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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Problem 2.3. (5 pts) A 0.500-kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, horizontal air track. (a) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm. (b) What is the velocity of the cart when the position is 2.00 cm? (c) Compute the kinetic and potential energies of the system when the position of the cart is 2.00 cm
The maximum speed of the cart is 26.07 cm/s, the velocity of the cart when the position is 2 cm is 0.141 m/s, and the kinetic and potential energies of the system are 4.97 ×10⁻³J and 4×10⁻³J.
From the given,
Mass of the cart = 0.5 kg
Force constant = 20 N/m
The amplitude of the motion = 3 cm = 0.03 m
A) maximum speed of the cart=?
ω = √k/m
= √(20/0.5) = 8.944
v = ω×amplitude = 8.944×3 = 26.07 cm/s.
B) Velocity of the cart when the position is 2 cm
v = √k/m(A²-x²)
= √(20/0.5)((0.03)²-(0.02)²)
= 0.141 m/s
C) Kinetic energy = 1/2 (mv²)
= 1/2 (0.5×(0.141)²)
= 4.97 × 10⁻³J
K.E = 4.97 ×10⁻³J
Potential energy = 1/2 kx²
= 1/2 (20×(2×10⁻²)²)
= 4 × 10⁻³J
P.E = 4 × 10⁻³J.
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When adding or subtracting two given data with uncertainties,we add the uncertainties and when multiplying and dividing,we add their percentage uncertainties.However,using the error propagation formulas none of the above rules work.Which one should I use?
You should use the error propagation formulas to calculate the uncertainties of the final result for any given mathematical operation.
How are the error propagation formulas most effective to use for final result?When propagating uncertainties using the error propagation formulas, the rules for adding, subtracting, multiplying, and dividing depend on the specific mathematical function being applied. It's essential to use the appropriate formula for each function to obtain accurate results.
Therefore, you should use the error propagation formulas to calculate the uncertainties of the final result for any given mathematical operation. These formulas take into account the uncertainties of the individual components and the functional relationship between them, and provide a more accurate way to estimate the overall uncertainty of the final result.
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that we odels, we 2. his type entists base tand somet of the real ents, we five elect period nd at particles a) Copy the table below into your books. b) In the first column, write down the names of the first 20 elements. c) Use the Periodic Table at the back of this book to complete the table. Element Symbol Number of Number of Number of protons electrons protons and neutrons Na V Number of neutrons The diagrams below show models of certain elements. a) Write down the number of protons, electrons and neutrons for each element. b) Identify each element. ents have number. Symbol for the Figure 11 Atomic information a Mass number and neutrons
The difference between an atom's mass number (A) and atomic number (Z) is equal to the number of neutrons.
1) H – Hydrogen - 1 proton, 1 electron, 0 neutrons
2) He – Helium - 2 protons, 2 electrons, 2 neutrons
3) Li – Lithium - 3 protons, 3 electrons, 4 neutrons
4) Be – Beryllium - 4 protons, 4 electrons, 5 neutrons
5) B – Boron - 5 protons, 5 electrons, 6 neutrons
6) C – Carbon - 6 protons, 6 electrons, 6 neutrons
7) N – Nitrogen - 7 protons, 7 electrons, 8 neutrons
8) O – Oxygen - 8 protons, 8 electrons, 8 neutrons
9) F – Fluorine - 9 protons, 9 electrons, 10 neutrons
10)Ne – Neon - 10 protons, 10 electrons, 10 neutrons
11) Na – Sodium - 11 protons, 11 electrons, 12 neutrons
12) Mg – Magnesium - 12 protons, 12 electrons, 12 neutrons
13) Al – Aluminium - 13 protons, 13 electrons, 14 neutrons
14) Si – Silicon - 14 protons, 14 electrons, 14 neutrons
15) P – Phosphorus - 15 protons, 15 electrons, 17 neutrons
16) S – Sulphur - 16 protons, 16 electrons, 16 neutrons
17) Cl – Chlorine - 17 protons, 17 electrons, 18 neutrons
18) Ar – Argon - 18 protons, 18 electrons, 22 neutrons
19) K – Potassium - 19 protons, 19 electrons, 20 neutrons
20) Ca – Calcium - 20 protons, 20 electrons, 28 neutrons
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which of the following is a form of potential energy
When the hydrogen in a star's core is used up, what occurs?
