The amplitude of oscillations A of the scale after the slices of turkey land on the plate is approximately 0.0159 meters.
When the slices of turkey are dropped on the plate, the total initial momentum is:
p = m × v
where m is the total mass of the turkey and v is the initial velocity of the turkey. Since the turkey is dropped from rest, v = 0, and the initial momentum is also zero.
When the turkey lands on the plate, it makes a totally inelastic collision, which means that the turkey and the plate stick together and move as one object. The final momentum of the turkey and the plate is therefore:
p' = (m + M) × V
where M is the mass of the plate, V is the velocity of the turkey and the plate together after the collision.
Since momentum is conserved in the collision, we have:
p = p'
which gives:
m × v = (m + M) × V
Solving for V, we get:
V = (m × v) / (m + M)
The kinetic energy of the turkey just before it lands on the plate is:
K = (1/2) × m × v^2
After the collision, the turkey and the plate are moving together, so their kinetic energy is:
K' = (1/2) × (m + M) × V^2
The difference between the initial and final kinetic energies is converted into potential energy of the spring, which is given by:
U = (1/2) × k × A^2
where k is the force constant of the spring and A is the amplitude of the oscillations.
Using conservation of energy, we have:
K - K' = U
Substituting the expressions for K, K', and V, and solving for A, we get:
A = sqrt[(m × g / k) × ((m + M) / (m^2 + 2 × m × M + M^2))]
Substituting the given values, we get:
A = sqrt[(0.100kg × 9.81m/s^2 / 200N/m) × ((0.100kg + 0.400kg) / (0.100kg^2 + 2 × 0.100kg × 0.400kg + 0.400kg^2))]
A = 0.0159m
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The given question is incomplete, the complete question is :
For lunch you and your friends decide to stop at the nearest deli and have a sandwich made fresh for you with 0.100kg{\rm kg} of turkey. The slices of turkey are weighed on a plate of mass 0.400kg{\rm kg} placed atop a vertical spring of negligible mass and force constant of 200N/m{\rm N/m} . The slices of turkey are dropped on the plate all at the same time from a height of 0.250m{\rm m} . They make a totally inelastic collision with the plate and set the scale into vertical simple harmonic motion (SHM). You may assume that the collision time is extremely small.
What is the amplitude of oscillations A of the scale after the slices of turkey land on the plate?
Learning Goal:
To understand the meaning of Kepler's second law of planetary motion.
Part A
Parts A through C all refer to the orbit of a single comet around the Sun.
Each of the four diagrams below represents the orbit of the same comet, but each one shows the comet passing through a different segment of its orbit around the Sun. During each segment, a line drawn from the Sun to the comet sweeps out a triangular-shaped, shaded area. Assume that all the shaded regions have exactly the same area. Rank the segments of the comet’s orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.
According to Kepler's Second Law, as a planet orbits the Sun, an imaginary line connecting them sweeps across the same amount of space. This means that planets need not travel along their orbits speed.
What purposes does Kepler's law serve?The study of the motion the planets, asteroids, or other space objects inside the solar system makes extensive use of Kepler's laws. They are still used today to create and launch satellites into orbit. The Kepler principles served as inspiration for Newton, who then proposed his original three laws of motion and the concept of universal gravitation.
What is the name of Kepler's first law?The planets' orbits are ellipses with the light at one focus, according to Kepler's First Law, sometimes referred to as The Law on Ellipses. The line between such a planet or the sun sweeps forth equal areas inside the plane of planetary system over equal times, according to Kepler's Second Law, often known as The Law for Equal Areas at Equal Time.
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Use the terms "force", "weight", "mass", and "inertia" to explain why it is easier to tackle a 220 lb football player than a 288 lb football player. << read less.
It would be easier to tackle the 220 lb player because less force is required to change their motion due to their lower inertia.
Force is the interaction between two objects that can cause a change in motion. Weight is a type of force that is caused by gravity acting on an object with mass. Mass is a measure of the amount of matter in an object, and it determines the strength of the gravitational force acting on the object. Inertia is the tendency of an object to resist changes in its state of motion.
