The acceleration will vary depending on the specific values of force and mass used in each of the four trials.
What would hypothesize about the value of "a" in this experiment?.Based on Newton's Second Law, we know that acceleration is directly proportional to the net force applied to an object and inversely proportional to its mass. Therefore, we can make some general hypotheses about the relationship between force, mass, and acceleration:
If the force applied to an object is increased while the mass is held constant, then the acceleration will also increase.If the mass of an object is increased while the force is held constant, then the acceleration will decrease.If both the force and mass are increased proportionally, then the acceleration will remain constant.Based on these hypotheses, we can predict that the acceleration will vary depending on the specific values of force and mass used in each of the four trials. If the force and mass are kept constant across all four trials, then the acceleration should also remain constant. If the force is varied while the mass is held constant, then the acceleration should increase or decrease accordingly. Similarly, if the mass is varied while the force is held constant, then the acceleration should decrease or increase accordingly.
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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)
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
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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Two objects of fixed mass are moved apart so that they are separated by three times their original distance. Compared to the original gravitational force between them, the new gravitational force is.
The gravitational force was multiplied by nine. Inversely proportionate to their squared distance, the two bodies' gravitational pull on one another.
In light of this, The gravitational force would rise by a factor of 9 as the distance shrunk to 1/3 of its initial amount.
What does a scientific force mean?A specific meaning is associated to the adjective "force." The terms "push" & "pull" are totally acceptable at this level to express forces. An object does not have a force inside of it or within it. Another object applies a force to the first. Both living things and non-living things can be considered to be parts of a force.
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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 6.0-kg rock is dropped from a height of 9.0 m. At what height is the rock's kinetic energy twice its potential energy?
Answer:
3 m
Explanation:
You want to know the height at which a rock dropped from a height of 9 m has twice as much kinetic energy as potential energy.
RatioThe ratio of KE to PE is given as ...
KE : PE = 2 : 1
This means the potential energy of the rock is 1/(2+1) = 1/3 of the total energy the rock has.
Potential energyWhen the rock is dropped, all of its energy is potential energy. As the rock falls, that potential energy is converted to kinetic energy. The remaining potential energy is proportional to the height of the rock.
If the remaining potential energy is 1/3 of the original potential energy, the height of the rock is 1/3 the original height:
(1/3)×(9 m) = 3 m
When the rock is 3 m high, the kinetic energy is twice the potential energy.
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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Drive an Expression for
The period of Oscilation
of a torsional pendulum
The period of oscillation of a torsional pendulum is T = 2π √(1/2 * MR^2 / k).
What is the expression for period of Oscillation?The period of oscillation of a torsional pendulum can be expressed as:
T = 2π √(I / k)
where;
T is the period of oscillation, I is the moment of inertia of the pendulum, and k is the torsion constant of the pendulum.The moment of inertia of the pendulum depends on its shape and mass distribution. For a simple pendulum consisting of a uniform disk of radius R and mass M suspended from a torsional spring at a distance L from its center, the moment of inertia can be expressed as:
I = 1/2 * MR^2
The torsion constant of the pendulum, k, is a measure of the resistance of the spring to twisting and can be determined experimentally.
Substituting the moment of inertia and torsion constant into the expression for the period of oscillation, we get:
T = 2π √(1/2 * MR^2 / k)
Therefore, the period of oscillation of a torsional pendulum depends on the moment of inertia of the pendulum and the torsion constant of the spring.
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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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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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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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Ants can carry food at a speed of 1 cm/s. How long will it take the ant to carry a cookie crumb a distance of 50 m from the kitchen table to the ant hill?.
5000 seconds, or almost 83.33 minutes time required by Ants to carry a cookie crumb a distance of 50 m from the kitchen table to the ant hill
As per the given information;
Speed = 1 cm/s = 0.01 m/s
Distance = 50 m
Here we have to find out the time required by Ants to carry a cookie crumb a distance of 50 m from the kitchen table to the ant hill.
As we know that:
Time = distance / speed
where distance denotes how far the ant must travel and
speed denotes how quickly it can transport the cookie crumbs.
By substituting the given values, we get:
Time = 50 m / 0.01 m/s
Time = 5000 s
Hence, The cookie crumbs will travel 50 metres from the kitchen table to the ant hill in 5000 seconds, or almost 83.33 minutes.
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Hunter designs two flags for his adventure club. What is the length of the base, x, of the larger flag? enter your answer, as a decimal, in the box. X = ft.
The required length of the base of larger flag when other sides are specified is calculated to be 6.25 ft.
The given two triangles are the flags of two different sizes. The lengths of various sides are specified.
The length of the base of the larger flag is to be found out.
The given two angles in small flag are equal to the corresponding angles in the large flag.
Two flags are the similar triangles as they look proportionate.
Both triangles' edges are proportional to one another.
So, from the figure, 4/5 = 5/x
x = 25/4 = 6.25 ft
Thus, the required x on the base of bigger flag is 6.25 ft
The given question is incomplete. The figure is missing. It is attached in the figure below.
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What ended the jim crow laws and when??
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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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:
3. A 3.4-kg fireworks rocket is launched vertically into the night sky with an initial speed of 44.2 m/s. The rocket explodes and breaks into two pieces 3.1 seconds later. The first piece has a mass of 2.1-kg and travels 22 m/s at 140 degrees from the point of explosion. (A) What is the mass of the second piece? (B) What is the velocity of the second piece after the explosion?
