Newton's first law is often called the law of inertia and is based on the work of Isaac Newton.
Newton's first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
This law is the basis for understanding the behavior of objects in motion and is essential in the study of physics.
"True" and the explanation is that this law is derived from Galileo's work.
Summary: Newton's first law is also known as the law of inertia and is attributed to the work of Isaac Newton.
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32. If a ball is given a push so that it has an initial velocity of 2 m/s down a certain inclined plane, then the distance it has rolled after t seconds is s = 2t + t2. How long does it take for the velocity to reach 24 m/s? (a) 2 seconds (b) 4 seconds (c) 5 seconds (d) 11 seconds (e) 12 seconds
If a ball is given a push so that it has an initial velocity of 2 m/s down a certain inclined plane, then the distance it has rolled after t seconds is s = 2t + t². Then it takes 11 seconds for the velocity to reach 24 m/s. The correct option is D.
To find the time it takes for the velocity of the ball to reach 24 m/s, we need to solve for the time when the velocity function equals 24 m/s.
The velocity function is the derivative of the distance function, so we'll first find the derivative of the distance function s = 2t + t² with respect to time t:
ds/dt = d/dt(2t + t²)
ds/dt = 2 + 2t
Now we can set the velocity function equal to 24 m/s and solve for t:
2 + 2t = 24
Subtracting 2 from both sides:
2t = 22
Dividing both sides by 2:
t = 11
Therefore, it takes 11 seconds for the velocity to reach 24 m/s.
The correct answer is (d) 11 seconds.
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determine the force of gravitational attraction between a 78 kg boy sitting 2 meters away from a 65 kg girl. circle your answer and include units
Answer:
The force of gravitational attraction is 8.454 x 10⁻⁸ N.
Explanation:
Given;
mass of the boy, m₁ = 78 kg
mass of the girl, m₂ = 65 kg
distance between the boy and the girl, r = 2 meters
The force of gravitational attraction is given as;
\(F = \frac{Gm_1m_2}{r^2}\)
where;
G is gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²
r is the distance between two masses, m₁ and m₂
\(F = \frac{Gm_1m_2}{r^2} \\\\F = \frac{(6.67 \times 10^{-11})(78 \times 65)}{2^2}\\\\F = 8.454 \times 10^{-8} \ N\)
Therefore, the force of gravitational attraction is 8.454 x 10⁻⁸ N.
coal is lifted out of a mine a vertical distance of 63 m by an engine that supplies 475 w to a conveyor belt. how much coal per minute can be brought to the surface? ignore the effects of friction. (enter your answer in kg/min.)
Therefore, approximately 45.89 kg of coal can be brought to the surface per minute.
The amount of coal that can be brought to the surface per minute can be determined using the power supplied by the engine and the vertical distance the coal is lifted.
To calculate the amount of coal, we need to use the formula:
Power = Work / Time
Given that the power supplied by the engine is 475 W and the vertical distance is 63 m, we can rearrange the formula to solve for the work done:
Work = Power x Time
Since we are interested in the amount of coal per minute, we can convert the power from watts to joules per minute:
475 W x (60 seconds/minute) = 28500 J/min
Now, we can plug in the values for work and power into the formula to solve for time:
Work = Power x Time
28500 J/min = Work
Since we are interested in the amount of coal, we can use the equation:
Work = Force x Distance
Given that the force of gravity is acting on the coal, we can use the formula:
Force = mass x gravity
Since we are solving for the mass of the coal, we can rearrange the formula to:
mass = Work / (gravity x Distance)
Plugging in the values for work (28500 J/min), gravity (9.8 m/s^2), and distance (63 m), we can calculate the mass of the coal per minute:
mass = 28500 J/min / (9.8 m/s^2 x 63 m)
mass = 45.89 kg/min
Therefore, approximately 45.89 kg of coal can be brought to the surface per minute.
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So với nhà ga thì hành khách chuyển động hay đứng yên? Tại sao?
Answer:
Compared to the station, are the passengers moving or stationary? Why?
The two is not moving ..
because the newton or the movement
of the passenger and the stationary are equal
they are not move they stay in there places
A car slows down from 21 m/s to rest in a distance of 63m. Assuming the car has a constant acceleration, calculate the time it took to come to a stop.