When tackling a football player, the player exerts a force on the tackler, and the tackler exerts an equal and opposite force on the player due to Newton's third law of motion. The player's weight is also a force acting on the tackler, and it depends on the mass of the player and the strength of the gravitational field.
The mass of an object determines its inertia, which is the resistance of the object to changes in its state of motion. In other words, an object with a greater mass has a greater inertia, and it requires a greater force to change its motion. Therefore, when tackling a football player, it is easier to tackle a player with a lower mass, or in other words, a lower weight, than a player with a higher mass, or a higher weight.
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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.
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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When does magnetic force push objects apart?
A: when opposite poles of two magnets are facing each other
B: never
C: when like poles of two magnets are facing each other
D: when the objects are made of wood
When two magnets' opposing poles are lined up with one another (option A).
Is strength equivalent to force?As a result of their seeming comparable definitions, force and power are frequently employed interchangeably. They are not equivalent, nevertheless, in physics. Power is a statement of energy used over time, of which force is a component, while force is the essential outcome of a collision between two objects.
What generates force?Every time two things interact, a force is applied to each of them. The force is lost when the interaction between the two items ends. Only through interactions can forces be created.
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WORTH 40 POINTS!!
Label the following geologic map. Click on a label below the map to select it, and then click on the appropriate box on the map to place the label.
1.) Rock age/name
2.) Strike and dip
3.) Rock type
4.) Contact line
5.) Fault line
Geologic map: The correct label as placed in the respective boxes are as follows- is attached to the answer.
What is Geologic map?A geologic map is a scientific illustration that depicts the physical features of a geographic area and the underlying geology. It is used to help interpret the geologic history of a region. Geologic maps are created by geologists and contain information about the distribution of different rock types and other subsurface features. This information is used to interpret the area’s geologic history, understand the resources available in the area, and plan for development and management of the area. Geologic maps include information such as the age and type of rocks, their structures and minerals, faults and folds, and the presence of any surface features such as rivers, lakes, and soils. Geologic maps are used by geologists, engineers, planners, and other professionals to help understand the underlying geology and make decisions about how to use the land.
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6. Find the total impulse of the following graph
The total impulse here is the sum of area of the rectangle and area of the triangle. Here, area of the rectangle is 18 Ns and area of the triangle is -2 Ns, then the total impulse is 16 N.s.
What is impulse ?
Impulse is a physical quantity which measures the change in momentum of the object. The change in momentum is equal to the product of force and time.
thus impulse = F t
From the graph, impulse = area of rectangle + area of triangle
area of rectangle = lb = 2 s × 6 N = 18 N s
area of triangle = 1/2 bh = 1/2 2 s × -2 N = - 2 N.s
Total impulse from the graph = -2 Ns + 18 Ns = 16 N.s.
Therefore, the total impulse of the object obtained from the graph is 16 N.s.
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What chemical did Dr Julian first synthesize that changed the world and why was this considered such an important discovery?
Answer:
Julian (1899-1975) first synthesized the drug physostigmine, previously only available from its natural source, the Calabar bean. His pioneering research led to the process that made physostigmine readily available for the treatment of glaucoma.
Answer:
Julian (1899-1975) first synthesized the drug physostigmine, previously only available from its natural source, the Calabar bean. His pioneering research led to the process that made physostigmine readily available for the treatment of glaucoma.
how many pattern block hexagons would 2 trapezoids create
To make two hexagons out of pattern blocks, you need 12 trapezoids.
Explain about the term hexagons?A closed, two-dimensional polygon containing six sides is what is known as a hexagon. Six vertices and six angles make up a hexagon.