A. The core collapses causing a huge explosion called a supernova.
B. The nitrogen core collapses and the outer layer expands into a red giant.
C. The helium core collapses and the outer layer expands into a red giant.
D. The outer layer drifts away leaving a hot dense white dwarf core.
The core will collapse under its own gravity, leading to a supernova explosion that expels the outer layers of the star into space, leaving behind either a neutron star or a black hole, depending on the mass of the core.
What happens when the Helium in the core gets used up?As the helium in the core is used up, the core will contract and heat up once again until it is hot enough to fuse heavier elements. This process will continue until the core is made up of iron, which cannot be fused further. At this point, the core will collapse under its own gravity, leading to a supernova explosion that expels the outer layers of the star into space, leaving behind either a neutron star or a black hole, depending on the mass of the core.
For high-mass stars, the process is similar, but the fusion reactions proceed more rapidly, leading to a shorter lifespan and a more violent supernova explosion. In both cases, the ultimate fate of the star depends on its mass and the resulting conditions in its core.
When the hydrogen in a star's core is used up, a series of events can occur depending on the mass of the star. For low to medium-mass stars, such as our Sun, the core will contract and heat up until it is hot enough to initiate the fusion of helium into carbon and oxygen. This process, known as the helium-burning phase, will cause the outer layers of the star to expand into a red giant.
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How many amperes of current are flowing through a circuit if the battery provides 7.0 V and the light bulb has a resistance of 39 Ω?
The amount of current flowing through the given circuit is 0.179 Amperes.
We can use Ohm's Law, which says that current (I) is equal to the voltage (V) divided by resistance (R), to figure out how much current is passing through the circuit. This can be shown mathematically as:
I = V / R
I = the amount of electricity in amperes
V = voltage in volts
R = resistance measured in ohms.
Given that the battery gives off 7.0 V and the light bulb has a resistance of 39, we can plug these numbers into the formula:
I = 7.0 V / 39 Ω
I = 0.1795 A (to four places after the decimal)
So, about 0.1795 amperes of current are moving through the circuit.
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Beta and gamma rays are produced when iodine-131 decays. When patients ingest iodine-131, the beta and gamma rays are used to image and treat cancer. A patient is administered a 20.0mg dose of iodine-131. After 21 days, 3.24mg of iodine-131 remains in the patient's body.
a) Calculate the decay constant of iodine-131.
b) Calculate the half-life of iodine-131.
c) How much iodine-131 will be present in the patient's body 50 days after it was administered?
a. The decay constant of iodine-131 is 0.0502 day^-1.
b. the half-life of iodine-131 is 13.8 days.
c. 1.29 mg of iodine-131 will be present in the patient's body 50 days after it was administered.
How to determine the decay constanta) To calculate the decay constant of iodine-131, we can use the formula:
N = N0 * e^(-λt)
where
N is the amount of iodine-131 remaining after time t,
N0 is the initial amount of iodine-131, and
λ is the decay constant.
We are given that N0 = 20.0 mg and N = 3.24 mg, and t = 21 days. Substituting these values into the formula and solving for λ, we get:
λ = ln(N0/N) / t
= ln(20.0/3.24) / 21
= 0.0502 day^-1
Therefore, the decay constant of iodine-131 is 0.0502 day^-1.
b) To calculate the half-life of iodine-131, we can use the formula:
t1/2 = ln(2) / λ
Substituting the value of λ we calculated in part (a), we get:
t1/2 = ln(2) / 0.0502
= 13.8 days
Therefore, the half-life of iodine-131 is 13.8 days.
c) To calculate how much iodine-131 will be present in the patient's body 50 days after it was administered, we can again use the formula:
N = N0 * e^(-λt)
We are given that t = 50 days,
N = 20.0 * e^(-0.0502*50)
= 1.29 mg
Therefore, 1.29 mg of iodine-131 will be present in the patient's body 50 days after it was administered.
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A cylinder with an area ratio of .5 and a diameter of 15cm extends at a velocity of 5 cm per second. What is the flow rate?
Answer:
To calculate the flow rate, we need to first find the cross-sectional area of the cylinder.
