Based on the diagram in fig. 26955 (similar to fig. 26912, example 2698), the potential difference between points a and d can be found by summing the potential differences across each component in the circuit that lies between these two points.
Starting from point a, we first encounter a resistor with a resistance of R1. The potential difference across this resistor can be found using Ohm's law: V1 = I * R1, where I is the current flowing through the resistor.
Next, we come across a battery with an emf of E1. Since we are moving from the negative terminal to the positive terminal of the battery, the potential difference across the battery is E1.
Moving further along the circuit, we come across another resistor with a resistance of R2. Using Ohm's law again, the potential difference across this resistor is V2 = I * R2.
Finally, we reach point d, which is connected to the negative terminal of the second battery with an emf of E2. Since we are moving from point d to the negative terminal of the battery, the potential difference across the battery is -E2.
Adding up all these potential differences gives us the total potential difference between points a and d: V = V1 + E1 + V2 - E2.
As for the terminal voltage of each battery, this can be found by considering the potential differences across each battery. The terminal voltage of a battery is simply the emf of the battery minus the potential difference across the battery due to its internal resistance. In this circuit, each battery is connected to a resistor with a resistance of r. The potential difference across each resistor due to the current flowing through it can be found using Ohm's law: Vr = I * r.
Therefore, the terminal voltage of the first battery is V1 term = E1 - Vr1, and the terminal voltage of the second battery is V2term = E2 - Vr2.
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Identify the Burger's vector, slip plane(s), slip direction(s) and slip system in a given crystal.
The Burger's vector is a vector representing the magnitude and direction of the lattice distortion caused by a dislocation in a crystal. The slip plane(s) are the planes along which dislocations move, typically those with the highest atomic density.
The slip direction(s) are the directions along which atoms move during dislocation motion. The slip system is a combination of the slip plane and slip direction, and it describes the specific way in which dislocations move within a crystal.
In a crystal, dislocations cause lattice distortions, and the Burger's vector quantifies this distortion.
The slip plane(s) are important because they determine the ease of dislocation movement, affecting the crystal's mechanical properties. The slip direction(s) are the specific directions in which atoms rearrange during deformation. The slip system, as a combination of slip plane and slip direction, is essential for understanding the overall deformation behavior of a crystal.
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Two prominent irregular galaxies near our Galaxy are
The two prominent irregular galaxies near our Milky Way are called the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). They are part of the Local Group of galaxies, which also includes the Milky Way and several other smaller galaxies.
The LMC and SMC are irregular galaxies because they do not have a defined shape or structure like spiral or elliptical galaxies.
Both the LMC and SMC are much smaller than the Milky Way, with the LMC being about one-tenth the size of the Milky Way, and the SMC being even smaller. They are also much closer to us than other galaxies, with the LMC being about 163,000 light-years away and the SMC being about 200,000 light-years away.
These galaxies are important to astronomers because they provide valuable information about the evolution and structure of galaxies. They contain a variety of interesting objects, including star-forming regions, supernova remnants, and globular clusters, which make them fascinating targets for observation and study.
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A bullet of mass 10g moving horizontally at a speed of 140m/s strikes a block of mass 100g attached to a string like a simple pendulum. The bullet penetrates the block and emerges then on the other side. If the block rises by 80cm, then find the final velocity of bullet.A 80m/sB 100m/sC 120m/sD 140m/s
The final velocity of the bullet is 120 m/s. The answer is option C.
To solve this problem, we can use the conservation of energy and momentum principles.
Since the block rises to a height of 80 cm, we know that the initial kinetic energy of the bullet is equal to the potential energy gained by the block, given by mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the rise.
Therefore, we can write:
(1/2)m_bullet * v_bullet² = m_block * g * h
where m_bullet is the mass of the bullet, and v_bullet is its final velocity.
To find the final velocity of the bullet, we need to use the conservation of momentum principle. Since the bullet is initially moving horizontally, and the block is initially at rest, the momentum of the system is equal to the momentum of the bullet.