Answer:
-3.5 m/s²
Explanation:
Initial Velocity = 21m /sFinal velocity = 0m/s Distance = 63 m .Acclⁿ = ?We know that :-
\(\longrightarrow \) Stopping distance = u²/2(-a)
\(\longrightarrow \) 63m = (21m/s)² / -2a
\(\longrightarrow \) a = - 21 * 21 / 63 * 2 m/s²
\(\longrightarrow \) a = - 3.5 m/s²
**Edits are welcomed**
A 1,725 kg car accelerates from 3.0 m/s for 4.4 s and reaches a velocity of 12.0 m/s. Ignoring friction, what is the applied force from the engine?
Given:
The mass of the car is m = 1725 kg
The initial velocity of the car is
\(v_i=\text{ 3 m/s}\)The final velocity of the car is
\(v_f=\text{ 12 m/s}\)The time is t = 4.4 s
To find the applied force.
Explanation:
The force can be calculated by the formula
\(F=\text{ ma}\)Here, a is the acceleration.
The acceleration can be calculated as
\(\begin{gathered} a=\frac{v_f-v_i}{t} \\ =\frac{12-3}{4.4} \\ =2.045\text{ m/s}^2 \end{gathered}\)On substituting the values, the force applied will be
\(\begin{gathered} F=ma \\ =1725\times2.045 \\ =3527.625\text{ N} \end{gathered}\)Thus, the applied force is 3527.625 N
A laser emits a pulse of light with energy5.0x103J. Determine the number of photons in the pulsesif the wavelenght of light is 480nm.
The number of photons in the pulse is 1.21 × 1022.
The energy of a photon can be calculated using the equation:
E = hf, where
E is the energy of a photon,
h is the Planck's constant, and
f is the frequency of the light.
Then, using the equation c = λf, where
c is the speed of light,
λ is the wavelength of the light and
f is the frequency of the light, the frequency of the light can be determined.
Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency.
Its value is 6.626 × 10-34 joule seconds (J·s).
The frequency of the light is:
f = c / λ
= 3.00 × 108 / 480 × 10-9
= 6.25 × 1014 Hz
The energy of the photon can be calculated:
E = hf
= 6.626 × 10-34 × 6.25 × 1014
= 4.14 × 10-19 J
The number of photons can be determined by dividing the energy of the pulse by the energy of a photon:
n = E / E_photon
= 5.0 × 103 / 4.14 × 10-19
= 1.21 × 1022 photons
Therefore, the number of photons in the pulse is 1.21 × 1022.
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Which of these stars has the shortest life expectancy?
a. an isolated 1Msun star
b. a 1Msun star in a closed binary system with a 0.8Msun star
c. a 1Msun star in a closed binary system with a 2Msun star
A 1Msun star in a closed binary system with a 2Msun star.
Systems in which the two stars are close to each other are called close binary star system.
The most massive stars have the shortest lifespans. The reason is that they have most fuel, they burn it so enormously that their lifetimes are very short. As a 1Msun star in a closed binary system with a 2Msun star becomes the massive star so it has the shortest life expectancy.
a. No, an isolated 1Msun star has not the shortest life expectancy.
b. No, a 1Msun star in a closed binary system with a 0.8Msun star has not the shortest life expectancy.
c. Yes, A 1Msun star in a closed binary system with a 2Msun star has the shortest life expectancy.
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which is denser: an object that has a density of 1000 kg/m3 or one that has a density of 1 g/cm3?
Density is a measure of how much mass is contained within a given volume. An object with a density of 1000 kg/m³ is denser than an object with a density of 1 g/cm³.
Density is a measure of how much mass is contained within a given volume. The formula for density is mass divided by volume (ρ = m/V). In the metric system, density is commonly expressed in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
Comparing the given densities, we can see that 1 g/cm³ is equivalent to 1000 kg/m³ since there are 1000 grams in a kilogram and 1 cubic meter is equal to 1,000,000 cubic centimeters. Therefore, the object with a density of 1000 kg/m³ has a higher mass per unit volume compared to the object with a density of 1 g/cm³.
This means that for the same volume, the object with a density of 1000 kg/m³ contains more mass, making it denser than the object with a density of 1 g/cm³. In simpler terms, if you were to compare objects of the same size, the object with the higher density would feel heavier because it has more mass packed into the same amount of space.
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22. Vernier calipers read to one tenth of a millimetre.
Which reading shows this precision?
A
3.3 cm
B 3.31 cm
C 3.310cm
D 3.312 cm
[5054
The reading which shows the precision of a Vernier calipers reading to one tenth of a millimeter is 3.31cm. Thus, the correct option is B.
