The maximum velocity of the sphere when it will reach the ground will be [tex]\sqrt{\dfrac{10gh}{7} }[/tex]. Thus, option A is correct.
What are the lowest and highest speeds?A minimum velocity is present at a position where acceleration is both negative to the left and positive to the right. A maximum velocity is at a location where acceleration is positive to the left and negative to the right.
The displacement diminishes as the mass comes closer to the equilibrium position, which also results in a decrease in the restoring force and acceleration. There is no restoring force when the mass reaches the equilibrium position. Since there is no acceleration, the mass is travelling at its fastest possible rate.
For the maximum velocity of the sphere when it reaches the ground, the loss in gravitational potential energy is equal to the gain in translational kinetic energy and rotational kinetic energy,
[tex]$ \Rightarrow \text{ mgh} = \frac{1}{2} mv^2 + \frac{1}{2} I \omega^2[/tex]
[tex]$ \Rightarrow \text{ mgh} = \frac{1}{2} mv^2 + \frac{1}{2} \left(\frac{2}{5}mR^2\right) \omega^2[/tex]
[tex]$ \Rightarrow \text{ mgh} = \frac{1}{2} mv^2 + \frac{1}{2} \times \frac{2}{5}m \times R \times R \times \omega \times \omega[/tex]
From the no-slip condition:
v = Rω
So, [tex]\mathrm{ R \times R \times \omega \times \omega = v \times v = v^2 }[/tex]
[tex]$ \Rightarrow \text{ mgh} = \frac{1}{2} mv^2 + \frac{2}{10} mv^2[/tex]
[tex]$\mathrm{ \Rightarrow \text{ mgh} = \frac{5}{10} mv^2 + \frac{2}{10} mv^2}[/tex]
[tex]$\mathrm{ \Rightarrow \text{ mgh} = mv^2\left(\frac{5 + 2 }{10} \right)}[/tex]
[tex]$\mathrm{ \Rightarrow \text{ mgh} = mv^2\left(\frac{7 }{10} \right)}[/tex]
[tex]$\mathrm{ \Rightarrow \frac{ mgh}{mv^2} = \left(\frac{7 }{10} \right)}[/tex]
[tex]$\mathrm{ \Rightarrow 7{v^2} ={10} gh }[/tex]
[tex]$\mathrm{ \Rightarrow {v^2} = \frac {10 gh} {7}}}[/tex]
[tex]$ \Rightarrow \text v = \sqrt{\frac{10gh}{7} }[/tex]
Thus, the maximum velocity of the sphere when it will reach the ground will be [tex]\sqrt{\dfrac{10gh}{7} }[/tex]. Thus, option A is correct.
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Electric dipole field] A positive point charge and a small electric dipole are arranged as shown in the figure. a) Find the exact formula for the total force exerted on the dipole by the charge Q. b) Derive an approximate formula for d« r. You should find that the force varies as x-3. [Use the Taylor expansion] c) What would be different if the dipole were oriented the other way? Give a qualitative explanation. Q -4 +9 X d
F = F1 - F2 = kQq/x^2 - kQ(-q)/x^2 = 2kQ*q/x^2
The force varies as x-3, since the second term is proportional to (d/x)^2 and the third term is proportional to (d/x)^4.
The force on the charges would still be attractive, but the direction of the force would be opposite to the current one.
What is dipole and derive the formula for total force?a)Coulomb's law, which states that the force a point charge exerts on another point charge is proportional to the product of the charges and inversely proportional to the square of the distance between them, can be used to determine the total force Q exerts on the electric dipole.The electric dipole consists of two point charges: a positive charge +q and a negative charge -q, separated by a small distance 2d.The force exerted on the positive charge by the charge Q is given by Coulomb's law as:F1 = kQq/x^2The force exerted on the negative charge by the charge Q is also given by Coulomb's law as:F2 = kQ(-q)/x^2The net force exerted on the dipole is the vector sum of the forces on the individual charges.F = F1 - F2 = kQq/x^2 - kQ(-q)/x^2 = 2kQ*q/x^2Where k is Coulomb's constant = 1/4πε, q is the magnitude of the charge on each point charge, x is the distance between the charge Q and the center of the dipole.b) To derive an approximate formula for d«r, we can use a Taylor series expansion of the function 2kQ*q/x^2.2kQq/x^2 = 2kQq*(1 - (d/x)^2 + (d/x)^4 - (d/x)^6 + ...)The first term (2kQ*q) is the force when the dipole is at point x = 0. The second term is the correction due to the displacement of the dipole along x-axis. The third term is the correction due to the displacement of the dipole along y-axis, and so on.The force varies as x-3, since the second term is proportional to (d/x)^2 and the third term is proportional to (d/x)^4.c) If the dipole were oriented the other way, the direction of the force would be reversed, but the magnitude of the force would be the same. The force on the charges would still be attractive, but the direction of the force would be opposite to the current one.To learn more about electric dipole refer:
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a stone of mass m is dropped and falls freely under the influence of gravity. ignoring any effects of air resistance, which one of the following expressions gives the momentum of the stone as a function of time t? the local acceleration due to gravity is g. a gt b 1/2 gt2 c 1/2 mgt2 d mg e mgt
The correct answer is b) m gt. When a stone of different mass Is dropped, it falls freely due to gravity.
