Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
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A wave oscillates 5.0 times a second and has a speed of 4.0 m/s
A.What is the frequency of this wave?
Express your answer to two significant figures and include the appropriate units.
b.What is the period of this wave?
Express your answer to two significant figures and include the appropriate units.
c.What is the wavelength of this wave?
Express your answer to two significant figures and include the appropriate units.
may or may not be lying. ＼(^_^)／
a. f = 5.0 Hz
b. T = 1/f
1/5.0 Hz
period of 0.20 s
c. λ = v/f
4.0 m/s / 5.0 Hz
wavelength of 0.80 m
IG:whis.sama_ent
A wave oscillates 5.0 times a second and has a speed of 4.0 m/s.
A. The frequency of any wave is the number of times it oscillates in one second. That's given in the question.
Frequency = 5.0 Hertz.
B. The period of any wave is the reciprocal of its frequency.
Period = (1 / 5.0 Hz)
Period = 0.2 second .
C. The wavelength of any wave is (speed / frequency).
Both of these numbers are given in the question.
Wavelength = (4.0 m/s) / (5.0 Hz) .
Wavelength = 0.8 meter .
What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when 1.00 x 10ᵌ V is appled to it? (Such a rod may be used to make nuclear-particle detectors, for example.)
Answer: 1.68 A (Amperes)
Explanation:
To calculate the current flowing through the silicon rod, we need to use Ohm's law, which states that the current (I) flowing through a conductor is equal to the voltage (V) applied across it divided by the resistance (R) of the conductor:
I = V/R
The resistance (R) of the silicon rod can be calculated using the formula:
R = ρL/A
where ρ is the resistivity of silicon, L is the length of the rod, and A is the cross-sectional area of the rod.
The resistivity of pure silicon at room temperature is approximately 2.3 x 10^-3 Ω m. The cross-sectional area of the rod can be calculated using the formula for the area of a circle:
A = πr^2
where r is the radius of the rod, which is half of its diameter. Substituting the given values, we get:
r = 2.54/2 = 1.27 cm = 0.0127 m
A = π(0.0127)^2 = 5.083 x 10^-4 m^2
Now we can calculate the resistance of the rod:
R = (2.3 x 10^-3 Ω m)(20.0 cm/100 cm)/5.083 x 10^-4 m^2 = 9.035 Ω
Finally, we can use Ohm's law to calculate the current flowing through the rod:
I = V/R = (1.00 x 10^3 V)/9.035 Ω = 1.68 A
Therefore, the current flowing through the silicon rod is 1.68 Amperes.
A team of students conducts a series of experiments to investigate collisions. In the first experiment, the two carts collide with each other on a smooth surface. The carts stick together and continue to move forward. In the second experiment, the two carts collide with each other on a rough surface. The carts stick together and quickly come to rest. In both experiments, the initial speeds of the carts are identical. Is there a difference in the total energy of the two experiments?
A.
No, because the kinetic energy of the two-cart system after the collision is the same in both the experiments.
B.
No, because the sum of the kinetic energy and thermal energy of the two-cart system after the collision is the same in both experiments.
C.
Yes, because the kinetic energy of the two-cart system in the second experiment after the collision is less than that of the first experiment.
D.
Yes, because the sum of the kinetic energy and thermal energy of the two cart system in the second experiment after the collision is less than that of the first experiment.
If a team of students conducts a series of experiments to investigate collisions. C. Yes, because the kinetic energy of the two-cart system in the second experiment after the collision is less than that of the first experiment.
What is difference in the total energy of the two experiments?In the first experiment, the two carts collide on a smooth surface and stick together, so the kinetic energy of the system after the collision is entirely in the form of translational kinetic energy of the combined carts.
In the second experiment, the two carts collide on a rough surface and stick together, so some of the kinetic energy is converted into thermal energy due to friction between the carts and the surface. This means that the kinetic energy of the system after the collision is less than in the first experiment.
Option A is incorrect because the kinetic energy is not necessarily the same in both experiments.
Option B is incorrect because the thermal energy is not necessarily the same in both experiments.
Option D is incorrect because the thermal energy is not considered in the calculation of the total energy of the system after the collision.
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US President Biden will sign an agreement to end the national emergency of COVID-19 in advance, which is strongly opposed by the White House spokesman
US President Biden signed an agreement to end the national emergency of COVID-19 in advance, but it was strongly opposed by the White House spokesman.
