Answer:
40 cm
Explanation:
Since Bob pulls with a force of F = 200 N when the spring is attached to the wall and it extends a length x = 20 cm, from Hooke's law,
F = kx where k = spring constant
So, k = F/x = 200 N/20 cm = 10 N/cm
Now, sine both Bob and Carlos pull with a force of F = 200 N in opposite directions, the spring stretches about its center and has an extension, x' in each direction.
So, from F = kx
x = F/k = 200 N/10 N/cm = 20 cm
So, the spring stretches 20 cm in both directions.
So, the total extension is thus x' + x' = 2x' = 2(20 cm) = 40 cm
The spring will stretch 40 cm.When a force is act om the spring the spring will stretch or compress depeds on the application of force.
What is hooke's law?Hooke's law states that the force used to extend the spring is directly equal to the amount of stretch.
The force needed to extend the spring is proportional to its displacement. It is stated as
F=Kx
The given data in the problem is;
F is the force of pull to bob= 200 N
x is the length of extension= 20 cm.
F' is the force act on the another end= 200 N
According to Hooke's law,
[tex]\rm F = Kx \\\\ \rm K= \frac{F}{x} \\\\ \rm K= \frac{200}{20} \\\\ \rm K=10 \ N/cm[/tex]
The extension due to another end force is found by;
[tex]\rm x' = \frac{F}{K} \\\\ \rm x' = \frac{200}{10} \\\\ \rm x' = 20[/tex]
The total extension of the spring will be;
[tex]\rm x_t = x+x' \\\\ \rm x_t = 2(20) \\\\ \rm x_t =40\ cm[/tex]
Hence the spring will stretch 40 cm.
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A 70 cm diameter wheel accelerates uniformly about its center from 130 rpm to 280 rpm in 4 s. Determine (a) its angular acceleration, and (b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2 s after it has started accelerating. Show all work and formulas for best rating.
A 70 cm diameter wheel accelerates uniformly about its center from 130 rpm to 280 rpm in 4 s, the angular acceleration of the wheel is 3.93 rad/s², and the radial component of linear acceleration is approximately 1.375 m/s², and the tangential component is approximately 165.86 m/s².
(a) The angular acceleration of the wheel can be determined using the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Given:
Initial angular velocity (ω₁) = 130 rpm
Final angular velocity (ω₂) = 280 rpm
Time (t) = 4 s
First, we need to convert the angular velocities from rpm to radians per second (rad/s):
ω₁ = 130 rpm * (2π rad/1 min) * (1 min/60 s) = 13.61 rad/s
ω₂ = 280 rpm * (2π rad/1 min) * (1 min/60 s) = 29.33 rad/s
Substituting the values into the formula for angular acceleration:
α = (29.33 rad/s - 13.61 rad/s) / 4 s = 3.93 rad/s²
Therefore, the angular acceleration of the wheel is 3.93 rad/s².
(b) To determine the radial and tangential components of the linear acceleration of a point on the edge of the wheel after 2 s, we can use the following formulas:
Radial acceleration (ar) = r * α
Tangential acceleration (at) = r * ω²
Given:
Radius of the wheel (r) = 70 cm / 2 = 35 cm = 0.35 m
Angular acceleration (α) = 3.93 rad/s²
Angular velocity (ω) at t = 2 s can be found using the formula:
ω = ω₁ + α * t
Substituting the values:
ω = 13.61 rad/s + 3.93 rad/s² * 2 s = 21.47 rad/s
Now we can calculate the radial and tangential components of linear acceleration:
ar = r * α = 0.35 m * 3.93 rad/s² ≈ 1.375 m/s²
at = r * ω² = 0.35 m * (21.47 rad/s)² ≈ 165.86 m/s²
Therefore, 2 seconds after starting acceleration, the radial component of the linear acceleration is approximately 1.375 m/s², and the tangential component is approximately 165.86 m/s².
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A meteorite is DIFFERENT from a comet mainly because it
A) has a tail of ice and dust.
B) enters the Earth’s atmosphere.
C) has a nucleus made of snow and rock.
Eliminate
D) is found in orbit between Mars and Jupiter.
When you think of the word "respiration," you might think about the process of breathing, which is actually called ventilation. (The respiratory system consists of the windpipe, lungs, etc.) How is breathing related to cellular respiration?
Answer:
Breathing and cellular respiration are complementary processes that enable the body to produce energy by taken in oxygen which is required for the chemicals contained in food to be broken down there by producing, energy, water and carbon dioxide. The breathing and cellular respiration process also enables the removal of the produced carbon dioxide finally through nose and/or mouth
Explanation:
In cellular respiration, glucose molecules in the presence of oxygen gas are broken down into carbon dioxide and water aerobically in living cells, to release energy and produce ATP as follows;
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
During breathing, oxygen is inhaled into the lungs from the atmosphere and carbon dioxide is exhaled from the longs into the atmosphere, such that the carbon dioxide produced during cellular respiration is transported out of the body through the veins respiratory system, from where is passes out through the nose, while oxygen used in cellular respiration comes from breathing in oxygen into the respiratory system
The oxygen is then transported to the cells through by blood in the blood vessels of the circulatory system to the cells, where the cells use the oxygen for cellular respiration to release energy.
At a certain instant, the earth, the moon, and a stationary 1470 kg spacecraft lie at the vertices of an equilateral triangle whose sides are km in length.