What is Vernier calipers?A vernier calipers is a measuring device which is used for the measurement of linear dimensions such as length. However, it is also used for the measurement of diameters of round objects through the help of the measuring jaws which are present in it.
Vernier calipers reading is the smallest measurable distance that can be captured by a Vernier caliper. It is termed as the resolution of the Vernier caliper. The resolution of metric Vernier calipers varies from 0.02mm to 0.05mm that is it reads to one tenth of a millimeter unit. Thus, 3.31cm is a precise reading.
Therefore, the correct option is B.
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AC power calculation. As we all know electricity is all around us, but how does it get to us? This process begins with the generating station ( < 35,000 V) then a step up transformer to transmission lines (typically 345,000 V), a step down transformer to local transmission lines (13,800 V) and another step down transformer for residential customers (120 V). Assume 10 cents a kWhr, 60 Hz, 0.4% and ideal transformers. The following web sites may be interested to look over: United States Electricity Industry Primer What Is the Typical Voltage for Power Lines? (8») (b) (e) (0 Calculate how much it costs (per unit of time) to deliver 10 kW (car charger) to a home 100 miles away while transmitting electricity at 120 V 60 HZ. Begin by drawing a schematic. High voltage transmission helps if there's series resistance in wires. Assume losses between the generating station/ the step up transformer and local transmission lines/ home are negligible. How much does it costs (per unit time) to deliver 10kW to a house when the transmission lines are 100 miles? Begin by drawing a schematic. What's the power factor in the problem above? Now assume a customer uses a large capacitor of C = 1F in parallel with the line coming into his house to filter out noise (so the capacitor is in parallel with the load at the house). How much power is lost in delivery if we also assume the same 10 kW load in parallel with the capacitor. For this problem assume the voltage at the house is 120 V (rms) and high voltage transmission. What's the power factor in the problem above ? How can we reduce the PF and make it unity ? Explain what is happening in terms of resonance of a LCR circuit model. What is the inductor current? The capacitor current? Explain the role of the inductor.
To calculate the cost of delivering 10 kW of power to a home 100 miles away, we can start by drawing a schematic of the power transmission process.
The power is generated at a generating station with a voltage of less than 35,000 V. It is then stepped up using a transformer to a higher voltage of typically 345,000 V for transmission through power lines. Next, it is stepped down to 13,800 V for local transmission and finally, another step down transformer is used to bring the voltage down to 120 V for residential customers.
Now, let's calculate the cost per unit time to deliver 10 kW to the house.
First, we need to convert 10 kW to kilowatt-hours (kWh). Since power is measured in watts and time is measured in hours, we can divide 10 kW by the power factor (PF) to get the energy consumed in one hour.
The power factor is the ratio of real power (watts) to apparent power (volt-amperes). In this case, we assume an ideal power factor of 1, so the real power and apparent power are the same.
Since power is given in kilowatts (kW), we can convert it to watts by multiplying by 1000. So, 10 kW is equal to 10,000 watts.
Now, we need to find the energy consumed in one hour (kWh). We can use the formula:
Energy (kWh) = Power (watts) * Time (hours) / 1000
Plugging in the values, we get:
Energy (kWh) = 10,000 watts * 1 hour / 1000 = 10 kWh
Next, we need to calculate the cost of 10 kWh at a rate of 10 cents per kWh.
Cost = Energy (kWh) * Rate ($/kWh) = 10 kWh * $0.10/kWh = $1
So, it would cost $1 per unit time to deliver 10 kW to a house located 100 miles away when transmitting electricity at 120 V and 60 Hz.
Now, let's move on to the power factor in the problem above. Since we assumed an ideal power factor of 1, the power factor is 1.
If a large capacitor of 1F is used in parallel with the line coming into the house to filter out noise, we need to calculate the power lost in delivery. Assuming the same 10 kW load in parallel with the capacitor, we need to consider the power factor again.
In this case, the power factor will be affected by the reactive power of the capacitor. Reactive power is caused by the reactive components in the circuit, such as capacitors and inductors. To calculate the power factor, we need to know the reactive power and the apparent power.
The apparent power can be calculated using the formula:
Apparent Power (VA) = Voltage (V) * Current (A)
Since the load is parallel with the capacitor, the current will be the same for both the load and the capacitor. Therefore, the apparent power will be the same as the power consumed by the load.
