To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:
(P1 x V1) / T1 = (P2 x V2) / T2
where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature, respectively.
First, let's convert the initial temperature of 30°C to Kelvin:
T1 = 30°C + 273.15 = 303.15 K
We can now set up the equation with the initial conditions:
(760 mmHg x V1) / 303.15 K = (P2 x 2V1) / 353.15 K
where V1 is the initial volume of the gas.
Simplifying this equation by multiplying both sides by 303.15 K and dividing by 2V1, we get:
P2 = (760 mmHg x 303.15 K) / (353.15 K) = 653.75 mmHg
Therefore, the final pressure of the gas is 653.75 mmHg when the volume is doubled and the temperature is increased to 80°C.
A fly accumulates 3.0 x 10-10 c of positive charge as it flies through the air. what is the
magnitude and direction of the electric field at a location 2.0 cm away from the fly?
The magnitude of the electric field at a location 2.0 cm away from the fly with 3.0 x 10^-10 C of positive charge is 5.39 x 10^(-2) N/C. The direction of the electric field is radially outward from the fly.
To find the magnitude and direction of the electric field at a location 2.0 cm away from the fly, we need to use the formula for the electric field due to a point charge:
E = k * Q / r^2
where E is the electric field, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), Q is the charge of the fly (3.0 x 10^-10 C), and r is the distance from the charge (2.0 cm or 0.02 m).
Step 1: Convert distance to meters: 2.0 cm = 0.02 m
Step 2: Plug in the values into the formula:
E = (8.99 x 10^9 N m^2/C^2) * (3.0 x 10^-10 C) / (0.02 m)^2
Step 3: Calculate the electric field magnitude:
E = 5.39 x 10^(-2) N/C
Since the fly has a positive charge, the electric field will be directed radially outward from the fly. This means that at any point 2.0 cm away from the fly, the electric field will be pointing away from the fly in a direction perpendicular to the line connecting the fly and the point.
Know more about electric field click here:
https://brainly.com/question/8971780
#SPJ11
A 3. 2-kg point-mass travels around a 0. 45-m radius circle with an angular velocity of 11. 0 rad/s. What is the magnitude of its angular momentum about the center of the circle?
The magnitude of the angular momentum of the point mass about the center of the circle is [tex]$7.1676\ \text{kg}\ \text{m}^2/\text{s}$[/tex].
The angular momentum of a rotating object is defined as the product of its moment of inertia and its angular velocity with respect to an axis of rotation. In this case, we have a point mass of 3.2 kg traveling around a circle of radius 0.45 m with an angular velocity of 11.0 rad/s.
To calculate the angular momentum of the point mass about the center of the circle, we first need to find its moment of inertia. For a point-mass rotating around an axis passing through its center of mass, the moment of inertia is simply the mass times the square of the radius, i.e., [tex]I = mr^2[/tex]. Thus, the moment of inertia of our point mass is:
[tex]I = (3.2 kg) \times (0.45 m)^2 = 0.6516 kg m^2[/tex]
Now, we can calculate the angular momentum L of the point-mass about the center of the circle using the formula:
L = I x w
where w is the angular velocity of the point mass. Plugging in the values we have:
[tex]$L = (0.6516 \text{ kg m}^2) \times (11.0 \text{ rad/s}) = 7.1676 \text{ kg m}^2/\text{s}$[/tex]
This value indicates the amount of rotational motion the point mass possesses, and it is conserved as long as there are no external torques acting on the system.
To learn more about magnitude
https://brainly.com/question/14452091
#SPJ4
Researchers are trying to use radiocarbon dating to determine when the wooden buildings at an archaeological site were constructed. They know that trees in the area would have been cut down for the construction, and that when the trees died, they would have a ratio of carbon-14 to carbon-12 of about one part per trillion (1 ppt). The half-life for the decay of carbon-14 is 5,730 years, and they discover the ratio of carbon-14 to carbon-12 to be about 0. 125 parts per trillion (ppt). What is the age of the buildings at the site? *
716. 25 years
5,730 years
17,190 years
0. 125 billion years
The age of the buildings at the site is approximately 17,190 years. The correct option is 17190 years.
To determine the age of the wooden buildings using radiocarbon dating, we can use the half-life formula:
N = N₀ * (1/2)^(t/T)
where:
- N is the current ratio of carbon-14 to carbon-12 (0.125 ppt)
- N₀ is the initial ratio of carbon-14 to carbon-12 when the trees were cut down (1 ppt)
- t is the time elapsed (the age of the buildings, which we want to find)
- T is the half-life of carbon-14 (5,730 years)
We can rearrange the formula to solve for t:
t = T * log2(N₀/N)
Plugging in the given values:
t = 5730 * log2(1/0.125)
t = 5730 * log2(8)
t = 5730 * 3
t = 17,190 years
So, the correct option is 17190 years.
For more about buildings:
https://brainly.com/question/23099874
#SPJ11
A person who weighs 715 N is riding a 98-N mountain bike. Suppose the entire weight of the rider and bike is supported equally by the two tires. If the gauge pressure in each tire is 6. 20 105 Pa, what is the area of contact between each tire and the ground?