What is COVID-19?The new coronavirus SARS-CoV-2 is the cause of the extremely contagious disease COVID-19. The virus was discovered for the first time in Wuhan, China, in December 2019, and it spread fast over the world, causing a pandemic. When an infected person coughs, sneezes, or talks, respiratory droplets from their mouth or nose are the main means of disease transmission.
On April 10, 2023, President Biden approved legislation written by Republicans that put an end to the COVID-19 pandemic's state of emergency. Notwithstanding the fact that the White House intended to stop making emergency declarations on May 11, the GOP's proposed legislation received some bipartisan support in Congress. The measure, according to the White House, "would generate widespread turmoil and uncertainty throughout the health care system – for states, for hospitals and doctor's offices, and, most crucially, for tens of millions of Americans," A White House representative, however, downplayed the significance of the law, stating that the end of the emergency "does not affect our ability to wind down authorities in an orderly manner."
A White House representative later minimized the bill's effects, saying they would not have an impact on the scheduled wind-down of authority on May 11.
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State the difference between positive and negative zero error of a vernier calliper
Equal volumes of two fluids are added to the U-shaped pipe as shown in the figure below. The pipe is open at both ends and the fluids come to equilibrium without mixing. What is the ratio B/A of the fluid densities? (Assume the ratio air/fluid for fluids A and B is small enough to be neglected. Use the following as necessary: h.)?
The ratio of density of fluid A to that of fluid B is 1/3.
From the figure,
The distance of the fluid A to the line B from the top of the fluid, d₁ = 3h
The distance of the fluid B to the line B from the top of the fluid, d₂ = h
According to Pascal's law, pressure of A is equal to that of B, along the same horizontal line.
P(A) = P(B)
ρ₁gd₁ = ρ₂gd₂
Therefore, the ratio of density of fluid A to that of fluid B,
ρ₁/ρ₂ = d₂/d₁
ρ₁/ρ₂ = h/3h
ρ₁/ρ₂ = 1/3
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Your question was incomplete. Attaching the image file here.
A ball has a mass 0f 2Kg and a diameter of 50cm calculate the buoyant force and water displaces...
The buoyant force acting on the ball is 5134.7 N and the water displaced by the ball is 0.5236 [tex]m^{3}[/tex] (or 523.6 L).
We use the following formula:
Weight of displaced water = Buoyant force
Volume of water displaced times water's density equals the weight of the water.
The first step is to calculate the volume of the ball:
Volume of ball = ([tex]\frac{4}{3}[/tex]) × π × [tex]\frac{diameter}{2}^3[/tex]
Volume of ball = ([tex]\frac{4}{3}[/tex]) × π × [tex](\frac{50 cm}{2})^3[/tex]
Volume of ball = 0.5236 [tex]m^{3}[/tex]
Next, calculate water displaced:
Density of water = 1000 [tex]\frac{kg}{m^3}[/tex](at standard conditions)
Weight of water displaced = 1000 [tex]\frac{kg}{m^3}[/tex] × 0.5236 [tex]m^{3}[/tex]
Weight of water displaced = 523.6 kg
Finally, we can calculate the buoyant force:
Buoyant force = weight of water displaced
Buoyant force = 523.6 kg x 9.81 [tex]\frac{m}{s^2}[/tex]
Buoyant force = 5134.7 N
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A simple pendulum consisting of a bob of mass m
attached to a string of length L
swings with a period T
.
Part A
If the bob's mass is doubled, approximately what will the pendulum's new period be?
Part B
If the pendulum is brought on the moon where the gravitational acceleration is about g/6
, approximately what will its period now be?
T/6
T/√6
√6T
6T
Part C
If the pendulum is taken into the orbiting space station what will happen to the bob?
View Available Hint(s)for Part C
If the pendulum is taken into the orbiting space station what will happen to the bob?
It will continue to oscillate in a vertical plane with the same period.
It will no longer oscillate because there is no gravity in space.
It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall.
It will oscillate much faster with a period that approaches zero.
Answer: Part A:
The period of a simple pendulum is given by the formula: T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If the mass of the bob is doubled, the period of the pendulum will change. To see how much it changes, we can use the fact that the period depends only on the length of the pendulum and the acceleration due to gravity, and not on the mass of the bob. Therefore, the new period of the pendulum will be the same as the old period: T.