Describe mass in mathematics with an example.
The amount of material that make up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, any chair, your bedroom, a football, weight glass, and even air.
As we know:
v = u + at
=> v = 0 + gt = gt
Hence change in momentum = ∆mv
=> ∆P = m∆v
=> ∆P = m (v-u)
=> ∆P = m gt
How does physics quantify mass?
The unit of measurement for mass, or mass in kilograms, is matter. A bird's bulk remains constant. No matter where you weigh something—on Heaven, the Moon, or Mars—it always weighs 15 grams.
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Complete question
A stone of mass m is dropped and falls freely under the influence of gravity. Ignoring air resistance, which of the following expressions given the momentum of the stone as function of time t? (Pleas show all work)
a) (1/2) mgt²
b) m gt
c) (1/2) gt²
d) gt
rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest.rank from largest to smallest. to rank items as equivalent, overlap them. if the ranking cannot be determined, check the box below.
To rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest, we need to consider the mass and velocity of each vehicle.
What is momentum and how the rank the automobile based on it?An object's momentum is equal to its mass times its velocity.
Therefore, a larger mass or a higher velocity will result in a larger momentum.
The ranking of the automobiles based on momentum would be as follows:
Car 1 (High mass and high velocity)
Car 3 (High mass and low velocity)
Car 4 (Low mass and high velocity)
Car 2 (Low mass and low velocity)
In this case, Car 1 has the highest momentum because it has high mass and high velocity. Car 3 also has high mass but lower velocity than Car 1 so its momentum is less.
Car 4 has low mass but high velocity than Car 3 so its momentum is less than Car 3. Car 2 has both low mass and low velocity so it has the lowest momentum.
It's worth noting that if we don't have the mass and velocity information of these vehicles it would be impossible to determine the ranking.
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Complete question is:
Rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest. Rank from largest to smallest. To rank items as equivalent, overlap them. If the ranking cannot be determined, check the box below. Reset Help 500 kg 2000 kg 1000kg 1000 kg 4000 kg 500 kg 20 m/s 10m/s 5 m/s 20 m/s 10 m/s 5 m/s smallest largest.
For the beam shown, determine (a) the maximum tensile and compressive bending stresses, (b) the maximum shear stress due to shear force V, and (c) the maximum shear stress in the beam. Plot the bending stress and the shear stress profiles.
The maximum tensile and compressive bending stresses in the beam are 5294 psi and -7456 psi, respectively. The neutral axis's maximum shear stress is 25350, which is induced by V at B, is 1875 psi.
The maximum shear stress measured in the beam is 3728 psi. Shear stress is the portion of a stress that is parallel to the cross section of a material. It is brought on by the shear force, a component of the force vector that is perpendicular to the cross section of the material. When a material is under compression, a compressive stress is being applied to it.
-18000(2.5)/8.5 = 5294 psi is the highest tensile bending stress.
Maximum compressive bending stresses are 25350(2.5)/8.5, which equates to -7456 psi.
Maximum bending force = 7456/2 = 3728 psi
Maximum shear stress = 3900(13) - 300(13)(13/2)
Maximum shear stress = 25350
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at the time a cup of chili is served, its temperature is 170 degrees fahrenheit. the chili's temperature is modeled by the function c, where c(t) is measured in degrees fahrenheit and t is measured in minutes. the rate at which the temperature of the chili is decreasing is given by c(t)
The rate at which the temperature of the chili is decreasing is given by
c(t)=[tex]22e^{-0.05t^{2} }[/tex] is 77.267⁰ F.
What do you mean by rate of change of temperature?The rate of change of temperature, also known as the temperature gradient, is a measure of how quickly the temperature of a system is changing at a given point in space and time. It is typically measured in units of degrees Celsius per second or degrees Fahrenheit per second. The temperature gradient is a vector quantity, with the direction of the gradient pointing in the direction of the greatest temperature change. The magnitude of the gradient is a measure of how quickly the temperature is changing in that direction. The rate of change of temperature can be positive, negative, or zero. A positive rate of change of temperature means that the temperature is increasing, a negative rate of change of temperature means that the temperature is decreasing
Rate of change of temperature over 0 [tex]\leq[/tex] t [tex]\leq[/tex] 5.