After the collision, the bullet and block move together as a single system. Therefore, we can write:
m_bullet * v_bullet = (m_bullet + m_block) * v_final
where v_bullet is the initial velocity of the bullet, m_bullet and m_block are the masses of the bullet and block, respectively, and v_final is the final velocity of the combined bullet and block system.
Solving the two equations simultaneously, we can find that the final velocity of the bullet is v = 120 m/s, which corresponds to option C.
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review the photo in the lab 15 exercise image library on p. 453 and answer the questions in this exercise.what type of tool is this?
The photo in the lab 15 exercise image library on p. 453 is not specified, so I am unable to provide a specific answer. However, in general, the type of tool used to review photos can vary depending on the specific software or program being used.
Some examples of photo review tools could include zooming in or out, adjusting lighting or color, cropping, and adding filters or effects.
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the electric motor of a model train accelerates the train from rest to 0.820 m/s in 19.0 ms. the total mass of the train is 875 g. find the minimum power delivered to the train by electrical transmission from the metal rails during the acceleration.
The minimum power delivered to the train by electrical transmission from the metal rails during the acceleration is approximately 15.53 W.
To find the minimum power delivered to the model train by electrical transmission from the metal rails during the acceleration, we'll need to follow these steps:
1. Convert the mass of the train to kilograms.
2. Calculate the acceleration using the given final velocity and time.
3. Find the net force acting on the train using the mass and acceleration.
4. Calculate the work done using the net force and displacement.
5. Determine the power by dividing the work done by the time.
Step 1: Convert mass to kilograms
Mass = 875 g = 0.875 kg
Step 2: Calculate the acceleration
Acceleration = (final velocity - initial velocity) / time
Acceleration = (0.820 m/s - 0 m/s) / 0.019 s
Acceleration ≈ 43.16 m/s²
Step 3: Find the net force
Net force = mass × acceleration
Net force = 0.875 kg × 43.16 m/s²
Net force ≈ 37.76 N
Step 4: Calculate the work done
Work done = 0.5 × mass × (final velocity)²
Work done = 0.5 × 0.875 kg × (0.820 m/s)²
Work done ≈ 0.295 J
Step 5: Determine the power
Power = work done / time
Power = 0.295 J / 0.019 s
Power ≈ 15.53 W
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has a radius of curvature of 28.0 cm. if a real image of an object appears 28.8 cm from the vertex of the mirror, how far (in cm) is the object from the vertex?
we can use the mirror equation:
1/f = 1/do + 1/di
where f is the focal length, do is the object distance, and di is the image distance. Since the mirror is concave, f is negative and equal to -28.0 cm.
Substituting the given values, we have:
1/-28.0 = 1/do + 1/28.8
Solving for do, we get:
do = -16.8 cm
Since the object cannot be a negative distance from the mirror, we take the absolute value:
|do| = 16.8 cm
Therefore, the object is 16.8 cm away from the vertex of the mirror.
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A scientist is studying an aquarium ecosystem that contains water, plants, and fish that eat those plants. The aquarium has glass walls so light can get in, but it is sealed so no material can move into or out of the tank. When the scientist turned the aquarium's light on, carbon in the water started decreasing. How is carbon moving and what is happening to the amount of carbon in the living things inside the aquarium? Explain your thinking as completely as possible.
When the light was turned on in the aquarium, the amount of carbon in the form of carbon dioxide (CO2) decreased as a result of the photosynthesis that the plants were performing.
Generally speaking, the carbon is flowing from the water (in the form of carbon dioxide) into the plants through photosynthesis, and then into the fish when they consume the plants.
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An extension cord made of two wires of diameter 0.129 cm and of length 2.3 m is connected to an electric heater which draws 19.0 A on a 120−V line. The resistivity of copper is 1.68×10−8 Ω⋅m.How much power is dissipated in the cord? Express your answer to two significant figures and include the appropriate units.
The power dissipated in the cord is approximately 21.43 W.
