To solve for the velocity of sound in air, we can use the formula:
v = fλ
where:
v = velocity of sound
f = frequency of the wave
λ = wavelength of the wave
In this problem, we are given the frequency and the length of the string, but we need to find the wavelength. For a string fixed at both ends, the wavelength is given by:
λ = 2L/n
where:
L = length of the string
n = harmonic number
In this case, the string is fixed at both ends, so the harmonic number will be an odd number:
n = 1, 3, 5, ...
We are given that the maximum frequency is 800 Hz, which corresponds to the fundamental frequency (n = 1). Therefore:
λ = 2L/n = 2(1.25 m)/1 = 2.5 m
Now we can substitute the values into the formula for the velocity of sound:
v = fλ = (800 Hz)(2.5 m) = 2000 m/s
Therefore, the velocity of sound in air is 2000 m/s.
a ball, kicked towards the south end of the field, moves a total of 130 meters in 20 seconds. find the velocity
Answer:
The velocity of the ball can be found by dividing the total distance (130 meters) by the total time (20 seconds). This gives a velocity of 6.5 m/s
A student sits on a rotating stool holding two
3 kg objects. When his arms are extended
horizontally, the objects are 1 m from the
axis of rotation, and he rotates with angular
speed of 0.64 rad/sec. The moment of inertia
of the student plus the stool is 8 kg m2
and is assumed to be constant. The student then
pulls the objects horizontally to a radius 0.3 m
from the rotation axis.
The student's final angular speed is roughly 0.60 radians per second.
What is an object's angular speed?The speed of an object in rotation is known as its angular speed. In radians, the distance traveled is denoted by the symbol. The amount of time is expressed in seconds. The angular speed is therefore expressed in radians per second, or rad/s.
This issue can be resolved using the conservation of angular momentum:
L = Iω
The student and the two objects initially have the following angular momentum:
L1 = (2 × 3 kg) × (1 m) × (0.64 rad/sec) = 3.84 kg m²/s
The moment of inertia of the student plus the stool is given as I = 8 kg m
I' = I + 2mr²
where m is the mass of each object (3 kg), and r is the new radius (0.3 m).
I' = 8 kg m² + 2 × 3 kg × (0.3 m)² = 8.54 kg m²
L1 = L2
I1 ω1 = I2 ω2
8 kg m² × 0.64 rad/sec = 8.54 kg m² × ω2
ω2 = (8 kg m² × 0.64 rad/sec) / (8.54 kg m²) = 0.60 rad/sec.
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What ended the jim crow laws and when??
A man with weight of 150 lb is holding to a balloon with both hands equally. Determine the tension in each of his hands when: a) the balloon rises with v=0.8t ft/s, and b) the balloon descents with v=0.4t ft/s.
1) a) T=153.8 lb, b) T=148.1 lb
2) a) T=135.0 lb, b) T=45.0 lb
3) a) T=74.1 lb, b) T=76.9 lb
4) a) T=76.9 lb, b) T=74.1 lb
a) The tension is 76.9 lb when the balloon rises with v=0.8t ft/s and b) The tension is 74.1 lb when the balloon descents with v = 0.4t ft/s.
What is Newton's second law?Newton's second law, states that the net force on an object is equal to its mass times its acceleration.
We can apply Newton's second law to the man and the balloon separately to determine the tension in each of his hands.
a) The net force on the balloon is equal to its mass times its acceleration, which is given by:
F(b) = mg + ma = mg + m(dv/dt)
= mg + m(d/dt(0.8 ft/s)
= (mg + 0.8m)/2
= [150 lb + (150b/32 ft/s²)(0.8 ft/s)]/2
T = 76.86 lb or 76.9 lb
b) When the balloon descends with a velocity of 0.4t ft/s, its acceleration is -0.4 ft/s² (negative because it is descending).
The net force on the man is still equal to the tension in his hands, which we can call T. Therefore:
T = m(m) × g - F(b)
where m(b) is the mass of the balloon, r is its radius, and ρₐ is the density of air,.