[tex]\int\limits^5_0 {c(t)} \, dt = 22\int\limits^5_0 {e^{0.05t^{2} } } \, dt[/tex]
using numerical integration we get value of
[tex]\int\limits^5_0 {e^{0.05t^{2} } } \, dt=3.51211\\\int\limits^5_0 {c(t)} \, dt= 22* 3.51211=77.26657= 77.267^{0} F[/tex]
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A student swings a ball at the end of a string of length R in a vertical circle as shown. The ball moves with the minimum speed necessary to complete a circular path at point 1. Consider the system of the ball. In terms of the mechanical energy of the system, which of the following claims is correct, and why? The system is open, because the ball is able to complete a full revolution around the circle. B The system is open, because a net force is exerted on the ball as it travels in a circle. C The system is closed, because the ball is able to complete a full revolution around the circle. The system is closed, because the speed of the ball remains constant as it travels in the vertical circle.
Previous question
Because a net force is applied to the ball as it travels in a circle, the ball moves at the slowest possible speed to complete a circular path when the system is open.
What does circular motion refer to?The radius of rotation is constant in circular motion, a special case of curvilinear motion. There is an acceleration in this instance toward the cente of 2r. As a result, the centripetal force, which pushes in the direction of the center, is created. The centrifugal reaction is how this force is reacted to.
Describe circular motion with an example.Circular motion is defined as the movement of a body in a circle. Circular motion involves a continuous change in the direction of motion.
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Macmillan Learning
While standing at the edge of the roof of a building, a man throws a stone upward with an initial speed of 6.07 m/s. The stone
subsequently falls to the ground, which is 18.1 m below the point where the stone leaves his hand.
At what speed does the stone impact the ground? Ignore air resistance and use g = 9.81 m/s² for the acceleration due to gravity.
impact speed:
How much time is the stone in the air?
elapsed time:
m/s
The stone is in the air for a total of 2.76 seconds, rising and falling for 0.68 seconds and 2.08 seconds, respectively.
How much time is the stone in the air?The stone will first rise till it reaches its highest point before beginning to descend until it touches the ground. Therefore, we can apply equation to determine the time increasing: Where Vf is the ultimate speed, Vi is the beginning speed, an is the acceleration, and t is the time, Vf = Vi + a*t. A = -g = -9.81 m/s2 in this instance because the stone defies gravity's pull. t = 6.71/9.81 = 0.68 seconds because 0 = 6.71 - 9.81*t The upward distance is calculated as follows: d = Vi*t + 1/2*a*t2 = 6.71*0.68 + 1/2*(-9.81)*0.682 d = 4.59-2.29 = 2.29 metres. The stone then begins to descend until it reaches the earth, which is 18.9 + 2.29 metres below, and it moves at a speed of 9.81 m/s2 since the stone moves in the same direction as gravity:t = 2.08 seconds since d = Vi*t + 1/2*a*t2 = 0*t+1/2*9.81*t2 = 21.19 = 4.905*t2
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the measure of how hot or cold an object is relative to another is its _____ , whereas ____ is the energy that flows between two objects.
Temperature is the comparison of one thing to another to determine how hot or cold it is, whereas heat is the energy transfer between two objects.
The degree to which an object is hot or cold is measured by its temperature. A thing's temperature describes how hot or cold it is. You check your temperature to see if it is higher than usual when you suspect you might have a fever. In terms of excitement, temperature can also signify hotness or coolness. Heat is the result of the movement of kinetic energy within a material or an item, or from an energy source to a material or an object. Radiation, conduction, and convection are the three mechanisms through which such energy can be transferred.
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DUE SOON PLEASE HELP. I GIVE BRIANLEST.
(a) The missing parts of the circuit are total current (I_T) 2.31 A, total resistance (R_T) 45.01 ohms, voltage 1 (V₁) 19 V, resistance 1 (R₁) 8.23 ohms, resistance 2 (R₂) 20.78 ohms, and the current in part of the circuit is the same with a value of 2.31 A.
(b) The voltage drop at resistor 1 is 19 V.
What is the equivalent current in the circuit?
The current flowing in each bulb in a series circuit is equal and it is calculated as follows;
I (tot) = I₁ = I₂ = I₃
I₃ = V₃ / R₃
I₃ = ( 37 V ) / ( 16 ohms )
I₃ = 2.31 A
The missing Voltage of the circuit is calculated as follows;
V₁ = VT - ( V₂ + V₃ )
V₁ = 104 V - ( 48 V + 37 V )
V₁ = 19 V
The missing resistance of the circuit is calculated as follows;
R₁ = V₁ / I₁
R₁ = ( 19 V ) / ( 2.31 A )
R₁ = 8.23 ohms
R₂ = V₂ / I₂
R₂ = ( 48 V ) / ( 2.31 A )
R₂ = 20.78 ohms
The total resistance of the circuit is calculated as follows;
R (t) = R₁ + R₂ + R₃
R (t) = 8.23 + 20.78 + 16
R (t) = 45.01 ohms
The voltage drop at resistor 1 = V₁ = 19 V
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use least squares regression to fit a 0th degree polynomial to the following data: where . what is the 0th degree polynomial solution?