Part B:
If the pendulum is brought to the moon, where the acceleration due to gravity is about g/6, the new period of the pendulum can be found using the same formula as before: T = 2π√(L/g). However, now we need to use the value of the acceleration due to gravity on the moon, which is g/6. Therefore, the new period of the pendulum is T' = 2π√(L/(g/6)) = 2π√(6L/g) = √6T.
Therefore, the answer is: T/√6.
Part C:
If the pendulum is taken into an orbiting space station, the bob will continue to oscillate in a vertical plane with the same period as it did on the surface of the Earth. This is because the period of the pendulum depends only on the length of the pendulum and the acceleration due to gravity, and not on the location of the pendulum. In the space station, both the pendulum and the point to which it is attached are in free fall, but they are falling together and maintaining their relative positions, so the pendulum will continue to oscillate as before.
After coming down a slope, a 60-kg skier is coasting northward on a level, snowy surface at a constant 15 m>s. Her 5.0-kg cat, initially running southward at 3.8 m>s, leaps into her arms, and she catches it. (a) Determine the amount of kinetic energy converted to internal energy in the Earth reference frame. (b) What is the velocity, measured in the Earth reference frame, of an inertial reference frame in which the cat’s kinetic energy does not change?
The velocity, measured in the Earth reference frame, of an inertial reference frame in which the cat's kinetic energy does not change is equal to the velocity of the skier before the collision. The velocity of the skier before the collision is 15 m/s.
What is law of conservation of momentum?According to the law of conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision. This can be expressed as m1*v1 + m2*v2 = (m1 + m2)*vf, where m1 and m2 are the masses of the skier and the cat respectively, v1 is the velocity of the skier, and vf is the velocity of the skier and the cat after the collision.
The kinetic energy converted to internal energy in the Earth reference frame can be determined by applying the law of conservation of momentum.
The amount of kinetic energy converted to internal energy can be calculated as follows:
m1*v1 = (m1 + m2)*vf
vf = (m1*v1)/(m1 + m2)
KE = (1/2)*m2*v2²
KE converted = KE initial - KE final
KE converted = (1/2)*m2*v2² - (1/2)*m2*((m1*v1)/(m1 + m2))²
KE converted = (1/2)*m2*v2² - (1/2)*m2*((60*15)/(60 + 5))²
KE converted = (1/2)*5*3.8² - (1/2)*5*(15²/65)
KE converted = 28.8 - 22.15
KE converted = 6.65 J
The velocity, measured in the Earth reference frame, of an inertial reference frame in which the cat's kinetic energy does not change is equal to the velocity of the skier before the collision.
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The chains of a swing on a playground swing set are 4.0 m
long. What is the period of this swing?
Express your answer to two significant figures and include the appropriate units.
Answer:
2.54 seconds
Explanation:
The period of a swing on a playground swing set can be calculated using the formula:
T = 2π√(L/g)
where T is the period, L is the length of the swing's chain, and g is the acceleration due to gravity, which is approximately 9.81 m/s².
Substituting the given values, we get:
T = 2π√(4.0 m/9.81 m/s²)
T = 2π√0.407
T = 2.54 s (rounded to two significant figures)
Therefore, the period of the swing is 2.54 seconds.
Hope this helps!
Calculate the range in cm of 400keV beta ray(2.27 MeV from 90Y in bone of density 1.9g/cm3
The range of a 400 keV beta particle (2.27 MeV from 90Y) in bone with a density of 1.9 g/cm3 is approximately 0.000197 cm.
Using the Bethe-Bloch formula, the range of a 400 keV beta particle in bone with a density of 1.9 g/cm3 can be calculated as:
[tex]R = 0.415 * (E/ \rho Z^2) * (1/\beta^2 - 1)[/tex]
where R is the range in cm, E is the kinetic energy of the beta particle in MeV, ρ is the density of the material in g/cm3, Z is the atomic number of the material, and β is the velocity of the beta particle as a fraction of the speed of light.