A. Find the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon.
B. Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon.
C. State the direction as an angle measured from a line connecting the earth and the spacecraft.
D. What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? You can ignore any gravitational effects due to the other planets or the sun.
The magnitude of the net gravitational force exerted on the spacecraft by the Earth and Moon is approximately 4.60 x 10^12 N, and the direction of the net gravitational force is towards the center of the equilateral triangle, forming an angle of 60 degrees with the line connecting the Earth and the spacecraft.
A. The magnitude of the net gravitational force exerted on the spacecraft by the Earth and Moon can be calculated using the formula for gravitational force:
Gravitational force (F) = G * ((m1 * m2) / r^2)
Where G is the gravitational constant (6.67430 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the objects (Earth, Moon, or spacecraft), and r is the distance between the objects.
Given:
Mass of Earth (mE) = 5.972 × 10^24 kg
Mass of Moon (mM) = 7.348 × 10^22 kg
Mass of spacecraft (mS) = 1470 kg
Length of the sides of the equilateral triangle (s) = km = 1,000 m
To find the magnitude of the net gravitational force on the spacecraft, we need to consider the gravitational forces between the spacecraft and both the Earth and the Moon. Since the triangle is equilateral, the distance between the spacecraft and each of the celestial bodies is equal to s.
F_Earth = G * ((mE * mS) / s^2)
F_Moon = G * ((mM * mS) / s^2)
Net gravitational force (F_net) = F_Earth + F_Moon
B. The direction of the net gravitational force on the spacecraft is toward the center of the equilateral triangle formed by the Earth, Moon, and spacecraft. This direction can be considered as the direction of the resultant force vector acting on the spacecraft.
C. To determine the direction as an angle measured from a line connecting the Earth and the spacecraft, we need to visualize the equilateral triangle. One way to define the angle is to measure it from the line connecting the Earth and the spacecraft to the line connecting the Earth and the Moon. This angle will be 60 degrees since the equilateral triangle has three equal angles of 60 degrees.
D. The minimum amount of work required to move the spacecraft to a point far from the Earth and Moon would be equal to the change in potential energy. As the spacecraft moves far away, the potential energy decreases. The work done is given by the formula:
Work (W) = ΔPE = PE_final - PE_initial
Since the potential energy depends on the distance from the Earth and Moon, moving the spacecraft to a point far away where the gravitational influence is negligible would result in a significant decrease in potential energy. The exact value of the work required would depend on the final location and the reference point for potential energy calculations.
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Explain how radioactive decay works for measuring the absolute age of ancient objects.
Answer: Radioactive decay is the breakdown of a material into stable isotopes which are used for determining the age of the ancient material.
Explanation:
The radioactive decay is a natural process in which an ancient or old material whether in the form of rock, object or fossil break down into elements. Carbon 14 is an unstable isotope which decays to produce stable elements, the dating procedure uses these stable elements and the rate of decay of the isotopes to determine the age of absolute ancient of the objects but exact age cannot be determined just an approximation can be accepted.
A guitar string 61 cm long vibrates with a standing wave that has three antinodes.
1-Which harmonic is this? Express your answer using one significant figure.
2-What is the wavelength of this wave? Express your answer using two significant figures.
1. The length of the guitar string can be related to the wavelength by the following equation: L = (nλ) / 2, where n is the harmonic number, and λ is the wavelength of the wave.
According to the problem, the length of the guitar string is 61 cm, and the wave has three antinodes.
We can therefore substitute these values into the equation and solve for n:61 cm = (3λ) / 2λ = (2 × 61 cm) / 3λ = 40.7 cm (rounded to one significant figure)
Therefore, the wavelength is 40.7 cm (rounded to two significant figures).
2. The wavelength: We can now use the above value of λ and the formula
v = fλ to calculate the frequency of the wave.
However, the velocity of a wave in a string is given by the formula
v = √(T/μ), where T is the tension in the string and μ is its linear mass density (mass per unit length).
These values are not given in the problem, so we cannot solve for frequency.
Instead, we can use another equation that relates the wavelength to the length of a string:λ = 2L / n,
where L is the length of the string and n is the harmonic number. Substituting the given values: L = 61 cm, n = 3λ = 40.7 cm (from part a).
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An electron moves along the z-axis with vz=3.8×107m/svz=3.8×107m/s. As it passes the origin, what are the strength and direction of the magnetic field at the following (xx, yy, zz) positions?
A. (2 cmcm , 0 cmcm, 0 cmcm)
B. (0 cmcm, 0 cmcm, 1 cmcm )
C. (0 cmcm, 2 cmcm , 1 cmcm )
At position A, the magnetic field is directed in the positive z-direction with a magnitude of [tex]9.5 * 10^{-2}[/tex] Tesla.
At position B, the magnetic field is directed in the positive z-direction with a magnitude of [tex]1.52 * 10^{-6}[/tex] Tesla.
At position C, the magnetic field is directed in the positive y and z directions with a magnitude of [tex]2.85 * 10^{-1}[/tex] Tesla in the y-direction and [tex]1.43 * 10^{-1}[/tex] Tesla in the z-direction.
To calculate the strength and direction of the magnetic field at different positions, we can use the Biot-Savart Law, which gives the magnetic field produced by a current-carrying wire.