The area ratio is defined as the ratio of the cross-sectional area of the extended cylinder to the cross-sectional area of the cylinder before it was extended.
Let's call the cross-sectional area of the cylinder before it was extended A1, and the cross-sectional area of the extended cylinder A2.
We know that the diameter of the cylinder is 15cm, so the radius is 7.5cm.
The cross-sectional area of a cylinder is given by the formula A = πr^2.
So,
A1 = π(7.5)^2 = 176.71 cm^2
To find A2, we can use the area ratio:
Area ratio = A2/A1 = 0.5
A2 = 0.5 * A1 = 0.5 * 176.71 = 88.36 cm^2
Now we can calculate the flow rate using the formula:
Flow rate = velocity * cross-sectional area
Flow rate = 5 cm/s * 88.36 cm^2 = 441.8 cm^3/s
Therefore, the flow rate is 441.8 cm^3/s.
A participant is exercising on a Monark cycle ergometer for 5 minutes at a resistance
of 4.5kp and a cadence of 80 RPM. Calculate i) the amount of work performed in 5min
and 2) mean power output for the 5 minutes
Ergometer is a device that standardizes the work and power output. The work done by the cycle ergometer is 109.5 kJ and the power output for the 5 minutes is 353.133 W.
Work done by the engine is defined as the product of force and distance and the unit of work done is the joule (J).
From the given,
resistance of the ergometer = 4.5kp
revolutions per minute = 80 rpm
time taken = 5 minutes
Work done (W) = F × d
= (4.5 × 9.81) × (80 rpm × 6 m/rev × 5)
= 105,948
Work done (W) = 105.94 kJ
Power is the ratio of the work done and time and the unit of power is the watt (W).
Power = Work done / time
= 105.94 × 10³ / 300 (5 minutes = 300 seconds)
= 353.13 W.
Hence the work done by the cycle ergometer is 105.94 kJ and the output power in 5 minutes (300 seconds) is 353.133 W.
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Question
A 1.50 kg copper pipe at 800.0° C is immersed into a 20.0°C bucket of water with a mass of 5.00 kg. What is the final
temperature of the copper-water mixture if the specific heat of copper is 0.386- and the specific heat of water is
8°C
4.184?
To solve this problem, we need to use the principle of conservation of energy, which states that the total energy in a system is constant. In this case, the energy lost by the copper pipe as it cools down will be gained by the water as it heats up. We can use the equation:
Q_copper = -Q_water
where Q_copper is the heat lost by the copper pipe, and Q_water is the heat gained by the water. The negative sign indicates that the energy flows from the copper to the water.
The heat lost by the copper pipe can be calculated using the formula:
Q_copper = mcΔT
where m is the mass of the copper pipe, c is the specific heat of copper, and ΔT is the change in temperature. We can assume that the final temperature of the copper-water mixture is the same, so we can write:
Q_copper = mc(800.0 - T)
where T is the final temperature of the mixture.
The heat gained by the water can be calculated using the formula:
Q_water = mwCΔT
where mw is the mass of the water, C is the specific heat of water, and ΔT is the change in temperature. We can assume that the initial temperature of the water is 20.0°C, so we can write:
Q_water = mwC(T - 20.0)
Now we can substitute these equations into the conservation of energy equation:
mc(800.0 - T) = -mwC(T - 20.0)
Solving for T:
mc(800.0 - T) = mwC(T - 20.0)
1500.0 * 0.386 * (800.0 - T) = 5.00 * 4.184 * (T - 20.0)
231480 - 579.6T = 20.92T - 418.4
600.52T = 231898.4
T = 386.6°C
Therefore, the final temperature of the copper-water mixture is 386.6°C.
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3. When 815 Joules of heat is added to a sample of solid copper, the temperature rises
from 12.0°C to 35°C. How many grams of copper were in the sample? Specific heat of Cu
is 0.385 J/g-K.
q=MCdeltaT
Answer:
79.3
Explanation:
We can use the formula:
q = m * c * deltaT
where:
q is the heat added to the system, which is 815 J in this case
m is the mass of the sample we want to find
c is the specific heat of copper, which is 0.385 J/g-K
deltaT is the change in temperature, which is (35 - 12) = 23°C
Plugging in the values given, we get:
815 J = m * 0.385 J/g-K * 23°C
Simplifying this expression yields:
m = 815 J / (0.385 J/g-K * 23°C)
Thus, the mass of the copper sample is:
m = 79.3 g
Therefore, there were approximately 79.3 grams of copper in the sample.