The magnitude of the magnetic field is [tex]2.56 * 10^{-4} T.[/tex]
The force on a charged particle moving in a magnetic field is given by the equation:
F = q v B sin θ
where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field, and θ is the angle between the velocity of the particle and the magnetic field.
The acceleration of the particle is related to the force on the particle by the equation:
F = m a
where m is the mass of the particle and a is the acceleration of the particle.
In this problem, the velocity of the particle is given as 2.0 km/s at an angle of 50° to the magnetic field.
We can resolve this velocity vector into components parallel and perpendicular to the magnetic field.
The component of the velocity parallel to the magnetic field does not experience any force, so we can ignore it.
The component of the velocity perpendicular to the magnetic field experiences a force that causes the particle to move in a circular path.
The magnitude of the velocity component perpendicular to the magnetic field is:
v_perp = v sin θ
v_perp = 2.0 km/s × sin 50°
v_perp = 1.53 km/s
We can convert this to meters per second:
v_perp = 1.53 km/s × 1000 m/km
v_perp = 1530 m/s
The force on the particle due to the magnetic field is:
F = q v_perp B
The mass of the particle is given as 5.0 mg. We can convert this to kilograms:
[tex]m = 5.0 mg *1 kg / (1000 mg) = 5.0 * 10^{-6} kg[/tex]
The acceleration of the particle is given as [tex]5.8 m/s^2[/tex]. We can substitute these values into the equation F = m a and solve for the magnetic field B:
F = m a
q v_perp B = m a
B = m a / (q v_perp)
Substituting the values we know, we get:
[tex]B = (5.0 * 10^{-6} kg) *(5.8 m/s^2) / (-4.0 C * 1530 m/s) = 2.56 * 10^{-4} T[/tex]
To know more about magnetic field refer here
https://brainly.com/question/14848188#
#SPJ11
A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 70.0 m above ground level, and the ball is fired with initial horizontal speed v0 . Assume acceleration due to gravity to be g = 9.80 m/s2 .
A)Assume that the cannon is fired at time t=0 and that the cannonball hits the ground at time tg . What is the y position of the cannonball at the time tg/2 ? Answer numerically in units of meters.
The vertical position of the cannonball at the time tg/2 is 87.5 meters above ground level.
What is the vertical position of the cannonball?The horizontal motion of the cannonball is independent of its vertical motion. Since the cannonball is fired horizontally, its initial vertical velocity is zero, and it only experiences a downward acceleration due to gravity.
We can use the following kinematic equation to determine the time it takes for the cannonball to hit the ground:
h = v₀_y * t + (1/2) * g * t²,
where;
h is the initial height of the cannonball, v₀_y is the initial vertical velocity of the cannonball (which is zero), and t is the time it takes for the cannonball to hit the ground.Solving for t, we get:
t = √(2*h/g)
Plugging in the given values, we get:
t = √(2*70/9.8) = 3.78 s
Therefore, the cannonball hits the ground at time t = 3.78 s.
Now, let's consider the vertical motion of the cannonball. At the time tg/2, the time elapsed since the cannon was fired is tg/2.
The vertical position of the cannonball at this time can be calculated using the following kinematic equation:
y = h + v₀_y * t + (1/2) * g * t²,
Since v₀_y is zero, we have:
y = h + (1/2) * g * (tg/2)²
Plugging in the given values, we get:
y = 70 + (1/2) * 9.8 * (3.78/2)² = 87.5 m (rounded to one decimal place)
Learn more about vertical position here: https://brainly.com/question/21026296
#SPJ1
(1]2] Which row links both the photoelectric effect and electron diffraction to the properties of
waves and particles?
[1 mark]
Photoelectric effect | Electron diffraction
a Particle property Particle property
8 | Wave property Wave property
Particle property Wave property
| Wave property Particle property
The row that links both the photoelectric effect and electron diffraction to the properties of waves and particles is the first row, which includes the terms "Particle property" and "Wave property".
The photoelectric effect refers to the phenomenon where electrons are emitted from a material when light shines on it, while electron diffraction refers to the scattering of electrons by a crystal lattice.
Both of these phenomena can be explained using the wave-particle duality of matter, which suggests that matter can exhibit both particle-like and wave-like properties. The photoelectric effect can be explained by treating light as a particle (photon) that transfers energy to an electron, while electron diffraction can be explained by treating electrons as waves that interfere with each other.
Understanding the properties of waves and particles is essential in understanding these phenomena and many other fundamental concepts in physics. The study of wave-particle duality has also led to the development of quantum mechanics, which is a cornerstone of modern physics. The correct option is "Particle property" and "Wave property".
For more about Particle property:
https://brainly.com/question/16550892
#SPJ11
A man is pulling a 20 kg cart up a hill that is 5 m high if he used 50 N force how far did he pull the cart for
The distance he pulled the cart for is 5 meters, as that is the height of the hill.
