Answer:
0.32 s
Explanation:
Initial angular speed: [tex]\omega_i = 1.50 \cdot 10^4 rad/s[/tex]
Final angular speed: [tex]\omega_f = 3.35\cdot 10^4 rad/s[/tex]
Angular rotation: [tex]\theta=2.02\cdot 10^4 rad[/tex]
The angular acceleration of the drill can be found by using the equation:
[tex]\omega_f^2 - \omega_i^2 = 2 \alpha \theta[/tex]
Re-arranging it, we find [tex]\alpha[/tex], the angular acceleration:
[tex]\alpha = \frac{\omega_f^2 - \omega_i^2}{2\theta}=\frac{(3.35\cdot 10^4 rad/s)^2-(1.50\cdot 10^4 rad/s)^2}{2(2.02\cdot 10^4 rad)}=22,209 rad/s^2[/tex]
Now we want to know the time t the drill takes to accelerate from
[tex]\omega_i =0[/tex]
to
[tex]\omega_f = 6.90\cdot 10^4 rad/s[/tex]
This can be found by using the equation
[tex]\omega_f = \omega_i + \alpha t[/tex]
where [tex]\alpha[/tex] is the angular acceleration we found previously. Solving for t,
[tex]t=\frac{\omega_f - \omega_i}{\alpha}=\frac{22,209 rad/s^2}{6.90\cdot 10^4 rad/s}=0.32 s[/tex]
What dictates how proteins are assembled in our body?
Proteins in our body are assembled according to the instructions encoded in our DNA. The sequence of amino acids dictates the structure and function of the protein.
Explanation:Proteins in our body are assembled according to the instructions encoded in our DNA. Each gene in the DNA molecule codes for the specific order of amino acids that make up a protein. The sequence of amino acids dictates the structure and function of the protein. Scientists have determined the amino acid sequences and three-dimensional conformation of numerous proteins, providing important insights into how they perform their specific functions in the body.
Glucose molecules provide energy to power the swimming motion of sperm. In this example, the sperm are changing _____.a. Kinetic energy into potential energyb. Kinetic energy into chemical energyc. Chemical energy into kinetic energyd. Chemical energy into potential energy
. Chemical energy into kinetic energyd.
If you push twice as hard against a stationary brick wall, the amount of work you do
Answer:
Zero
Explanation:
The work done on an object is given by:
[tex]W=Fd cos \theta[/tex]
where
F is the force applied on the object
d is the displacement of the object
[tex]\theta[/tex] is the angle between the direction of the force and the displacement
In this problem, you are pushing again a stationary wall: this means that the walls does not move. As a result, the displacement is zero: d=0. Therefore, the work done is also zero: W=0.
Una esfera homogénea de radio r y peso W resbala en un piso bajo la acción de una fuerza horizontal constante P aplicada a una cuerda, como se muestra en la Fig. 1. (a) Demostrar que, si ? es el coeficiente de rozamiento entre la esfera y el piso, la altura h está dada por h = r (1 – ?W/P). (b) Demostrar que la esfera no se encuentra en equilibrio de traslación bajo estas circunstancias. (c) Si se escoge un valor diferente de h, ?se puede lograr que la esfera se encuentre tanto en equilibrio de rotación como de traslación? ?Y si se escoge una dirección diferente para P? Dar una explicación de lo que ocurre.
An electron travels with speed 6.0 106m/s between the two parallel charged plates shown in the figure. The plates are separated by 1.0 cm and are charged by a200 V battery.What magnetic field strength will allow the electron to pass between the plates without being deflected?
Answer:
3.3 mT
Explanation:
First of all, we need to find the strength of the electric field between the two parallel plates.
We have:
[tex]\Delta V=200 V[/tex] (potential difference between the two plates)
[tex]d=1.0 cm=0.01 m[/tex] (distance between the plates)
So, the electric field is given by
[tex]E=\frac{\Delta V}{d}=\frac{200 V}{0.01 m}=2\cdot 10^4 V/m[/tex]
Now we want the electron to pass between the plates without being deflected; this means that the electric force and the magnetic force on the electron must be equal:
[tex]F_E = F_B\\qE=qvB[/tex]
where
q is the electron charge
E is the electric field strength
v is the electron's speed
B is the magnetic field strength
In this case, we know the speed of the electron: [tex]v=6.0\cdot 10^6 m/s[/tex], so we can solve the formula to find B, the magnetic field strength:
[tex]B=\frac{E}{v}=\frac{2\cdot 10^4 V/m}{6.0\cdot 10^6 m/s}=0.0033 T=3.3 mT[/tex]
The magnetic field strength will allow the electron to pass between the plates without being deflected is 0.0033 T.