Answer:
Explanation:
We can use the equation q = mCΔT, where q is the amount of heat transferred, m is the mass of the sample, C is the specific heat capacity of the material, and ΔT is the change in temperature.
First, we need to calculate the change in temperature, which is:
ΔT = T₂ - T₁ = 35°C - 12.0°C = 23°C
Next, we can rearrange the equation to solve for the mass of the sample:
m = q / (CΔT)
Substituting the values we have:
m = 815 J / (0.385 J/g-K × 23°C) ≈ 90.2 g
Therefore, the sample of solid copper had a mass of approximately 90.2 grams.
How can astronomers use how long it takes an objects brightness to vary to say something about the physical size of the object?
Astronomers can use how long it takes an object's brightness to vary to estimate the physical size of the object through a method known as photometry. This method involves observing an object's brightness over time and analyzing the patterns of variation.
For example, consider a binary star system in which two stars orbit each other. As one star passes in front of the other, the combined brightness of the system will decrease. The duration of this decrease in brightness can be used to estimate the physical size of the stars, as the duration of the decrease is related to the size of the stars and the distance between them.
Similarly, if an asteroid or other small body passes in front of a star, the star's brightness will decrease for a short period of time. The duration of this decrease can be used to estimate the size of the asteroid, as the duration is related to the size of the asteroid and the distance between it and the observer.
In general, the size of an object can be estimated using photometry by comparing the observed variation in brightness to the expected variation based on the physical characteristics of the object. This can provide valuable information about the properties and behavior of celestial objects and can help astronomers to better understand the structure and evolution of the universe.
A radioactive sample consists of a mixture of a S-35 and P-32 .initially 5% of the activity is due to the S-35 and 95% due to the P-32 .At what subsequent time will the activities of the two nucleide be equal
The time at which the activities of the two nuclides be equal is 2.7 s.
Radioactivity is the process of an unstable atomic nucleus spontaneously splitting or disintegrating and emitting radiation in the form of α-rays, β-rays, or γ-rays.
λ₁ = 0.05
λ₂ = .95
According to the law of radioactive decay, the total number of nuclei in a sample material is directly proportional to the number of nuclei that are undergoing the decaying process in that sample material per unit time.
λ₁N₁ = λ₂N₂
λ₁N₀e⁻(λ₁t) = λ₂N₀e⁻(λ₂t)
λ₁/λ₂ = e⁻(λ₁ - λ₂)t
ln(λ₁/λ₂) = (λ₁ - λ₂)t
Therefore time,
t = ln(λ₁/λ₂)/(λ₁ - λ₂)
t = ln(0.05/.95)/(0.95 - 0.05)
t = -2.94 x -0.9
t = 2.7 s
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An 80 Ώ resistor has a voltage difference of 12 Volts across its leads.
(a) What is the current through the resistor?
(b) What is the power being dissipated in this resistor?
The resistor is dissipating 1.8 W of power. As a result, 0.15 A is the current flowing through the resistor.
What kind of power does the resistor dissipate?Any equation linking power to current, voltage, and resistance may be used to calculate the power wasted by each resistor because all three variables are known. Since each resistor receives its full voltage, let's use P=V2R P = V 2 R.
(a) We may determine the current flowing through the resistor using Ohm's Law as follows:
I = V/R
where R is the resistance and V is the voltage difference across the resistor.
Therefore, the resistor's current is as follows:
I = 12 V / 80 Ω = 0.15 A
Therefore, the current through the resistor is 0.15 A.
(b) The power being dissipated in the resistor can be calculated using the formula:
P = VI = I²R = V²/R
where P is the power, V is the voltage difference across the resistor, I is the current through the resistor, and R is the resistance.
Substituting the given values, we get:
P = VI = (0.15 A)(12 V) = 1.8 W
Alternatively, we can use the third formula to calculate the power:
P = V²/R = (12 V)²/ 80 Ω = 1.8 W
So, the power being dissipated in the resistor is 1.8 W.
