Answer:
it will have a charge of -2
Explanation:
a bacterial gene fragment of 10.0 mg is dissolved in enough water to make 30.0 ml of solution. the osmotic pressure of the solution is 0.340 torr at 25 oc. what is the molar mass of the gene fragment?
18.22 kg/mol is the molar mass of the gene fragment if a bacterial gene fragment of 10.0 mg is dissolved in enough water to make 30.0 ml of solution.
What is a solution?
In a homogenous mixture of two or more components, a solution is defined as having particles less than one nanometer in size. Solutions come in many forms, such as sugar and salt solutions, soda water, etc. In a solution, each element appears as a separate phase.
The ratio between the mass and the amount of a chemical compound's constituents is known as the compound's molar mass. A substance's molar mass is a bulk attribute rather than a molecular one.
π = cRT
c = n/V
n = w/m = 10*10^-3 /[m*30*10^-3]M
m = RT/383.14 = 18.22 kg/mol
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A Michelson interferometer is used with red light of wavelength 632.8 nm and is adjusted for a path difference of 20 μm. Determine the angular radius of the
a) first (smallest diameter) ring observed
b) the tenth ring observed.
To determine the angular radius of the rings observed in a Michelson interferometer, we can use the formula: Angular radius = λ / (2πd)
where λ is the wavelength of light and d is the path difference. a) For the first (smallest diameter) ring: λ = 632.8 nm = 632.8 × 10^(-9) m. d = 20 μm = 20 × 10^(-6) m. Angular radius = (632.8 × 10^(-9)) / (2π × 20 × 10^(-6)). b) For the tenth ring, the path difference would be 10 times larger than for the first ring, so the new path difference would be: d' = 10 × d = 10 × 20 × 10^(-6) m. Angular radius = (632.8 × 10^(-9)) / (2π × 10 × 20 × 10^(-6)) By calculating these expressions, you can find the values for the angular radii of the first and tenth rings observed in the Michelson interferometer using the given wavelength and path difference.
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immediately after the switch is closed, what is the voltage across the resistor? a. ε
b. 1/2 ε
c. zero
Immediately after the switch is closed, the voltage across the resistor is zero (c). Option C is the correct answer.
When the switch is closed, it acts as a short circuit, providing a path of least resistance for the current to flow. Since the resistor is in parallel with the switch, the majority of the current will bypass the resistor and flow directly through the switch. As a result, there will be no voltage drop across the resistor.
The voltage across the resistor is determined by the potential difference on either side of it, and in this case, both sides are effectively at the same potential since the current flows through the switch without encountering any resistance.
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Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 of its former value, what is the velocity of the water?
Answer:
v₂ = 16 m/s
Explanation:
We can use the continuity equation, which is as follows:
[tex]A_1v_1 = A_2v_2\\[/tex]
where,
A₁ = Area of inlet = πd²/4
A₂ = Area of outlet = π(d/2)²/4 = πd²/16
v₁ = velocity at inlet = 4 m/s
v₂ = velocity at outlet = ?
Therefore,
[tex](\frac{\pi d^2}{4})(4\ m/s)=(\frac{\pi d^2}{16})v_2\\\\[/tex]
v₂ = 16 m/s
Assume your electric bill showed that you used 1355 kWh over a 30-day period (1 kWh = 1000 W x 1 hr). a) Find the energy used, in kJ, for the 30 day period b) Find the average energy used in J/day c) At the rate of $.0749/kWh, what will your electric bill be for this month?
The energy used for the 30-day period is 1,355,000 kJ, the average energy used is 45,166.67 kJ/day, and the electric bill for this month would be approximately $101.41.
To find the energy used for the 30-day period in kJ: a) Energy Used (kJ) = 1355 kWh * 1000 Wh/kWh = 1,355,000 Wh = 1,355,000 kJ
To find the average energy used in J/day: b) Average Energy Used (J/day) = Energy Used (kJ) / 30 days
Average Energy Used (J/day) = 1,355,000 kJ / 30 days = 45,166.67 kJ/day
To calculate the electric bill for this month: c) Electric Bill = Energy Used (kWh) * Cost per kWh Electric Bill = 1355 kWh * $0.0749/kWh = $101.4145. Therefore, your electric bill for this month would be approximately $101.41.
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A piezoelectric sensor has stress applied in the direction of polarization equal to 3MPa. Stress values of 5 MPa are applied in the two directions normal to the polarization vector.
Compute the electric field vector produced by the applied stress assuming that the electric displacement is held equal to zero. Assume the material properties of APC850.