The work done by the man to pull the cart up the hill is given by the formula W = F dcos(theta), where W is the work done, F is the force applied, d is the distance traveled, and theta is the angle between the force and the direction of motion.
Since the force and the direction of motion are in the same direction, theta = 0. Therefore, W = F * d.
Substituting the given values, we get W = 50 N * 5 m = 250 J. This is the amount of work done by the man. The distance he pulled the cart for is 5 meters, as that is the height of the hill.
To know more about motion, refer here:
https://brainly.com/question/22810476#
#SPJ11
2) A pallet is pulled 125 m across a floor by a cable that makes an angle of 45° with the
floor. If 1150 N is exerted on the cable, how much work is done?
The work done in pulling the pallet 125 m across the floor with a cable making an angle of 45° with the floor and a force of 1150 N is 96,875 J.
To calculate the work done, we need to use the formula W = Fdcosθ, where F is the force applied, d is the distance moved, and θ is the angle between the force and the direction of motion.
In this case, the force exerted on the pallet is 1150 N, and the distance moved is 125 m. The angle between the force and the direction of motion is 45°.
So, W = (1150 N)(125 m)cos45° = 96,875 J
Therefore, the work done in pulling the pallet 125 m across the floor with a cable making an angle of 45° with the floor and a force of 1150 N is 96,875 J.
To know more about force , refer here:
https://brainly.com/question/13191643#
#SPJ11
Using a lever, a person applies 60 n of force and moves the lever 1 m. this moves a 200-newton rock at the other end by 0. 2 m
The force required to move the 200-newton rock using the lever is 300 N.
We can use the principle of mechanical advantage to determine the force required to move the rock using the lever. Mechanical advantage is the ratio of the output force (the force required to move the rock) to the input force (the force applied by the person). It is given by the formula:
mechanical advantage = output force / input force
In this case, the input force is 60 N and the output force is the force required to move the rock, which we can calculate as follows:
output force = input force x mechanical advantage
The mechanical advantage of a lever is determined by the ratio of the distance from the input force to the fulcrum (the pivot point) to the distance from the output force to the fulcrum. This is known as the lever arm ratio.
In this question, we are told that the person moves the lever 1 m and the rock moves 0.2 m. Therefore, the lever arm ratio is:
lever arm ratio = output distance / input distance
= 0.2 m / 1 m
= 0.2
The mechanical advantage is the inverse of the lever arm ratio:
mechanical advantage = 1 / lever arm ratio
= 1 / 0.2
= 5
Substituting this value in the formula for output force, we get:
output force = input force x mechanical advantage
= 60 N x 5
= 300 N
To know more about lever, here
https://brainly.com/question/3977835
#SPJ4
A bar of length L = 0. 36m is free to slide without friction on horizontal rails. A uniform magnetic field B = 2. 4T is directed into the plane. At one end of the rails there is a battery with emf = 12V and a Switch S. The bar has the mass 0. 90kg and resistance 5. 0ohm. Ignore all the other resistance in the circuit. The switch is closed at time t = 0. A) Just after the switch is closed, what is the acceleration of the bar? b)what is the acceleration of. The bar when its speed is 2. 0m/s? c) what is the bar's terminal speed?
The acceleration of the bar just after the switch is closed is [tex]6.91 m/s^2[/tex]. When the bar's speed is 2.0 m/s, its acceleration is zero. The terminal speed of the bar is 1.49 m/s.
To solve this problem, we will use the equation of motion for an object under the influence of a force and the equation for the current in a circuit under the influence of an emf and resistance.
a) Just after the switch is closed, the current in the circuit will be given by Ohm's Law:
I = emf / R = 12 V / 5.0 Ω = 2.4 A
The bar will experience a magnetic force due to the magnetic field that is perpendicular to its motion. The magnetic force can be calculated using the formula:
F = BIL
where B is the magnetic field, I is the current, and L is the length of the bar. The bar will experience a force in the direction opposite to its motion. Therefore, the acceleration of the bar can be calculated using Newton's second law:
a = F / m = (BIL) / m
Substituting the given values, we get:
a = (2.4 T)(2.4 A)(0.36 m) / 0.90 kg = [tex]6.91 m/s^2[/tex]
Therefore, the acceleration of the bar just after the switch is closed is [tex]6.91 m/s^2[/tex].
b) To calculate the acceleration of the bar when its speed is 2.0 m/s, we need to use the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration, and t is the time.