In this case, we can consider the electron's velocity as a current and calculate the magnetic field using the equation:
B = (μ₀/4π) * (v × r) / r²
where B is the magnetic field, μ₀ is the permeability of free space [tex](4\pi * 10^{-7} T.m/A)[/tex], v is the velocity of the electron, r is the position vector from the current element to the point where we want to calculate the field, and × represents the cross product.
Let's calculate the magnetic field at each given position:
A. (2 cm, 0 cm, 0 cm):
First, convert the position to meters: (0.02 m, 0 m, 0 m)
The position vector, r = (0.02 m, 0 m, 0 m), points in the positive x-direction.
Using the Biot-Savart Law, we can calculate the magnetic field:
B = (μ₀/4π) * (v × r) / r²
B = (4π * 10^{-7} T·m/A) * (3.8 × 10^7 m/s) * (0 m, 0 m, 1 m) / (0.02 m)²
B = (4π × 10^{-7} T·m/A) * (3.8 × 10^7 m/s) * (0 m, 0 m, 1 m) / (0.0004 m)
B = 9.5 × 10^{-2} T * (0 m, 0 m, 1 m) = (0 T, 0 T, 9.5 × 10^{-2} T)
Therefore, at position A, the magnetic field is directed in the positive z-direction with a magnitude of 9.5 × 10^{-2} Tesla.
B. (0 cm, 0 cm, 1 cm):
First, convert the position to meters: (0 m, 0 m, 0.01 m)
The position vector, r = (0 m, 0 m, 0.01 m), points in the positive z-direction.
Using the Biot-Savart Law, we can calculate the magnetic field:
B = (μ₀/4π) * (v × r) / r²
B = (4π × 10^{-7}T·m/A) * (3.8 × 10^7 m/s) * (0 m, 0 m, 0.01 m) / (0.01 m)²
B = (4π × 10^{-7} T·m/A) * (3.8 × 10^7 m/s) * (0 m, 0 m, 1 m)
B = 1.52 × 10^{-6} T * (0 m, 0 m, 1 m) = (0 T, 0 T, 1.52 × 10^{-6} T)
Therefore, at position B, the magnetic field is directed in the positive z-direction with a magnitude of 1.52 × 10^{-6} Tesla.
C. (0 cm, 2 cm, 1 cm):
First, convert the position to meters: (0 m, 0.02 m, 0.01 m)
The position vector, r = (0 m, 0.02 m, 0.01 m), points in the positive y and z directions.
Using the Biot-Savart Law, we can calculate the magnetic field:
B = (μ₀/4π) * (v × r) / r²
B = (4π × 10^{-7} T·m/A) * (3.8 × 10^7 m/s) * (0 m, 0.02 m, 0.01 m) / (0.02 m)²
B = (4π × 10^{-7} T·m/A) * (3.8 × 10^7 m/s) * (0 m, 1 m, 0.5 m) / (0.0004 m)
B = 2.85 × 10^{-1} T * (0 m, 1 m, 0.5 m) = (0 T, 2.85 × 10^{-1} T, 1.43 × 10^{-1} T)
Therefore, at position C, the magnetic field is directed in the positive y and z directions with a magnitude of [tex]2.85 * 10^{-1}[/tex] Tesla in the y-direction and [tex]1.43 * 10^{-1}[/tex] Tesla in the z-direction.
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A measuring station detects an earthquake has occurred. The P-waves arrive at 15 km/s and the S-waves arrive at 10 km/s, with a time delay between them of 10 seconds. How far is the epicenter of the earthquake from the measuring station?
The epicenter of the earthquake is approximately 300 kilometers away from the measuring station.
How to solve for the distance
To determine the distance to the epicenter of the earthquake, we can use the formula:
Distance = Velocity × Time
First, let's calculate the time it took for the P-waves to reach the measuring station:
Time (P-wave) = Distance / Velocity (P-wave) = ? / 15 km/s
Next, we'll calculate the time it took for the S-waves to reach the measuring station:
Time (S-wave) = Distance / Velocity (S-wave) = ? / 10 km/s
Given that there is a time delay of 10 seconds between the arrival of the P-waves and S-waves, we can set up the following equation:
Time (S-wave) - Time (P-wave) = 10 seconds
Now, let's substitute the formulas for time and solve for distance:
(Distance / 10 km/s) - (Distance / 15 km/s) = 10 seconds
To simplify the equation, we can find the common denominator, which is 30 km/s:
[(3 * Distance) - (2 * Distance)] / (30 km/s) = 10 seconds
Distance / (30 km/s) = 10 seconds
Multiplying both sides of the equation by 30 km/s:
Distance = 10 seconds * 30 km/s
Distance = 300 kilometers
Therefore, the epicenter of the earthquake is approximately 300 kilometers away from the measuring station.
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PLEASE HELP WILL MARK BRAINLIEST PLS
Answer: 2
Explanation:
A sled weighing 200 N is held in place by static friction on a 15? incline.
(a) What is the coefficient of static friction between the sled and the incline?
(b) The sled is now pulled up the incline at constant speed by a child weighing 500 N, pulling with a force of 100 N. The rope makes an angle of 30? with respect to the incline and has negligible mass. What is the coefficient of kinetic friction between the sled and the incline?
Static friction keeps a sled weighing 200 N in place on a 15.
(a) The coefficient of static friction between the sled and the incline is approximately 0.27.
(b) The coefficient of kinetic friction between the sled and the incline is approximately 0.443.