You need to utilize a total of 12 trapezoids to make two hexagons using pattern blocks. You will also need 2 hexagons to employ all twelve trapezoids because each hexagon has six trapezoids in it. Trapezoids can be arranged in a pattern with two triangles, 2 parallelograms, 2 rhombuses, and 2 trapezoids to create the two hexagons. These 12 trapezoids can be used to form two full hexagons.Thus,
You need 12 trapezoids to build two hexagons out of pattern blocks.Six trapezoids form each hexagon.Since you require two hexagons, a total of 12 trapezoids are required.To know more about the hexagons, here
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What is INTEGRITY? Why is it necessary in our school community? Why is it necessary in society in general? What does it look like in practice?
Integrity is the quality of being honest, truthful, and morally upright. It means doing the right thing even when no one is watching, and being accountable for one's actions.
Why is Integrity necessary?
In our school community, integrity is essential as it ensures that students and faculty members act with honesty and ethics in all their interactions. It creates a safe and trustworthy environment where individuals are respected, and their contributions are valued. Without integrity, academic performance, reputation, and character can be damaged, which can negatively impact the school community.
Integrity is also necessary in society in general, as it ensures that individuals act with honesty, ethics, and fairness in all their interactions. It helps to create a sense of trust and respect among people, which is essential for building positive relationships and fostering a healthy community. In business and professional settings, integrity is crucial as it helps to build credibility, establish trust, and maintain good relationships with clients and stakeholders.
In practice, integrity looks like individuals acting with honesty, ethics, and moral values in all their interactions. It means taking responsibility for one's actions, being accountable for one's mistakes, and working towards making things right when something goes wrong. It also means being respectful of others, treating them with dignity, and valuing their contributions. In the school community, it looks like students and faculty members conducting themselves with honesty and integrity in academic and personal settings.
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please answer this question!!
Answer:
14.75m
Explanation:
k=504N/m
m=11.2g =0.0112kg
x=7.66cm =0.0766m
9=9.8
h = kx^2/2mg
=504×(0.0766)^2/2×0.0112×9.8
=2.95/0.2
h=14.75m
How to solve this problem
The displacement vectors in component form are A = 1.732 km i + 1 km j and B = -2.955 km i - 0.522 km j.
The distance from home when cell phone rings is 1.309 km.
The direction from home when phone rings is 21.48° West of South.
How to express displacement vectors?(a) The displacement vector A can be expressed in component form as:
A = 2 km [cos(30°) i + sin(30°) j] = 2 km [√3/2 i + 1/2 j] ≈ 1.732 km i + 1 km j
The displacement vector B can be expressed in component form as:
B = 3 km [cos(280°) i + sin(280°) j] = 3 km [-0.985 i - 0.174 j] ≈ -2.955 km i - 0.522 km j
(b) The total displacement vector (C) is the sum of vectors A and B, which can be found by adding the corresponding components:
C = A + B = (1.732 - 2.955) km i + (1 - 0.522) km j = -1.223 km i + 0.478 km j
The magnitude of the resulting vector C can be found using the Pythagorean theorem:
|C| = √((-1.223)² + (0.478)²) ≈ 1.309 km
Therefore, you are about 1.309 km away from home when your cell phone rings.
(c) The direction of the resulting vector C can be found using the inverse tangent function:
θ = tan^-1(0.478/-1.223) ≈ -21.48°
Since the direction is measured with respect to the positive x axis, the direction from "home" to "you" when the phone rings is about 21.48° West of South.
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in an electroscope being charged by induction, what happens when the charging rod is moved away before the ground is removed from the knob?
The electroscope will remain charged and continue to show the presence of an electric charge if the ground is withdrawn from the knob before the charging rod is removed.
An early scientific tool used to find electrical charge on a body is called an electroscope. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.
There are three traditional electroscope types: the needle electroscope, the gold-leaf electroscope, and the pith-ball electroscope (third).
electroscopes are utilized to determine whether a body has an electric charge. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.
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the volume of a cylinder is given by (pi)r^2h where r is the radius of the cylinder and h is the height. which expression represents the volume of this can? 3(pi)x^23
Answer:
Explanation:
The volume of a cylinder is given by the formula V = (pi)r^2h, where V is the volume, r is the radius, and h is the height. To represent the volume of a cylinder with a specific radius and height, we would substitute those values into the formula.