A polynomial with zero coefficients is one that has all of its components equal to zero. In other words, the degree of a zero polynomial seems to be either undefined or set to -1.
What does the 0 in a polynomial mean?
The zeros of a polynomial, p(x), are all x-values that make it equal to zero. They intrigue us for a number of reasons, such as the fact of they reveal the polynomial's x-intercepts on the graph. We will also see that they are related to a polynomial's factors.
What exactly is a quadratic of degree zero?
When all of the factors in a polynomial have degrees of 0, it is said to have zero degrees. Examples include 6 x 0 & 9 a 0.Therefore, any number is an usually negligible polynomial, whether it is positive or negative.
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Complete question
Is there a way, given a set of values (x,f(x)), to find the polynomial of a given degree that best fits the data?
I know polynomial interpolation, which is for finding a polynomial of degree n given n+1 data points, but here there are a large number of values and we want to find a low-degree polynomial (find best linear fit, best quadratic, best cubic, etc.). It might be related to least squares...
More generally, I would like to know the answer when we have a multivariate function -- points like (x,y,f(x,y)), say -- and want to find the best polynomial (p(x,y)) of a given degree in the variables. (Specifically a polynomial, not splines or Fourier series.)
Both theory and code/libraries (preferably in Python, but any language is okay) would be useful.
Which of the following is the major difference between the inner planets as a group and the outer planets as a group?composition
Now, the inner planets are closer to the sun and are rocky, the outer planets are far from the Sun and are mostly made of gases.
The composition, which includes one of the following, is the primary distinction between the outer planets as a group and the inner countries as a group.
Which planet most closely resembles Earth?
Venus and Mars are the two planets that are closest to Earth, though in different ways. Dimensions, average density, volume, and surface gravity of Venus and Earth are strikingly similar. But in other ways, Earth and Mars are the most similar.
Which planet is the best place to live?
Mars has a small amount of atmosphere that can protect people from solar and cosmic radiation, bearable temperatures, and liquid water. The gravity on Mars is 38% greater than that on Earth.
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write a statement that describes the relationship between the force you applied to the spring and the extent to which it was compressed
The amount of force applied to the spring is directly proportional to the extent to which it is compressed. As more force is applied,the spring will compress more as less force is applied,the spring will compress less.
What is force?Force is an influence that causes a physical object to change its motion, direction, or shape. It can be thought of as a push or pull on an object. Force is measured in terms of magnitude, direction, and point of application. Magnitude refers to the amount of force applied, direction refers to the direction in which the force is applied, and point of application refers to the location on an object to which the force is being applied. Some examples of forces include gravity, friction, magnetism, and electricity. All of these forces are at work in the world around us. Force can be used to create motion, change direction, and change shape.
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A torsion pendulum is used as the timing element in a clock as shown. The speed of the clock is adjusted by changing the distance of two small disks from the rotation axis of the pendulum. If we adjust the disks so that they are closer to the rotation axis, the clock runs: a. Faster b. Slower C. No change in speed
If we adjust the disks so that they are closer to the rotation axis, the clock runs slower. So correct option is b.
What do you mean by rotation?All of the particles within an object move in a circular motion around an axis of rotation when the item rotates or is said to have a rotational motion. Consider a bicycle wheel as an example, with the axle serving as the axis of rotation. This is the most basic form of rotational motion. The rotation of ceiling fans, merry-go-rounds, and the earth around its axis are more examples.
A torsion pendulum is a device that consists of a weight attached to a thin rod or wire that is free to rotate about its axis. The speed of the clock is adjusted by changing the distance of two small disks from the rotation axis of the pendulum.
When the disks are closer to the rotation axis, the moment of inertia of the pendulum decreases, which means that the pendulum has less resistance to rotation. This causes the pendulum to rotate more slowly, which results in a slower clock.
On the other hand, if we moved the disks away from the rotation axis, the moment of inertia would increase, making the pendulum more resistant to rotation, thus causing it to rotate more quickly and the clock to run faster.
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true/false. the best example of a shortage is limited amounts of group of answer choices water available for irrigating a crop trees available to manufacture paper towels food available because the trucks carrying it are on strike coal available at a mine due to natural resources running out
The given statement is True. The best example of a shortage is limited amounts of water available for irrigating a crop.
What is irrigating?Irrigating is a type of agricultural practice that involves providing water to plants and crops. The practice of irrigation includes supplying water to land for the purpose of growing crops, increasing crop yields, and maintaining soil fertility.