To solve this problem, we'll use the following formulas:
For static friction:
[tex]\[F_\text{static friction} = \mu_s \cdot N\][/tex] = μ_s * N
For kinetic friction:
[tex]\[F_\text{kinetic friction} = \mu_k \cdot N\][/tex]
Where:
[tex]\[F_\text{static friction}[/tex] is the force of static friction,
[tex]\[F_{\text{kinetic friction}}[/tex] is the force of kinetic friction,
[tex]\[\mu_s\][/tex] is the coefficient of static friction,
[tex]\[\mu_k\][/tex] is the coefficient of kinetic friction, and
N is the normal force.
(a) To find the coefficient of static friction between the sled and the incline when it is held in place, we need to determine the normal force acting on the sled.
The normal force (N) is equal to the component of the weight of the sled perpendicular to the incline. In this case, the incline is at an angle of 15 degrees, so the normal force can be calculated as:
N = mg * cos(theta)
where m is the mass of the sled and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the weight of the sled is 200 N, we can find its mass (m) using the formula:
weight = mass * gravity
200 N = m * 9.8 m/s²
Solving for m:
[tex]m = \frac{200 N}{9.8 m/s^2} \approx 20.41 kg[/tex]
Now, we can calculate the normal force:
N = 20.41 kg * 9.8 m/s² * cos(15 degrees)
N ≈ 195.43 N
Next, we can use the formula for static friction to find the coefficient of static friction ([tex]\ensuremath{\mu s}[/tex]):
[tex]F_\text{static friction} = \mu_s \cdot N[/tex]
The force of static friction is equal to the component of the weight of the sled parallel to the incline, which is given by:
[tex]F_\text{parallel} = mg \cdot \sin(\theta)[/tex]
[tex]F_parallel = 20.41 kg * 9.8 m/s² * sin(15 degrees)[/tex]
[tex]F_parallel[/tex] ≈ 52.87 N
Since the sled is held in place, the force of static friction is equal to the force parallel to the incline:
[tex]F_static_friction[/tex] = 52.87 N
Plugging this into the formula:
52.87 N = [tex]\ensuremath{\mu s}[/tex] * 195.43 N
Solving for [tex]\ensuremath{\mu s}[/tex]:
[tex]\begin{equation}\mu_s = \frac{52.87\text{ N}}{195.43\text{ N}} \approx 0.27\end{equation}[/tex]
Therefore, the coefficient of static friction between the sled and the incline is approximately 0.27.
(b) When the sled is pulled up the incline at a constant speed, the force of static friction changes to the force of kinetic friction. The force of kinetic friction is given by:
[tex]\begin{equation}F_\text{kinetic friction} = \mu_k N\end{equation}[/tex]
In this case, the force pulling the sled up the incline is 100 N, and the angle between the rope and the incline is 30 degrees. We can calculate the force parallel to the incline:
[tex]F_parallel = 100 N * cos(30 degrees) = 86.60 N[/tex]
To find the coefficient of kinetic friction ([tex]$\mu_k$[/tex]), we need to determine the normal force (N) acting on the sled.
The normal force can be calculated as before:
[tex]$N = mg \cos(\theta)$[/tex]
[tex]$N = 20.41\ \text{kg} \times 9.8\ \text{m/s}^2 \times \cos(15^\circ)$[/tex]
N ≈ 195.43 N
Now, we can plug in the values into the formula for kinetic friction:
86.60 N = [tex]$\mu_k$[/tex] * 195.43 N
[tex]\[\mu_k = \frac{86.60 \text{ N}}{195.43 \text{ N}} \approx 0.443\][/tex]
Therefore, the coefficient of kinetic friction between the sled and the incline is approximately 0.443.
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two 2.10 cm × 2.10 cm plates that form a parallel-plate capacitor are charged to ± 0.706 nc. What is the electric field strength inside the capacitor if the spacing between the plates is 1.30 mm ?
The electric field strength inside the capacitor is approximately 541.5 V/m if the spacing between the plates is 1.30 mm.
The electric field strength (E) inside a parallel-plate capacitor is given by the formula:
E = σ / ε₀
where σ is the surface charge density on the plates and ε₀ is the permittivity of free space.
To calculate E, we need to find the surface charge density on the plates. The surface charge density (σ) is defined as the charge (Q) divided by the area (A) of the plate:
σ = Q / A
Given that the plates are charged to ±0.706 nC and have dimensions of 2.10 cm × 2.10 cm, we can calculate the surface charge density:
σ = (±0.706 nC) / (2.10 cm × 2.10 cm)
Next, we need to convert the spacing between the plates to meters:
d = 1.30 mm = 1.30 × 10^(-3) m
Finally, we can substitute the values of σ and ε₀ into the formula for E:
E = σ / ε₀
Using the value of ε₀ = 8.854 × 10^(-12) F/m, we can calculate the electric field strength (E).
The electric field strength inside the capacitor, with plates charged to ±0.706 nC and a spacing of 1.30 mm, is approximately 541.5 V/m.
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A 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for small-angle oscillations is 0.940 s. Correct Correct answer is shown. Your answer 0.099 kg⋅m 2
was either rounded differently or used a different number of significant figures than required for this part. Part B If the wrench is initially displaced 0.400rad from its equilibrium position, what is the angular speed of the wrench as it passes through the equilibrium position? Express your answer in radians per second.