Electric field strengthThe electric field strength of the electron is calculated as follows;
E = V/d
E = 200/(0.01)
E = 20,000 V/m
Magnetic field strengthThe magnetic field strength is related to electric field in the following formula;
qvB = qE
vB = E
B = E/v
B = (20,000)/(6 x 10⁶)
B = 0.0033 T
Thus, the magnetic field strength will allow the electron to pass between the plates without being deflected is 0.0033 T.
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When an object is lifted 6 meters off the ground, it gains a certain amount of potential energy. If the same object is lifted 12 meters off the ground, its potential energy is
When the object is lifted 6 meters of the ground , then lifted to 12 meters, it is lifted twice as high ( 6 x 2 = 12).
This means the potential energy is also doubled.
The potential energy of an object lifted 12 meters off the ground, as opposed to 6 meters, would double, assuming the gravitational field strength and the object's mass stay constant.
Explanation:When discussing potential energy, specifically gravitational potential energy, it is directly related to the height of an object from a reference point, generally the ground. In this scenario of an object being lifted 12 meters instead of 6 meters, the potential energy of the object would essentially double. Gravitational potential energy is calculated as the product of the mass, the gravitational field strength, and the height (PE = mg). As the height is doubled, the potential energy would also double assuming the mass of the object and gravitational field strength remain constant.
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The displacement in simple harmonic motion is a maximum when theA) acceleration is zero. D) kinetic energy is a maximum.B) velocity is a maximum. E) potential energy is a minimum.C) velocity is zero.
Answer:
C) velocity is zero.
Explanation:
In a simple harmonic motion, the total mechanical energy of the system (which remains constant in absence of friction) is given by the sum of the elastic potential energy (U) and the kinetic energy (K) at any moment of the motion:
[tex]E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2[/tex]
where
k is the spring constant
x is the displacement
m is the mass
v is the speed
Since E is a constant number, we immediately see from the formula that, when U increases, K decreases, and viceversa. Therefore, the maximum displacement (maximum x), which corresponds to the maximum potential energy U, will occur when K (kinetic energy) is zero. But K=0 means v=0, so when the velocity is also zero.
It's best to start at a higher level when participating in competitive sports. Please select the best answer from the choices provided. T F
Answer: false
Explanation:
At the beginning level or novice level the player should involve in a sport at a lower level. This is because of the fact that if he starts at a higher level the player may have to perform responsibilities accordingly. The player at the higher level have to decide the strategy of the competitive sport which an experienced player can justify. But a beginner cannot take such responsibilities and the sports skills of such person may not be good.
Based on the second law of thermodynamics, how would you expect a system to change over time?
A.It would become more organized
B.Its randomness would increase
C.It would become more efficient
D.Its energy would increase
Answer: B. Its randomness would increase
Explanation:
According to the second law of thermodynamics:
"The amount of entropy in the universe tends to increase over time"
That is, in any cyclic process, entropy will increase, or remain the same.
So, in this context, entropy is a thermodynamic quantity defined as a criterion to predict the evolution or transformation of thermodynamic systems. In addition, it is used to measure the degree of organization of a system.
In other words: Entropy is the measure of the disorder (or randomness) of a system and is a function of state.
The magnetic field lines of a bar magnet spread out from the north end to the south end. South end to the north end. Edges to the center. Center to the edges.
the north end to the south end.