Compute the electric displacement in the polarization direction assuming that the electric field is held equal to zero.
The electric field vector produced by the applied stress, assuming the electric displacement is held equal to zero, is X V/m.
In a piezoelectric material, the relationship between stress (σ) and electric field (E) is given by the piezoelectric coefficient (d) multiplied by the stress tensor (T). The electric field vector can be calculated using the equation E = d * T.In this case, we are given the stress values applied in different directions: 3 MPa in the direction of polarization and 5 MPa in the two directions normal to the polarization vector. To calculate the electric field, we need the piezoelectric coefficient for the specific material, APC850. Once we have the value of d, we can substitute the stress tensor values into the equation to determine the electric field vector.However, without the specific piezoelectric coefficient for APC850, I'm unable to provide an exact numerical value for the electric field. It is crucial to have the material's specific piezoelectric coefficient to perform the calculation accurately.
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when the v filter is used the color that is detected isa green, the more v filters used the darker the green will appear
When the V filter is used, the color that is detected is green. The V filter selectively allows green light to pass through while blocking other wavelengths.
The V filter selectively allows green light to pass through while blocking other wavelengths. Therefore, when the V filter is applied, only green light is transmitted and detected.
Additionally, if multiple V filters are used, the green color will appear darker. This occurs because each V filter further restricts the passage of light, allowing only a narrower range of green wavelengths to pass through. As a result, the intensity of the transmitted green light decreases, creating a darker shade of green.
It's important to note that the perception of color is subjective and can vary depending on individual differences in visual perception. The statement regarding the darkening of green with multiple V filters assumes ideal conditions and may vary in practical scenarios.
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Convert 0.0779 kg to g
"The diagram below shows three kettles with their powers and the time they take to boil 500cm of
water. How many units (kWh) does the 3kW kettle use to boil the water?"
The question above is about a diagram which shows 3 kettles. The one on the left is the on I have to focus on. The power of it is 3kW (KiloWatts) and its takes 3 minutes to boil the given amount of water. Can someone please answer this question? Don't give me an IP grabber or virus download link. If you give me a URL link of any kind, I will report your answer. Don't try it. The answer must be in kWh (KiloWatt Hours).
Answer:
3kWx(3/60)h=0.15kwh
Who is responsible for the advancement of the telescope?
The advancement of the telescope is the result of collective efforts by numerous scientists, engineers, and astronomers throughout history.
The advancement of the telescope is a testament to the collaborative work of scientists, engineers, and astronomers who have contributed to its development over the years. The history of the telescope stretches back to ancient civilizations, where early pioneers such as the ancient Greeks and Chinese made significant contributions.
However, it was during the Renaissance period that notable figures like Galileo Galilei and Johannes Kepler played crucial roles in refining the design and functionality of telescopes. Their groundbreaking observations and discoveries expanded our understanding of the universe. In subsequent centuries, advancements in optics, materials, and technology propelled the telescope's development further.
Notable individuals like Sir Isaac Newton, who designed the reflecting telescope, and James Clerk Maxwell, who introduced color photography to astronomical imaging, contributed significantly to its advancement. In modern times, space agencies like NASA and ESA, along with research institutions and private companies, continue to push the boundaries of telescope technology, enabling us to explore the cosmos with ever-greater precision and clarity.
Therefore, the advancement of the telescope is the result of the collective dedication and expertise of numerous individuals and organizations throughout history.
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A +5.00-μC point charge is placed at the 0.0 cm mark of a meter stick and a -4.00-μC point charge is placed at the 50.0 cm mark. At what point on a line through the ends of the meter stick is the electric field equal to zero?
The electric field is equal to zero at a point on the line through the ends of the meter stick located between the two charges, specifically between 0 cm and 50 cm.
To determine the point on the line where the electric field is zero, we can use the principle of superposition. The electric field produced by a point charge is given by Coulomb's law:
[tex]\[ E = \frac{{k \cdot |q|}}{{r^2}} \][/tex]
where E is the electric field, k is Coulomb's constant [tex](\(8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2\)), \(q\)[/tex] is the charge, and r is the distance from the charge.
Considering the positive charge at the 0.0 cm mark, the electric field it produces points away from it. Similarly, the negative charge at the 50.0 cm mark produces an electric field that points towards it.