T = 150 lb × 32.2 ft/s² - (4/3)πr³ × ρₐ × 0.4 ft/s²
Dividing the tension equally between the man's hands, we get:
T(h) = T/2 = 75 lb × 32.2 ft/s² - (2/3)πr³× ρₐ × 0.4 ft/s²
Substituting the value of r and ρₐ, we get:
T(h) = 74.1 lb
Therefore, the answer is option 4) a) T=76.9 lb, b) T=74.1 lb.
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A physics student performed an experiment in which the potential difference V between the ends of a long straight wire was varied. The current I in the wire was measured at each value of the potential difference with an ammeter and the results of the experiment are shown in the table.
Which one of the following statements is the best conclusion based on the data?
a The wire obeys Ohm's law over the range of potential differences between 5 and 30 V.
b The wire obeys Ohm's law over the range of potential differences between 5 and 20 V.
c The resistance of the wire is 20 Ω.
d The wire does not obey Ohm's law.
e The current in the wire is directly proportional to the applied potential difference.
(a) The wire Obeys over the range differences of Ohm's law Potential between 5 & 20 V.
What is Ohm's law?The relationship between current, voltage, and resistance is described by Ohm's law. The voltage or potential difference across a large number of materials determines how much constant current flows through them.
Given, A table of voltage and current shown in the picture below:
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and the constant of proportionality is the resistance of the conductor. In other words, Ohm's law can be expressed as:
V = IR
where V is the potential difference across the conductor,
"I" is the current flowing through the conductor,
and R is the resistance of the conductor.
A) V =IR for Voltage, 5 - 20V it obeys. The range between Ohm's law Over on the potential differences. 5 & 20v, So This option is true
B) You Can't Say that Resistance the Range 5 -40 after 20 V Changes, Check it, at 25
dV/ dI = (25 -20)/(1.5 -1) = 10 ohm
C) Since Obey's accuracy, is not within 5V-20V it is Ohm's law with good this option is not true.
D) After 20V this option is not true also.
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Complete question:
Once ______ is locked, pain causing chemicals cannot transmit their messages.
Once the nerve cell membrane is locked, pain causing chemicals cannot transmit their messages.
What is the membrane ?The membrane is a thin, selective barrier which separates two distinct environments. It is the most fundamental structural and functional element of all living cells, regulating the passage of molecules into and out of the cell. Membranes are composed of a lipid bilayer and proteins. The lipid bilayer is made of phospholipids, which are amphipathic molecules, meaning they have both hydrophilic (water-attracting) and hydrophobic (water-repelling) regions. The membrane proteins embedded in the lipid bilayer provide the cell with selective permeability, allowing for the controlled passage of molecules into and out of the cell, and providing an effective barrier to the external environment. The proteins also provide receptors for signaling molecules, enzymes for metabolic reactions, and a scaffold for organizing the cell’s internal architecture.
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What is the mass of a product if the reactants have mass of 44. 6 grams (fe) and 12. 8 grams (o2)?.
The mass of the product Fe₂O₃ when the masses of the reactants are specified is calculated to be 57.4 g.
The mass of the product when Fe reacts with O₂ will be equal to the summation of the masses of the reactants i.e,Σ(M₁ + M₂) and this is because of the law of conservation of mass.
We know,
Fe + O₂ → Fe₂O₃
Mass of Fe is given as 44.6 g
Mass of O₂ is given as 12.8 g
So, the mass of Fe₂O₃ is 57.4 g.
Thus, the required mass of the product Fe₂O₃ formed when the masses of reactants are given is 57.4 g.
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Photons and photon flux a. Consider a 1 kW AM radio transmitter at 700 kHz. Calculate the number of photons emitted fro-m the antenna per second. b. The average intensity of sunlight on Earth's surface is about 1 kW m^-2. The maximum intensity is at a wavelength of around 800 nm. Assuming that all the photons have an 800 nm wavelength, calculate the number of photons arriving on Earth's surface per unit time per unit area. What is the magnitude of the electric field in the sunlight? c. Suppose that a solar cell device can convert each sunlight photon into an electron, which can then give rise to an external current. What is the maximum current that can be supplied per unit area (m^2) of this solar cell device?