We can rearrange this equation to solve for time:
t = (v - u) / a = v / a
Substituting the given values, we get:
t = 2.0/ 6.91 = 0.289 s
Now we can use the equation of motion again to calculate the distance traveled by the bar during this time:
[tex]$s = ut + \frac{1}{2}at^2 = \frac{1}{2}at^2$[/tex]
Substituting the given values, we get:
[tex]$s = \frac{1}{2}(6.91 , \mathrm{m/s^2})(0.289 , \mathrm{s})^2 = 0.115 , \mathrm{m}$[/tex]
Therefore, the distance traveled by the bar when its speed is 2.0 m/s is 0.115 m. To calculate the acceleration, we can use the formula:
a = F / m = (BIL) / m
Substituting the given values and using the fact that the bar is now moving at a constant speed (i.e., the net force on the bar is zero), we get:
a = 0
Therefore, the acceleration of the bar when its speed is 2.0 m/s is zero.
c) The terminal speed of the bar can be calculated using the formula:
[tex]$v_{\text{terminal}} = \frac{\text{emf}}{\text{BRL}} \cdot \left(1 - e^{-\frac{\text{BRL}}{\text{m}}}\right)$[/tex]
where emf is the emf of the battery, B is the magnetic field, R is the resistance of the bar, L is the length of the bar, and m is the mass of the bar.
Substituting the given values, we get:
[tex]$v_{\text{terminal}} = \frac{12 , \mathrm{V}}{(2.4 , \mathrm{T})(5.0 , \Omega)(0.36 , \mathrm{m})} \cdot \left(1 - e^{-\frac{(2.4 , \mathrm{T})(5.0 , \Omega)(0.36 , \mathrm{m})}{0.90 , \mathrm{kg}}}\right)$[/tex]
Simplifying this expression, we get:
v_terminal = 1.49 m/s
Therefore, the terminal speed of the bar is 1.49 m/s.
To learn more about acceleration
https://brainly.com/question/12550364
#SPJ4
which statement must be true for a rocket to travel from earth to another planet? group of answer choices it must have large engines. it must attain escape velocity from earth. it must carry a lot of extra fuel. it must be launched from space, rather than from the ground.
For a rocket to travel from Earth to another planet, it must attain escape velocity from Earth. Option B is correct.
This is the minimum velocity needed to escape the gravitational pull of Earth and enter into space. Once a rocket achieves escape velocity, it can continue on its trajectory toward the other planet without the need for extra fuel or engines. While having large engines and carrying extra fuel can certainly be beneficial for a rocket's journey, they are not absolute requirements for traveling from Earth to another planet.
Additionally, launching from space rather than from the ground is not a requirement, as many successful missions have been launched from Earth's surface. Therefore, the key requirement for a rocket to travel from Earth to another planet is to attain escape velocity from Earth's gravitational pull. Option B is correct.
To know more about the Rocket, here
https://brainly.com/question/10488794
#SPJ4
Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass. What wavelength of light is emitted when electrons transition from an energy level of 1. 67 ev to 0. 50 ev?.
The wavelength of the emitted light is approximately 1.05 micrometers.
We can use the equation:
$\lambda = \frac{hc}{E}$
where $\lambda$ is the wavelength, $h$ is Planck's constant, $c$ is the speed of light, and $E$ is the energy of the transition.
First, we need to convert the energies from electron volts (eV) to joules (J):
$E_1 = 1.67 \text{ eV} \times 1.602 \times 10^{-19} \text{ J/eV} = 2.68 \times 10^{-19} \text{ J}$
$E_2 = 0.50 \text{ eV} \times 1.602 \times 10^{-19} \text{ J/eV} = 8.01 \times 10^{-20} \text{ J}$
Now, we can calculate the wavelength:
$\lambda = \frac{hc}{E_1 - E_2} = \frac{(6.626 \times 10^{-34} \text{ J s})(2.998 \times 10^{8} \text{ m/s})}{2.68 \times 10^{-19} \text{ J} - 8.01 \times 10^{-20} \text{ J}} \approx \boxed{1.05 \times 10^{-6} \text{ m}}$
To know more about Planck's constant refer here
https://brainly.com/question/30763530#
#SPJ11
A capacitor of capacitance 8. 1x10-6 F is discharging through a 1. 3 M Ω resistor. At what time will the energy stored in the capacitor be half of its initial value?
Answer in seconds and upto 1 decimal place
TimeTime when energy stored in the capacitor will be half of its initial value=7.3s
To find the time at which the energy stored in the capacitor will be half of its initial value, we can use the formula for the time constant (τ) of an RC circuit and the fact that energy is halved when the voltage across the capacitor is reduced to 1/√2 of its initial value.
The time constant (τ) of the RC circuit is given by τ = R * C, where R is the resistance and C is the capacitance.
τ = (1.3 * 10^6 Ω) * (8.1 * 10^-6 F) = 10.53 seconds
Now, we can use the formula for discharging a capacitor: V(t) = V_initial * e^(-t/τ)
We need to find the time (t) when V(t) = V_initial / √2. So:
V_initial / √2 = V_initial * e^(-t/10.53)
Divide both sides by V_initial:
1 / √2 = e^(-t/10.53)
Take the natural logarithm of both sides:
-ln(√2) = -t / 10.53
Now, solve for t:
t = 10.53 * ln(√2) ≈ 7.3 seconds
So, the energy stored in the capacitor will be half of its initial value at approximately 7.3 seconds.
Visit https://brainly.com/question/29301875 to learn more about capacitors
#SPJ11
What is the tension in the string when the meterstick is vertical?.