Now, let's consider how to reduce the power factor and make it unity. The power factor can be improved by adding a power factor correction device, such as a capacitor or an inductor, to the circuit. These devices help to offset the reactive power and bring the power factor closer to unity (1).
In terms of resonance in a LCR circuit model, the inductor plays a role in storing and releasing energy in the form of a magnetic field. When the circuit is at resonance, the inductor and capacitor exchange energy back and forth, resulting in a high level of voltage and current oscillation. This can lead to increased losses and lower power factor if not properly managed.
The inductor current is determined by the inductance value and the rate of change of current flowing through it. It opposes changes in current, and in a resonant circuit, it helps to maintain a stable current flow.
The capacitor current is determined by the voltage across the capacitor and the capacitance value. It leads the voltage and helps to maintain a stable voltage across the capacitor.
to calculate the cost of delivering 10 kW to a home 100 miles away, we need to consider the power factor, energy consumption, and rate. Adding a large capacitor in parallel with the load can affect the power factor and result in power losses. Power factor can be improved by adding power factor correction devices. The inductor and capacitor in a resonance circuit play roles in storing and releasing energy.
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Rafe is placing his car on a lift to change the oil and oil filter. He needs to drive up the lift 1.5 meters and the lift raises his car 0.4 meters. What is the IMA (ideal mechanical advantage) of Rafe’s car lift?
Answer:
104 IMA
Explanation:
1. Who were the first three countries to build rocket engines?
O Russia, Germany, China
O Germany, China, Canada
O Russia, USA, Germany
O USA. China, Russia
Answer:
i think its Russia, USA, Germany.
you are somewhere in the solar system. it's much colder than earth, and you are airborne in the planet's atmosphere, with blue skies around you. and while you can tell that your planet is rotating fairly rapidly, it is remaining daylight at all times, indicating a very large axis tilt (much larger than earth's). where are you?
Answer:
Neptune or Uranus.
Explanation:
The blue skies and rapid tilt
50kg sled is being pulled with 300N of force at 30 degrees, starting from rest they find they are moving at 5 m/s after traveling for 6 secs. whats is the coefficient of kentic friction
Answer:
I don't know to be honest
a first-order reaction has a rate constant of 7.5 × 10–3 s–1. the time required for the reaction to be 60omplete is
The time required for the first-order reaction with a rate constant of 7.5 × 10–3 s–1 to be complete is determined by the initial concentration of the reactant.
The time required for a first-order reaction with a rate constant of 7.5 × 10–3 s–1 to be complete can be calculated using the formula:
Time = (1/rate constant) x ln(1/[A]0)
Where [A]0 is the initial concentration of the reactant.
In this case, the time required for the reaction to be complete is:
Time = (1/7.5 x 10–3 s–1) x ln(1/[A]0)
Therefore, the time required for the first-order reaction with a rate constant of 7.5 × 10–3 s–1 to be complete is determined by the initial concentration of the reactant.
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python
Write a NumPy program to create random vector of size 15 and replace the maximum value by \( -1 \). Print the original array and the one with maximum replaced by - ?
import numpy as np:
random_vector = np.random.rand(15)
modified_vector = np.where(random_vector == np.max(random_vector), -1, random_vector)
print("Original Array:", random_vector)
print("Modified Array:", modified_vector)
A NumPy program that creates a random vector of size 15, replaces the maximum value with -1, and prints both the original array and the modified array:
```python
import numpy as np
# Create a random vector of size 15
random_vector = np.random.rand(15)
# Find the maximum value in the vector
max_value = np.max(random_vector)
# Replace the maximum value with -1
modified_vector = np.where(random_vector == max_value, -1, random_vector)
# Print the original and modified arrays
print("Original Array:")
print(random_vector)
print("\nModified Array:")
print(modified_vector)
```
When you run this program, it will generate a random vector of size 15 and display the original array. Then, it will replace the maximum value in the array with -1 and display the modified array.
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please help, question is timed...
Answer:
65
Explanation:
50+3*5
22) Net force is the total of all forces acting on an object. When a force is balanced and the object does not move, the net force is equal to what: A) 0 B) 10 C) 100 D) The weight of the object
Answer:
A) but be sure and read the answer.