The number of photons emitted per second is 2.16 x 10^28 photons/s. The magnitude of the electric field in the sunlight is 3.22 x 10^-5 V/m. The maximum current that can be supplied per unit area by the solar cell device is 1.29 microamperes per square meter.
How to find number of photons emitted per second?a. The energy of a single photon is given by E = hf, where h is Planck's constant and f is the frequency. We can find the frequency of the radio wave as follows:
f = 700 kHz = 700,000 Hz
The energy of a single photon at this frequency is:
E = hf = (6.626 x 10^-34 J s) x (700,000 Hz) = 4.64 x 10^-26 J
The power of the transmitter is 1 kW = 1000 J/s. Therefore, the number of photons emitted per second is:
(1000 J/s) / (4.64 x 10^-26 J/photon) = 2.16 x 10^28 photons/s
b. The energy of a photon with a wavelength of 800 nm can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength.
We can then calculate the number of photons arriving on Earth's surface per unit time per unit area as follows:
E = hc/λ = (6.626 x 10^-34 J s) x (3.00 x 10^8 m/s) / (800 x 10^-9 m) = 2.48 x 10^-19 J
The number of photons arriving per unit time per unit area (i.e., the photon flux) is given by the intensity I divided by the energy of a single photon:
I = 1 kW/m^2 = 1000 J/s/m^2
Photon flux = I/E = (1000 J/s/m^2) / (2.48 x 10^-19 J/photon) = 4.03 x 10^21 photons/s/m^2
The magnitude of the electric field in the sunlight can be found using the formula I = ε0cE^2/2, where ε0 is the permittivity of free space and c is the speed of light:
E = sqrt(2I/ε0c) = sqrt(2 x 1000 J/s/m^2 / (8.85 x 10^-12 F/m x 3.00 x 10^8 m/s)) = 3.22 x 10^-5 V/m
c. The maximum current that can be supplied per unit area by the solar cell device is equal to the photon flux multiplied by the charge of an electron (q) and the efficiency of the solar cell (η):
I = ηqPhoton flux = ηq(4.03 x 10^21 photons/s/m^2)
The charge of an electron is q = 1.602 x 10^-19 C, and the efficiency of a typical silicon solar cell is around 20%. Therefore:
I = 0.2 x (1.602 x 10^-19 C) x (4.03 x 10^21 photons/s/m^2) = 1.29 x 10^-6 A/m^2
So, the maximum current that can be supplied per unit area by the solar cell device is 1.29 microamperes per square meter.
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The painting the starry night by vincent van gogh is rectangular in shape with height 29 inches and width 36. 25 inches. If a reproduction was made where each dimension is the corresponding original dimension, what is the height of the reproduction, to the nearest hundredth of an inch?.
The height of the reproduction is 29 inches, which is the same as the height of the original painting with dimensions.
To find the height of the reproduction of Vincent Van Gogh's painting "The Starry Night," we can use the concept of proportional scaling. Since the reproduction has the same dimensions as the original painting, the ratio of the height and width of the reproduction must be the same as the ratio of the height and width of the original painting.
The ratio of height to width of the original painting can be calculated as:
29 / 36.25 = 0.8
Therefore, the ratio of height to width of the reproduction must also be 0.8. We can set up a proportion to solve for the height of the reproduction, which we'll call h:
h / 36.25 = 0.8
To solve for h, we can multiply both sides by 36.25:
h = 36.25 * 0.8
h = 29
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Problem
Assume that you have created a mechanical robot that can perform the following tasks:
• Stand up.
• Sit down.
• Turn left 90 degrees.
• Turn right 90 degrees.
• Take a step.