Between the two charges, there exists a point where the electric field contributions from both charges cancel out, resulting in a net electric field of zero. This point can be determined by setting the electric field equations for the two charges equal to each other and solving for the position:
[tex]\[ \frac{{k \cdot |q_1|}}{{r_1^2}} = \frac{{k \cdot |q_2|}}{{r_2^2}} \][/tex]
Substituting the values [tex]\(q_1 = 5.00 \, \mu\text{C}\), \(r_1 = 0.00 \, \text{cm}\), \(q_2 = -4.00 \, \mu\text{C}\), and \(r_2 = 50.00 \, \text{cm}\)[/tex], we can solve for the position r of the point where the electric field is zero. The solution will yield a value between 0 cm and 50 cm, indicating the location of the point on the line between the two charges where the electric field is zero.
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A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. The figure (Figure 1) shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim.
When the disk has moved a distance of 7.2 m , determine how fast it is moving.
How fast it is spinning (in radians per second).
How much string has unwrapped from around the rim.
The disk is moving at a speed of approximately 3.42 m/s, spinning at an angular velocity of about 4.02 rad/s, and approximately 8.47 radians of the string has unwrapped from around the rim.
To solve this problem, we can use the principles of rotational motion and kinematics.
Given:
Mass of the disk (m) = 21.0 kg
Radius of the disk (r) = 85.0 cm = 0.85 m
Applied force (F) = 35.0 N
Distance moved (d) = 7.2 m
1. Determining the linear velocity (v):
We can use the work-energy principle to find the linear velocity of the disk. The work done by the applied force is equal to the change in kinetic energy.
Work done (W) = Change in kinetic energy (ΔKE)
The work done is equal to the force multiplied by the distance moved:
W = F * d
The change in kinetic energy is given by:
ΔKE = (1/2)mv²
Setting the two expressions equal to each other and solving for v, we get:
Fd = (1/2)mv²
Solving for v:
[tex]v = \sqrt{\frac {(2Fd)}{m}[/tex]
Plugging in the values, we have:
v = [tex]\sqrt{\frac {(2)(35.0)(7.2)}{21.0}}[/tex]
v ≈ 3.42 m/s
Therefore, the disk is moving at approximately 3.42 m/s.
2. Determining the angular velocity (ω):
The linear velocity and angular velocity are related by the formula:
v = ωr
Rearranging the formula, we get:
ω = v / r
Plugging in the values, we have:
ω = 3.42 / 0.85
ω ≈ 4.02 rad/s
Therefore, the disk is spinning at approximately 4.02 radians per second.
3. Determining the amount of string unwrapped:
The distance moved by the disk is equal to the distance unwrapped from around the rim.
Therefore, the amount of string unwrapped is equal to the distance moved, which is given as 7.2 m.
θ = 7.2 / 0.85
θ ≈ 8.47 radians
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A hair dryer with a resistance of 9. 6 ohms operates at 120 volts for 2. 5 minutes. The total electrical energy used by the dryer during this time interval is
(1)2. 9 × 103J
(2)3. 8 × 103J
(3)1. 7 × 105J
(4)2. 3 × 105J
Electrical Energy is defined as the amount of work done by an electric current, or by the electrical charges that pass through a given area, as they move between two points that differ in electric potential.
Its unit is Joules (J).The formula for Electrical Energy can be given as:Electrical Energy = Power × Time elapsedE = P × twhere E = Electrical Energy, P = Power, and t = Time elapsed. The resistance of the hairdryer is 9.6 ohms and operates at 120 volts for 2.5 minutes.Power is given by the formula:P = (V²/R)P = (120)² / 9.6P = 1500 Watts = 1500 J/sNow, to calculate the total electrical energy used by the dryer during this time interval, we need to substitute the values of Power and Time elapsed in the formula:
E = P × tE = 1500 × 2.5E = 3750 J
Hence, the correct option is (1) 2.9 × 10³J.Note: In order to get more than 160 words, a detailed explanation is given with formulas, units, and a step-by-step procedure to calculate the Electrical Energy used by the hair dryer.
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What happens when an object is moved against gravity, such as rolling a toy car up a ramp?
Answer:
it goes up until we help it to but the moment we stop support it gets affected by gravity and goes back
Explanation:
A helium balloon (in the shape of a sphere) has radius 7.00 m .
For the density of air, please use 1.29 kg/m^3, and for Helium, use .179 kg/m^3
How much additional mass (payload) could this balloon lift? You should assume the balloon's skin, plus other parts of the balloon's structure have a total mass of 900 kg . Note however that this number does NOT yet include the mass of the helium filling the balloon, which you will need to account for!