Plugging in the given values, we get:
[tex]R = 0.415 * (0.4 / (1.9 * 22.5^2)) * (1 / (1 - (0.4 / 2.27)^2)) \\R = 0.415 * (0.4 / 966.375) * (1 / 0.858) \\R = 0.000197 cm[/tex]
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A 25.00-V battery is used to supply current to a Ω10-kΩ resistor. Assume the voltage drop across any wires used for connections is negligible. (a) What is the current through the resistor? (b) What is the power dissipated by the resistor? (c) What is the power input from the battery, assuming all the electrical power is dissipated by the resistor? (d) What happens to the energy dissipated by the resistor?
a. The current through the resistor is 2.50 milliamperes. b. The power dissipated by the resistor is 62.5 milliwatts. c. The power input from the battery is also 62.5 milliwatts. d. The energy dissipated by the resistor is converted into heat energy and is lost to the surroundings.
The current through the resistor can be found using Ohm's law:
I = V/R = 25.00 V / 10 kΩ = 2.50 mA
The power dissipated by the resistor can be found using the formula:
P = I² R
Substituting the values, we get:
P = (2.50 x 10⁻³ A)² x 10 kΩ = 62.5 mW
The power input from the battery can be found using the formula:
P = IV
Substituting the values, we get:
P = (2.50 x 10⁻³ A) x 25.00 V = 62.5 mW
The energy dissipated by the resistor is converted into heat energy and is lost to the surroundings. This is known as joule heating or ohmic heating, where the electrical energy is converted into thermal energy due to the resistance of the material.
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How does our viewing angle from earth affect what type of agn we observe?
Our viewing angle from Earth can affect the type of AGN (Active Galactic Nuclei) we observe. If we view an AGN from the direction of its accretion disk, we see a quasar, which is an incredibly bright object.
How does the viewing angle from earth affect how we observe?if we view the same AGN from a different angle, we may see a less bright active galactic nucleus, such as a Seyfert galaxy or a blazar. This is because the orientation of the accretion disk and the angle of the jets relative to our line of sight can affect the amount of radiation that reaches us.
In some cases, the orientation of the AGN can also affect the appearance of its emission lines. For example, in a type 2 Seyfert galaxy, which is viewed at an angle where the accretion disk is obscured by a thick torus of dust and gas, the broad emission lines that are typically seen in type 1 Seyfert galaxies may be absent or significantly narrower. Thus, the viewing angle from Earth plays an important role in the study of AGN and their properties.
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Spin-offs from the aerospace industry have contributed to Floridas economy and the economy of the United States what is a spinoff
A spinoff, in the context of the aerospace industry, refers to the transfer of technology or knowledge developed for a specific space or aviation program to other fields or industries.
The technology and knowledge developed for aerospace programs often have applications beyond the aerospace industry, and these applications can lead to the creation of new products, services, and industries.
For example, the development of lightweight, high-strength materials for use in spacecraft can also be applied to other industries such as the automotive, sporting goods, and construction industries. Similarly, the development of advanced computer systems and software for use in spacecraft can be applied to other industries such as healthcare, finance, and telecommunications.
Spinoffs from the aerospace industry have contributed to the economy of Florida and the United States by creating new jobs, new products, and new industries. The transfer of technology and knowledge from the aerospace industry to other fields has also led to advancements in a wide range of areas, from medicine to transportation to telecommunications, that have improved the quality of life for people around the world.
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a student rises their 15 kg back pack from the froor at a constant velocity of 5.0 m/s. How much force must the student apply
a student rises their 15 kg back pack from the floor at a constant velocity of 5.0 m/s then they apply of 37.5 N of force.
Force is responsible for the motion of an object. it produces acceleration in the body. According to newton's second law force is mass times acceleration i.e. F =ma. Its SI unit is N which is equivalent to kg.m/s². There are two types of forces, balanced force and unbalanced force.
In this problem student rises 15 kg of backpack at constant velocity and it happens in 2s, so consider time t = 2s.
Force is change in velocity with respect to time multiplied by mass.
F = m dv/dt
F = 15 kg × 5.0 m/s/2s
F = 37.5 N
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After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 51.0 cm
. The explorer finds that the pendulum completes 110 full swing cycles in a time of 133 s
.
Part A
What is the magnitude of the gravitational acceleration on this planet?
Express your answer in meters per second per second.
The period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
We can rearrange this formula to solve for g:
g = (4π²L)/T²
Plugging in the given values:
L = 51.0 cm = 0.510 m
T = 133 s / 110 = 1.209 s
(Note that we divide the total time by the number of cycles to get the time for one cycle.)