Assuming that the meterstick is in equilibrium, the sum of the forces acting on it must be zero. At the top of the meterstick, the tension in the string is pulling upward with a force of T, while the weight of the meterstick is pulling downward with a force of mg, where m is the mass of the meterstick and g is the acceleration due to gravity.
Since the meterstick is vertical, the weight is acting straight down and the tension is acting at an angle of 90 degrees. Therefore, we can use the following equation to find the tension:
T = mg/cosθ
where θ is the angle between the string and the meterstick (which is 90 degrees in this case). Plugging in the values given:
T = (0.5 kg)(9.8 m/s^2)/cos(90°) = 0 N
Therefore, the tension in the string when the meterstick is vertical is 0 N.
To know more about meterstick refer here
https://brainly.com/question/29690562#
#SPJ11
when approaching a railroad crossing with no warning device, the speed limit is ___
When approaching a railroad crossing with no warning device, the speed limit is determined by state law and may vary depending on the specific location and circumstances.
However, there are some general guidelines to keep in mind:
1. Slow down: It is always recommended to slow down when approaching a railroad crossing, regardless of whether there is a warning device or not.
2. Look and listen: Take the time to look and listen for trains before proceeding across the tracks. Even if you don't see or hear a train, it's still important to exercise caution.
3. Be prepared to stop: Be prepared to come to a complete stop if necessary. If you see a train approaching, do not try to beat it across the tracks.
4. Obey signs and signals: Follow any posted signs or signals that indicate the speed limit or provide other warnings about the crossing.
5. Yield to trains: Remember that trains always have the right of way. If a train is approaching, yield to it and wait until it has passed before proceeding.
In general, it's important to approach all railroad crossings with caution, even if there are no warning devices present.
The exact speed limit may vary depending on the location and circumstances, so it's always best to exercise caution and be prepared to stop if necessary.
To know more about speed limit refer here
https://brainly.com/question/29632218#
#SPJ11
A 76 kg surfer travels through the barrel of a wave at 11 m/s. What is his
kinetic energy (KE) in Joules?
A 76 kg surfer traveling through the barrel of a wave at 11 m/s has a kinetic energy of 4,958 Joules.
The kinetic energy (KE) of the surfer can be calculated using the formula KE = 1/2mv^2, where m is the mass of the surfer and v is the velocity at which he is traveling through the wave.
Given that the mass of the surfer is 76 kg and his velocity is 11 m/s, we can plug these values into the formula:
KE = 1/2(76 kg)(11 m/s)^2
KE = 4,958 Joules
Therefore, the kinetic energy of the surfer traveling through the barrel of the wave is approximately 4,958 Joules.
This represents the energy of motion or the energy that the surfer possesses due to his velocity. As the surfer moves through the wave, his kinetic energy is constantly changing due to factors such as friction with the water and changes in velocity.
Understanding the concept of kinetic energy is important in many fields, including physics, engineering, and sports science.
Learn more about kinetic energy at: https://brainly.com/question/8101588
#SPJ11
What is the approximate velocity of the object at 5 seconds ?
The actual answer may differ depending on the true values of those variables.
The approximate velocity of the object at 5 seconds can be determined using the following steps:
1. Identify the given information: You are asked to find the velocity of the object at a specific time (5 seconds).
2. Determine the equation needed:
To find the velocity at a certain time, you will need to use the equation:
v = u + at,
where
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time.
3. Gather necessary data: To use the equation, you need to know the initial velocity (u) and the acceleration (a) of the object. This information is not provided in your question,
so it is not possible to give an exact answer. However, I will assume some values for u and a to provide an example calculation.
4. Example calculation: Let's assume the initial velocity (u) is 0 m/s and the acceleration (a) is 2 m/s². Plug these values, along with the given time (t = 5 seconds), into the equation:
v = u + at
v = 0 + (2 × 5)
v = 0 + 10
v = 10 m/s
In this example, the approximate velocity of the object at 5 seconds is 10 m/s. Note that this answer is based on the assumed values for initial velocity and acceleration,
So the actual answer may differ depending on the true values of those variables.
To know more about approximate velocity refer here
brainly.com/question/28605419#
#SPJ11
What is the probability of each possible sample if (a) a random sample of size n=4 is to be drawn from a finite population of size N=12; (b) a random sample of size n=5 is to be drawn from a finite population of size N=22?
The probability of each possible sample is (sample) = 1/495. The probability of each possible sample is P(sample) = 1/28,544.