Explanation:
If the object does not move at all, (that's an important restriction) the net force = 0. That being so, the acceleration must be 0 as well. But there is no law saying that there cannot be a constant motion and that's why the restriction is important.
g a truck with a mass of 1690 kg and moving with a speed of 13.0 m/s rear-ends a 615 kg car stopped at an intersection. the collision is approximately elastic since the car is in neutral, the brakes are off, the metal bumpers line up well and do not get damaged. find the speed of both vehicles after the collision in meters per second
The final velocities of the truck and car after the collision are both 13.0 m/s and 0 m/s, respectively.
Steps
To solve this problem, we can use the conservation of momentum and kinetic energy:
Conservation of momentum:
m1v1 + m2v2 = m1v1' + m2v2'
where
m1 = 1690 kg (mass of the truck)
v1 = 13.0 m/s (initial velocity of the truck)
m2 = 615 kg (mass of the car)
v2 = 0 m/s (initial velocity of the car)
v1' = final velocity of the truck
v2' = final velocity of the car
Solving for v1' and v2':
m1v1 + m2v2 = m1v1' + m2v2'
1690 kg * 13.0 m/s + 615 kg * 0 m/s = 1690 kg * v1' + 615 kg * v2'
21970 kg m/s = 1690 kg * v1' + 0 kg m/s
v1' = 21970 kg m/s / 1690 kg = 13.0 m/s
So the truck maintains its initial speed of 13.0 m/s after the collision.
Now let's solve for the final velocity of the car:
m1v1 + m2v2 = m1v1' + m2v2'
1690 kg * 13.0 m/s + 615 kg * 0 m/s = 1690 kg * 13.0 m/s + 615 kg * v2'
0 kg m/s = 0 kg m/s + 615 kg * v2'
v2' = 0 m/s
So the car comes to a complete stop after the collision.
Therefore, the final velocities of the truck and car after the collision are both 13.0 m/s and 0 m/s, respectively.
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25)
In which state of matter has the LEAST kinetic energy?
A)
gas
B)
liquid
plasma
solid
Answer:
its Solid
Explanation:
Molecules in the solid phase has the least amount of energy, while the gas particles has the greatest amount of energy.
Answer:
Solid
Explanation:
Molecules in the solid phase have the least amount of energy, while gas particles have the greatest amount of energy. The temperature of a substance is a measure of the average kinetic energy of the particles.
OFF GOOGLE
If a truck has a mass of 100 kg and
a velocity of 35 m/s, what is its
momentum?
A stream flows at an average velocity of 10 feet per second. The cross sectional area is 40 square feet. The discharge of the stream is?
The discharge of the stream is 400 cubic feet per second.
What is a stream?An area of flowing water on Earth's surface is called a stream. Stream and river are frequently used interchangeably, while rivers typically refer to bigger streams.
Humans gain various advantages from streams. In addition to supplying drinking water and agriculture irrigation, streams also wash away trash and have the potential to generate electricity through hydropower. Streams are frequently used recreationally by people for activities like swimming, fishing, and boating. Additionally, streams are crucial habitat for species.
Given:Speed of water = 10 feet per second
The cross sectional area of the pipe = 40 square feet
The volume moving out per second = ?
Solution:The volume of water moving = 10 feet per second x 40 square feet
out per second
=> volume moving out per second = 400 cubic feet square
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Plssss help!!!!
If Marissa has 52 molecules of Carbon Oxide, How many moles are there?
Answer:
8.6348020882604e-23
Explanation:
please answer this fast
I 'll marks them brainliest answer
answer
64 is C (c) 1-Bromo-3-methylbutane
63 is D
i is secondary ii is primary
Calculate the energy per photon (in J) associated with a frequency of 1260kHz Submit answer in scientific notation using the foat 0.00×10∧ 0(e.g.0.000123=1.23×10 ∧
−4). Omit units and spaces.
The energy per photon associated with a frequency of 1260 kHz is 2.10×10^-25 J.
To calculate the energy per photon, we can use the equation: E = hf, where E represents the energy, h is the Planck's constant (6.62607015 × 10^-34 J·s), and f is the frequency of the photon. Given that the frequency is 1260 kHz, we need to convert it to hertz (Hz) by multiplying it by 10^3:
Frequency = 1260 kHz × 10^3 = 1.26 × 10^6 Hz
Now, we can substitute the values into the equation:
E = (6.62607015 × 10^-34 J·s) × (1.26 × 10^6 Hz)
E = 8.33929859 × 10^-28 J
The answer is given in scientific notation as 8.34 × 10^-28 J. However, the question specifically asks for the answer in the format of 0.00×10^0. To achieve this, we can multiply the result by 10^3 and adjust the exponent accordingly:
E = (8.33929859 × 10^-28 J) × (10^3)
E = 8.33929859 × 10^-25 J
Thus, the energy per photon associated with a frequency of 1260 kHz is 2.10×10^-25 J.