Irrigation systems help promote efficient use of already-scarce water resources, minimize losses from evaporation, and reduce water wastage. Common irrigation techniques are sprinkler, drip, and surface irrigation. Sprinkler irrigation involves the spraying of water from sprinklers over the crop fields. Drip irrigation is a method of delivering water directly to the root zone of the plant, while surface irrigation is the most common type of irrigation, which involves the spreading of water over the soil surface.
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A bar is hung from the ceiling by its center. On one side a block with a mass of 33kg is hanging 1.5m away from the center, on the other side of the bar a second block is hanging 2.1 from the center. Calculate the mass of the second block.
The mass of the second block is 118.6.
The tension of a hanging mass can be determined in what ways?The equation T = mg + ma is used to determine the force of tension, as we are aware.A net torque about the axis is created when the individual torques combine. The net torque about the specified axis is the sum of the individual torques when the proper sign (positive or negative) is applied to the magnitudes of the individual torques about the specified axis: →τnet=∑i|→τi|.Tension is equal to 2g(m1)(m2)/(m2+m1) for a system with two masses suspended from a vertical pulley, where "g" denotes the gravitational acceleration and "m1" and "m2" denote the masses of the objects.Explanation:
T = 33*1.5 + 33*2.1
= 49.5 + 69.1
= 118.6.
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Consider the hypothesis test below. H0:p1−p2≤0Ha:p1−p2>0 The following results are for independent samples taken from the two populations. Sample 1n1=200pˉ1=0.22 Sample 2n2=300pˉ2=0.16 Use pooled estimator of P. a. What is the pryalue (to 4 decimals)? Use Table 1 from Appendix a.
Give an explanation of null hypothesis and an illustration.
The null hypothesis states that any difference between the chosen characteristics you notice in a set of data is a result of chance. If the expected earnings for the gambling game are actually equal to zero, then any discrepancy between the average earnings in the data and zero, for example, is due to chance.Sample 1 demonstrates that theTo know more about null hypothesis visit:
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What do you mean by the density of ice is 920 kg/m3 ?
Explanation:
The density of ice is given by the mass/volume of a given amount of ice so what they simply mean is that when a particular cup filled with ice is weighed for it's mass and measured for it's volume and further divided by each other you are going to get 920 kilograms per meter cube
assume we had accidentally submerged our cube in such a fashion that a few mm of the cube were actually above the surface of the water. which of the following describes the effect of this poor experimental technique?
The following describes the effect of this poor experimental technique- "the pressure inside the box is lower on top than it is at the bottom. The sides balance one another out, making them equal."
What is pressure?The force applied perpendicularly to an object's surface per unit area over which that force is distributed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units. Pressure is the term for the force acting on a unit area of a surface. It operates perpendicular to the surface being applied pressure to. Pressure is a force and the space that it acts in. Greater force results from smaller area. The concept of pressure is crucial to fluid mechanics and is used to describe a gas's energy in the ideal gas law, among many other physical applications.
Here,
The following describes the effect of this poor experimental technique- "On top of the box, there is less pressure than there is at the bottom. The sides are equal because they counterbalance one another."
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If the stone is thrown downward with a speed of 2 m/s, how long does it take to reach the ground? (round your answer to two decimal places.)
The stone takes 3 seconds to reach the floor as a result. It is crucial to verify motion equations with t = 0 in order to remember any irregularities, if any in the motion.
What does motion mean?In physics, motion is defined as a change in a body's position or orientation over time. Translation is the term for movement across a plane or a curve. Rotation is another motion that modifies a body's orientation.
Describe an abnormality?Anomalies, then, are phenomena that stick out since they appear peculiar or unexpected.
An observation that deviates from the predictions made by a well-established scientific theory Unusual observations may motivate researchers to reevaluate, revise, or develop.
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The isomerization of cyclopropane to propene has an activation energy of 273 kJ/mol. When the reaction is run at 750 K, the rate constant, k_1, is 1.8 times 10^-4 s^-1. What is the value of the rate constant, k_2, at 850 K? A. 3.1 times 10^-2 s^-1 B. 1.2 times 10^-8 s^-1 C. 4.1 times 10^-4 s^-1 D. 2.7 times 10^-3 s^-1
The activation energy of cyclopropane to propene is 273 kJ/mol. At 750 K, the rate constant, k 1, is 1.8 times 10⁻⁴ s⁻¹, while at 850 K, the rate constant, k 2, is 3.1*10⁻² s⁻¹.
T1 = 750 K
T2 = 850 K
K1 = 1.8*10⁻⁴ s⁻¹
Ea = 273 KJ/mol
= 273000 J/mol
use:
ln(K2/K1) = (Ea/R)*(1/T1 - 1/T2)
ln(K2/1.8*10⁻⁴) = (273000/8.314)*(1/750 - 1/850)
ln(K2/1.8*10⁻⁴) = 32836*(1.569*10⁻⁴)
K2 = 3.1*10⁻² s⁻¹
We frequently use the word "energy" in our everyday speech. Energy has a specific physical meaning even if the term is frequently used figuratively. Energy is defined in physics as something's capacity to perform work. Numerous types of energy are possible. Energy is always either kinetic or potential. Let's examine the definition of energy and the many types of energy in detail in this article.