(a) The probability of each possible sample of size n=4 being drawn from a finite population of size N=12 can be calculated using the formula:
P(sample) = (number of ways to choose the sample) / (total number of possible samples)
The number of ways to choose a sample of size 4 from a population of size 12 is:
C(12,4) = 12! / (4! * 8!) = 495
The total number of possible samples of size 4 from a population of size 12 is:
C(12,4) = 495
Therefore, the probability of each possible sample is:
P(sample) = 1/495
(b) The probability of each possible sample of size n=5 being drawn from a finite population of size N=22 can be calculated using the same formula:
P(sample) = (number of ways to choose the sample) / (total number of possible samples)
The number of ways to choose a sample of size 5 from a population of size 22 is:
C(22,5) = 22! / (5! * 17!) = 28,544
The total number of possible samples of size 5 from a population of size 22 is:
C(22,5) = 28,544
Therefore, the probability of each possible sample is:
P(sample) = 1/28,544
Learn more about probability here:-
https://brainly.com/question/30034780
#SPJ11
What is (fnet3)x , the x-component of the net force exerted by these two charges on a third charge q3 = 48.0 nc placed between q1 and q2 at x3 = -1.145 m ? your answer may be positive or negative, depending on the direction of the force.
The x-component of the net force exerted by [tex]q_1[/tex] and [tex]q_2[/tex] on [tex]q_3[/tex] is -5.33 x [tex]10^{-3}[/tex] N, indicating that [tex]q_3[/tex] is attracted towards [tex]q_1[/tex].
What is Charge?
Charge is a fundamental property of matter that describes the amount of electrical energy that a particle possesses. It is a physical property that can be either positive or negative and is measured in units of coulombs (C).
To calculate the x-component of the net force, we need to consider the x-components of the distances and forces. Since [tex]q_3[/tex] is placed between [tex]q_1[/tex]and [tex]q_2[/tex], we can calculate the distances as follows:
[tex]r_1[/tex] = [tex]x_3[/tex] - [tex]x_1[/tex] = (-1.145 m) - (0 m) = -1.145 m
[tex]r_2[/tex] = [tex]x_2[/tex] - [tex]x_3[/tex] = (0.855 m) - (-1.145 m) = 2 m
Note that we use the signs of the distances to indicate the directions of the forces.
The x-components of the forces can be calculated using trigonometry:
F[tex]x_1[/tex] = F1 * cos(theta1) = k * [tex]q_1[/tex] * [tex]q_3[/tex] / [tex]r_1[/tex] * cos(theta1)
F[tex]x_2[/tex] = F2 * cos(theta2) = k * [tex]q_2[/tex] * [tex]q_3[/tex] / [tex]r_2[/tex] * cos(theta2)
where theta1 and theta2 are the angles between the forces and the x-axis.
Since [tex]q_1[/tex] and [tex]q_2[/tex] are both positive, they repel each other and the force on [tex]q_3[/tex] is negative, indicating that it is attracted towards the negative side of the x-axis, which is towards [tex]q_1[/tex].
Using trigonometry, we can calculate the angles as follows:
theta1 = arctan(y1 / [tex]x_1[/tex]) = arctan(0 / (-1.145 m)) = 0 rad
theta2 = arctan(y2 / [tex]x_2[/tex]) = arctan(0 / (0.855 m)) = 0 rad
Therefore, the x-components of the forces are:
F[tex]x_1[/tex] = k *[tex]q_1[/tex] *[tex]q_3[/tex] / [tex]r_1[/tex]^2 * cos(0 rad) = -3.31 x [tex]10^{-3}[/tex] N
F[tex]x_2[/tex] = k * [tex]q_2[/tex] *[tex]q_3[/tex] / [tex]r_2[/tex]^2 * cos(0 rad) = -2.02 x [tex]10^{-3}[/tex] N
The net force on [tex]q_3[/tex] is the sum of the forces:
Fnetx = F[tex]x_1[/tex] + F[tex]x_2[/tex] = -5.33 x [tex]10^{-3}[/tex] N
To know more about Charge visit;
https://brainly.com/question/18102056
#SPJ4
A speeding car traveling at 41 m/s passes a parked police car. One second after getting passed, the police car begins pursuit. The police car accelerates at a rate of 7.5 m/s/s. The police car catches up after 12.8 seconds and the police car travels 527 meters.
What is the velocity of the police car when it catches up to the speeding car?
Answer:
To solve this problem, we can use the equation:
distance = initial velocity x time + 1/2 x acceleration x time^2
First, we need to find the initial distance between the two cars. The speeding car travels for 1 second before the police car begins pursuit, so its initial distance from the parked police car is:
initial distance = 41 m/s x 1 s = 41 m
Now we can use the equation to find the time it takes for the police car to catch up to the speeding car:
distance = initial velocity x time + 1/2 x acceleration x time^2
527 m = 0 m/s x t + 1/2 x 7.5 m/s^2 x t^2
Simplifying:
t = sqrt((2 x 527 m) / 7.5 m/s^2) = 12.92 s
So the police car catches up to the speeding car after 12.92 seconds. Now we can use the equation:
final velocity = initial velocity + acceleration x time
to find the velocity of the police car when it catches up to the speeding car:
final velocity = 0 m/s + 7.5 m/s^2 x 12.92 s = 96.9 m/s
Therefore, the velocity of the police car when it catches up to the speeding car is 96.9 m/s.