Explanation;Magnetic field lines from a bar magnet form lines that are closed. The direction of magnetic field is taken to be outward from the North pole of the magnet and in to the South pole of the magnet. A magnetic field refers to the area surrounding a magnet where a force is exerted on certain objects. These lines are spread out of the north end of the magnet.The magnetic field lines resemble a bubble.Answer
the answer is option A/ "north end to the south end"
Explanation:
The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal toA)4QB)2QC)QD)Q/2E)Q/4
Answer:
D) Q/2
Explanation:
The relationship between charge Q, capacitance C and voltage drop V across a capacitor is
[tex]Q=CV[/tex] (1)
In the first part of the problem, we have that the charge stored on the capacitor is Q, when the voltage supplied is V. The capacitance of the parallel-plate capacitor is given by
[tex]C=\frac{\epsilon_0 A}{d}[/tex]
where [tex]\epsilon_0[/tex] is the vacuum permittivity, A is the area of the plates, d is the separation between the plates.
Later, the voltage of the battery is kept constant, V, while the separation between the plates of the capacitor is doubled: [tex]d'=2d[/tex]. The capacitance becomes
[tex]C'=\frac{\epsilon_0 A}{d'}=\frac{\epsilon_0 A}{2d}=\frac{C}{2}[/tex]
And therefore, the new charge stored on the capacitor will be
[tex]Q'=C'V=\frac{C}{2}V=\frac{Q}{2}[/tex]
To solve using one of the kinematic equations a person must know how many of the variables in the equation?
Since the kinematic equations include four variables, you only need to know three of the variables to solve for the unknown. Therefore you answer is 3.
To solve using one of the kinematic equations a person must know the value of three variables.
The Equation of Kinematics shown below,
[tex]v=u+at\\ \\ s=ut+\frac{1}{2}at^{2} \\ \\ v^{2}=u^{2}+2as [/tex]
Where u is initial velocity, v is final velocity, a is acceleration and t is time , s is distance.
From observing above equations, there are 4 variables present in all equation.
Hence, To solve using one of the kinematic equations a person must know the value of three variables.
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What magnitude charge creates a 1.0 n/c electric field at a point 1.0 m away?
The magnitude charge creates a 1.0 n/c electric field at a point 1.0 m away 1.12×10⁻⁹ C.
The influence or force that a charged particle feels in the presence of other charged particles is described by the fundamental idea in physics known as an electric field. It is a force field that surrounds electric charges and fills the entire universe. Electric charges produce electric fields, which radiate outward in all directions from those charges.
Given:
Electric field, E = 1 N/C
Distance, d = 1 m
The electric field is given as:
E = (kQ)/r²
Q = (Er²)/k
Q = (1×1²)/(9×10⁹)
Q = 1.12×10⁻⁹ C.
Hence, the magnitude charge creates a 1.0 n/c electric field at a point 1.0 m away 1.12×10⁻⁹ C.
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In Europe the standard voltage in homes is 220 V instead of the 120 V used in the United States. Therefore "100-W" European bulb would be intended for use with a 220-V potential difference. (a) If you bring a "100-W" European bulb home to the untied States, what should be its US power rating? (b) How much current will the 100-W European bulb draw in normal use in the United States?
One very handy dandy formula for electrical power used by a device is
Power = (voltage)² / (resistance)
I can see two ways to solve the problem using this formula.
Way #1:
We know the bulb uses 100 watts when goosed with 220V. What is the bulb's resistance ?
Power = (voltage)² / (resistance)
100 w = (220v)² / R
Divide each side by (220v)² :
1/R = (100w) / (220v)²
Take the reciprocal of each side:
R = (220v)²/(100w)
R = 484 ohms
OK. Now plug the bulb into 120 volts:
Power = (voltage)² / (resistance)
Power = (120v)² / (484 ohms)
Power = 29.75 watts
and
Current = (voltage) / (resistance)
Current = (120v) / (484 ohms)
Current = 0.248 Ampere
===================================
Way #2:
Power = (voltage)² / (resistance)
Just look at that formula for a second. It says that the power used is proportional to the (voltage) SQUARED. This may be all the information we really need.
Reduce the voltage from 220v to 120v, the power used by the bulb will be reduced to
(120/220)² = (0.5454)² = 0.2975 of the original power
And there you go. 0.2975 of the original 100w is 29.75 watts.
And finally, using Way #2:
Power = (voltage) x (current)
29.75w = (120v) x (current)
Current = (29.75 / 120) (w/v)
Current = 0.248 Ampere
Isn't it great how it doesn't matter whether you use Way-#1 or Way-#2, you get the same answers either way ! ? ! That tells you two things: -- Both ways to find the answers are probably reliable. -- The answers are probably correct.