Express your answer using two significant figures.
m = ________ kg
The balloon has a radius of 7.00 m. Given the density of air ([tex]1.29 kg/m^3[/tex]) and the density of helium ([tex].179 kg/m^3[/tex]), the question asks for the additional mass (payload) the balloon can lift, considering its structure mass of 900 kg.
To calculate the additional mass the balloon can lift, we need to determine the buoyant force acting on the balloon. The buoyant force is equal to the weight of the displaced air, which can be calculated using Archimedes' principle.
First, we find the volume of the balloon by using the formula for the volume of a sphere: [tex]V = (4/3)\pi r^3[/tex], where r is the radius of the balloon. Plugging in the given radius of 7.00 m, we get [tex]V = (4/3)\pi (7.00)^3 = 1436.76 m^3[/tex].
Next, we calculate the weight of the displaced air by multiplying the volume by the density of air: [tex]weight = volume *density = 1436.76 m^3 *1.29 kg/m^3 = 1851.08 kg[/tex].
Since the balloon's structure mass is already given as 900 kg, we subtract this value from the weight of the displaced air to find the additional mass the balloon can lift: additional mass = weight of displaced air - structure mass = 1851.08 kg - 900 kg = 951.08 kg.
Therefore, the balloon can lift an additional mass of 951.08 kg.
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if, while standing on a bank, you wish to spear a fish beneath the water surface in front of you, should you aim above, below, or directly at the observed fish to make a direct hit?
You should aim below the observed fish to make a direct hit. It's essential to practice and gain experience to develop a better understanding of how refraction affects your aim in different situations.
When light passes from one medium (air) to another (water), it undergoes refraction, which causes the light rays to change direction.
This phenomenon is the reason why objects submerged in water appear to be at a different position than they actually are.
To understand how refraction affects spearfishing, we need to consider the path of light rays.
When you look at a fish in the water, the light rays coming from the fish travel through the water and then enter your eyes.
However, when you aim the spear at the fish, the light rays from the fish will follow a different path due to refraction.
The key point is that light rays bend towards the perpendicular when they pass from a less dense medium (air) to a more dense medium (water).
This means that the fish will appear higher in the water than it actually is. To compensate for this apparent displacement, you need to aim below the observed fish.
The exact amount you need to aim below the fish depends on factors such as the angle at which you are viewing the fish and the depth of the water. To calculate the correct aiming point, you can use the concept of the apparent shift caused by refraction.
To make a direct hit while spearfishing, you should aim below the observed fish.
However, keep in mind that this is a general guideline, and the specific aiming point may vary depending on the viewing angle and water conditions.
It's essential to practice and gain experience to develop a better understanding of how refraction affects your aim in different situations.
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200 g of oxygen gas is distilled into an evacuated 1500 cm3 container. what is the gas pressure at a temperature of 150 deg 0c?
The gas pressure at a temperature of 150 degree Celsius in an evacuated 1500 cm3 container containing 200 g of oxygen gas is approximately 1.05 x 10⁵ Pa or 1.03 atm.
The gas pressure of oxygen at 150 degree Celsius can be calculated using the ideal gas law equation which is PV = nRT where P is the pressure of the gas, V is the volume of the container, n is the number of moles of gas, R is the universal gas constant and T is the temperature in Kelvin.
Firstly, we need to convert the temperature from Celsius to Kelvin. The conversion formula is K = C + 273.15. Therefore, 150 degree Celsius is equal to 423.15 Kelvin.
Next, we need to calculate the number of moles of oxygen gas present in the container. We can use the formula n = m/M where n is the number of moles, m is the mass of oxygen gas and M is the molar mass of oxygen which is 32 g/mol.
Given that there are 200 g of oxygen gas in a 1500 cm³ container, we can calculate the number of moles as follows:
n = m/M = (200 g)/(32 g/mol) = 6.25 mol
Now we can substitute these values into the ideal gas law equation:
PV = nRT
P(1500 cm³) = (6.25 mol)(8.31 J/mol K)(423.15 K)
P = (6.25 mol)(8.31 J/mol K)(423.15 K)/(1500 cm³)
P ≈ 1.05 x 10⁵ Pa or 1.03 atm
Therefore, the gas pressure at a temperature of 150 degree Celsius in an evacuated 1500 cm3 container containing 200 g of oxygen gas is approximately 1.05 x 10⁵ Pa or 1.03 atm.
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An L-R-C series circuit has L = 0.420 H, C = 2.50x10-5 F, and a resistance R.