On earth, energy comes in a variety of shapes and sizes. The sun is regarded as the earth's fundamental source of energy. Energy is a quantifiable property that can be transferred from an item to perform work in physics. Thus, the ability to perform any kind of physical action can be described as having energy.
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Athin hoop of mass M. radius R. and rotational inertia MR is released from rest from the top of the ramp of length Labove. The ramp makes se angle with respect to a horizontal tabletop to which the ramp is fixed. The table is height H above the floor. Assume that the hoop rolls without slipping down the ramp and across the table. Express all algebraic answers in terms of given quantities and fundamental constants. (a) Derive an expression for the acceleration of the center of mass of the hoop as it rolls down the ramp. (b) Derive an expression for the speed of the center of mass of the hoop when it reaches the bottom of the ramp. (c) Derive an expression for the horizontal distance from the edge of the table to where the hoop lands on the floor (d) Suppose that the hoop is now replaced by a disk huving the same mess M and radius R. How will the distance from the edge of the table to where the disk lands on the floor compare with the distance determined in part te) for the hoop? Less than The same as Greater than Briefly justify your response
Derive an expression for the speed of the center of mass of the hoop when it reaches the bottom of the ramp.
What is meant by speed ?
Speed is what it means. the speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined.Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.To learn more about speed refer to
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A thin rod extends from
x = 0
to
x = 15.0 cm.
It has a cross-sectional area
A = 8.00 cm2,
and its density increases uniformly in the positive x-direction from 2.50 g/cm3 at one endpoint to 19.5 g/cm3 at the other.
(a)
The density as a function of distance for the rod is given by
= B + Cx,
where B and C are constants. What are the values of B (in g/cm3) and C (in g/cm4)?
B =
g/cm3
C =
g/cm4
(b)
Finding the total mass of the rod requires integrating the density function over the entire length of the rod. The integral is written as follows.
m =
allmaterial
dv =
all x
A dx =
15.0 cm
0
(B + Cx)(8.00 cm2) dx
What is the total mass of the rod (in kg)?
kg
(a) For the density function, the value of B is 2.5 g/cm³ and the value of C is 1.3 g/cm⁴
(b) The total mass of the rod is 1470 g.
What is the density function?The density of the rod is a function of distance and it is given as;
ρ = B + Cx
where;
B and C are constantsρ = 2.5 g/cm³ + (19.5 g/cm³ ) / ( 15 cm ) x
ρ = 2.5 g/cm³ + 1.3 g/cm⁴ x
The total mass of the rod is calculated by integrating the function;
dm = ( B + Cx)(8 cm² ) dx
m = 8B + 8Cx
m = 8Bx + 8Cx² / 2
m = ( 8 x 2.5 x 15 ) + ( 8 x 1.3 x 15² ) / 2
m = 1470 g
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As you travel down the highway in your car, an ambulance approaches you from the rear at a high speed (Figure) sounding its siren at a frequency of 500 Hz. Which statement is correct? (a) You hear a frequency less than 500 Hz. (b) You hear a frequency equal to 500 Hz. (c) You hear a frequency greater than 500 Hz. (d) You hear a frequency greater than 500 Hz, whereas the ambulance driver hears a frequency lower than 500 Hz. (e) You hear a frequency less than 500 Hz, whereas the ambulance driver hears a frequency of 500 Hz.
A fixed distance away from the siren, the ambulance driver can hear the siren's true frequency. A frequency higher than the real 500 Hz will be audible to you because of the shrinking distance between you and the siren.
what is frequency?The quantity of waves passing a fixed place in a unit of time is known as the frequency in physics. A body in harmonic oscillator undergoes how many cycles or vibrations in one unit of time, according to this definition.
How do you determine frequency?Divide the quantity of times the event happens over the period of time to determine the frequency. Example: Anna divides the time by the quantity of page clicks (236). (one hour, or 60 minutes). She discovers that her clickthrough rate is 3.9 per minute.
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A 1,030-kg car is pulling a 285-kg trailer. Together, the car and trailer have an acceleration of 2.00 m/s2 in the positive x-direction. Neglecting frictional forces on the trailer, determine the following. (Indicate the direction with the sign of your answer. Take the forward direction to be positive. Assume the trailer's weight is entirely supported by it's own tires.)
(a) the net force on the car
_______N
(b) the net force on the trailer
_______N
(c) the force exerted by the trailer on the car
________N
(d) the resultant force exerted by the car on the road
magnitude _______ N
direction _________
The net force on the car is 2060N,the net force on trailer is 570N.