Additionally, the robot can determine the answer to one test condition:
• Am I touching something?
a. Place two chairs 20 feet apart, directly facing each other. Draw a structured flowchart or write pseudocode describing the logic that would allow the robot to start from a sitting position in one chair, cross the room, and end up sitting in the other chair. Have a fellow student act as the robot and carry out your instructions.
b. Draw a structured flowchart or write pseudocode describing the logic that would allow the robot to start from a sitting position in one chair, stand up and circle the chair, cross the room, circle the other chair, return to the first chair, and sit. Have a fellow student act as the robot and carry out your instructions.
a. Here's the pseudocode for the robot to move from one chair to the other chair and sit down:
Start in a sitting position on the first chair.
Stand up.
Take a step forward until the robot is no longer touching the first chair.
Turn left 90 degrees.
Take a step forward until the robot is touching the second chair.
Turn left 90 degrees.
Take a step forward until the robot is no longer touching the second chair.
Turn left 90 degrees.
Take a step forward until the robot is facing the second chair.
Sit down on the second chair.
b. Here's the pseudocode for the robot to move from one chair to the other chair, circle both chairs, and return to the first chair:
Start in a sitting position on the first chair.
Stand up.
Turn right 90 degrees.
Take a step forward and turn right to circle the first chair.
Repeat step 4 for a complete circle.
Turn right 90 degrees.
Take a step forward until the robot is no longer touching the first chair.
Turn left 90 degrees.
Take a step forward until the robot is touching the second chair.
Turn left 90 degrees.
Take a step forward and turn left to circle the second chair.
Repeat step 11 for a complete circle.
Turn left 90 degrees.
Take a step forward until the robot is no longer touching the second chair.
Turn right 180 degrees.
Take a step forward until the robot is touching the first chair.
Turn right 90 degrees.
Take a step forward and turn right to circle the first chair.
Repeat step 18 for a complete circle.
Turn right 90 degrees.
Take a step forward until the robot is facing the first chair.
Sit down on the first chair.
Note: The above pseudocode assumes that the chairs are placed in a rectangular configuration with the backs of the chairs facing each other. If the chairs are placed in a different configuration, the pseudocode may need to be modified accordingly.
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an opaque spot called a may develop on the lens, which limits the amount of light transmitted into the eye.
An opaque spot called a cataract may develop on the lens, which limits the amount of light transmitted into the eye.
Describe the cataract?A cataract is described as a condition that affects the lens of the eye, causing it to become cloudy and opaque.
The lens is responsible for sending visual information to the brain, and also is described as a transparent structure in the eye that helps to focus light onto the retina.
Cataracts are most commonly associated with older people, but in some cases can be caused by other factors such as genetics, certain medical conditions.
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two speakers are emitting identical sound waves with a wavelength of 4.0 m. the speakers are 8.0 m apart explained
a 5.0 kg block accelerates a .80 m/s2 along a horizontal surface when a horizontal 12.0 N force acts on it. Show that the force of friction on the block is 8.0 N
The value of the frictional force acting on the block will be equal to 8 N.
How to get the frictional force?Force is defined as the product of mass and acceleration, and it acts on the body to move it.
Because an external force is acting on the block, a frictional force opposes the block's movement. The frictional force is denoted by f(k) and is given by
f(k) = external force - (ma)
f(k) = 12N - (5×0.8)
f(k) = 12- 4
f(k) = 8 N
f(k) = 8 N and since it opposes the external force then the sign will be negative that is f(k) = -8N.
Therefore, the frictional force will be 8 N.
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Water flows steadily along a horizontal pipe at a rate of 8 × 10-3 m3/s. If the cross-section of the pipe is 40 × 10-4 m2, calculate the;
a). Flow velocity of water total pressure in the pipe if the static pressure in the horizontal pipe is 3×104 Pa. (Density of water is 1000 kg/m3)
b).new flow velocity if the total pressure is 3.6 × 104 Pa.
The flow velocity of the water is 2 m/s and the total pressure in the pipe is 3.5 × 10⁴ Pa and the new flow velocity of the water is 109.5 m/s.
What is static pressure?Static pressure is the pressure exerted by a fluid or gas that is not in motion or is at rest. It is equal in all directions and is caused by the molecules of the fluid or gas colliding with the walls of the container in which it is held.