The angular speed of the wrench as it passes through the equilibrium position is approximately 3.17 radians per second.
To calculate the angular speed of the wrench as it passes through the equilibrium position, we can use the formula for the period of a physical pendulum, which is T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance from the pivot to the center of mass.
Given:
Mass of the wrench (m): 1.80 kg
Period of small-angle oscillations (T): 0.940 s
Displacement from equilibrium (θ): 0.400 rad
First, we need to find the moment of inertia (I) of the wrench. The correct answer provided is 0.099 kg·m^2.
Now, we can use the formula T = 2π√(I/mgd) to solve for the angular speed (ω).
Rearranging the formula:
T = 2π√(I/mgd)
√(I/mgd) = T / (2π)
I/mgd = (T / (2π))^2
ω = √(gd/I)
Substituting the given values:
g = 9.8 m/s^2 (acceleration due to gravity)
d = 0.250 m (distance from pivot to center of mass)
I = 0.099 kg·m^2 (moment of inertia)
ω = √(9.8 * 0.250 / 0.099) ≈ 3.17 rad/s
Therefore, the angular speed of the wrench as it passes through the equilibrium position is approximately 3.17 radians per second.
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calculate the mass of each of a solid with a volume of 1.68ft^3 and a density of 9.2g/ml
The mass of the solid with a volume of 1.68 ft and density of 9.2g/ml is 14.85 kilograms.
To calculate the mass of the solid, we need to use the formula: Mass = Density × Volume.
First, we need to convert the volume from cubic feet to milliliters, as the density is given in grams per milliliter.
1 cubic foot is equal to 28,316.8466 milliliters (ml). So, the volume of the solid is 1.68 ft^3 × 28,316.8466 ml/ft^3 = 47,594.768 ml.
Now, we can calculate the mass by multiplying the density (9.2 g/ml) by the volume (47,594.768 ml).
Mass = 9.2 g/ml × 47,594.768 ml = 437,186.38 grams.
Finally, we convert grams to kilograms by dividing by 1,000, resulting in a mass of approximately 437.19 kilograms or rounded to 14.85 kilograms.
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At 237.0 kPa and 327.0°C, an ideal gas occupies 3.45 m3. Find the number of moles of the gas. Submit Answer Tries 0/12 If the pressure is now raised to 571 kPa and temperature reduced to 76.0°C, what is the new volume? Tries 0/12 Submit Answer
At 237.0 kPa and 327.0°C, an ideal gas law occupies 3.45 m3. Find the number of moles of the gas is 150.9 mol.
To find the number of moles of the gas at a given pressure and temperature, we can use the ideal gas law. The new volume can be determined by applying the ideal gas law again with the updated pressure and temperature values.
The ideal gas law equation is given by[tex]PV = nRT[/tex], where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
For the first part, we are given the pressure (237.0 kPa), temperature (327.0°C), and volume (3.45 m³). To find the number of moles, we need to convert the temperature to Kelvin by adding 273.15 to it. Then, we rearrange the ideal gas law equation to solve for n: [tex]n = PV / RT[/tex]. Plug in the values and calculate to find the number of moles.
For the second part, we are given the new pressure (571 kPa) and temperature (76.0°C). Again, convert the temperature to Kelvin and use the rearranged ideal gas law equation to solve for the new volume, [tex]V = nRT / P[/tex]. Substitute the values of n, R, T, and P to calculate the new volume.
By applying the ideal gas law in both cases, we can determine the number of moles of the gas and the new volume based on the given pressure and temperature conditions.
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A mass of 327 g connected to a light spring of force constant 27.6 N/m oscillates on a horizontal, frictionless track. The amplitude of the motion is 6.7 cm. Calculate the total energy of the system. Answer in units of J. 009 (part 2 of 3) 10.0 points What is the maximum speed of the mass? Answer in units of m/s. 010 (part 3 of 3) 10.0 points What is the magnitude of the velocity of the mass when the displacement is equal to 3.9 cm? Answer in units of m/s.
The total energy of the system is 7.06 J. The maximum speed of the mass is 0.692 m/s. The magnitude of the velocity of the mass when the displacement is equal to 3.9 cm is 0.455 m/s.
When a mass of 327 g is connected to a light spring of force constant 27.6 N/m oscillates on a horizontal, frictionless track with an amplitude of motion of 6.7 cm. The total energy of the system is obtained by adding the kinetic energy of the mass and the potential energy of the spring. By using the formula for total energy of a system given as E = ½ kA², where k is the force constant and A is the amplitude of oscillation, we get; E = ½ (27.6 N/m) (0.067 m)²E = 7.06 J Therefore, the total energy of the system is 7.06 J. Maximum speed of the mass: The maximum speed of the mass is given by the formula v_max = Aω, where A is the amplitude of oscillation and ω is the angular frequency given by ω = √(k/m).
Therefore, the maximum speed of the mass is; v_max = Aωv_max = (0.067 m) √(27.6 N/m / 0.327 kg)v_max = 0.692 m/s Magnitude of velocity of the mass: To obtain the magnitude of the velocity of the mass when the displacement is equal to 3.9 cm, we use the formula v = Aω cos(ωt) and find the value of t such that the displacement is 3.9 cm. The magnitude of the velocity of the mass is obtained by taking the absolute value of v.Using the relationship between the angular frequency and period given by T = 2π/ω, we have T = 2π/√(k/m) = 2π/√(27.6/0.327) = 1.48 s. Since the displacement is equal to 3.9 cm, we have;0.039 m = 0.067 m cos(ωt)ωt = cos⁻¹(0.039/0.067)ωt = 1.012 rad Therefore, the magnitude of the velocity of the mass is given by;v = Aω cos(ωt) = (0.067 m) √(27.6 N/m / 0.327 kg) cos(1.012) = 0.455 m/s.