What is force?When an object interacts with another object, there is a push or pull applied to the object. An item can accelerate, change direction, or remain in the same location as a result of forces.
How do you determine it?(a) By utilising the equation F=ma, where m is the car's mass and a represents its acceleration, one may calculate the net force acting on the vehicle.
F=(1.030 kg X 2.00 m/s2) = 2060 N
(b) The equation F=ma, where m is the mass of the trailer and an is the acceleration, can also be used to calculate the net force on the trailer.
570 N is equal to F = (285 kg X 2.00 m/s2).
(c) The force the automobile exerts on the trailer is equal to and opposing the force the trailer exerts on the car. The trailer pulls on the car with a force of -570 N since they are going in the same direction.
(d) The force the car exerts on the road is 2060 N since the net force acting on the car is 2060 N.
2060 N in a forward-moving direction (positive x-direction)
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t (minutes) 0 4 9 15 20 W t( ) (degrees Fahrenheit) 55.0 57.1 61.8 67.9 71.0The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W, where W t( ) is measured in degrees fahrenheit and t is measured in minutes. At time t = 0, the temperature of the water is 55 F. ° The water is heated for 30 minutes, beginning at time t = 0. Values of W t( ) at selected times t for the first 20 minutes are given in the table above. (a) Use the data in the table to estimate W′( ) 12 . Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. (b) Use the data in the table to evaluate ( )20 0 W t dt ′ . Using correct units, interpret the meaning of ( ) 20 0 W t dt ′ in the context of this problem. (c) For 0 20, ≤ ≤t the average temperature of the water in the tub is ( ) 20 0 1 . 20 W t dt Use a left Riemann sum with the four subintervals indicated by the data in the table to approximate ( ) 20 0 1 . 20 W t dt Does this approximation overestimate or underestimate the average temperature of the water over these 20 minutes? Explain your reasoning. (d) For 20 25, ≤ ≤t the function W that models the water temperature has first derivative given by Wt t t ′( ) = 0.4 cos 0.06 . ( ) Based on the model, what is the temperature of the water at time t = 25 ?
(a) Rate of change of the temperature of the water at time t = 12 minutes is 2 degrees Fahrenheit per minute. b)Total change in the temperature of the water over 20 minutes is 7.5 degrees Fahrenheit. c)average temperature = 60.5. d) At t = 25, W(25) = W(20) + ∫20 25W′(t)dt = W(20) + ∫20 25(0.4 cos(0.06t))dt
What is theorem of calculus?The fundamental theorem of calculus states that integral of the derivative of a function is equal to difference between function evaluated at the upper and lower limits.
(a) To estimate W′(12), use the formula for the slope of a line between two points: (W(y2) - W(y1)) / (x2 - x1). Using data in the table, estimate W′(12) by taking slope between points (12, 67) and (10, 63) : (67 - 63) / (12 - 10) = 4 / 2 = 2. So, rate of change of the temperature of the water at time t = 12 minutes is 2 degrees Fahrenheit per minute.
(b) To evaluate integral of W′(t) from t = 0 to t = 20; W′(t) = 0.4t + 0.5, so the integral is equal to W(20) - W(0) = (0.420 + 0.5) - (0.40 + 0.5) = 8 - 0.5 = 7.5. Total change in the temperature of the water over 20 minutes is 7.5 degrees Fahrenheit.
(c) To approximate the average temperature of the water over these 20 minutes : (5/20)(55 + 57 + 63 + 67) = (5/20)(242) = 60.5. As the temperature of the water is increasing, average temperature will be greater than temperature of water at the start of the time period and less than temperature of the water at end of the time period, so approximation will overestimate average temperature.
(d) For 20 <= t <= 25, W′(t) = 0.4 cos(0.06t). At t = 25, W(25) = W(20) + ∫20 25W′(t)dt = W(20) + ∫20 25(0.4 cos(0.06t))dt. To find the definite integral we need to evaluate it with the limit from 20 to 25. As the temperature of the water is increasing as the derivative is positive.
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Why is the metric system of units considered superior to most other systems of units?
Oscilloscope trigger problem. The 'trigger' settings determine when the trace begins. Suppose you have displayed a sine wave with V = Vo sin (ωt) on the screen, where Vo = 5V and ω/2π = 5kHz. EXAMPLE:
Suppose you double the amplitude of the wave without changing any oscilloscope settings. What are V and ωt now when the scope is triggered? [Answer: the level hasn't changed so the scope still triggers when V=2.5V V=2.5=10sin(ωt)
ωt=sin^-1(2.5/10)=14.4775121851511 degrees.]
QUESTION:
Assume that you reduce Vo back to 5 V and switch the trigger slope polarity from '+' to '-' without changing the trigger level dial. What are V and ωt when the scope is triggered now?