Equation:a) To find the flow velocity of the water, we can use the equation:
Q = A * v
where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the flow velocity.
Given Q = 8 × 10⁻³ m³/s and A = 40 × 10⁻⁴ m², we can solve for v:
v = Q / A
v = (8 × 10⁻³ m³/s) / (40 × 10⁻⁴ m²)
v = 2 m/s
To find the total pressure in the pipe, we can use the Bernoulli's equation:
P + (1/2)ρv² = P0
where P is the total pressure, ρ is the density of water, v is the flow velocity, and P0 is the static pressure.
Given ρ = 1000 kg/m³, v = 2 m/s, and P0 = 3 × 10⁴ Pa, we can solve for P:
P + (1/2)(1000 kg/m³)(2 m/s)² = 3 × 10⁴ Pa
P = 3.5 × 10⁴Pa
Therefore, the flow velocity of the water is 2 m/s and the total pressure in the pipe is 3.5 × 10⁴ Pa.
b) To find the new flow velocity, we can use the Bernoulli's equation again:
P + (1/2)ρv² = P0
Given P = 3.6 × 10⁴ Pa, ρ = 1000 kg/m³, and P0 = 3 × 10⁴ Pa, we can solve for v:
(1/2)(1000 kg/m³)v² = (3.6 × 10⁴ - 3 × 10⁴) Pa
v² = 1.2 × 10⁴ m²/s²
v = √(1.2 × 10⁴) m/s
v = 109.5 m/s
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Explain the independent roles of the approach motivation and the avoidance motivation on producing feelings of contentment in a relationship.
Both approach and avoidance motivation can impact feelings of contentment in a relationship. Approach motivation can lead to positive feelings of contentment by promoting behaviors that enhance intimacy and closeness, while avoidance motivation can help prevent negative experiences.
Explain the term approach motivation.Approach motivation can lead to positive feelings of contentment in a relationship by driving individuals to seek out and engage in behaviors that promote intimacy, closeness, and positive interactions with their partner.
Explain the term avoidance motivation.Avoidance motivation can also impact feelings of contentment in a relationship, but in a different way. It can lead individuals to engage in behaviors that prevent or mitigate negative experiences in the relationship.
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A fireman standing on a 10 m high ladder. operates a water hose with a round nozzle of diameter 2.74 inch. The lower end of the hose (10 m below the nozzle) is connected to the pump outlet of diameter 4.19 inch. The gauge pressure of the water at the pump is P(gauge) pump = P (abs) pump − Patm = 50.3 PSI = 346.806 kPa. Calculate the speed of the water jet emerging from the nozzle. Assume that water is an incompressible liquid of density 1000 kg/m3 and negligible viscosity. The acceleration of gravity is 9.8 m/s^2. Answer in units of m/s.
Answer:
The speed of the water jet emerging from the nozzle can be calculated using Bernoulli's equation as follows:
V^2 = 2gP(gauge) pump/ρ
Substituting the given values in the above equation, we get
V^2 = 2*9.8*346.806*1000/1000
V = 166.905 m/s
Which of the following best describes energy transfer in a closed system?
The best description of energy transfer in a closed system is that it occurs within the system and does not involve any exchange of energy with the surroundings.
What is Energy?
Energy is a property of objects or systems that can be transferred to other objects or systems, or converted into different forms. It is a scalar physical quantity that can be defined as the ability to do work or produce heat. Energy exists in many forms, such as mechanical, thermal, electrical, chemical, nuclear, and electromagnetic, and can be transformed from one form to another. The SI unit of energy is the joule (J), but other units such as the calorie (cal) or the electronvolt (eV) are also commonly used in different contexts.
In a closed system, energy transfer occurs between different parts of the system, but no energy is exchanged with the surroundings. Energy can be transformed from one form to another within the closed system, but the total amount of energy remains constant. Therefore, the best description of energy transfer in a closed system is that it occurs within the system and does not involve any exchange of energy with the surroundings.