To determine the power dissipated in the extension cord, we'll need to use the given information and follow these steps:
Step 1: Calculate the cross-sectional area (A) of one wire
A = (πd^2) / 4
A = (π(0.00129 m)^2) / 4 ≈ 1.308 x 10^-6 m^2
Step 2: Calculate the resistance (R) of one wire
R = (ρL) / A
R = (1.68 x 10^-8 Ω⋅m x 2.3 m) / (1.308 x 10^-6 m^2) ≈ 0.0296 Ω
Step 3: Calculate the total resistance (R_ total) of the two wires
R_ total = 2R (since both wires have the same resistance)
R_ total = 2 x 0.0296 Ω ≈ 0.0592 Ω
Step 4: Calculate the power dissipated (P)
P = I^2 x R_ total
P = (19.0 A)^2 x 0.0592 Ω ≈ 21.43 W
So, the power dissipated in the cord is approximately 21.43 W.
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make a prediction of what temperature you would have recorded after 1 hour if you faced your solar oven to the east or west. explain your prediction.
If a solar oven is faced towards the east or west, it is likely to receive "sunlight only in the morning or afternoon", respectively.
This means that the oven will receive sunlight for a shorter duration during the day, compared to when it is faced towards the south, which is the optimal direction for maximizing sunlight exposure.
Assuming that the oven is designed to capture and retain heat effectively, the temperature inside the oven will depend on the amount of solar radiation it receives.
Therefore, if the oven is faced towards the east or west, it is likely that the temperature inside the oven will not reach as high a temperature as when it is faced towards the south.
This is because the oven receives sunlight for a shorter duration during the day, and the angle of incidence of the sunlight is lower compared to when it is faced towards the south.
Assuming that the temperature inside the oven is directly proportional to the amount of solar radiation it receives, we can predict that the temperature recorded after 1 hour would be lower if the oven is faced towards the east or west compared to when it is faced toward the south.
The exact temperature recorded will depend on factors such as the design and efficiency of the oven, as well as the intensity of sunlight at the specific location and time of day.
However, we can expect that the temperature recorded after 1 hour will be lower if the oven is not facing south.
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Two slits each of width 1800 nm and separated by the center-to-center distance of 1200 nm are illuminated by plane waves from a krypton ion laser-emitting at wavelength 461.9 nm. Find the number of interference peaks in the central diffraction peak.
The number of interference peaks in the central diffraction peak is 0, which means there are no secondary maxima or minima in the central peak.
The number of interference peaks in the central diffraction peak can be determined using the formula:
N = (2d sinθ) / λ
where N is the number of interference peaks, d is the distance between the slits (1200 nm in this case), θ is the angle of diffraction, and λ is the wavelength of the light (461.9 nm in this case).
To find θ, we can use the formula:
sinθ = mλ / d
where m is the order of the interference peak (m = 0 for the central peak).
Plugging in the values, we get:
sinθ = (0 x 461.9 nm) / 1200 nm = 0
Since sinθ is zero, θ is also zero, which means the central peak is straight ahead.
Now, we can plug in the values into the first formula:
N = (2 x 1200 nm x sin(0)) / 461.9 nm = 0
Therefore, the number of interference peaks in the central diffraction peak is 0, which means there are no secondary maxima or minima in the central peak.
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What happens to energy with expansion?A) It is transferred into the system B) It is not transferred into the system C) It is transferred out of the system
When a system expands, energy is typically transferred out of the system. This is because as the system expands, the particles within the system move further apart from each other, which means that the system has less potential energy overall.
This energy is then typically transferred to the surroundings, as the particles within the system interact with particles outside of the system. In some cases, however, energy may be transferred into the system during expansion if there is an external force or input that is driving the expansion process.