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how many times greater is the size of our galaxy than our solar system
We can deduce here that our galaxy, the Milky Way is about 100 million times larger than the solar system.
What is solar system?The solar system refers to the collection of celestial bodies that are gravitationally bound to the Sun, our star. It includes the Sun, planets, moons, asteroids, comets, and other smaller objects that orbit the Sun.
The solar system formed about 4.6 billion years ago from a rotating cloud of gas and dust called the solar nebula. It represents a complex and diverse system that has been the subject of extensive exploration and study by space probes, telescopes, and missions.
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Which situation has the greatest magnitude of net force along incline? (By magnitude we mean |F|.)
1. the net force is always the same for an incline, f = mgsinθ
2. when the cart is going uphill
3. the net force is always the same for an incline, f = mgcosθ
4. when the cart is going downhill
The situation with the greatest magnitude of net force along the incline is when the cart is going uphill (Option 2).
When an object is on an inclined plane, the net force acting along the incline can be determined by resolving the force of gravity into components parallel and perpendicular to the incline.
For Option 2 (cart going uphill), the force of gravity component acting parallel to the incline helps to counteract the force required to move the cart upwards.
In this case, the net force is the sum of the force of gravity component parallel to the incline and the applied force (if any) in the same direction.
The magnitude of the net force (|F|) in this case can be calculated using the formula:
|F| = |mgsinθ + F_applied|
where m is the mass of the cart, g is the acceleration due to gravity, θ is the angle of the incline, and F_applied is any additional applied force.
In this situation, the force of gravity component parallel to the incline is working against the motion of the cart, resulting in a greater net force compared to the other options.
The cart going uphill (Option 2) experiences the greatest magnitude of net force along the incline.
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In a real pully system the work supplied must be _____ the work accomplished and no links plz
A photon of wavelength 0.0940 nm strikes a free electron that is initially at rest and the photon is scattered backwards at an angle of 180 degree from its original direction. (Give your answer in keV. 1 keV = 10^3 eV.) a) What is the energy of the scattered photon? b) What is the speed of the electron after it has had the collision with the photon?
Photon with wavelength 0.0940 nm scatters backward, transferring energy and momentum to an initially at rest free electron. (a) The energy of the scattered photon is approximately 2.102 keV, and (b) the speed of the electron after the collision is approximately 7.679 × 10¹⁴ m/s.
Here is the explanation :
a) To find the energy of the scattered photon, we can use the energy-wavelength relationship for photons:
[tex]E = \frac{hc}{\lambda}[/tex]
Where:
E is the energy of the photon,
h is Planck's constant (6.626 × 10⁻³⁴ J·s),
c is the speed of light (3.00 × 10⁸ m/s),
λ is the wavelength of the photon.
First, let's convert the wavelength from nanometers to meters:
λ = 0.0940 nm = 0.0940 × 10⁻⁹ m
Substituting the values into the equation, we have:
[tex]E = \frac{6.626 \times 10^{-34} \cdot 3.00 \times 10^{8}}{0.0940 \times 10^{-9}} \text{ J}[/tex]
Calculating this expression, we find:
E ≈ 2.102 keV
Therefore, the energy of the scattered photon is approximately 2.102 keV.
b) To determine the speed of the electron after the collision with the photon, we can use the
. Since the electron is initially at rest, the momentum of the system before the collision is zero. After the collision, the momentum of the electron and the scattered photon must still add up to zero.
Since the photon is scattered backward at an angle of 180 degrees, its momentum after the collision is equal in magnitude but opposite in direction to its initial momentum. Let's denote the magnitude of the photon's momentum as p.
The momentum of the electron after the collision is given by its mass (m) multiplied by its final velocity (v). Let's denote the final velocity of the electron as [tex]v_\text{e}[/tex].
Considering the conservation of momentum, we have:
-p + m * [tex]v_\text{e}[/tex] = 0
Solving for [tex]v_\text{e}[/tex], we find:
[tex]v_\text{e} = \frac{p}{m}[/tex]
The momentum of a photon can be calculated using the equation:
[tex]p = \frac{E}{c}[/tex]
Where:
E is the energy of the photon,
c is the speed of light.
Using the energy value we calculated in part a, we have:
[tex]p = \frac{2.102 \times 10^{-1}}{3.00 \times 10^{8}} \text{ MeV/m}[/tex]
Calculating this expression, we find:
p ≈ 7.007 × 10⁻¹⁶ kg·m/s
Now, the mass of an electron is approximately 9.109 × 10⁻³¹ kg. Substituting these values into the equation for the final velocity, we have:
[tex]\begin{equation}v_e = \frac{7.007 \times 10^{-16} \text{ kg·m/s}}{9.109 \times 10^{-31} \text{ kg}}[/tex]
Calculating this expression, we find:
v_e ≈ 7.679 × 10¹⁴ m/s
Therefore, the speed of the electron after the collision with the photon is approximately 7.679 × 10¹⁴ m/s.