For example, if the radius of a cylinder is 4 cm and the height is 10 cm, the volume can be calculated as:
V = (pi)(4 cm)^2(10 cm) = 160(pi) cubic centimeters
Vectors A and B have equal magnitudes of 5.7 u. If the sum of the vectors is 1.2 j. Determine the angle in radians between the vectors.
The angle in radians between the vectors is; 2.93 radians
What is the angle between the vectors?We are given that Vectors A and B have equal magnitudes of 5.7
The sum of the vectors is 1.2j. Thus;
A + B = 1.2 j^
Thus;
(A_x + B_x)i^ + (A_y + B_y)j^ = 0i^ + 1.2 j^
Because the vectors have the same magnitude and x components of equal magnitude but of opposite sign, the vectors are reflections of each other in the y axis. Therefore, the two vectors have the same y components:
A_y = B_y = (1/2) * 1.2 = 0.6
If θ is the angle between either A or B and the y axis, then;
cos θ = 0.6/5.7
cos θ = 0.1053
θ = 83.96°
Thus;
Angle between two vectors is;
2 * 83.96° = 167.92°
Converting to radians gives 2.93 radians
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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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How can motion be measured?
Motion can be measured in several ways, depending on the context and the specific parameters that need to be quantified.
What is Motion?
Motion is a fundamental concept in physics and is described by the laws of motion formulated by Sir Isaac Newton. These laws state that an object at rest tends to remain at rest and an object in motion tends to remain in motion with the same velocity . The study of motion is important in many fields, including physics, engineering, and astronomy.
Motion can be measured in several ways, depending on the context and the specific parameters that need to be quantified. Some common methods of measuring motion include:
Displacement: Displacement is the change in position of an object over a certain period of time. It can be measured using a ruler, tape measure, or other distance-measuring tools.
Speed: Speed is the rate at which an object moves, and it can be measured using a stopwatch or other timing device to determine the time it takes for an object to travel a certain distance.
Velocity: Velocity is similar to speed, but it takes into account both the speed and direction of motion. It can be measured using a velocity sensor or other motion-tracking tools.
Acceleration: Acceleration is the rate at which an object's speed or velocity changes over time, and it can be measured using an accelerometer or other motion-tracking tools.
Gyroscopic sensors: Gyroscopic sensors can be used to measure the rotational motion of an object, such as the rotation of a wheel or the movement of a drone.
Video analysis: Video analysis software can be used to track the movement of an object or a person, using visual markers or other reference points to determine motion.
Inertial measurement units (IMUs): IMUs are electronic sensors that can measure motion, acceleration, and rotation in three-dimensional space, and are commonly used in robotics, virtual reality, and other applications.
These are just a few examples of methods used to measure motion, and there are many other tools and techniques that can be used depending on the specific context and requirements.
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QUESTION 4
What's the speed of electromagnetic waves (light waves)?
300,000 km/s
300, 000 m/s
30,000 km/s
It depends on wavelength.
Explanation:
answer is mention in above pdf please check it
A ball with mass m is suspended from a roof with a rope of length L. The ball spins in a circle making a constant angle θ with the vertical as shown. Write an expression for the speed v of the ball in terms of m, L, θ, and g.
The speed v of the ball can be determined using the centripetal force equation Fc = mv^2/r.
The centripetal force is provided by the tension in the rope and the weight of the ball. We can write the equation as:
Tcosθ - mg = mv^2/L
From this equation, we can solve for the speed v: v = sqrt((Tcosθ - mg)L/m).
We can also express the tension T in terms of the angle θ and the length L using the equation Tsinθ = mv^2/L.
Substituting this into the previous equation gives us: v = sqrt((Lsinθcosθ - mgL)/m)
This is the expression for the speed v of the ball in terms of m, L, θ, and g.
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A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?.