Explanation:
Marci drops a ball off the top of the Empire state building. How fast is the ball traveling after 4 seconds? (assuming there is no air)
Answer:We can use the kinematic equation:
v = vo + at
where:
v = final velocity (what we want to find)
vo = initial velocity (which is zero since the ball is dropped)
a = acceleration due to gravity (-9.8 m/s^2, negative since it is acting in the opposite direction of the ball's motion)
t = time (4 seconds)
Substituting the values, we get:
v = 0 + (-9.8 m/s^2)(4 s)
v = -39.2 m/s
Note that the negative sign indicates that the ball is moving downward.
Explanation:
Find the temperature of an ideal gas being quasi-statically compressed by 700 j of work to one-third of its initial volume
The temperature of an ideal gas being quasi-statically compressed by 700 j of work to one-third of its initial volume can be found using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the work done on the system plus the heat added to the system.
Since the gas is considered ideal, the heat added is assumed to be zero. Therefore, the change in internal energy is simply equal to the work done, which is 700 j. Since internal energy is proportional to temperature, the temperature of the gas can be found by dividing the work done by the gas's specific heat capacity.
The temperature will increase as the gas is compressed, and the final temperature can be determined by multiplying the initial temperature by the ratio of the final volume to the initial volume. In this case, the final temperature would be three times the initial temperature.
To know more about thermodynamics, click here:
https://brainly.com/question/1368306
#SPJ4
ii. how long it takes to travel 294 m below the point of projection.
It takes 10 seconds for the stone to travel 294 m below the point of projection. That's how long it take to travel.
How do we calculate how long it take to travel 294 m below the point of projection.?The equation to use to find how long it take to travel 294m below the point of projection is:
4.9t² - 19.6t - 294 = 0
We need the quadratic equation
t = [-b ± √(b² - 4ac)] / (2a)]
a = 4.9, b = -19.6, and c = -294.
t = [19.6 ± √((-19.6)² - 44.9(-294))] / (2×4.9)
t = [19.6 ±√384.16 + 5745.6)] / 9.8
t = [19.6 ± √(6129.76)] / 9.8
t = [19.6 ± 78.3] / 9.8
The possible answers are;
t1 = (19.6 + 78.3) / 9.8 = 10 seconds
t2 = (19.6 - 78.3) / 9.8 = -6 seconds
considerinf that the answer cannot be in the negative, therefore t₁ is the answer.
Find more exercises on how long it takes to travel;
https://brainly.com/question/4836382
#SPJ1
Question 5
A ball is thrown straight down with an initial speed of 4.30 m/s, from a height of
8.80 m. What is the velocity of the ball when it reaches a height of 5.80?
Answer:We can use the kinematic equations of motion to solve this problem. The equation we need to use is:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (which is -9.81 m/s^2), and s is the displacement.
Initially, the ball is thrown straight down with an initial speed of 4.30 m/s and a height of 8.80 m. Let's take the upward direction as positive. Using the equation of motion for displacement, we can find the time it takes for the ball to reach a height of 5.80 m:
s = ut + (1/2)at^2
-3 = 4.3t + (1/2)(-9.81)t^2
-4.905t^2 + 4.3t - 3 = 0
Using the quadratic formula, we find that the time it takes for the ball to reach a height of 5.80 m is t = 0.956 s (rounded to three significant figures).
Now, we can use the equation of motion for velocity to find the velocity of the ball at this point:
v^2 = u^2 + 2as
v^2 = (4.3 m/s)^2 + 2(-9.81 m/s^2)(-3 m)
v = -5.08 m/s
The negative sign indicates that the velocity is in the downward direction. Therefore, the velocity of the ball when it reaches a height of 5.80 m is 5.08 m/s downward.
Explanation:
What is the angle of incidence for this ray?
Answer:
35
Explanation:
Let Angle of Incident ray be i.
Let Angle of Reflected ray be r.
By laws of reflection
i = r
Here
i + r = 70
i + i = 70
2i = 70
i = 70/2
i = 35
Hence
The angle of incidence for this ray is 35.
Instruction: Answer all questions Time: 1. 5hrs An electron is placed in a uniform electric field with field strength of 150kvm Calculate the duration for it to travel 30mm from its stationary Position Give an explanation for your answer.
The duration for the electron to travel 30 mm in a uniform electric field with a field strength of 150 kV/m is approximately 6.37 x 10⁻⁸ seconds.
What is acceleration?The rate at which velocity changes with respect to time.
To solve this problem, we can use the equation for the acceleration of an electron in an electric field:
a = F/m = qE/m
where a is the acceleration, F is the force, m is the mass of the electron, q is the charge of the electron, and E is the electric field strength.
We can rearrange this equation to solve for the time it takes for the electron to travel a certain distance:
t = √(2d/a)
where d is the distance traveled.
Plugging in the given values, we get:
a = (1.602 x 10⁻¹⁹ C)(150 x 10³ V/m)/(9.109 x 10⁻³¹ kg) = 2.62 x 10¹⁴ m/s²
d = 30 mm = 0.03 m
t = √(2 x 0.03 m / 2.62 x 10¹⁴ m/s²) = 6.37 x 10⁻⁸ s
Therefore, the duration for the electron to travel 30 mm in a uniform electric field with a field strength of 150 kV/m is approximately 6.37 x 10⁻⁸ seconds.