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Kepler's second law, which states that as a planet moves around its orbit it sweeps out equal areas in equal times, implies that A) a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. B) planets have circular orbits. C) the period of a planet does not depend on its mass. D) planets that are farther from the Sun move at slower average speeds than nearer planets. E) a planet's period does not depend on the eccentricity of its orbit.
Answer: an object's orbital speed is faster when nearer to the Sun and slower when farther away
Explanation:
Kepler's second law, which states that as a planet moves around its orbit, it sweeps out equal areas at equal times, implies that a planet travels faster when it is nearer to the sun and slower when it is farther from the sun, which is option a.
Kepler states that when a planet gets closer to the sun in its orbit, it generally covers a greater distance in a given amount of time, resulting in a higher speed. On the other hand, at the same time, the planet moves a small distance when it is farther from the sun. Here the Kepler second is explained.
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when two objects slide against one another, which of the following statements about the force of friction between them is true?
Friction is the pressure that happens when two objects rub together. Microscopic bumps on the surface of each object obstruct the action of the different as the surfaces slide throughout one another.
What is the force of friction between the two objects?Friction is constantly contrary to the course of motion. The frictional pressure between two surfaces in attempting to slide one object throughout the different however neither objects are transferring with admire to every other. The friction is usually equal to the internet force parallel to the surface.
What type of pressure is when one object is sliding across another?We can outline sliding friction as the resistance created by using any two objects when sliding against each other. This friction is also recognised as kinetic friction and is defined as the pressure that is needed to keep a surface sliding along any other surface.
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a turntable is rotating at 3313rpm . you then flip a switch, and the turntable speeds up, with constant angular acceleration, until it reaches 78rpm . part g suppose you are asked to find the amount of time t , in seconds, it takes for the turntable to reach its final rotational speed. which of the following equations could you use to directly solve for the numerical value of t ?
Once t can be located, more details are required.You would need further information (namely, the amount of the rotational motion ) before you could discover a numerical value for t; knowing and 0 would not be sufficient to enable you to solve for t.
What does rotation about just a fixed axis entail?When every particle in a body revolves in a circle around a single line, this is known as pure rotational motion.The rotational axis is this line.Then, at the same time, the same deflection occurs in all of the radii vectors from of the shaft to all of the particles.
What quantity is regarded when the rotation's axis is fixed—angular velocity?A spinning object's angular velocity is defined as a vector quantity in more sophisticated investigations of rotational motion.This vector has magnitude and points exteriorly along the axis of rotation for an object revolving anticlockwise about a fixed axis.
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The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
At which of the labeled points will the electric field have the greatest magnitude?
A) G
B) I
C) A
D) H
E) D
The answer is B) I. The electric field will have the greatest magnitude at point I because it is the closest point to the charged conductors. The closer to the conductors, the greater the electric field magnitude.
What is electric field?Electric field is an invisible force field that surrounds any object that has an electric charge. It is measured in terms of volts per meter (V/m) and is responsible for the attraction or repulsion of two objects with different electric charges. The force of the electric field is determined by the amount of charge on the objects and the distance between them. Any changes in the electric field will cause a corresponding change in the force felt by the objects. Electric fields can be created by moving charges, such as those found in electric currents, or by static charges, such as those found on a charged object. Electric fields are essential for the transmission of electrical signals and are used in many applications, from telecommunications to medical imaging.
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A 1.67m wooden beam that weighs 100 pounds is resting on two supports. The first support is 0.2 m from one end of the beam, and the second support is 0.3 m from the other end. Assume the axis of rotation would be the center of the beam
a. Find the torques acting on the wooden beam
b. Find the net torque acting on the wooden beam
The torque acts on a distance of 0.2 m from one end of the beam is 88.96 Nm and the torque acting upon a the distance of 0.3 m from the other end of the beam is 133.4 Nm. Then, the net torque of the mass is 44.48 Nm.
What is torque ?Torque is the rotational analogue of force on an object. It is the measure of force that acts on the object to rotate the object about an axis.
It is the cross product of force and distance from the end of axis. Torques generates the angular momentum in the object.
Given the mass m= 100 pounds.