So,
g = (4π² × 0.510 m) / (1.209 s)²
= 9.57 m/s²
Therefore, the magnitude of the gravitational acceleration on this planet is approximately 9.57 m/s².
*IG:whis.sama_ent*
Answer: 7.68 m/s²
Explanation: The period of a simple pendulum is given by the formula:
T = 2π√(L/g)
where T is the period, L is the length of the pendulum, and g is the gravitational acceleration.
In this problem, the pendulum completes 110 full swing cycles in a time of 133 s, which means that the period of the pendulum is:
T = 133 s / 110 = 1.209 s
Substituting this into the formula above and solving for g, we get:
g = (4π²L) / T² = (4π²)(0.51 m) / (1.209 s)² ≈ 7.68 m/s²
Therefore, the magnitude of the gravitational acceleration on this planet is approximately 7.68 m/s².
A 47 Ώ (Ohm) resistor and a 28 Ώ (Ohm) resistor are connected in series to a 12-V battery.
(a) What is the current flowing through each resistor?
(b) What is the voltage difference across each resistor?
(a)
To find the current flowing through each resistor, we can use Ohm's Law, which states that the current (I) through a resistor is equal to the voltage (V) across the resistor divided by the resistance (R) of the resistor:
I = V / R
As there is only one path for the current to go in the series circuit, the current flowing through both resistors is the same.
We can determine the current flowing through the circuit using the values provided in the problem by doing the following:
Total resistance (Rt) = 47 Ώ + 28 Ώ = 75 Ώ
Total current (It) = V / Rt = 12 V / 75 Ώ = 0.16 A
Therefore, the current flowing through each resistor is 0.16 A.
(b)
We may apply Ohm's Law once more to determine the voltage difference between each resistor, but this time we will solve for the voltage:
V = I x R
The voltage difference across each resistor can be determined using the values provided in the problem as follows:
Voltage across 47 Ώ resistor = 0.16 A x 47 Ώ = 7.52 V
Voltage across 28 Ώ resistor = 0.16 A x 28 Ώ = 4.48 V
Therefore, the voltage difference across the 47 Ώ resistor is 7.52 V, and the voltage difference across the 28 Ώ resistor is 4.48 V.
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The angle of reflection is 15°, and the incident ray is bent 15° below the normal
What will be the difference in thinking when you turn it?
The angle of reflection is the angle between the reflected ray and the normal to the surface
What is the difference in thinking?The angle of reflection is the angle made by the reflected ray with the surface, measured relative to the normal, and is equal to the angle of incidence, which is the angle between the incident ray and the normal.
The angle of reflection can be determined using the law of reflection, which states that the angle of incidence is equal to the angle of reflection. This law applies to the reflection of light, sound, and other waves from a smooth, flat surface, such as a mirror or a still body of water.
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phet circuit lab pls help
Series (ckt II) will have greater resistor voltage equal to 20v as the voltage will add in series.
What is Battery Current?
Battery current refers to the flow of electric charge in a circuit that is provided by a battery. In simpler terms, it is the amount of electric current that is being drawn from or supplied to a battery. Battery current is measured in amperes (A) and can be either positive or negative, depending on whether the battery is being charged or discharged.
When a battery is being discharged, the current flows from the battery's positive terminal through the external circuit and back to the negative terminal. This is referred to as the discharge current, and its magnitude is determined by the resistance of the circuit and the voltage of the battery.
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If the air inside a balloon exerts a force of 1 N on an area of 0.5 m^2 what is the pressure inside the balloon
Answer:
2 Pascal (Pa)
Explanation:
Pressure is defined as the force acting per unit area. Mathematically, it is expressed as:
Pressure (P) = Force (F) / Area (A)
Given:
Force exerted by the air inside the balloon (F) = 1 N
Area of the balloon (A) = 0.5 m^2
Plugging in the given values into the formula for pressure, we get:
P = F / A
P = 1 N / 0.5 m^2
Using basic arithmetic, we can calculate the pressure inside the balloon:
P = 2 N/m^2
So, the pressure inside the balloon is 2 N/m^2, which is also commonly referred to as 2 Pascal (Pa) since 1 Pascal is equal to 1 N/m^2.