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6.1 62 6.3 64 quency of sound waves emitted by a stationary source. the relationship between the observed frequency and the The learner moves towards the source at a constant velocity and records the observed frequency (f) for a given source frequency (fs). This process is repeated for different frequencies of the source, with the learner moving at the same constant velocity each time The graph below shows how the observed frequency changes as the frequency of sound waves emitted by the source changes. fL (Hz) fs (Hz) Name the phenomenon illustrated by the graph Name ONE application in the medical field of the phenomenon in QUESTION 6.1. O Write down the type of proportionality that exists between f and fs, as illustrated by the graph. The gradient of the graph obtained is found to be 1,06. (1) of the
The highlighted phenomenon in the graph is called the Doppler effect, which involves a modification of frequency for sound waves (or any kind of wave) due to the difference in motion between the observed and the source.
How to explain the effectAn example of this effect present in the medical field is through ultrasound imaging; doctors use it to measure the velocity and route of blood circulating throughout the patient's body by sending out high-frequency sound waves and analyzing the reflected waves.
What appears in the graphed illustration specifically is linear proportionality, meaning that there is a direct correlation between f and fs, the former being the observed frequency and the latter the source frequency.
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2/10
If two forces act on an object in the same direction, the net
force is equal to the
of the two forces.
Answer:
The net force on an object when two forces act on it in the same direction is equal to the sum of the two forces.
The caloric theory is the most workable model of heat today.
True
False
Answer:
False
Explanation:
The modern kinetic-molecular model is better than the caloric model, not because it is true, but because it produces more workable results. credited to be the first to demonstrate a clear connection between mechanical energy and heat.
In a stable star, nuclear fusion pushes _________ and gravity pushes _________.
A. outward, outward
B. outward, inward
C. inward, inward
D. inward, outward
Answer:
In a stable star, the force of nuclear fusion is balanced by the force of gravity. The high temperatures and pressures in the core of the star cause atoms to collide and fuse together, releasing energy in the process. This energy is what keeps the star from collapsing under the force of gravity. The outward pressure from the energy released by nuclear fusion pushes outward, while the force of gravity pulls inward. In a stable star, these two forces are balanced, with the inward force of gravity being counteracted by the outward pressure from fusion. This balance allows the star to maintain a stable size and temperature.
Therefore the answer is A. outward, inward.
If Ja Morant has a vertical leap of 1.35m, then what speed does he leave the ground and what is his
total hang time?
Ja Morant's total hang time is 0.53 seconds.
The initial vertical velocity, Vi, is 0 since he starts from rest. The final vertical displacement, Δy, is 1.35m. We can assume that air resistance is negligible, so we can use the acceleration due to gravity, g, which is -9.81 m/s².
To find the speed he leaves the ground, we can use the equation:
Vf² = Vi² + 2gΔy
Vf² = 0 + 2(-9.81)(1.35)
Vf = 5.89 m/s
Therefore, Ja Morant leaves the ground at a speed of 5.89 m/s.
To find the total hang time, we can use the equation:
Δy = ViT + 1/2 gT²
1.35 = 0T + 1/2(-9.81)T²
[tex]T = \sqrt{(2(1.35)/9.81)[/tex]
T = 0.53 seconds
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i need too get them right because me and my friend are challeging each other
6. Water - B. has a positive and negative end, 7. Nucleic acids - A. contains instructions, 8. Proteins - D. Some help break down nutrients, 9. Lipids - E. do not mix with water, and 10. carbohydrates - C. sugar is one.
6. Water - B. has a positive and negative end: Water is a polar molecule, which means it has a partial positive charge on one end and a partial negative charge on the other. This polarity is due to the asymmetric arrangement of the hydrogen and oxygen atoms in the molecule, with the oxygen atom having a stronger attraction for electrons than the hydrogen atoms. The positive and negative ends of the water molecule allow it to form hydrogen bonds with other polar molecules, including other water molecules, which gives water many of its unique properties, such as high surface tension, high boiling and melting points, and its ability to dissolve many substances.
7. Nucleic Acids - A. contain instructions: Nucleic acids are biomolecules that store and transmit genetic information in living organisms. They are composed of long chains of nucleotides, which are made up of a nitrogenous base, a sugar molecule, and a phosphate group. The two main types of nucleic acids are DNA (deoxyribonucleic acid) and RNA (ribonucleic acid). DNA contains the genetic information that is passed down from one generation to the next, while RNA helps to transcribe and translate that information into functional proteins that perform various cellular processes.