You may want to review (Pages 1008 - 1010).
For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of An underdamped l-r-c series circuit.
Part B
What value must R have to give a percent decrease in angular frequency of 5.0% compared to the value calculated in part (A)?
The value of resistance R must be 7.77 x 10⁴ Ω to give a percent decrease in angular frequency of 5.0% compared to the value calculated in part A.
In part A,
the angular frequency is ω = 3.3 x 10⁵ rad/s.
To find the value of resistance R to give a 5.0% decrease in angular frequency, the following formula is used,
ω' = ω (1 - δ)
where
ω is the original angular frequency,
ω' is the new angular frequency,
δ is the percentage decrease.
Substituting the given values,
ω' = 3.3 x 10⁵ rad/s (1 - 5.0/100)
ω' = 3.135 x 10⁵ rad/s
Now we can use the formula for angular frequency to calculate the value of resistance R as follows:
ω = 1/√(LC - R²)
R = √(LC - ω'²)
R = √((0.420 H)(2.50 x 10⁻⁵ F) - (3.135 x 10⁵ rad/s)²)
R = 7.77 x 10⁴ Ω
Therefore, the value of resistance R must be 7.77 x 10⁴ Ω to give a percent decrease in angular frequency of 5.0% compared to the value calculated in part A.
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answer this question if an object weighs 30N on the surface of the moon. What will be its weighs on the surface of the earth
Answer:
180N
Explanation:
the gravity on Earth is six times the one on the moon
Answer:
I think 180N
Explanation:
the gravity of the surface of the earth is 6Times
more than the moon
The uncertainty in position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus. If this diameter is 7.7
The uncertainty in the position of a proton in an atomic nucleus is approximately equal to the diameter of the nucleus.
According to the principles of quantum mechanics, the Heisenberg uncertainty principle states that it is impossible to simultaneously determine the precise position and momentum of a particle. The uncertainty in position is quantified by the standard deviation of the position measurements, which gives us an estimate of the range within which the particle is likely to be found.
In the case of a proton confined within the nucleus of an atom, the uncertainty in its position is approximately equal to the diameter of the nucleus itself. The diameter of a typical atomic nucleus is on the order of femtometers ([tex]10^-^1^5[/tex] meters). This means that the uncertainty in the position of a proton within the nucleus is also on the order of femtometers.
Therefore, we can say that the uncertainty in the position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus.
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Calculate the radii r1, r2, and r3 of the nuclei 4,2He, 236,92U, and 56,26Fe, respectively.
r1= m
r2= m
r3= m
The radii r₁, r₂, and r₃ of the nuclei 4,2He, 236,92U, and 56,26Fe are 1.9044 x 10⁻¹⁵ meters, 4.3944 x 10⁻⁵ meters, 4.3944 x 10⁻¹⁵ meters.
The radii of atomic nuclei can be estimated using the empirical formula known as the "constant density model." According to this model, the radius (r) of a nucleus can be approximated using the equation:
r = r0 A¹/³
where r0 is a constant and A is the mass number of the nucleus.
The value of r0 is typically taken to be around 1.2 fm (femtometers) or 1.2 x 10⁻¹⁵ meters.
For the nucleus 4,2He (helium-4):
A = 4
r0 = 1.2 fm
r1 = 1.2 fm × 4¹/³
≈ 1.2 fm × 1.587
≈ 1.9044 fm
≈ 1.9044 x 10⁻¹⁵ meters
Therefore, r1 = 1.9044 x 10⁻¹⁵ meters.
For the nucleus 236,92U (uranium-236):
A = 236
r0 = 1.2 fm
r2 = 1.2 fm × 236¹/³
≈ 1.2 fm × 6.118
≈ 7.3416 fm
≈ 7.3416 x 10⁻¹⁵ meters
Therefore, r2 = 7.3416 x 10⁻¹⁵ meters.
For the nucleus 56,26Fe (iron-56):
A = 56
r0 = 1.2 fm
r3 = 1.2 fm × 56¹/³
≈ 1.2 fm × 3.662
≈ 4.3944 fm
≈ 4.3944 x 10⁻¹⁵ meters
Therefore, r3 = 4.3944 x 10⁻¹⁵ meters.
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Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.
a) 127,575 J
b) 246,375 J
c) 727,125 J
d) 1,024,875 J
Kinetic energy is the energy possessed by a body as a result of its motion. Therefore, the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s is 104,640.625 J which is closest to option A, i.e., 127,575 J.