___ volts
___ degrees
Assume that you reduce Vo back to 5 V and switch the trigger slope polarity from '+' to '-' without changing the trigger level dial. V and ωt when the scope is triggered now 2.5 volts 150 degrees.
An oscilloscope (informally a scope) is a sort of digital take a look at instrument that graphically shows various electrical voltages as a -dimensional plot of one or extra signals as a feature of the time. the main functions are to show repetitive or unmarried waveforms on the screen that might in any other case arise too briefly to be perceived via the human eye.
The displayed waveform can then be analyzed for homes consisting of amplitude, frequency, upward thrust time, time c program language period, distortion, and others. at first, the calculation of these values required manually measuring the waveform in opposition to the scales built into the display of the instrument. current digital units might also calculate and display those residences without delay.
Oscilloscopes are used within the sciences, medicine, engineering, car, and telecommunications industry. general-reason devices are used for the preservation of digital devices and laboratory paintings. unique-motive oscilloscopes may be used to analyze an automobile ignition device or to show the waveform of the heartbeat as an electrocardiogram, for instance.
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The height of a rocket, launched from the ground, is given by the function y = 30t - 5t2, where y is in meters and t is in seconds. An observer is sitting at ground level a distance d from the launch point. If r is the distance between the observer and where the rocket is, show that dr/dt = ((30t - 5t2)(30 - 10t)) / sqrt((30t - 5t2)2 + d2)
Rate of change of r with respect to time is ((30t - 5t^2)(30 - 10t)) / sqrt((30t - 5t^2)^2 + d^2)
What is projectile?Projectile is an object that is propelled by the application of external force and then moves freely under the influence of gravity and air resistance.
Given, height of the rocket is, y = 30t - 5t^2, and distance between the observer and the rocket is r.
As, r = sqrt(d^2 + (y - 0)^2)
So, r = sqrt(d^2 + (30t - 5t^2 - 0)^2)
r = sqrt(d^2 + (30t - 5t^2)^2)
Then, dr/dt = (d^2 + (30t - 5t^2)^2)^(1/2) (2(30t - 5t^2)(-10t + 30)) / (2(d^2 + (30t - 5t^2)^2)^(1/2))
So, dr/dt = (30t - 5t^2)(30 - 10t) / sqrt((30t - 5t^2)^2 + d^2)
Therefore, rate of change of r with respect to time is ((30t - 5t^2)(30 - 10t)) / sqrt((30t - 5t^2)^2 + d^2).
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which of the following statements about the motion of the electrons in the given reference frame will be true at the instant the two electrons reach their minimum separation?
At the instant the two electrons reach their minimum separation, the motion of the electrons in the given reference frame will be that both electrons are momentarily stationary.
This is because, since the electrons are repelling each other, their velocities will be in opposite directions and will cancel out, resulting in no net velocity. As for the acceleration, it will also be zero, since the velocity of the electrons is not changing. Therefore, at the instant the two electrons reach their minimum separation, the motion of the electrons in the given reference frame will be that both electrons are momentarily stationary, with zero velocity and acceleration.
Complete question:
Two electrons, each with mass m and charge q, are released from positions very far from each other. With respect to a certain reference frame, electron A has initial nonzero speed v toward electron B in the positive x direction, and electron B has initial speed 3vtoward electron A in the negative x direction. The electrons move directly toward each other along the x axis(very hard to do with real electrons). As the electrons approach each other, they slow due to their electric repulsion. This repulsion eventually pushes them away from each other.
a)Which of the following statements about the motion of the electrons in the given reference frame will be true at the instant the two electrons reach their minimum separation?
Electron A is moving faster than electron B. Electron B is moving faster than electron A. Both electrons are moving at the same (nonzero) speed in opposite directions. Both electrons are moving at the same (nonzero) speed in the same direction. Both electrons are momentarily stationary.
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Lauren feels a cold coming on, and her friend recommends taking a high dose vitamin C supplement. But Lauren isn't just taking her friend's word for it. Before she takes a supplement, she wants to at least be sure it's safe. Which of the following DRI values would assist Lauren in determining the highest amount of the supplement that would be safe for her to consume? Estimated Average Requirement (EAR) Acceptable Macronutrient Distribution Range (AMDR) Recommended Dietary Allowance (RDA) Tolerable Upper Intake Level (UL)
The term "tolerable upper intake level" (UL) refers to the maximum daily food intake that is most likely to not put almost all members of the general population at risk for negative health impacts.
Which 4 dietary reference intakes are there?
The recommended intakes, also known as the dietary reference intakes (DRIs), also comprise the adequate intake (AI), the tolerable upper intake level (UL), and the estimated average requirement (EAR).
What are the six main dietary requirements?
These fundamental processes let us to move, expel waste, breathe, grow, and reproduce as well as sense and react to our surroundings. The body needs nutrients from six different classes in order to function and maintain general health.
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