Which describes Hans Oersted’s work with electricity and magnetism?
He discovered electromagnetic induction after seeing a compass needle deflected by a flowing electric current.
He discovered electromagnetism after seeing a compass needle deflected by a flowing electric current.
He discovered electromagnetic induction after seeing a changing magnetic field generate an electric current. ( not C)
He discovered electromagnetism after seeing a changing magnetic field generate an electric current.
The correct statement is" He discovered electromagnetic induction after seeing a changing magnetic field generate an electric current."The correct option is C.
Hans Oersted was a physicist who conducted a number of experiments in the early 19th century that contributed to our understanding of the relationship between electricity and magnetism. In one of his most famous experiments, he discovered electromagnetic induction, which is the process by which a changing magnetic field generates an electric current in a nearby conductor.
Option A is incorrect because Oersted did not discover electromagnetic induction by seeing a compass needle deflected by a flowing electric current. Instead, he noticed that a compass needle was deflected when a current-carrying wire was brought near it.
Option B is incorrect because although Oersted observed a compass needle is deflected, it was not solely due to the flowing electric current. It was the interaction between the electric current and the magnetic field that caused the deflection.
Option D is incorrect because although a changing magnetic field can generate an electric current, Oersted's discovery was based on the observation of a current-carrying wire creating a magnetic field that affected a nearby compass needle.
Therefore, the correct option is C because Oersted discovered electromagnetic induction by seeing a changing magnetic field generate an electric current, which is the core concept of this phenomenon.
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(Please help it will mean a lot)
(
1. The graph above represents the nuclear decay of a radioactive element, measured using a radiation-detecting device. What is the half-life, in days, of this hypothetical element?
2. If the half-life of a given substance is 65 days, how long will it take for a
100-gram sample of the substance to decay until there is only 25 grams of the radioactive material remaining?
3. If a sample of radioactive isotopes takes 60 minutes to decay from 200 grams to
50 grams, what is the half-life of the isotope? Hint: First, determine how many times the sample has lost half of its mass, which tells you how many half-life cycles have occurred.
4. If a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years, what is the half-life of technetium-99
1. The half-life is 2 days
2. The time taken is 130 days
3. The half-life is 30 minutes
4. The half-life is 213000 years
1. How do i determine the half-life?The half-life of a material is the time taken for half the material to decay.
From the above diagram, the following were obtained
Original amount = 80Half of original amount = 80 / 2 = 40Half-life =?From the diagram, we can see that the time taken to get to half of the element is 2 days.
Thus, we can conclude that the half-life is 2 days
2. How do i determine the time taken?First, we shall determine the number of half lives that has elapsed. This is obtained as follow:
Original amount (N₀) = 100 gAmount remaining (N) = 25 gNumber of half-lives (n) =?2ⁿ = N₀ / N
2ⁿ = 100 / 25
2ⁿ = 4
2ⁿ = 2²
n = 2
Finally, we shall determine the time taken. Details below
Half-life (t½) = 65 daysNumber of half-lives (n) = 2 Time taken (t) =?t = n × t½
t = 2 × 65
Time taken = 130 days
3. How do i determine the half-life?First, we shall determine the number of half lives that has elapsed. This is obtained as follow:
Original amount (N₀) = 200 gAmount remaining (N) = 50 gNumber of half-lives (n) =?2ⁿ = N₀ / N
2ⁿ = 200 / 50
2ⁿ = 4
2ⁿ = 2²
n = 2
Finally, we shall determine the half-life. Details below
Number of half-lives (n) = 2 Time taken (t) = 60 minutes Half-life (t½) = ?t½ = t / n
t½ = 60 / 2
Half-life = 30 minutes
4. How do i determine the half-life?First, we shall determine the number of half lives that has elapsed. This is obtained as follow:
Original amount (N₀) = 500 gAmount remaining (N) = 62.5 gNumber of half-lives (n) =?2ⁿ = N₀ / N
2ⁿ = 500 / 62.5
2ⁿ = 8
2ⁿ = 2³
n = 3
Finally, we shall determine the half-life. Details below
Number of half-lives (n) = 3 Time taken (t) = 639000 yearsHalf-life (t½) = ?t½ = t / n
t½ = 639000 / 3
Half-life = 213000 years
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A uniform horizontal rod of mass 1.5 kg and length 1.9 m is free to pivot about one end as shown. The moment of inertia of the rod about an axis perpendicular to the rod and through the center of mass is given by
m.02
I=
12
930.