The total initial momentum of the rocket is 150.28 kg m/s. The total final momentum of the mass fractions is equal to the initial value. From this, the mass of the second piece is 1.3 kg with a velocity of 80 m/s.
What is momentum ?Momentum of an object is the product of its mass and velocity. During a collision, the total momentum will be conserved. Thus, total initial momentum of the system is equal to its total final momentum.
Here, mass of the rocket = 3.4 kg
velocity = 44.2 m/s
then momentum = 3.4 kg × 44.2 m/s = 150.28 kg m/s
The mass of one piece = 2.1 kg.
then mass of second piece of the rocket = 3.4 - 2.1 = 1.3 kg.
velocity of first piece = 22 m/s
then, momentum = 2.1 kg × 22 m/s = 46.2 kg m/s.
Now, momentum of first piece + momentum of second piece = 150.28 kg m/s.
then momentum of second piece = 150.28 - 46.2 = 104 kg m/s.
Therefore, velocity = momentum/mass
v = 104 kg m/s /1.3 kg = 80 m/s.
Therefore, the velocity of the second piece of the rocket after explosion is 80 m/s.
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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
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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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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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 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
The constant of proportionality in a relationship is 0. 5. What equation represents this relationship?.
The equation that represents the relationship with a constant of proportionality of 0.5 is y = 0.5x.
When two variables are related proportionally, it means that their values are related by a constant factor. In other words, if we increase one variable by a certain factor, the other variable will increase by the same factor.
This constant factor is known as the constant of proportionality. It can be represented by the letter k, and is usually determined experimentally by collecting data and analyzing the relationship between the variables.
In this case, we are given that the constant of proportionality is 0.5. This means that for every unit increase in one variable (let's say x), the other variable (let's say y) increases by 0.5 units.
To represent this relationship mathematically, we can use the equation y = kx. Since k is equal to 0.5, the equation becomes y = 0.5x. This equation tells us that if we increase x by one unit, y will increase by 0.5 units.
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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.
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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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 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
URGENT HELP:
Two sine waves of equal frequency are to be compounded, (1) a1= 3.0 × 10–6 m and ϕ0 = 60° and (2) a2= 4.0 × 10–6 m and ϕ0 = 150°. (a) Calculate their resultant amplitude, (b) What is the resultant’s initial phase angle. (c) Draw a circle of reference and a time graph for the sine waves.
Answer:
Explanation:
To solve this problem, we can use the following equations for the addition of two sinusoidal waves:
y1 = A1 sin(ωt + φ1)
y2 = A2 sin(ωt + φ2)
where A1 and A2 are the amplitudes of the waves, ω is the angular frequency, t is time, and φ1 and φ2 are the initial phase angles.
(a) To find the resultant amplitude of the two waves, we can use the following equation:
Ar = √(A1^2 + A2^2 + 2A1A2cos(φ2 - φ1))
where Ar is the resultant amplitude.
Substituting the given values, we get:
Ar = √((3.0 × 10^(-6))^2 + (4.0 × 10^(-6))^2 + 2(3.0 × 10^(-6))(4.0 × 10^(-6))cos(150° - 60°))
Ar ≈ 5.03 × 10^(-6) m
Therefore, the resultant amplitude is approximately 5.03 × 10^(-6) m.
(b) To find the resultant's initial phase angle, we can use the following equation:
tan(φr) = (A1sin(φ1) + A2sin(φ2))/(A1cos(φ1) + A2cos(φ2))
where φr is the initial phase angle of the resultant wave.
Substituting the given values, we get:
tan(φr) = (3.0 × 10^(-6)sin(60°) + 4.0 × 10^(-6)sin(150°))/(3.0 × 10^(-6)cos(60°) + 4.0 × 10^(-6)cos(150°))
φr ≈ 142.85°
Therefore, the resultant's initial phase angle is approximately 142.85°.
(c) The circle of reference and the time graph for the sine waves can be drawn as follows:
Sine Waves
The blue and red arrows represent the maximum displacement of the waves. The black arrow represents the displacement of the resultant wave. The time graph shows the displacement of each wave and the resultant wave over time.
Hair Growth
WARNING: This homework problem is out of left field. It has nothing to do with anything covered in the class. It is just a fun problem to practice unit conversions. It really annoys some people, but it has become a tradition so I'm leaving it in. Buckle up. The subsequent problems will all be on topic.
1a) Suppose your hair grows at the rate of 1/35 in per day. Find the rate at which your hair grows in nm/s.
1b) If an atomic layer is approximately 0.1nm thick, how fast are the protein synthesis machines working in atomic layer/s?
(a) The rate at which your hair grows is approximately 20.3 nm/s.
(b) The protein synthesis machines are working at a rate of approximately 203.2 atomic layers/s.
What is the rate at which your hair grows in nm/s?
First, we need to convert the rate of hair growth from inches per day to nanometers per second. There are 2.54 centimeters in an inch, and 10 million nanometers in a centimeter.
So, we can calculate:
1/35 inch per day = (1/35) x 2.54 cm/inch x 10^7 nm/cm x 1 day/86400 s
= 20.319 nm/s (rounded to three significant figures)
If an atomic layer is approximately 0.1nm thick, then the number of atomic layers formed in one second will be the ratio of the growth rate of the protein synthesis machines to the thickness of an atomic layer.
We can use the growth rate we calculated in part (a) and divide it by 0.1 nm to find the number of atomic layers formed per second:
20.319 nm/s / 0.1 nm/layer = 203.19 layers/s
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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 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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