1 pound = 4.448 N
then Force by the weight F = 100 × 4.448 = 444.8 N.
Then, the torque acts over 0.2 m from one end = F .r = 444.8 × 0.2 = 88.96 Nm.
Then, the torque acts over 0.3 m from one end = F .r = 444.8 × 0.3 = 133.4 Nm.
Therefore, the net torque acting on the mass is 133.4 -88.96 = 44.48 Nm.
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Explain the independent roles of the approach motivation and the avoidance motivation in producing feelings of contentment in a relationship
Motivation sometimes really helpful to a person when he or she confuses for the next step or hesitates in taking decisions. It helps to heal the problems in a relationship.
What is role of motivation?In psychology theory and research, the dichotomy between the drive to pursue rewards and the drive to avoid risks has a long and significant history.
For instance, Pavlov's description of two distinct systems that direct an organism towards or away from a stimulus prefigured more recent evidence from cognitive neuroscience that identifies various brain activity patterns related to the presentation of incentives and dangers.
The fact that approach and avoidance motives and goals are mostly independent of one another is a recurrent finding in research on these topics.
For instance, Gable, Reis, conducted a series of confirmatory component analyses on individual difference measures of approach and avoidance constructs to support a two-factor model of these constructs.
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A student sits on a rotating stool holding two
3 kg objects. When his arms are extended
horizontally, the objects are 1 m from the
axis of rotation, and he rotates with angular
speed of 0.64 rad/sec. The moment of inertia
of the student plus the stool is 8 kg m2
and
is assumed to be constant. The student then
pulls the objects horizontally to a radius 0.3 m
from the rotation axis.
part A. The final angular speed of the student is 1.28 rad/s.
part B. The change in kinetic energy of the system is 7.04 J.
How do we calculate?We have that the moment of inertia of the system is assumed to be constant, we then write:
Iω = I'ω'
The moment of inertia of the objects is written in the form of :
I_objects = 2MR^2
Therefore, the initial moment of inertia is gotten as:
I = M_student R_stool^2 + 2MR^2
The final moment of inertia is gotten as:
I' = M_student R_stool^2 + 2M(0.3)^2
The angular momentum is conserved, we ten have:
Iω = I'ω'
Solving for ω', we get:
ω' = (Iω)/(I') = ω (I/I')
ω' = 0.64 rad/s (M_student R_stool^2 + 2MR^2) / (M_student R_stool^2 + 2M(0.3)^2)
ω' = 1.28 rad/s
part b.
The initial kinetic energy is
K = 1/2 I ω^2
K = 1/2 (8 kg m^2) (0.64 rad/s)^2 = 1.6384 J
The final kinetic energy is given by:
K' = 1/2 I' ω'^2
K' = 1/2 (8 kg m^2 + 2(3 kg)(0.3 m)^2) (1.28 rad/s)^2 = 8.6784 J
The change in kinetic energy is therefore calculated as:
ΔK = K' - K = 8.6784 J - 1.6384 J = 7.04 J
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a passenger car traveling down a rough road bounces up and down at 1.1 hz with a maximum vertical acceleration of 0.24 m/s2 both typical values. What are the (a) amplitude and
(b) maximum speed of the oscillation?
The frequency of the oscillation. In this case, the amplitude is 0.218 m. and B. the maximum speed of the oscillation is 0.636 m/s.
What is frequency?Frequency is a measure of the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency.
a) The amplitude of the oscillation is the maximum displacement of the car from its equilibrium position. It is equal to the maximum acceleration divided by the frequency of the oscillation. In this case, the amplitude is 0.24 m/s² / 1.1 hz = 0.218 m.
b) The maximum speed of the oscillation is related to the amplitude and frequency of the oscillation. It can be calculated using the formula v = √(2*a*f), where a is the maximum acceleration and f is the frequency of the oscillation. In this case, the maximum speed of the oscillation is v = √(2*0.24 m/s² * 1.1 hz) = 0.636 m/s.