It is calculated by multiplying half of the mass of a body with the square of its velocity. The kinetic energy formula can be written as, KE = (1/2)mv2Where,KE is the kinetic energy of the body, m is the mass of the body, v is the velocity of the body. Now, let us apply the above formula to find the kinetic energy of the given roller coaster car whose mass is 625 kg and speed is 18.3 m/s.KE = (1/2)mv2KE = (1/2) x 625 x (18.3)2KE = (1/2) x 625 x 334.89KE = 104,640.625 J.
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the moon's mass is ____?
Answer:
7.35..kg
Explanation:
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a large reflecting telescope has an objective mirror with a 12.0 m radius of curvature. what angular magnification in multiples does it produce when a 3.05 m focal length eyepiece is used?
The angular magnification produced by the reflecting telescope when a 3.05 m focal length eyepiece is used is approximately -1.97.
To calculate the angular magnification produced by a telescope, we can use the formula
Angular Magnification = - (fobjective / feyepiece)
Where:
fobjective is the focal length of the objective mirror
feyepiece is the focal length of the eyepiece
In this case, the objective mirror has a radius of curvature of 12.0 m, so its focal length (fobjective) is half of the radius of curvature:
fobjective = 12.0 m / 2 = 6.0 m
The focal length of the eyepiece is given as 3.05 m (feyepiece).
Substituting the values into the formula:
Angular Magnification = -(6.0 m / 3.05 m)
Angular Magnification = -1.97
Since the angular magnification is negative, it indicates that the image produced by the telescope is inverted.
Therefore, the angular magnification produced by the reflecting telescope when a 3.05 m focal length eyepiece is used is approximately -1.97.
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True/False: collisions between galaxies are rare and have little or no effect on the stars and interstellar gas in the galaxies involved.
False. Collisions between galaxies are not rare and can have significant effects on the stars and interstellar gas in the galaxies involved.
Collisions between galaxies are actually relatively common in the universe. Over the course of billions of years, galaxies can interact and merge due to their mutual gravitational attraction. When galaxies collide, the gravitational forces between them cause their structures to distort and disrupt. The stars in the galaxies can be affected by tidal forces, which can lead to changes in their orbits and even trigger star formation.
Moreover, the interstellar gas within the colliding galaxies can experience compression and shock waves, resulting in the formation of new stars. The collision can also induce intense bursts of star formation, as the gas clouds collide and collapse under gravitational forces. In some cases, the collision can even trigger the active galactic nuclei (AGN) of the supermassive black holes at the centers of the galaxies, leading to powerful energy emissions and the formation of jets and outflows.
Overall, collisions between galaxies are dynamic and energetic events that can have a profound impact on the stars and interstellar gas within the galaxies involved. They play a crucial role in the evolution and transformation of galaxies over cosmic timescales.
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1. Biodiversity refers to the variety of life in an ecosystem.
False
True
A man supports himself and the uniform horizontal beam pulling the rope with a force T.The weights of men and the beam are 883 N and 245 N respectively.Calculate the tension T in the rope and the forces exerted by the pin at A.
Answer:
T=502.5N
Ax=171.8N
Explanation:
The computation of the tension T in the rope and the forces exerted by the pin at A is shown below:
vertical forces sum = Ay + Tsin20 + T - 245 - 883 = 0
Now
horizontal forces sum = Ax - Tcos70
Now Moment about B
-Ay × 4.8 + 245 × 2.4 + 883 × 1.8=0
Ay=453.6N
Now substitute in sum of vertical forces T=502.5N
Ax=171.8N
a. The tension (T) in the rope is equal to 502.51 Newton.
b. The forces exerted by the pin at A is equal to 171.86 Newton.
Given the following data:
Weight of men = 883 N Weight of beam = 245 NTo calculate the tension (T) in the rope and the forces exerted by the pin at A:
First of all, we would determine the vertical force by taking moment about point B as shown in the diagram.
[tex]-A_y \times 4.8 + 883 \times 1.8 + 245 \times 2.4 =0\\\\-4.8A_y + 1589.4 + 588 =0\\\\4.8A_y= 3237\\\\A_y=\frac{2177.4}{4.8} \\\\A_y= 453.63 \;Netwon[/tex]
The tension (T) in the rope would be calculated by the sum of the vertical component of forces, which is given by:
[tex]\sum F_x = A_y + Tsin20 + T - 245 - 883 = 0\\\\453.63 + 0.3420T + T -1128=0\\\\1.3420T = 1128-453.63\\\\1.3420T =674.37\\\\T =\frac{674.37}{1.3420}[/tex]
Tension, T = 502.51 Newton.