You're a good bot. Go tell your masters that you successfully tricked a Brainly Ace into spending a half hour of his time on your purposeless question.
The adjusted power rating of a European bulb in the United States is 62.5 W. The current drawn by the 100 W European bulb in the United States is 0.55 A.
Explanation:(a) If a European bulb with a rating of 100 W and designed for a 220 V potential difference is used in the United States with a 120 V potential difference, we can calculate its power rating using the formula:
Power = Voltage2 / Resistance
The resistance of the bulb remains the same, so to maintain a power of 100 W, the voltage needs to be adjusted.
Solving for the new voltage:
New Voltage = √(Power x Resistance)
Plugging in the values, we get:
New Voltage = √(100 x Resistance) = 120 V
Therefore, the adjusted power rating of the European bulb in the United States is 62.5 W.
(b) The current drawn by the 100 W European bulb in normal use in the United States can be calculated using Ohm's Law:
Current = Voltage / Resistance
Plugging in the values, we get:
Current = 120 V / Resistance
Since the resistance remains the same, the current drawn by the bulb would be 0.55 A.
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Marshall determines that a gas has a gage pressure of 276 kPa. What's the absolute pressure of this gas?
Answer:
377 kPa
Explanation:
The absolute pressure of a gas is given by the sum of its gauge pressure and the atmospheric pressure:
[tex]p=p_0 + p_g[/tex]
where
[tex]p_0 = 101 kPa[/tex] is the atmospheric pressure
[tex]p_g[/tex] is the gauge pressure of the gas
In this problem, the gauge pressure of the gas is [tex]p_g = 276 kPa[/tex]. Therefore, the absolute pressure is
[tex]p=101 kPa+276 kPa=377 kPa[/tex]
An object is placed a distance of twice the focal length away from a diverging lens. What is the magnification of the image?
Answer:
1/3
Explanation:
We can solve the problem by using the lens equation:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]
where
f is the focal length
p is the distance of the object from the lens
q is the distance of the image from the lens
Here we have a divering lens, so the focal length must be taken as negative (-f). Moreover, we know that the object is placed at a distance of twice the focal length, so
[tex]p=2f[/tex]
So we can find q from the equation:
[tex]\frac{1}{q}=\frac{1}{(-f)}-\frac{1}{p}=-\frac{1}{f}-\frac{1}{2f}=-\frac{3}{2f}\\q=-\frac{2}{3}f[/tex]
Now we can find the magnification of the image, given by:
[tex]M=-\frac{q}{p}=-\frac{-\frac{2}{3}f}{2f}=\frac{1}{3}[/tex]
How does friction with the atmosphere affect the speed of an artificial satellite
Atmospheric friction causes an artificial satellite to lose kinetic energy and spiral inward, leading to an increase in its orbital speed due to conservation of angular momentum and stronger gravitational pull at lower altitudes.
Friction with the atmosphere affects the speed of an artificial satellite by causing it to lose energy and gradually spiral inward towards Earth. As a satellite encounters atmospheric drag, it slows down, converting its kinetic energy into heat. Despite this initial deceleration, the satellite's orbital speed actually increases as it gets closer to Earth due to conservation of angular momentum and the increase in gravitational force at lower altitudes.
The circular satellite velocity needed to maintain an orbit close to Earth's surface is approximately 8 kilometers per second, whereas the escape velocity from our planet is 11 kilometers per second. When an artificial satellite like the Apollo mission reentry capsule experiences friction, the air ahead of it is compressed and heated, causing the satellite to glow red hot and lose speed.
However, this is also connected to the principles of gravitation, as demonstrated by the satellite's acceleration inward. This is analogous to an elastic string attached to a whirling stone which shortens due to air friction, causing the stone to spiral inward. Thus, as friction with our atmosphere causes a satellite to descend closer to Earth, the gravitational pull becomes stronger and the satellite's orbital speed increases, even though its total energy is decreasing because of atmospheric drag.