Explanation: The acceleration of the electron in the electric field is independent of its initial velocity. Hence, the electron will continue to accelerate at a constant rate until it reaches the end of the distance. Once it reaches the end, it will have attained a maximum velocity and will continue to move at a constant velocity if there are no other forces acting on it. Therefore, the time taken to travel the distance depends only on the acceleration and the distance traveled.
Learn more about acceleration on:
https://brainly.com/question/25876659
#SPJ4
In a laboratory, nakisha mixes a sodium hydroxide solution with an indicator called phenolphthalein. when combined, they create a pink solution. nakisha wonders if mixing other solutions with phenolphthalein will also create this pink color. how could nakisha use the scientific inquiry process to determine whether mixing other solutions with phenolphthalein will also create a pink color? check all that apply.
Nakisha can systematically investigate her question and determine the conditions under which: mixing phenolphthalein with other solutions will create a pink color
To determine whether mixing other solutions with phenolphthalein will also create a pink color, Nakisha could use the scientific inquiry process as follows:
1. Ask a question: Nakisha's question is whether mixing other solutions with phenolphthalein will create a pink color.
2. Conduct background research: Nakisha can research the properties of phenolphthalein and its reactions with different types of solutions, such as acids, bases, or neutral substances.
3. Form a hypothesis: Based on the background research, Nakisha can form a hypothesis about the possible outcomes when mixing phenolphthalein with various solutions. For example, she might hypothesize that phenolphthalein will only turn pink when mixed with basic solutions.
4. Design and perform an experiment: Nakisha can set up a controlled experiment where she tests different solutions with phenolphthalein. She can use a variety of solutions, such as hydrochloric acid, acetic acid, sodium hydroxide, ammonia, and distilled water, and observe their reactions with phenolphthalein.
5. Record and analyze data: Nakisha should carefully record the color changes that occur when mixing phenolphthalein with each solution. She can then analyze this data to determine which types of solutions cause a pink color change.
6. Draw conclusions: Based on her experimental results, Nakisha can draw a conclusion about which types of solutions create a pink color when mixed with phenolphthalein. If her hypothesis is supported, she can determine that only basic solutions create a pink color with phenolphthalein.
7. Communicate results: Finally, Nakisha can share her findings with others in the scientific community, either through a lab report, presentation, or published article.
By following the scientific inquiry process, Nakisha can systematically investigate her question and determine the conditions under which mixing phenolphthalein with other solutions will create a pink color.
To know more about phenolphthalein, refer here:
https://brainly.com/question/14037314#
#SPJ11
How thermal energy is transferred throughout the water
Answer:
Explanation: Thermal energy is transferred through water by conduction, convection, and radiation. Conduction occurs when heat is transferred through direct contact between water molecules with different thermal energy. Convection occurs when warmer water rises to the top and cooler water sinks to the bottom, creating a circular motion that distributes heat. Radiation is the transfer of energy through electromagnetic waves, but it is not significant in water due to poor conduction. The specific mechanism that dominates heat transfer depends on various factors such as temperature gradient, depth, and presence of other materials.
What would the RPM be if we were turning a 1. 00" diameter work piece made out of mild
steel, using HSS cutting tool?
The recommended RPM for turning a 1.00" diameter mild steel workpiece using an HSS cutting tool would be approximately 400 RPM.
To calculate the RPM for turning a 1.00" diameter workpiece made of mild steel using an HSS (high-speed steel) cutting tool, you can use the following formula:
RPM = (Cutting Speed x 4) / Workpiece Diameter
For mild steel, the recommended cutting speed with HSS tools is approximately 100 surface feet per minute (SFM). Using this value and the given workpiece diameter, we can calculate the RPM:
RPM = (100 SFM x 4) / 1.00" Diameter
RPM = 400 / 1.00
RPM ≈ 400
So, the recommended RPM for turning a 1.00" diameter mild steel workpiece using an HSS cutting tool would be approximately 400 RPM.
To learn more about speed, refer below:
https://brainly.com/question/28224010
#SPJ11
You find some limestone rock in southern Indiana and notice that it has fossil trilobites in it. Later you find the same fossil trilobites in a limestone in Colorado. From this you determine that the two rock types were deposited during the same time period using what concept or principle?
The concept or principle used to determine that the two rock types were deposited during the same time period is the principle of faunal succession.
This principle states that fossils of similar organisms found in rocks from different locations were deposited during the same time period, as the distribution of fossils in the rock layers is related to the relative ages of the rocks.
By finding the same fossil trilobites in both the Indiana and Colorado limestone rocks, it can be inferred that the rocks were deposited during the same time period and were likely part of the same geologic formation.
To know more about faunal succession, refer here:
https://brainly.com/question/13674871#
#SPJ11