8. Proteins - D. Some help break down nutrients: Proteins are complex biomolecules that perform a variety of functions in the cell, including catalyzing chemical reactions, transporting molecules, and providing structural support. Some proteins, known as enzymes, are specialized molecules that help to break down nutrients in the body by catalyzing chemical reactions that convert them into usable forms. Other proteins, such as antibodies and hormones, have other important roles in the immune system and in cellular communication.
9. Lipids - E. do not mix with water: Lipids are a diverse class of biomolecules that are characterized by their insolubility in water. They include fats, oils, phospholipids, and steroids, among others. Lipids are composed of long chains of hydrocarbons and contain a polar head group and a nonpolar tail. The nonpolar tail makes lipids insoluble in water, while the polar head group allows them to interact with other polar molecules. Lipids are important for energy storage, as a component of cell membranes, and as signaling molecules.
10. Carbohydrates - C. sugar is one: Carbohydrates are a class of biomolecules that are composed of carbon, hydrogen, and oxygen atoms. They include sugars, starches, and fibers, among others. Sugars are simple carbohydrates that consist of one or two sugar molecules linked together, while starches and fibers are complex carbohydrates made up of many sugar molecules linked together. Carbohydrates are an important source of energy for the body and play important roles in cellular processes such as cellular respiration and photosynthesis.
Hence, The correct answer is 6. Water - B. has a positive and negative end, 7. Nucleic acids - A. contains instructions, 8. Proteins - D. Some help break down nutrients, 9. Lipids - E. do not mix with water, and 10. carbohydrates - C. sugar is one
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If you do 12 J of work to push 0.001 C of charge from point A to point B in an electric field, what iS the potential difference between points A and B? B). What will be the increase in kinetic energy of an
electron if it has been accelerated through a potential difference of 20 million volts? (Assume that e 1.6 X 10-19 C)
If you do 12 J of work to push 0.001 C of charge from point A to point B in an electric field, then the potential difference between points A and B is 12 kV.
The increase in kinetic energy of an electron if it has been accelerated through a potential difference of 20 million volts is 8000 J.
a )When a charge is accelerated through potential difference then the energy gained by the charge is,
E = eV where E is energy e is charge and V is potential difference.
V = E/e = 12/0.001 = 12 kV
b) E = eV, E = 0.001 × 20×10⁶
E = 20000 J
Increase in the kinetic energy will be, 20000 - 12000 = 8000 J
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The 0.100 kg
sphere in (Figure 1) is released from rest at the position shown in the sketch, with its center 0.400 m
from the center of the 5.00 kg
mass. Assume that the only forces on the 0.100 kg
sphere are the gravitational forces exerted by the other two spheres and that the 5.00 kg
and 10.0 kg
spheres are held in place at their initial positions.
What is the speed of the 0.100 kg sphere when it has moved 0.150 m to the left from its initial position?
As per the given data, the speed of the 0.100 kg sphere when it has moved 0.150 m to the left from its initial position is 0.736 m/s.
Since only the gravitational forces are acting on the 0.100 kg sphere, we can use the conservation of energy principle to find its speed at any position.
We can use the initial position of the sphere as the reference point for potential energy and write the initial total energy as the sum of the potential energy and kinetic energy.
At any other position, the total energy will still be the sum of the potential energy and kinetic energy, but their values will be different.
The initial total energy of the system is:
E_i = m_0gh
Where m_0 is the mass of the 0.100 kg sphere, g is the acceleration due to gravity, and h is the height of the sphere above the reference position. In this case, h = 0.4 m.
The final total energy of the system is:
[tex]E_f = m_0v^2/2 + m_0gh_f[/tex]
Where v is the speed of the sphere, and h_f is the height of the sphere above the reference position at the final position.
Since the system is isolated, the initial and final energies must be equal:
E_i = E_f
[tex]m_0gh = m_0v^2/2 + m_0gh_f[/tex]
Solving for v, we get:
v = sqrt(2gh - 2gh_f)
To find the final height h_f, we can use the fact that the center of mass of the system remains fixed throughout the motion.