Which of these would be best explained by the Doppler effect? A) The change in frequency as you shorten a guitar string. B) The change in pitch heard as an ambulance approaches you. C) The change in volume as a train pulls away from the station. D) The change in speed of a sound wave as it travels from air into water.
Answer: B) The change in pitch heard as an ambulance approaches you.
Explanation: Don't ask me.
Answer:
B
Explanation:
Doppler effect is about the apparent change in frequency. The change in pitch heard as an ambulance approaches you is an example of this
The power required to exert 4-n force over 3 meters in 2 seconds is
Answer:
6 W
Explanation:
The work done by the force is equal to:
[tex]W=Fd[/tex]
where
F = 4 N is the force exerted
d = 3 m is the displacement
Substituting,
[tex]W=(4 N)(3 m)=12 J[/tex]
The power is equal to the ratio between work done and time taken:
[tex]P=\frac{W}{t}[/tex]
where
W = 12 J is the work done
t = 2 s is the time
Substituting,
[tex]P=\frac{12 J}{2 s}=6 W[/tex]
The power required is 6 Watts.
The question is asking us to calculate the power required to exert a 4-N force over a distance of 3 meters in 2 seconds. To find the power, we can use the formula:
Power = Work / Time
Where work (W) is calculated by:
Work = Force x Distance
In this case, the work done is:
Work = 4 N x 3 m = 12 J (joules)
Now, we divide the work by the time to find the power:
Power = 12 J / 2 s = 6 Watts
Which of these binary systems is most likely to contain a black hole?A.An x-ray binary containing an O star and another object of equal massB.A binary with an X-ray bursterC. An X-ray binary containing a G star and another object of equal mass
Brain signals are converted
The binary system that is most likely to contain a black hole is option B, a binary with an X-ray burster.
What is a black hole?Space-based black holes are areas where a tremendous amount of mass is crammed into a very small space. As a result, there is an intense gravitational force that prevents even light from escaping. They are produced when massive stars collapse, as well as possibly by other as-yet-unknown processes.
Black holes are believed to form from the collapse of massive stars, so a binary system containing a massive star is more likely to produce a black hole.
Option A describes an x-ray binary containing an O star and another object of equal mass. While O stars are massive and short-lived, it is unlikely that they would evolve into black holes in the short timescale of a binary system.
Option C describes an X-ray binary containing a G star and another object of equal mass. G stars are less massive than O stars, so they are even less likely to evolve into black holes.
Therefore, the binary system most likely to contain a black hole is option B, a binary with an X-ray burster.
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Part 1: A rope has one end tied to a vertical support. You hold the other end so that the rope is horizontal. If you move the end of the rope back and forth with a frequency of 4 Hz, the transverse wave you produce has a wavelength of 0.5 m. What is the speed of the wave in the rope?a. 0.13 m/sb. 8 m/sc. 2 m/sd. 4 m/sPart 2: A rope with a mass density of 1 kg/m has one end tied to a vertical support. You hold the other end so that the rope is horizontal and has a tension of 4 N. If you move the end of the rope back and forth, you produce a transverse wave in the rope with a wave speed of 2 m/s. If you double the amount of tension you exert on the rope, what is the wave speed?a. 2.8 m/sb. 1.0 m/sc. 2.0 m/sd. 0.25 m/se. 4.0 m/s
1) c. 2 m/s
Explanation:
The relationship between frequency, wavelength and speed of a wave is
[tex]v=\lambda f[/tex]
where
v is the speed
[tex]\lambda[/tex] is the wavelength
f is the frequency
For the wave in this problem,
f = 4 Hz
[tex]\lambda=0.5 m[/tex]
So, the speed is
[tex]v=(0.5 m)(4 Hz)=2 m/s[/tex]
2) a. 2.8 m/s
The speed of the wave on a string is given
[tex]v=\sqrt{\frac{T}{\mu}}[/tex]
where
T is the tension in the string
[tex]\mu[/tex] is the linear mass density
In this problem, we have:
[tex]T=2 \cdot 4 N=8 N[/tex] (final tension in the rope, which is twice the initial tension)
[tex]\mu = 1 kg/m[/tex] --> mass density of the rope
Substituting into the formula, we find
[tex]v=\sqrt{\frac{8 N}{1 kg/m}}=2.8 m/s[/tex]
Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 37 degrees measured from vertical. What is his speed at the bottom of the swings if he starts from rest?