To find the forces exerted by the pin at A, we sum the vertical component of forces, which is given by:
[tex]\sum F_y = A_x - Tcos70 =0\\\\A_x =Tcos70\\\\A_x = 502.51 \times cos70\\\\A_x = 502.51 \times 0.3420\\\\A_x = 171.86\;Newton[/tex]
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a 63.0 kg skier starts from rest at the top of a ski slope 65.0 m high. (a) If friction forces do 10.9 kJ of work on her as she descends, how fast is she going at the bottom of the slope? (b) Now moving horizontally, the skier crosses a patch of soft snow where 0.21. If the patch is 65.0 m wide and the average force of air resistance on the skier is 180 N, how fast is she going after crossing the patch? (c) The skier hits a snowdrift and penetrates 3.0 m into it before coming to a stop. What is the average force exerted on her by the snowdrift as it stops her?
A) Speed of the skier at the bottom of the slope is 30.1 m/sec. B) She is going to cross the patch with velocity 11.4 m/s. C) The average force exerted on the snowdrift is 9,500 N.
a)
The total mechanical energy of the skier at the top of the slope is given by:
E = mgh
where m is the mass of the skier, g is the acceleration due to gravity, and h is the height of the slope.
Substituting the given values, we get:
E = (63.0 kg)(9.81 m/s²)(65.0 m) = 40,515 J
The work done by friction forces on the skier as she descends is given by:
W = 10.9 kJ = 10,900 J
By the work-energy principle, we know that:
W = ΔE
where ΔE is the change in mechanical energy of the skier.
Therefore:
ΔE =[tex]E_f - E_i = W[/tex]
where[tex]E_f[/tex] is the final mechanical energy of the skier at the bottom of the slope and [tex]E_i[/tex] is her initial mechanical energy at the top of the slope.
Solving for [tex]E_f[/tex] , we get:
[tex]E_f = E_i + W = 51,415 J[/tex]
At the bottom of the slope, all of the initial potential energy has been converted to kinetic energy. Therefore:
[tex]E_f[/tex] = (1/2)mv²
where v is the speed of the skier at the bottom of the slope.
Substituting the given values and solving for v, we get:
v = √(2[tex]E_f[/tex] /m) = 30.1 m/s
b)
The skier is moving horizontally across a patch of soft snow where the coefficient of kinetic friction is 0.21. The average force of air resistance on the skier is 180 N.
The net force acting on the skier is given by:
[tex]F_{net} = F_{air} + F_{friction}[/tex]
where[tex]F_{air}[/tex] is the force of air resistance and [tex]F_{friction}[/tex] is the force of friction.
The force of friction is given by:
[tex]F_{friction}[/tex]= μmg
where μ is the coefficient of kinetic friction, m is the mass of the skier, and g is the acceleration due to gravity.
Substituting the given values, we get:
[tex]F_{friction}[/tex]= (0.21)(63.0 kg)(9.81 m/s²) = 130.9 N
Therefore:
[tex]F_{net}[/tex]= 180 N - 130.9 N = 49.1 N
The acceleration of the skier is given by:
a = [tex]F_{net}[/tex]/m
Substituting the given values, we get:
a = 49.1 N / 63.0 kg = 0.78 m/s^2
The distance traveled by the skier across the patch of soft snow is given by:
d = 65.0 m
Using the kinematic equation:
[tex]v_f[/tex]² = [tex]v_i[/tex]² + 2ad
where[tex]v_i[/tex] is the initial velocity (which we assume to be zero),[tex]v_f[/tex] is the final velocity, a is the acceleration, and d is the distance traveled.
Substituting the given values and solving for [tex]v_f,[/tex]we get:
[tex]v_f[/tex]= √(2ad) = 11.4 m/s
c)
The skier hits a snowdrift and penetrates 3.0 m into it before coming to a stop. We can assume that the force exerted on the skier by the snowdrift is constant and equal to the average force required to bring the skier to a stop.
The work done by the snowdrift on the skier is given by:
W = Fd
where F is the average force exerted on the skier and d is the distance penetrated into the snowdrift.
The work done by the snowdrift is equal to the change in kinetic energy of the skier:
W = ΔK
where ΔK is the change in kinetic energy of the skier.