The conservation of mechanical energy is independent of mass because the energy is proportional to both mass and velocity, and any changes in one factor are balanced out by changes in the other factor.
The conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy in a closed system remains constant over time, provided that no external forces act on the system.
When a ball falls from a shelf, its potential energy (due to its position above the ground) is converted into kinetic energy (due to its motion as it falls). The total amount of mechanical energy in the system (the ball and the Earth) is conserved, even though the mass of the ball is different from the mass of Earth.
This is because the potential energy of the ball is proportional to its mass and height above the ground, while the kinetic energy of the ball is proportional to its mass and velocity. As the ball falls, its potential energy decreases, while its kinetic energy increases by an equal amount, such that the total mechanical energy of the system (ball and Earth) remains constant.
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Answer: Mass is eliminated when equating gravitational potential energy with kinetic energy.
Explanation:
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.
For a system in simple harmonic motion, which of the following is the time required to complete a cycle of motion?
(a) Amplitude
(b) Period
(c) Frequency
(d) Revolution.
The period of a system in simple harmonic motion is the time required to complete a single cycle of motion.
What is harmonic motion?Harmonic motion is a type of motion that is periodic and repetitive. It is characterized by motion in a single plane and can be described as a sinusoidal wave. This type of motion is most commonly encountered in oscillatory systems, such as springs, pendulums, and electrical circuits. The motion is caused by a restoring force that pushes the system back to its equilibrium position when it has been displaced. The restoring force causes the system to oscillate between two points, which are known as the equilibrium points.
The amplitude, frequency, and revolution are all related to the period, but they do not directly refer to the amount of time required to complete a cycle.
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calculate the temperature of a blackbody if the spectral distribution peaks at each of the following wavelengths.
a. gamma rays, λ = 10^-14 m
_____ K
b. x rays, λ = 1.03 nm
_____ K
c. red light, λ = 690 nm
_____ K
d. broadcast television waves, λ = 1 m
_____ K
e. AM radio waves, λ = 224 m
_____ K
The temperature of a blackbody if the spectral distribution peaks at each of the following wavelengths:
a. gamma rays, λ = 10^-14 m 2.898 × 10^11 K.
b. x rays, λ = 1.03 nm 2.811 × 10^6 K.
c. red light, λ = 690 nm 4,203 K.
d. broadcast television waves, λ = 1 m 2.898 × 10^-3 K.
e. AM radio waves, λ = 224 m 1.295 × 10^-5 K.
What do you mean by wavelength?
Wavelength is a fundamental concept in physics and refers to the distance between consecutive peaks or troughs in a wave. It is commonly represented by the Greek letter lambda (λ).
In the context of electromagnetic waves, which include light, radio waves, X-rays, and other types of radiation, wavelength refers to the distance between two adjacent peaks or troughs of the wave. In a vacuum, all electromagnetic waves travel at the same speed, known as the speed of light, which is approximately 3.00 × 10^8 meters per second (m/s). The wavelength of electromagnetic waves is typically measured in units of meters, but can also be expressed in units such as nanometers (10^-9 meters) or micrometers (10^-6 meters), depending on the scale of the wave being measured.
The peak wavelength of a blackbody's spectral distribution is related to its temperature through Wien's displacement law:
λ_peak = b / T
where λ_peak is the peak wavelength of the spectral distribution, T is the temperature of the blackbody, and b is a constant known as Wien's displacement constant, with a value of approximately 2.898 × 10^-3 m K.
a. For a peak wavelength of λ = 10^-14 m, we have:
T = b / λ_peak = 2.898 × 10^-3 m K / 10^-14 m = 2.898 × 10^11 K
b. For a peak wavelength of λ = 1.03 nm, we have:
T = b / λ_peak = 2.898 × 10^-3 m K / (1.03 × 10^-9 m) = 2.811 × 10^6 K
c. For a peak wavelength of λ = 690 nm, we have:
T = b / λ_peak = 2.898 × 10^-3 m K / (690 × 10^-9 m) = 4,203 K
d. For a peak wavelength of λ = 1 m, we have:
T = b / λ_peak = 2.898 × 10^-3 m K / 1 m = 2.898 × 10^-3 K
(Note that this temperature is extremely low, near absolute zero, and is not physically realistic for a blackbody.)
e. For a peak wavelength of λ = 224 m, we have:
T = b / λ_peak = 2.898 × 10^-3 m K / 224 m = 1.295 × 10^-5 K
(Note again that this temperature is extremely low and not physically realistic for a blackbody.)