The initial center of mass is at a distance of 0.4 m from the center of the 5.00 kg sphere, and the masses of the 5.00 kg and 10.0 kg spheres are 5.00 kg and 10.0 kg, respectively.
Therefore, the initial center of mass is at:
x_cm,i = (0.4*0.1 + 5*0 + 10*0)/(0.1 + 5 + 10) = 0.032 m
where we have taken the x-axis to be horizontal and passing through the centers of the 5.00 kg and 10.0 kg spheres.
At the final position, the center of mass must still be at the same horizontal position:
x_cm,f = (5*0.1*(-0.15) + 10*0)/(0.1 + 5 + 10) = -0.011 m
where we have taken the leftward direction as positive.
The final height of the sphere is then:
h_f = 0.4 - x_cm,f = 0.4 + 0.011 = 0.411 m
Substituting the values of g, h, and h_f in the equation for v, we get:
v = sqrt(2*9.81*0.4 - 2*9.81*0.411) = 0.736 m/s (rounded to three significant figures)
Therefore, the speed of the 0.100 kg sphere when it has moved 0.150 m to the left from its initial position is 0.736 m/s.
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A single resistor is connected to a 1.5V battery. The resistor emits 10W of power. What is the resistance of the resistor?
Answer:
[tex]0.225\; {\rm \Omega}[/tex] (assuming that internal resistance in the battery is negligible.)
Explanation:
Let [tex]R[/tex] denote the resistance of this resistor.
Let [tex]V[/tex] denote the voltage across this resistor. In this question, it is given that [tex]V = 1.5\; {\rm V}[/tex].
By Ohm's Law, the current [tex]I[/tex] going through this resistor would be equal to:
[tex]\displaystyle I = \frac{V}{R}[/tex].
The power [tex]P[/tex] consumed in an electric circuit is equal to the product of voltage and current:
[tex]P = V\, I[/tex].
Substitute [tex]I = (V / R)[/tex] into this equation:
[tex]\displaystyle P = \frac{V^{2}}{R}[/tex].
Rearrange to find resistance [tex]R[/tex]:
[tex]\begin{aligned} R &= \frac{V^{2}}{P} \\ &= \frac{(1.5\; {\rm V})^{2}}{(10\; {\rm W})} \\ &=0.225\; {\rm \Omega}\end{aligned}[/tex].
9. A brick weighs 21 N. Measured underwater, it weighs 12 N. What is the
size of the buoyant force exerted by the water on the brick?
33 N
21 N
12 N
9N
1
Answer:
9N
Explanation:
The difference between the weight of the brick in air and the weight of the brick underwater is equal to the buoyant force exerted by the water on the brick.
Weight of the brick in air = 21 N
Weight of the brick underwater = 12 N
Therefore, the buoyant force exerted by the water on the brick is:
Buoyant force = Weight of the brick in air - Weight of the brick underwater
Buoyant force = 21 N - 12 N
Buoyant force = 9 N
So the size of the buoyant force exerted by the water on the brick is 9 N. Answer: 9N.
Hope this helps!
21. A rock is thrown straight down with an initial velocity of 14.5 m/s from a cliff. What is the rock’s displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2 .) a. 28 m
b. 49 m
c. 55 m
d. 64 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
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
a vertical spring scale can measure weights up to 175N the scale extends by an amount of 13.0cm from its equilibrium position at 0N to the 175 N mark. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.35 Hz. Ignore the mass of the spring, what is the mass Mof the fish
Answer:
Approximately 0.024 kg
Explanation:
We can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be written as:
F = -kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. The negative sign indicates that the force is in the opposite direction of the displacement.
We can use the given information to find the spring constant:
k = F/x = 175 N / 0.13 m = 1346.15 N/m
The fish is oscillating vertically, which means that the force of gravity is acting on it. The weight of the fish can be calculated as:
W = mg
where W is the weight, m is the mass, and g is the acceleration due to gravity (9.81 m/s^2).
The oscillation frequency of the fish can be related to its mass and the spring constant using the formula:
f = 1/2π * sqrt(k/m)
where f is the frequency of oscillation, π is a constant (approximately 3.14), and sqrt is the square root function.