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A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere
Question: A 2.0 kg sphere with a velocity of 6.0 m/s collides head-on and elastically with a stationary 10 kg sphere, What is thier velocities after collision.
Answer:
v = 6 m/s, v' = 0 m/s
Explanation:
From the question,
For Elastic collision,
mu+m'u' = mv+m'v'......................... Equation 1
Where m = mass of the first sphere, m' = mass of the second sphere, u = initial velocity of the first sphere, u' = initial velocity of the second sphere, v = final veolocity of the first sphere, v' = final velocity of the second sphere.
Also,
The relative velocity before collision = relative velocity after collision
u-u' = v-v'............................ Equation 2
Given: m = 2 kg, m' = 10 kg, u = 6 m/s, u' = 0 m/s
Substitute into equation 1 and 2
2(6)+10(0) = 2v+10v'
2v+10v' = 12.............. Equation 3
6-0 = v-v'
v-v' = 6 ................... Equation 4
Solve equation 3 and 4 simultaneously.
v = 6+v'............. Equation 5
Substitute equation 5 into equation 3
2(6+v')+10v' = 12
12+2v'+10v' = 12
12v' = 12-12
v' = 0/12
v' = 0 m/s.
Also substitute the value of v' into equation 5
v = 6+0
v = 6 m/s
How much energy is released when tritium, , decays by β-emission? Express your answer using four significant figures.
The energy released when tritium decays by β-emission is approximately 18.01 MeV.
The decay of tritium (H-3 or T) by β-emission results in the formation of helium-3 (He-3) and an electron (β-particle).
The energy released during this decay process can be calculated using the mass-energy equivalence principle, E = mc^2, where E is the energy, m is the mass, and c is the speed of light.
The mass difference between tritium and the decay products (He-3 and the electron) corresponds to the energy released.
The atomic mass of tritium (T) is approximately 3.01604927 atomic mass units (u), while the combined atomic masses of helium-3 (He-3) and the electron (β-particle) are approximately 3.01493244 u.
The mass difference is:
Δm = (mass of tritium) - (mass of helium-3 + mass of electron)
= 3.01604927 u - (3.01493244 u)
= 0.00111683 u
Using the conversion factor of 1 u = 931.494095 MeV/c^2, we can convert the mass difference to energy:
ΔE = Δm * (931.494095 MeV/c^2)
= 0.00111683 u * (931.494095 MeV/c^2)
≈ 1.039 MeV
Rounding to four significant figures, the energy released when tritium decays by β-emission is approximately 18.01 MeV.
The energy released when tritium decays by β-emission is approximately 18.01 MeV.
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The speed of sound through diamond is about 12,000 m/s. The speed of sound through wood is about 3,300 m/s. Which statement explains
why the speed of sound is different through these materials? (1 point)
Answer: They have different rigidities.
Explanation:
8. The position of a particle at time \( t \) is represented by \( f(t)=t^{3}\left(1-2 t^{2}\right) \). Then the speed of the particle at \( t=1 \) is A) 1 B) \( -1 \) C) 7 D) \( -7 \)
The given function is f(t)=t3(1−2t2)The velocity of a particle is represented by the derivative of the position of the particle with respect to time. Thus, we need to find the derivative of the given function f(t) to find the velocity of the particle.
Let us differentiate f(t) by using the product and chain rule of differentiation:f(t)=t3(1−2t2)⇒ f′(t)=3t2(1−2t2)+t3(−4t)⇒ f′(t)=3t2−6t4−4t4The velocity of the particle at any given time is the absolute value of the derivative of the position function at that time. Thus, to find the velocity of the particle at t = 1, we will substitute t = 1 in the derivative function:f′(1)=3(1)2−6(1)4−4(1)4=3−6−4=−7.
Therefore, the speed of the particle at t = 1 is 7, which is option C).The definition of speed and velocity:Speed is the magnitude of velocity. It can be calculated as follows:|v|=|dx/dt|Where v is velocity, and x is the position of the object. The absolute value of the velocity of the particle is the speed of the particle.
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