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a)write an equation for the magnitude of this systems acceleration. use the variables from the problem statement together with g for acceleration from gravity in order to write you equation.b) calculate the magnitude of the systems acceleration in m/s^2
The equation for the magnitude of the system's acceleration is a = g + (2M/m), where g is the acceleration due to gravity and M and m are the masses of the two objects.
What is acceleration ?Acceleration is the rate of change of velocity in an object over time. It is the rate of change of the speed of an object, and is defined as the change in velocity divided by the change in time. In other words, it is the rate at which an object's speed changes. Acceleration can be caused by a change in the speed of an object, or by a change in its direction. It is usually measured in meters per second squared (m/s2). Acceleration can be either positive or negative, depending on the direction of the change in velocity.
a = g + (2M/m)
a = 9.81 m/s^2 + (2(8 kg)/(3 kg)) = 13.87 m/s^2
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A cat chasses a mouse across a 1.0 m high table. The mouse steps out of the way and the car slides off the table and strikes the floor 2.2m from the edge of the table. When the cat slid off the table, what was its speed?
The speed of the cat when it slid off the table would be 4.43 m/s.
What is speed?Speed is defined as the rate of motion or action, or the rate of change of something. It is typically measured in terms of distance over time, such as kilometers per hour (km/h) or miles per hour (mph). Speed can also be expressed in terms of velocity, which is the rate of change in position. Velocity is measured in meters per second (m/s). In physics, speed is a scalar quantity, meaning it is a magnitude, or numerical value, without direction.
The speed of the cat can be calculated using the equation v^2=2gh, where v is the speed, g is the acceleration due to gravity (9.81 m/s^2), h is the height of the table (1.0 m).
So, the speed of the cat when it slid off the table would be:
v = sqrt(2*9.81*1.0) = 4.43 m/s
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In a 42 s interval, 597 hailstones strike a glass window of area 0.597 m2 at an angle 50◦ to the window surface. Each hailstone has a mass of 6 g and speed of 6.3 m/s. If the collisions are elastic, find the average force on the window.
Answer in units of N.
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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What is rill erosion
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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A pickup truck, parked on a hill that is 11.8 m high, is accidently left in neutral without the parking brake applied.
The truck begins rolling down the hill. At the bottom, it continues rolling along a horizontal road. A 104.3-kg man jumps in the back, causing the truck's speed to reduce to 14.5 m/s. What is the mass of the truck? Ignore friction
The mass of the truck is equal to (104.3 kg x 14.5 m/s) / 11.8 m/s, which is approximately 119.4 kg.
What is mass?Mass is a measure of the amount of matter contained in an object. It can be measured using scales, balances or other measuring instruments. Mass is a fundamental property of all matter, and its measurement is the basis for many scientific and engineering calculations. Mass is not the same as weight, which is a measure of the force exerted by gravity on an object. Mass is often expressed in units such as kilograms or grams.
The mass of the truck can be determined using the law of conservation of momentum. Momentum is defined as the product of mass and velocity, so the momentum of the truck before the man jumps in is equal to the momentum of the truck and man after the man jumps in.
The momentum of the truck before the man jumps in is equal to the truck's mass multiplied by its velocity, which is 11.8 m/s. The momentum of the truck and man after the man jumps in is equal to the mass of the truck plus the man, multiplied by the reduced velocity of 14.5 m/s.
Therefore, the mass of the truck is equal to (104.3 kg x 14.5 m/s) / 11.8 m/s, which is approximately 119.4 kg.
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