-pivot
1.5 kg
1.9 m -
If a 1.5 N force at an angle of 95° to the hot-izontal acts on the rod as shown, what is the magnitude of the resulting angular acceleration about the pivot point? The acceleration of gravity is 9.8 m/s?
Answer in units of rad/s?
The magnitude of the resulting angular acceleration about the pivot point is approximately 0.0021 rad/s^2.
Magnitude of the resulting angular accelerationTo solve this problem, we need to use the equation for the torque on a rigid body:
τ = Iα
where τ is the torque, I is the moment of inertia, and α is the angular acceleration. We can also use the fact that the torque is given by:
τ = r × F
where r is the vector from the pivot point to the point of application of the force, and F is the force. The vector cross product r × F gives the torque about the pivot point.
First, we need to find the vector r. Since the force is acting at an angle of 95° to the horizontal, the vertical component of the force is given by:
Fy = F sin(95°) = 1.5 sin(95°) ≈ 0.15 N
The horizontal component of the force is given by:
Fx = F cos(95°) = 1.5 cos(95°) ≈ 0.04 N
The vector r points vertically downward from the pivot point and has a magnitude equal to half the length of the rod:
|r| = 0.5(1.9 m) = 0.95 m
Therefore, the vector r is given by:
r = -0.95j
where j is the unit vector in the vertical direction.
The torque about the pivot point is given by:
τ = r × F = (-0.95j) × (0.04i + 0.15j) = -0.15k
where i is the unit vector in the horizontal direction and k is the unit vector in the direction perpendicular to the plane of the rod and pointing out of the page.
Substituting the moment of inertia and torque into the equation for angular acceleration, we have:
α = τ/I = (-0.15k)/(930.02/12) ≈ -0.0021 rad/s^2
Therefore, the magnitude of the resulting angular acceleration about the pivot point is approximately 0.0021 rad/s^2.
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The model of a ceiling fan shown in the figure consists of a uniform solid cylinder, of radius R = 0.067 m and mass MC = 1.8 kg, and two long uniform rods, each of length L = 0.94 m and mass MR = 3.4 kg, that are attached to the cylinder and extend from its center. Ignore the vertical rod that connects the fan to the motor.
(a) Enter an expression, in terms of the quantities defined in the problem, for the moment of inertia of each rod about the rotation axis.
(b) Enter an expression, in terms of the quantities defined in the problem, for the moment of inertia of the cylinder about the rotation axis.
(c) Enter an expression, in terms of the quantities defined in the problem, for the moment of inertia of the whole fan about the rotation axis.
(d) Calculate the moment of inertia, in units of kilogram meters squared, of the whole fan about the rotation axis.
a) The moment of inertia of each rod about the rotation axis is MR*L2/12.
What is axis?Axis is a reference line used for plotting points on a graph. It is used to indicate a direction and to measure distances. In a two-dimensional graph, the x-axis is typically used to represent the horizontal axis, while the y-axis is used to represent the vertical axis. In a three-dimensional graph, an additional z-axis is used to represent the third dimension. On the x-axis, the points are typically labeled with the independent variable, while the y-axis is labeled with the dependent variable. By plotting points on a graph, relationships between two or more variables can be seen and analyzed. This can be used to identify trends and make predictions about data.
b) The moment of inertia of the cylinder about the rotation axis is MC*R2.
c) The moment of inertia of the whole fan about the rotation axis is the sum of the moment of inertia of the rods and the cylinder, so it is MR*L2/12 + MC*R2.
d) Substituting in the values from the problem, the moment of inertia of the whole fan about the rotation axis is 3.4*0.942/12 + 1.8*0.0672 = 0.4086 kg m2.
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describe the energy changes in a mass spring system that is oscillating horizontally explain how this changes of the system is vibrating vertically
Answer:
Below
Explanation:
In a mass-spring system that is oscillating horizontally, the energy changes between potential energy and kinetic energy. When the mass is at its maximum displacement from the equilibrium position, it has maximum potential energy and zero kinetic energy. As the mass starts to move towards the equilibrium position, its potential energy decreases while its kinetic energy increases. At the equilibrium position, the mass has zero potential energy and maximum kinetic energy. As the mass moves away from the equilibrium position, its kinetic energy decreases while its potential energy increases. This cycle repeats as long as the system is oscillating.