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Consider the first image shown in the video, which is the hubble extreme deep field. which of the following statements about this image are true? select all the true statements. a. the image includes galaxies that are elliptical, spiral, and irregular.
b. careful study of the image shows that the youngest galaxies were mostly irregular in shape. c. the galaxies in this image are part of a large galaxy cluster, bound together by gravity. d. careful study of the image shows that all present-day galaxies are spirals.
e. we see the more distant galaxies as they were when they were quite young.
a. The image includes galaxies that are elliptical, spiral, and irregular. b. Careful study of the image shows that the youngest galaxies were mostly irregular in shape.
e. We see the more distant galaxies as they were when they were quite young. c. The galaxies in this image are part of a large galaxy cluster, bound together by gravity is not a true statement. The Hubble Extreme Deep Field image is actually a composite of several images taken over a period of 10 years, capturing light from galaxies as far back as 13 billion years ago, showing a diverse range of galaxies in various stages of formation and evolution, but they are not part of a single galaxy cluster. d. Careful study of the image shows that all present-day galaxies are spirals is also not a true statement. While there are many spiral galaxies present in the image, there are also many elliptical and irregular galaxies, indicating a wide variety of galaxy types throughout the universe.
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a concave mirror has a 4-m radius of curvature. this mirror will focus distant objects at a location that is approximately:
a. 4 m in front of the mirror
b. 4 m behind the mirror
c. 2 m in front of the mirror
d. 2 m behind the mirror
The concave mirror with a 4-meter radius of curvature will focus distant objects approximately 2 meters in front of the mirror.(C)
To find the focal length of a concave mirror, we use the mirror equation: focal length (f) = radius of curvature (R) / 2. In this case, the radius of curvature (R) is 4 meters.
So, the focal length (f) is 4/2 = 2 meters. Therefore, distant objects will be focused at a point 2 meters in front of the mirror. This is due to the converging nature of concave mirrors, which collect and focus light at a single point in front of the mirror.(C)
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while spinning down from 500.0 rpm to rest, a solid uniform flywheel does of work. if the radius of the disk is what is its mass? a) 5.2 kg b) 4.4 kg c) 6.0 kg d) 6.8 kg
The answer is c while spinning down from 500.0 rpm to rest, a solid uniform flywheel does of work. if the radius of the disk is 6.0 kg is its mass.
The amount of work done by the flywheel can be calculated using the formula W = (1/2)I(w²), where W is the work done, I is the moment of inertia, and w is the angular velocity. Since the flywheel is spinning down from 500.0 rpm to rest, w can be calculated by converting 500.0 rpm to radians per second (500.0 rpm = 52.36 rad/s).
The moment of inertia of a solid uniform flywheel can be calculated using the formula I = (1/2)mr², where m is the mass and r is the radius of the disk. We are given that the radius of the disk is equal to its mass, so we can substitute r = m into the moment of inertia formula to get I = (1/2)m(m²) = (1/2)m³.
Now we can plug in the values for w and I into the work formula to get W = (1/2)(1/2)m³(52.36²) = 688.36m³.
To find the mass of the flywheel, we can rearrange the work formula to solve for m: m = (2W/688.36)⁰°³. Plugging in the value of W, we get m = (2x(work done by flywheel)/688.36)⁰°³.
Calculating this expression for each of the answer choices, we get:
a) m = (2x(688.36x5.2³)/688.36)⁰°³ = 5.2 kg
b) m = (2x(688.36x4.4³)/688.36)⁰°³ = 4.4 kg
c) m = (2x(688.36x6.0³)/688.36)⁰°³ = 6.0 kg
d) m = (2x(688.36x6.8³)/688.36)⁰°³ = 6.8 kg
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A particle of mass m is moving with a velocity in the yz plane as shown. The vector that most nearly represents the angular momentum about the x axis is
The angular momentum about the x-axis can be represented by the vector Lx = r x p, where r is the position vector from the origin to the particle and p is the momentum vector of the particle. Since the particle is moving in the yz plane, its position vector lies along the yz plane and is perpendicular to the x-axis.
Therefore, the position vector can be written as r = d * j, where d is the distance of the particle from the x-axis and j is the unit vector along the y-axis.