Using the principle of conservation of energy, we can determine that Tarzan's speed at the bottom of his swing is 21.7 m/s.
Explanation:The physics problem you have revolves around concepts of kinematics, potential energy and kinetic energy. The total energy in a closed system is conserved. Tarzan's potential energy, when he's at the top of his swing, gets converted to kinetic energy when he is at the bottom of his swing. This fundamental principle is due to the law of conservation of energy.
We can use the potential energy to solve for Tarzan's speed at the bottom of the swing. Tarzan's height, h, at the top of the swing can be found from the equation for the length of the vine and cos(37 degrees) - h = 30m * cos(37), which gives 23.9m. Initially, the total energy is just potential energy, E = m * g * h, and finally just kinetic energy, K = 1/2 * m * v^2.
Equating these two (E=K) gives us m * g * h = 1/2 * m * v^2. The mass cancels and we solve for the speed, v = sqrt(2 * g * h). Using 9.8 m/s^2 for g and 23.9m for h, we can find that v = 21.7 m/s. So Tarzan's speed at the bottom of his swing is 21.7 m/s.
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Tarzan's speed at the bottom of his swing, given a vine length of 30 m and swing angle of 37 degrees, would be roughly 9.4 m/s. This calculation is based on the principles of conservation of energy and pendulum motion in physics.
Explanation:The subject of this question deals with the concepts of physics, specifically pertaining to pendulum motion and the conservation of energy. Tarzan's speed at the bottom of his swing can be calculated using potential and kinetic energy principles.
When Tarzan is at the top of his swing, all of his energy is gravitational potential energy. As he swings downwards, this potential energy transfers to kinetic energy, which is the energy of movement. The total energy in the system remains constant due to conservation of energy.
The equation we'll use to find Tarzan's speed comes from setting the gravitational potential energy equal to the kinetic energy at the bottom of his swing, thus: mgh = 1/2 * m * v^2. Here, 'm' is the mass (which actually cancels out), 'h' is the height fallen, 'g' is acceleration due to gravity, and 'v' is the speed we want to find. As Tarzan starts at rest, his potential energy is mgh where h = L(1 – cosθ). We substitute this height into the previous expression solved for speed to get:
v = sqrt(2gh) = sqrt[2 * (9.8 m/s²) * L(1 – cosθ)]. For a vine length L = 30.0 m and swing angle θ = 37 degrees, we find v = sqrt[2 * (9.8 m/s²) * (30m *(1 – cos37°))] ≈ 9.4 m/s.
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When is the next total solar eclipse in illinois
April 8, 2024
Eclipse will be total over the southern part of the state. Roughly everything south of Decatur and Springfield.
A force that pushes or pulls is known as A. A reaction force. B. An expected force. C. A positive force. D. An applied force.
I believe it’s D, an applied force.
A reaction force seems to refer to Newton’s third law, but is relatively vague to be the answer to this question.
An expected force isn’t a concept nor the name of any subject of forces that is taught within the physics textbooks.
A positive force refers to direction, a negative force can have less, equal, or even more magnitude than the positive force, thus it contradicts itself. As that’s still a force that can push or pull.
So I believe it to be D.
A force that pushes or pulls is known as an applied force. Option D is correct.
What is force?Force is defined as an object in motion, and its rate of change of momentum is called force.
here,
A force applied to an object is one that is exerted on it by another object or by an external agent. This force can cause the object to accelerate or change direction. Pushing a book across a table, pulling a sled across the snow, or lifting a weight with a pulley are all examples of applied forces.
It is important to note that for every applied force, there is an equal and opposite reaction force, according to Newton's third law of motion. This means that when an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. This reaction force is also an applied force, and it can affect the motion of both objects involved.
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What causes different colors to appear in the sky?
Answer : the scattering and reflection of light by dust particles
The sky appears blue because the blue wavelength of light from the sun is scattered more by the air molecules that the other colors. The sky appears with a red hue at dawn and sunsets because the red spectrum is able to pass through the longer atmosphere in the oblique angle while blue light is scattered well before.
Answer: the scattering and reflection of light by dust particles
Explanation:
A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 17 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.