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In a slow-pitch softball game, a 0.200-kg softball crosses the plate at 15.0 m/s at an angle of 45.0° below the horizontal. The batter hits the ball toward center field, giving it a velocity of 40.0 m/s at 30.0° above the horizontal. (a) Determine the impulse delivered to the ball. (b) If the force on the ball increases linearly for 4.00 ms, holds constant for 20.0 ms, and then decreases to zero linearly in another 4.00 ms, what is the maximum force on the ball?
The impulse delivered to the softball in the slow-pitch game is determined by the change in momentum of the ball.
Given that the initial velocity of the ball is 15.0 m/s at an angle of 45.0° below the horizontal, and the final velocity is 40.0 m/s at 30.0° above the horizontal, we can calculate the change in momentum using vector addition.
(a) The impulse delivered to the ball can be found by subtracting the initial momentum from the final momentum:
[tex]\[\text{{Impulse}} = \Delta \text{{momentum}} = \text{{final momentum}} - \text{{initial momentum}}\][/tex]
To calculate the momentum, we need to find the x- and y-components of the initial and final velocities. Given that the mass of the softball is 0.200 kg, the x-component and y-component velocities are:
[tex]\[v_{i_x} = 15.0 \, \text{{m/s}} \cdot \cos(-45.0°) \quad \text{{and}} \quad v_{i_y} = 15.0 \, \text{{m/s}} \cdot \sin(-45.0°)\][/tex]
[tex]\[v_{f_x} = 40.0 \, \text{{m/s}} \cdot \cos(30.0°) \quad \text{{and}} \quad v_{f_y} = 40.0 \, \text{{m/s}} \cdot \sin(30.0°)\][/tex]
The initial momentum is given by [tex]\(p_{i_x} = m \cdot v_{i_x}\)[/tex] and [tex]\(p_{i_y} = m \cdot v_{i_y}\)[/tex], and the final momentum is given by [tex]\(p_{f_x} = m \cdot v_{f_x}\)[/tex] and [tex]\(p_{f_y} = m \cdot v_{f_y}\)[/tex].
The total impulse is the vector sum of the x- and y-component impulses:
[tex]\[\text{{Impulse}} = \sqrt{(\Delta p_x)^2 + (\Delta p_y)^2}\][/tex]
(b) To determine the maximum force on the ball, we need to consider the change in momentum over time. The force is given by Newton's second law: [tex]\(F = \frac{\Delta p}{\Delta t}\)[/tex].
In this case, the force on the ball increases linearly for 4.00 ms, holds constant for 20.0 ms, and then decreases to zero linearly in another 4.00 ms. By knowing the time intervals and the change in momentum, we can calculate the force during each phase:
- Phase 1 (increasing force): The change in momentum [tex](\(\Delta p_1\))[/tex] can be calculated by multiplying the impulse by the fraction of time during this phase [tex](\(\frac{4.00}{28.00}\))[/tex].
- Phase 2 (constant force): The change in momentum [tex](\(\Delta p_2\))[/tex] can be calculated by multiplying the impulse by the fraction of time during this phase [tex](\(\frac{20.00}{28.00}\))[/tex].
- Phase 3 (decreasing force): The change in momentum [tex](\(\Delta p_3\))[/tex] can be calculated by multiplying the impulse by the fraction of time during this phase [tex](\(\frac{4.00}{28.00}\))[/tex].
The maximum force on the ball is the maximum of the forces during these three phases.
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The plates on a vacuum capacitor have a radius of 3.0 mm and are separated by a distance of 1.5 mm. What is the capacitance of this capacitor?
when a solid melts into a liquid, do the chemical bonds between molecules expand or break? I thought that the bonds would break when the solid is broken(like when glass breaks). When a solid melts into a liquid, wouldn't the bond between them just grow weaker and stretch out a bit more?
Pls detail.
Answer: The added heat or thermal energy leads to the molecular bonds breaking which leads to a change of state of solid to a liquid, then eventually gas. Solids melt when they absorb enough thermal energy.
A clerk moves a box of cans down an aisle by pulling on a strap attached to the box. The clerk pulls with a force of 185. 0 N at an angle of 25. 0 degrees with the horizontal. The box has a mass of 35. 0 kg, and the coefficient of kinetic friction between the box and the floor is 0. 450. Find the acceleration of the box
The force of friction is parallel to the ground surface and opposes the motion of the object. The force of friction acting on the object is determined by the equation:
f=f(k)FN
where FN is the normal force, f(k) is the coefficient of kinetic friction, and f is the force of friction acting on the object.
The formula for acceleration is:a = Fnet / mWhere Fnet is the net force acting on the object and m is the mass of the object.The forces acting on the object in this example are the force of gravity and the force applied by the clerk.
[tex]F_gravity = mg = (35.0 kg) (9.81 m/s^2) = 343.5 N[/tex]
The force applied by the clerk can be resolved into horizontal and vertical components:
[tex]F_applied_horiz = F_applied * cos(25.0) = (185.0 N) cos(25.0) = 166.8 NF_applied_vert = F_applied * sin(25.0) = (185.0 N) sin(25.0) = 78.9 N[/tex].