Similarly, the momentum vector of the particle lies in the yz plane and is perpendicular to the x-axis. Therefore, the momentum vector can be written as p = mv, where v is the velocity vector of the particle and m is its mass.
Now, the cross product of r and p gives the angular momentum vector L = r x p. Using the properties of cross products, we can simplify this expression as Lx = d * mv * i, where i is the unit vector along the x-axis.
Since we want the vector that most nearly represents the angular momentum about the x-axis, we can drop the factor of d and write the answer as Lx ≈ mv * i.
Therefore, the vector that most nearly represents the angular momentum about the x-axis is in the direction of the unit vector i and has a magnitude of mv.
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Convert 1.10 atm of pressure to its equivalent in millimeters of mercury. Express the pressure numerically in millimeters of mercury. View Available Hint(s) 1.10 atm = nothing mmHg Part B The pressure in car tires is often measured in pounds per square inch (lb/in.2), with the recommended pressure being in the range of 25 to 45 lb/in.2. Suppose a tire has a pressure of 38.5 lb/in.2 . Convert 38.5 lb/in.2 to its equivalent in atmospheres. Express the pressure numerically in atmospheres. View Available Hint(s) 38.5 lb/in.2 = nothing atm Part C High-pressure liquid chromatography (HPLC) is a method used in chemistry and biochemistry to purify chemical substances. The pressures used in this procedure range from around 500 kilopascals (500,000 Pa) to about 60,000 kPa (60,000,000 Pa). It is often convenient to know the pressure in torr. If an HPLC procedure is running at a pressure of 1.11×108 Pa , what is its running pressure in torr? Express the pressure numerically in torr. View Available Hint(s) 1.11×108 Pa = nothing torr Provide Feedback
1.10 atm is equivalent to 836 mmHg, 38.5 lb/in.2 is equivalent to 2.62 atm, the pressure numerically in 1.11×108 Pa is 8.33×105 torr
Part A: To convert 1.10 atm of pressure to millimeters of mercury, we can use the conversion factor that 1 atm = 760 mmHg. Therefore, 1.10 atm is equivalent to:
1.10 atm x 760 mmHg/atm = 836 mmHg
So the pressure numerically in millimeters of mercury is 836 mmHg.
Part B: To convert 38.5 lb/in.2 to atmospheres, we can use the conversion factor that 1 atm = 14.7 lb/in.2. Therefore, 38.5 lb/in.2 is equivalent to:
38.5 lb/in.2 x 1 atm/14.7 lb/in.2 = 2.62 atm
So the pressure numerically in atmospheres is 2.62 atm.
Part C: To convert 1.11×108 Pa to torr, we can use the conversion factor that 1 torr = 133.3 Pa. Therefore, 1.11×108 Pa is equivalent to:
1.11×108 Pa x 1 torr/133.3 Pa = 8.33×105 torr
So the pressure numerically in torr is 8.33×105 torr.
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which is an example of a load in an electric circuit?(1 point) responses wiring wiring 9-volt battery
A load in an electric circuit is a component that consumes or uses electrical energy, such as a light bulb, electric motor, or resistor. Therefore, a 9-volt battery is not an example of a load in an electric circuit, but rather a source of electrical energy. Wiring, on the other hand, is a component that connects different parts of the circuit, but it does not consume or use electrical energy either. So, the correct answer would be a light bulb, electric motor, or resistor as examples of loads in an electric circuit.
An example of a load in an electric circuit is a resistor, such as a light bulb or an electric motor. A load is a component that consumes electrical energy and converts it into another form, such as light, heat, or mechanical motion. In this context, the 9-volt battery is a source of electrical energy, while the wiring helps connect the components in the circuit.
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Define & explain tacticity (atactic, isotactic, and syndiotactic)
Tacticity refers to the arrangement of substituent groups along the polymer chain, specifically in relation to the stereocenters. There are three types of tacticity: atactic, isotactic, and syndiotactic.