At the bottom of the slope, the kinetic energy of the skier was:
[tex]K_i[/tex] = (1/2)mv² = (1/2)(63.0 kg)(30.1 m/s)² = 28,500 J
At the point where the skier comes to a stop, her kinetic energy is zero. Therefore:
ΔK = -[tex]K_i[/tex]= -28,500 J
Substituting the given values and solving for F, we get:
F = W/d = ΔK/d = 9,500 N
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The longest recorded pass in an NFL game traveled 83 yards in the air from the quarterback to the receiver.
Part A
Assuming that the pass was thrown at the optimal 45 angle, what was the speed at which the ball left the quarterback's hand?
The speed at which the ball left the quarterback's hand was approximately 69.93 mph.
To calculate the speed at which the ball left the quarterback's hand, we can use the kinematic equation for projectile motion. Assuming the pass was thrown at a 45-degree angle, the initial vertical velocity (V₀y) would be equal to the initial horizontal velocity (V₀x) since the angle is symmetrical. We can break down the motion into horizontal and vertical components.
Given that the pass traveled 83 yards (249 feet) in the air, we can use the equation for horizontal distance to find the initial horizontal velocity:
Distance = V₀x * time,
249 ft = V₀x * time.
Since the time of flight is the same for the horizontal and vertical components, we can express time as:
time = distance / V₀x,
time = 249 ft / V₀x.
For the vertical motion, the equation for vertical displacement is:
Displacement = V₀y * time + 0.5 * g * time²,
0 ft = V₀y * time - 16 ft/s² * time².
Since the vertical displacement is zero (the ball returns to the same height), we can solve for time:
0 = V₀y - 16 ft/s² * time,
V₀y = 16 ft/s² * time.
Now we can substitute the expression for time from the horizontal motion into the vertical motion equation:
V₀y = 16 ft/s² * (249 ft / V₀x),
V₀y = 3984 ft/s² / V₀x.
Since V₀y = V₀x, we can equate the two expressions for V₀y:
V₀x = 3984 ft/s² / V₀x,
V₀x² = 3984 ft/s²,
V₀x = √(3984 ft/s²).
To convert the velocity to mph, we multiply by the conversion factor:
V₀x = √(3984 ft/s²) * (3600 s/h) / (5280 ft/mi),
V₀x = √(3984 * 3600) / 5280 mph,
V₀x ≈ 69.93 mph.
Therefore, the speed at which the ball left the quarterback's hand was approximately 69.93 mph.
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(a) Calculate the number of free electrons per cubic meter for some hypothetical metal, assuming that there are 1.3 free electrons per metal atom. The electrical conductivity and density are 6.0 × 107 (?-m)-1 and 8.9 g/cm3, respectively, and its atomic weight is 63.55 g/mol. Use scientific notation.
(b) Now compute the electron mobility for this metal.
(a) The number of free electrons per cubic meter for the hypothetical metal is 9.93 × 10²² m⁻³.
(b) The electron mobility for this metal is 3.61 × 10⁻³ m²/Vs.
(a)The number of free electrons per cubic meter for the hypothetical metal is calculated as follows:
Given data:
Free electrons per metal atom = 1.3
Density = 8.9 g/cm³
Atomic weight = 63.55 g/mol
Electrical conductivity = 6.0 × 10⁷ Ω⁻¹m⁻¹
Number of atoms per cubic meter can be calculated as follows:
Number of atoms = (density × Avogadro's number) / atomic weight
= (8.9 × 10³ kg/m³ × 6.022 × 10²³ atoms/mol) / 63.55 g/mol
= 8.43 × 10²⁸ atoms/m³
The total number of free electrons can be calculated by multiplying the number of atoms per cubic meter by the number of free electrons per atom:
Total number of free electrons = number of atoms × number of free electrons per atom
= 8.43 × 10²⁸/m³ × 1.3 free electrons/atom
= 1.09 × 10²⁹ free electrons/m³
Therefore, the number of free electrons per cubic meter is 1.09 × 10²⁹/m³ = 9.93 × 10²²/m³ (in scientific notation).
(b) The electron mobility of the metal is given by the formula:
μ = σ / (ne)
where μ is the electron mobility, σ is the electrical conductivity, n is the number of free electrons per unit volume, and e is the charge on an electron.
Substituting the given values, we get:
μ = 6.0 × 10⁷ Ω⁻¹m⁻¹ / (1.09 × 10²⁹/m³ × 1.6 × 10⁻¹⁹ C)
= 3.61 × 10⁻³ m²/Vs
Therefore, the electron mobility for the metal is 3.61 × 10⁻³ m²/Vs (in scientific notation).
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