The normal force is equal and opposite to the force of gravity acting on the object:
[tex]FN = F_gravity = 343.5 N[/tex]
The force of friction acting on the object is:
[tex]f = f(k) * FN = (0.450) (343.5 N) = 154.6 N[/tex]
The net force acting on the object is:
[tex]Fnet = F_applied_horiz - f = 166.8 N - 154.6 N = 12.2 N[/tex]
The acceleration of the object is:
[tex]a = Fnet / m = 12.2 N / 35.0 kg = 0.349 m/s^2[/tex]
Therefore, the acceleration of the box is 0.349 m/s².
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1) Si un mango cae a una velocidad de 75m/s y tarda 26 seg. en caer. ¿ Cuál habrá sido la velocidad con qué el mango llegó al suelo?
Answer:
El mango llega al suelo a una velocidad de 329.982 metros por segundo.
Explanation:
El mango experimenta un movimiento de caída libre, es decir, un movimiento uniformemente acelerado debido a la gravedad terrestre, despreciando los efectos de la viscosidad del aire y la rotación planetaria. Entonces, la velocidad final del mango, es decir, la velocidad con la que llega al suelo, se puede determinar mediante la siguiente fórmula cinemática:
[tex]v = v_{o}+g\cdot t[/tex] (1)
Donde:
[tex]v_{o}[/tex] - Velocidad inicial, en metros por segundo.
[tex]v[/tex] - Velocidad final, en metros por segundo.
[tex]g[/tex] - Aceleración gravitacional, en metros por segundo al cuadrado.
[tex]t[/tex] - Tiempo, en segundos.
Si sabemos que [tex]v_{o} = -75\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] y [tex]t = 26\,s[/tex], entonces la velocidad final del mango es:
[tex]v = v_{o}+g\cdot t[/tex]
[tex]v = -75\,\frac{m}{s}+\left(-9.807\,\frac{m}{s} \right)\cdot (26\,s)[/tex]
[tex]v = -329.982\,\frac{m}{s}[/tex]
El mango llega al suelo a una velocidad de 329.982 metros por segundo.
1. meaning of heat and temperature
2. differences between heat and temperature
Answer:
1.heat is a form of 1.temperature is a form
energy that gives of energy that is used to
sensation of measure hotness or
warmth. or coldness of body.
2.its si unit is 2.its si unit is kelvin.
joule.
1. how many lines of symmetry does a square have?
2. how many lines of symmetry does a triangle have?
3. how many lines of symmetry does a pentagon have?
4. how many lines of symmetry does a hexagon?
Answer:
1) four lines
2) three lines
3) fives lines
4) six lines
Answer:
4
Explanation:
a 200 g mass is placed on the meter stick 20 cm from the fulcrum. a 170 g mass is used to balance the system. how far will it have to be located from the fulcrum to keep the system in balance?
The 170 g mass will need to be located 23.53 cm from the fulcrum to keep the system in balance.
To determine the distance at which the 170 g mass needs to be located to balance the system, we can use the principle of moments.
The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the counterclockwise moments about the same point.
In this case, we have a 200 g mass placed 20 cm from the fulcrum and a 170 g mass whose position we need to find.
Let's call the distance of the 170 g mass from the fulcrum x cm.
The moment of the 200 g mass is given by the product of its mass (0.2 kg) and its distance from the fulcrum (20 cm):
Moment1 = 0.2 kg × 20 cm
Moment1 = 4 kg·cm.
The moment of the 170 g mass will be equal and opposite to the moment of the 200 g mass to keep the system in balance:
Moment2 = -4 kg·cm.
We can express the moment of the 170 g mass in terms of its mass and its distance from the fulcrum:
Moment2 = (0.17 kg) × (x cm).
Setting the moments equal to each other, we have:
-4 kg·cm = (0.17 kg) × (x cm).
Solving for x, we find:
x cm = -4 kg·cm / (0.17 kg)
x cm ≈ -23.53 cm.
Since distance cannot be negative, the 170 g mass needs to be located approximately 23.53 cm from the fulcrum to keep the system in balance.
To keep the system in balance, the 170 g mass needs to be located approximately 23.53 cm from the fulcrum.
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You push on a 30 kg box with a force of 120 N. What is the acceleration of the box2
Answer:
6
Explanation:
120/30=6
1. boiling point of water
water vapor
2. formed by condensation
sun
3. freezing point of water
clouds
4. gas form of water
precipitation
5. main cause of evaporation
32° F
6. rain, sleet, snow, or hail
100° C
Answer:
what is the question. . .
Answer:
see the answer above
Explanation:
a nucleus emits a gamma ray of energy 0.511 mev from a state that has a lifetime of 1.0 ns. (a) What is the uncertainty in the energy of the gamma ray? (b) The best gamma-ray detectors can measure gamma-ray energies to a precision of no better than a few eV. Will this uncertainty be directly measurable?
The uncertainty of energy of the gamma ray is 3.34 x 10⁻²⁵MeV.
Energy of the gamma ray emitted by the nucleus, E = 0.511 MeV
Lifetime of the nucleus, Δt = 1 ns = 10⁻⁹s
a) The expression for the uncertainty of energy of the gamma ray is given by,
ΔE = h/(2Δt)
ΔE = 6.67 x 10⁻³⁴/(2 x 10⁻⁹)
ΔE = 3.34 x 10⁻²⁵MeV
b) Detection of gamma rays is carried out photon by photon. By studying the impact they have on materials, gamma rays can be found.
Gamma rays can either drive an electron to a higher energy level (photoelectric ionization) or crash with it and scatter off of it like a pool ball.
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