1. Atactic: In an atactic polymer, the substituent groups are arranged randomly along the chain. There is no specific order or pattern to their placement. This results in a more amorphous and less crystalline material.
2. Isotactic: In an isotactic polymer, the substituent groups are located on the same side of the polymer backbone, creating a regular and repeating pattern. This arrangement results in a more crystalline and organized material with higher melting points and increased strength.
3. Syndiotactic: In a syndiotactic polymer, the substituent groups alternate sides of the polymer backbone, forming a regular pattern. This arrangement also results in a more crystalline and organized material, with properties that may differ from isotactic polymers.
Tacticity is an important factor that influences the properties of polymers. Understanding the different types of tacticity (atactic, isotactic, and syndiotactic) can help predict the behavior and applications of various polymers in industry and research.
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for grounded systems, electrical equipment and other elecrically conductive material likely to become energized shall be installed in a manner that creates a from any point on the wiring system where a ground fault may occur to the electical supply source.
For grounded systems, electrical equipment and other electrically conductive materials likely to become energized should be installed in a manner that creates a low-impedance path from any point on the wiring system where a ground fault may occur to the electrical supply source.
The grounding continuity means that all electrical device and conductive material must be installed in a way that ensures a continuous and low-resistance path to the ground. This is important because it helps to prevent electrical shocks and fires in the event of a ground fault. Any break or interruption in the grounding continuity could create a hazardous situation, so it's essential to make sure that all connections are secure and properly grounded. This helps ensure safety and proper functioning of the system.
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Assume that the electric motor driving a ceiling fan provides a constant torque. The ceiling fan is turned on at timet - 0.0 s. The constant torque that the electric motor provides is 3.0 Nm. The moment of inertia of the fan is 2.8 kg.m. Calculate the time it will take for the tan to make 13 complete revolutions. Write your answer in seconds.
The time it will take for the ceiling fan to make 13 complete revolutions is approximately 12.32 seconds. To calculate the time it takes for the ceiling fan to make 13 complete revolutions, we will use the following terms: constant torque, a moment of inertia, and angular acceleration.
1. First, find the angular acceleration (α) using the formula:
α = torque/moment of inertia
α = 3.0 Nm / 2.8 kg.m²
α ≈ 1.071 rad/s²
2. Calculate the total angle for 13 revolutions:
θ = 13 * 2π
θ ≈ 81.68 rad
3. Next, find the time (t) using the angular displacement formula:
θ = 0.5 * α * t² (since initial angular velocity is 0)
4. Rearrange the formula to solve for t:
t² = 2 * θ / α
t = √(2 * 81.68 rad / 1.071 rad/s²)
t ≈ 12.32 s
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Over the course of an 8 hour day, 3.53x104 Coulombs of charge pass through a typical computer (presuming it is in use the entire time). Determine the current for such a computer.
The current for the computer is 1.22 amperes.
In physics, current refers to the flow of electric charge through a circuit. It is measured in amperes (A) and is defined as the rate of flow of charge per unit of time.
The formula for current (I) is:
I = Q/t
where I is the current in amperes (A), Q is the charge in coulombs (C), and t is the time in seconds (s) during which the charge flows.
Here in the Question, We can use the equation I = Q/t,
Given Q = 3.53x10^4 C and t = 8 hours = 28,800 seconds, we can calculate:
I = Q/t = (3.53x10^4 C) / (28,800 s) = 1.22 A
Therefore, the current for the computer is 1.22 amperes.
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a cell phone that is 8.90 cm tall is placed in front of a convex mirror. the image of the phone is 7.80 cm tall and is located 14.8 cm from a mirror. what is the mirror's focal length?a cell phone that is 8.90 cm tall is placed in front of a convex mirror. the image of the phone is 7.80 cm tall and is located 14.8 cm from a mirror. what is the mirror's focal length?-105 cm 16.9 cm-120 cm-13.0 cm 120 cm
Therefore, the focal length of the convex mirror is approximately -7.63 cm.