Now, if the support of the system is vibrating vertically, the energy changes that occur during horizontal oscillations cause the mass to move vertically as well. As the mass moves to its maximum displacement from the equilibrium position horizontally, it also moves upwards, gaining potential energy due to its increased height from the ground. As the mass moves towards the equilibrium position horizontally, it also moves downwards, losing potential energy and gaining kinetic energy due to its increased speed towards the ground. At the equilibrium position, the mass has zero potential energy but maximum kinetic energy, which is all in the vertical direction. As the mass moves away from the equilibrium position horizontally, it also moves upwards, gaining potential energy again. The cycle repeats, causing the mass to oscillate vertically as well.
Therefore, the energy changes that occur during horizontal oscillations in a mass-spring system can cause the system to vibrate vertically if the support is vibrating vertically.
List four states of matter. Which states of matter are most common on
Earth?
12. Which of the following quantities, if any, is a
scalar quantity?
(A) A velocity of -2.0 m/s
(B) A potential energy of -2.0 J
(C) A momentum of -2.0 N.S
(D) A displacement of -2.0 m
(E) None of the above is a scalar quantity.
The correct answer is (B) A potential energy of -2.0 J.
A scalar quantity is a physical quantity that has magnitude only and no direction.
Potential energy is a scalar quantity because it is a measure of the energy stored in an object or system, which does not depend on direction or orientation.
Velocity (A) and displacement (D) are vector quantities, as they have both magnitude and direction. Momentum (C) is also a vector quantity, as it is the product of mass and velocity and therefore has both magnitude and direction.
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A loop of area 0.100 m² is oriented at
a 15.5 degree angle to a 0.500 T
magnetic field. It rotates until it is at a
45.0 degree angle with the field. What
is the resulting CHANGE in the
magnetic flux?
[?] Wb
Answer:
Flux = Area * Field
A1 = .1 m^3 * cos 64.5 since we need perpendicular area
A1 = .043 m^2 perpendicular to field
A2 = .1 m^3 * cos 45 = .071 m^2
A = (.071 - .043) m^2 = .028 m^2 change in area
Change in flux = .028 m^2 ^ .5 T = .014 T m^2
What does the open universe theory say?
A. The universe is unchanging and will remain that way.
B. The mass of the universe is large enough for gravity to begin making it contract.
C. The universe may begin contracting due to gravity and lead to another big bang and continue this cycle over and over.
D. The mass of the universe is not large for its gravity to slow down the expansion, and it will continue indefinitely.
The open universe theory, states that the mass of the universe is not large enough for its gravity to slow down the expansion caused by the Big Bang, and it will continue expanding indefinitely.
What does the Open Universe Theory suggest?This theory also known as the unbounded or infinite universe theory suggests that the geometry of the universe is flat, meaning that parallel lines will never meet or intersect, and that the total energy of the universe is zero. In an open universe, the expansion will not stop, and galaxies will continue to move away from each other at an increasing rate. This theory is supported by observations of the cosmic microwave background radiation, which provide evidence for the early expansion of the universe.
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Can anyone explain how to tackle this problem please:
Figure 15.5 shows a 50 kg lead cylindrical piston which floats on 0.37 mol of compressed ideal air at 30°C. How far does the piston move if the temperature is increased to 300°C?
A. 65 cm
B. 140 cm
C. 73 cm
D. 730 cm
Answer:
P V = N R T ideal gas equation
V2 / V1 = T2 / T1 since P, N, R are constant
V2 = 573 / 303 * V1 = 1.89 V1
V = π R^2 h volume of cylinder
V1 = 3.14 * .05^2 * h1 = .00785 h1
V2 = .0148 h1
A (h1 + h) = A * h2
h = h2 - h1 = (.0148 - .00785) h1 = .00695 h1 distance moved by piston
Use V1 = N R T1 / P1 = A h1 to calculate h1
h1 = N R T1 / (A * P1) A * F/A = F to simplify denominater
h1 = .37 * 8.31 * 303 / (50 * 9.8) = 1.90 m P = F / A
Δh = .00695 h1 = .0132 m = 1.32 cm
Math should be checked!