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What force is required to accelerate a 10kg object at 5m/s²? (Force = mass x acceleration)
Answer:
Force = 50 N
Explanation:
Force = 50 N
Formula: Force = mass x acceleration
Answer: Force = 10kg x 5m/s²
Force = 50 N
Give the SI base unit of each of these quantities Enter the abbreviation rather than the name of the unit: time: mass: Kg length:m
Time: s (second)
Mass: kg (kilogram)
Length: m (meter)
What are the SI units?The SI units (International System of Units) are a standard system of measurement used in science, engineering, and many other fields. They provide a universal language for expressing and comparing measurements. The SI units are based on seven fundamental physical quantities, and each of these quantities is associated with a specific base unit, which is defined independently of any other unit.
Seven base units of the SI system are:
Length: meter (m)
Mass: kilogram (kg)
Time: second (s)
Electric current: ampere (A)
Temperature: kelvin (K)
Amount of substance: mole (mol)
Luminous intensity: candela (cd)
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The notes produced by a violin range in frequency from approximately 196Hz to 2637 Hz. Find the possible range of wavelengths in air produced by this instrument when the speed of sound in air is 340 m/s
Answer: low = 1.73 m and high = 0.129 m
Explanation: All you have to do is use the formula (Wavelength = Velocity/Frequency. Which would be 340m/s divided by 196 Hz and then 340m/s divided by 2637Hz.
The wavelength of a wave is its speed divided by frequency. The wavelength corresponds to the lower frequency of 196 Hz is 1.73 m and that for 2637 Hz is 0.12 m. Hence the wavelength range is 1.73 m to 0.12 m.
What is frequency ?Frequency of a wave is the number of wave cycles per unit time. It is the inverse of the time period. Thus, its unit is s⁻¹ which is equal to Hz. Frequency of a wave is inversely proportional to the wavelength.
The relation between speed and frequency with wavelength of the wave is given by,
c = νλ
Given frequency ν1 = 196 Hz.
speed of sound wave c = 340 m/s
then, wavelength at this frequency λ1 = 340 m/s / 196 Hz = 1.73 m.
For a frequency ν2 = 2637 Hz.
λ2 = 340 m/s/ 2637 Hz = 0.12 m.
Therefore, the range of wavelength of the notes from the violin will be in between 1.73 m to 0.12 m.
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A 1.17 kg book is held stationary in the hand. Find the forces acting on the book and the reaction forces to each of these. The hand now exerts an upward force of 14.9 N on the book. Find the book's acceleration. As the book moves upward, the hand is quickly removed from the book. Find the forces on the book and its acceleration
When the hand exerts an upward force of 14.9 N on the book, the book's acceleration is a = F/m = 14.9 N/1.17 kg = 12.7 m/s^2.
What is acceleration ?Acceleration is a measure of the rate of change of velocity of an object over time. It is a vector quantity and is measured in meters per second squared (m/s2). It is usually denoted by the symbol ‘a’. Acceleration can be positive, negative, or zero, depending on the direction of the change in velocity. Positive acceleration is an increase in velocity, negative acceleration is a decrease in velocity, and zero acceleration is no change in velocity.
The forces on the book when it is held stationary in the hand are the downward force of gravity (Fg = m*g = 1.17 kg * 9.8 N/kg = 11.5 N) and the upward force of the hand (Fh = 14.9 N). The reaction forces to these are the upward force of the hand (14.9 N) and the downward force of the book on the hand (11.5 N).
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In a 41 s interval, 580 hailstones strike a glass window of area 1.346 m2 at an angle 31◦ to the window surface. Each hailstone has a mass of 7 g and speed of 6.7 m/s. If the collisions are elastic, find the average force on the window. Answer in units of N.
Answer:
N = hailstones / sec = 580 / 41 = 14.1 stones / sec
mass = .007 kg
v = 6.7 m/s * sin 31 = 3.45 speed of stones perpendicular to surface
Δp = 2 m Δv change in momentum dur to striking window
F = N Δp force required to repel hailstones
F = 2 N m Δv = .68 N force on window pane
Pressure = force / area (don't need window area for force)