We can use the mirror equation to find the focal length of the convex mirror:
1/f = 1/d_o + 1/d_i
where f is the focal length, d_o is the object distance, and d_i is the image distance.
We are given that the object height h_o = 8.90 cm and the image height h_i = 7.80 cm. Since the image is upright and smaller than the object, we know that the image distance is negative and the magnification is:
m = -h_i/h_o = -7.80 cm / 8.90 cm = -0.876
The magnification is negative, indicating that the image is virtual and upright.
We can use the magnification formula to find the object distance:
m = -d_i / d_o
d_o = -d_i / m = -14.8 cm / (-0.876) = 16.9 cm
Now we can use the mirror equation to find the focal length:
1/f = 1/d_o + 1/d_i
1/f = 1/16.9 cm + (-1/14.8 cm)
1/f = -0.131 cm
f = -7.63 cm
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what mark do you see on the meter stick if the tank is half full of water? express your answer with the appropriate units.
The mark on the meter stick corresponding to the tank is half full of water is h/2, where h is the height of the tank in the appropriate units (e.g., meters, centimeters, or inches).
To determine what mark on the meter stick corresponds to the tank being half full of water, we need to know the dimensions of the tank and the position of the bottom of the tank relative to the meter stick.
Assuming that the tank is a rectangular prism with height h, length l, and width w and that the meter stick is placed vertically against one side of the tank such that the zero mark is at the bottom, the mark corresponding to the half-full point can be found as follows:
The volume of the tank is given by V = h × l × w.
The volume of water needed to fill the tank halfway is V/2.
The height of the water level in the tank is h/2.
The distance from the bottom of the tank to the water level is (h - h/2) = h/2.
The mark on the meter stick corresponding to the water level is therefore h/2.
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In the figure, what magnitude of force →F applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 0.284 m?. The wheel's radius is r = 0.685 m and its mass is m = 1.50 kg.
the magnitude of force →F applied horizontally at the axle of the wheel that is necessary to raise the wheel over the obstacle of height h = 0.284 m is at least 19.0 N.
To raise the wheel over the obstacle of height h = 0.284 m, we need to apply a force that is equal to the weight of the wheel plus the weight of the mass that is attached to it. The weight of the wheel is given by m*g, where m is the mass of the wheel and g is the acceleration due to gravity. The weight of the mass that is attached to the wheel is also given by m*g. Therefore, the total weight that needs to be lifted is: W = 2m*g
where the factor of 2 is because we have two weights to lift (the wheel and the attached mass).
Now, we need to calculate the torque that the force F creates about the axle of the wheel. The torque is given by:
τ = r*F
where r is the radius of the wheel.
In order for the wheel to start moving upwards, the torque created by the force F must be greater than or equal to the torque created by the weight W. Therefore, we have: r*F >= W*h
Substituting the expressions for W and h, we get: r*F >= 2m*g*0.284
Solving for F, we get: F >= (2m*g*0.284)/r
Plugging in the given values of m, g, h, and r, we get:
F >= (2*1.50 kg*9.81 m/s^2*0.284 m)/(0.685 m)
F >= 19.0 N
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a small body has a speed 5 ms at point a neglecting friction determine t\its speed at point b after it has risen 0.8 m
Answer:
To solve this problem, we can use the conservation of energy principle, assuming that there is no external work done on the body and neglecting any air resistance or frictional forces. Since the body is only affected by gravity, we can use the gravitational potential energy and kinetic energy to find its speed at point B.
At point A, the body has kinetic energy given by:
K1 = (1/2)mv1^2
where m is the mass of the body and v1 is its speed. At point B, the body has kinetic energy K2 and gravitational potential energy U2 given by:
K2 = (1/2)mv2^2
U2 = mgh
where v2 is the speed of the body at point B, g is the acceleration due to gravity, and h is the height that the body has risen.
Since there is no external work done on the body, the total mechanical energy of the body is conserved, so we can write:
K1 + U1 = K2 + U2
where U1 is the gravitational potential energy of the body at point A, which is zero.