We can rearrange this equation to solve for the mass of the fish:
m = k/(4π^2 * f^2)
Substituting the given values, we get:
m = 1346.15 N/m / (4 * 3.14^2 * (2.35 Hz)^2) ≈ 0.024 kg
Therefore, the mass of the fish is approximately 0.024 kg.
18.
As air temperature decreases, the speed of sound in air decreases.
True
False
Answer:
True
the velocity of sound in air decreases with decrease in temperature.
String 1 in the figure has linear density 2.60 g/m and string 2 has linear density 3.30 g/m. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. She wants both pulses to reach the ends of the strings simultaneously.
What should the string length L1 be?
What should the string length L2 be?
Explanation:
We can use the formula for the speed of waves on a string:
v = sqrt(T/μ)
where v is the speed of the wave, T is the tension in the string, and μ is the linear mass density (mass per unit length) of the string.
Let's denote the tension in both strings by T. Since the pulses must reach the ends of both strings simultaneously, we must have:
L1/v1 = L2/v2
where L1 and L2 are the lengths of the strings, v1 is the speed of the wave on string 1, and v2 is the speed of the wave on string 2.
Using the formula above and solving for T, we can eliminate T from this equation to get:
sqrt(μ1/ T)/ L1 = sqrt(μ2/T)/ L2
Squaring both sides and rearranging, we obtain:
L2/L1 = sqrt(μ2/μ1)
Substituting the given values for μ1 and μ2, we get:
L2/L1 = sqrt(3.30/2.60) = 1.126
Solving for one of the lengths, say L1, in terms of the other, we get:
L1 = L2/1.126
Now we need to find the values of L1 and L2 that satisfy the condition that both pulses reach the ends of the strings simultaneously. To do this, we can use the fact that the time it takes for a wave to travel a distance L on a string is given by:
t = L/v
where v is the speed of the wave on the string.
Therefore, if the pulses are to arrive at the ends of the strings simultaneously, we must have:
L1/v1 + L2/v2 = 2L1/v1
Simplifying this equation using the relation L1 = L2/1.126 and the formula for v, we get:
sqrt(T/μ1)L2/1.126/2.60 + sqrt(T/μ2)L2/3.30 = 2L2/1.126sqrt(T/μ1)
Simplifying further and eliminating T, we obtain:
L2 = (2.60/3.30)^2(1.126) L1
Substituting the expression for L1 in terms of L2 that we found earlier, we get:
L2 = (2.60/3.30)^2(1.126) L2/1.126
Solving for L2, we find:
L2 = 2.196 L1
Finally, using the relation L1 = L2/1.126, we get:
L1 = 1.91 m
L2 = 4.20 m
Therefore, the length of string 1 should be 1.91 m and the length of string 2 should be 4.20 m in order for both pulses to reach the ends of the strings simultaneously.
A 18.0-m-long bar of steel expands due to a temperature increase. A 10.0-m-long bar of copper also gets longer due to the same temperature rise. The two bars were originally separated by a gap of 1.1 cm. Assume the steel and copper bars are fixed on the ends.
α(Steel) = 13 x 10^-6 K^-1
α(Copper) = 16.5 x 10^-6 K^-1
1) Calculate the change in temperature if the gap is exactly "closed" by the expanding bars. (Express your answer to two significant figures.)
2) Calculate the distances that the steel stretches. (Express your answer to two significant figures.)
3) Calculate the distances that the copper stretches. (Express your answer to two significant figures.)
1. It is important to make your own decisions. At the same time, it is good to ask for help. Identify a
situation where you absolutely need to be thinking for yourself and one in which turning to others
is best when it comes to making decisions about your health.
Answer:
Explanation:
Decision making is the process of making choices and it is important for a person to make their own decisions in life as it makes them accountable for the choices they made.
What is decision making?
Decision making is the process of making your own choices by identifying a decision, gathering the information, and assessing alternative resolutions for the decision.
Each person has the right to make their own decisions and have choices about how they live their life in their own way. Each person has different ideas about what is important and what makes them feel best in life. Making own choices about things in life is very important because it gives the life meaning.
Being responsible in making own decisions means being accountable, taking charge of the course of the actions and the consequences of choices, however it is also important to turn to others in cases of making decisions about health as this helps in making the best decision by understanding things from other perspectives.