 )]
= cp [2T1-Ta -T2]
= cp*T1[2- Ta/at1 - T2/T1]
Ta/T1 = (Pi/P1)^x
T2/T1 = (P2/Pi)^x
and x =(k-1)/k
So , w =c p*T 1 [2−( P1/Pi)^ x−( Pi/P2)^x ]
In case of maximum work done , dw/di = 0
Substituting it in above equation gives:
P1*P2 = (Pi)^2x
Pi/P2 = P1/Pi
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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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