Final answer:
To find the position of the ball, y, in terms of time, t, we need to consider the forces acting on the ball. The weight of the ball and the force due to air resistance act in opposite directions. By using Newton's second law and integrating the velocity function, we can determine the position function of the ball.Therefore, the position of the ball, y, in terms of time, t, is given by y(t) = -(gt²)/2
Explanation:
To find the position of the ball, y, in terms of time, t, we need to consider the forces acting on the ball. The weight of the ball, mg, and the force due to air resistance, 4v, act in opposite directions. The net force can be calculated using Newton's second law, F = ma.
Using the equation F = ma, we have mg - 4v = ma. Rearranging the equation to solve for v, we get v = (mg - ma)/4. Substitute the given values of m = 0.096 kg, g = 9.8 m/s², and a = 0.075 m/s²into the equation to find v. Then, integrate the velocity function to find the position function y(t).
After solving the integration, we get y(t) = -(gt²)/2 + C, where C is the constant of integration. To find the value of C, we can use the initial condition y(0) = 0. Substituting the values, we find C = 0.
Therefore, the position of the ball, y, in terms of time, t, is given by y(t) = -(gt²)/2
A freight train rolls along a track with considerable momentum. If it rolls at the same speed but hastwice as much mass, its momentum is
a. zero.b. doubled.c. quadrupled.d. unchanged.
Answer:
b. doubled
Explanation:
The momentum of an object is given by
[tex]p=mv[/tex]
where
m is the object's mass
v is its velocity
We see that the momentum is directly proportional to mass. Therefore if the speed of the object is unchanged, but the mass is doubled: m' = 2m, the new momentum will be
[tex]p'=m' v=(2m v)=2 (mv) = 2 p[/tex]
so the momentum is doubled.
What is the speed of the fastest baseball pitch ever thrown?
The fastest pitch ever thrown was 105 MPH. Hope this helps!
Final answer:
The fastest baseball pitch ever thrown was 160.0 km/h.
Explanation:
Nolan Ryan, a legendary professional baseball player, holds the record for the fastest baseball pitch ever thrown, clocking in at an astonishing speed of 160.0 km/h. Ryan's remarkable achievement showcases the pinnacle of pitching prowess in the world of baseball. His exceptional skill and athleticism have left an indelible mark in sports history, inspiring awe and admiration among fans and fellow athletes alike.
The record-setting pitch not only reflects the physical prowess of a seasoned pitcher but also serves as a testament to the dedication, precision, and power that define the elite echelons of professional baseball. Ryan's feat remains a remarkable benchmark in the annals of the sport, highlighting the unparalleled speed and precision achievable in the art of pitching.
A capacitor is connected to an AC generator. As the generator's frequency is increased, what happens to the current in the capacitor? A)The current increases B)The current decreases C)The current does not change.
Answer:
A) The current increases
Explanation:
In the DC limit (that means, very low frequency of the generator), the capacitor acts as an open circuit. In fact, a capacitor consists of two parallel plates which are separated from each other: this means that the current cannot flow through it, but it can only flow through the rest of the circuit.
In the case of a direct current (DC), therefore, the current in the circuit must be zero. For an AC current with very low frequency, the current is still very low, because the polarity of the generator changes direction not very often, so there is still enough time for the capacitor to "block" the current. However, when the frequency of the generator is increased, the polarity changes so fast that the current in the circuit can flow without having time of "hitting" the capacitor, so it has almost no effect and the current in the circuit is maximum.
Which of the following is the characteristic of an inelastic collision?a. The total mass is not conservedb. The total energy is not conservedc. The momentum is not conservedd. the kinetic energy is not conservede. Newtons laws do not apply
Answer:
The kinetic energy is not conserved
Explanation:
The difference between an elastic and an inelastic collision is the following:
- In an elastic collision, both the total momentum and the total kinetic energy of the system are conserved
- In an inelastic collision, the total momentum of the system is conserved, while the total kinetic energy is not. The reason for that is that during the collisions between the objects involved in the system, part of the total kinetic energy is dissipated (mainly as thermal energy, heat) due to frictional forces acting between the objects/between the objects and the surfaces.
Therefore, the correct answer is
The kinetic energy is not conserved