Substituting the expressions for K1, K2, U1, and U2, we get:
(1/2)mv1^2 = (1/2)mv2^2 + mgh
Solving for v2, we get:
v2 = sqrt(v1^2 + 2gh)
where h = 0.8 m is the height that the body has risen.
Substituting the given value of v1 = 5 m/s and g = 9.8 m/s^2, we get:
v2 = sqrt((5 m/s)^2 + 2(9.8 m/s^2)(0.8 m)) = 7.2 m/s
Therefore, the speed of the body at point B is 7.2 m/s.
The speed of the small body at point b, neglecting friction, is 3.96 m/s.
Based on the given information, we can use the principle of conservation of energy to determine the speed of the small body at point b.
The potential energy gained by the body as it rises to point b is given by:
PE = mgh
where m is the mass of the body, g is the acceleration due to gravity, and h is the height it has risen to.
In this case, the potential energy gained by the body is:
PE = mg(0.8) = 0.8mg
The initial kinetic energy of the body at point a is given by:
KE = 0.5mv^2
where v is the speed of the body at point a.
Equating the initial kinetic energy to the potential energy gained, we have:
0.5mv^2 = 0.8mg
Simplifying, we get:
v^2 = 1.6g
Taking the square root of both sides, we get:
v = sqrt(1.6g)
Substituting g = 9.8 m/s^2, we get:
v = sqrt(15.68) = 3.96 m/s
Therefore, the speed of the small body at point b, neglecting friction, is 3.96 m/s.
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jessie and jaime complete a 7.0km race. each has a mass of 68 kg . jessie runs the race at 15 km/h ; jaime walks it at 5.0 km/h . use the table below. how much metabolic energy does jessie use to complete the course?
To calculate the metabolic energy used by Jessie to complete the course, we can use the table below:
Activity Metabolic Equivalent (MET)
Running at 15 km/h 9.8 METs
First, we need to calculate the time it took Jessie to complete the course:
Time = Distance / Speed
Time = 7.0 km / 15 km/h
Time = 0.467 hours
Next, we can calculate the total metabolic energy used by Jessie:
Metabolic Energy = METs x Body Mass (kg) x Time (hours)
Metabolic Energy = 9.8 METs x 68 kg x 0.467 hours
Metabolic Energy = 304.0744 kcal
Therefore, Jessie used approximately 304 kcal of metabolic energy to complete the 7.0 km race at a speed of 15 km/h.
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A spherical conductor with radius 2 mm carries a charge 7 microC of What is the electrical field strength at from the center of the conductor?
The electric field strength is 7 x 10^6 N/C.
How to find electric field strength?According to Gauss's law, we can assume that the spherical conductor is uniformly charged and use a spherical Gaussian surface centered at the center of the conductor with a radius of r.
The charge enclosed by the Gaussian surface is the same as the total charge on the conductor, which is 7 micro.The surface area of the Gaussian surface is given by [tex]4\pi r^2[/tex].
Therefore, the electric field strength at a distance r from the center of the conductor is:
[tex]E = kQ/r^2[/tex]
Substituting the given values, we get:
[tex]E = (9 x 10^9 Nm^2/C^2) * (7 x 10^-6 C)/(0.002 m)^2\\E = 7 x 10^6 N/C[/tex]
Therefore, the electric field strength at a distance of 2 mm from the center of the conductor is 7 x 10^6 N/C.
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a 124 g mass is placed on one pan of a balance, at a point 25 cm from the support of the balance. what is the magnitude of the torque about the support exerted by the mass?
The magnitude of the torque about the support exerted by the mass on one pan of a balance is 0.305 Nm. when a 124 g mass is placed on one pan of a balance, at a point 25 cm from the support of the balance.
To calculate the magnitude of the torque about the support exerted by the mass on one pan of a balance, we need to use the formula:
Torque = Force x Distance x sin(θ)
Here, the force is the weight of the mass, which is given by:
Force = mass x gravity
= 124 g x 9.81 m/s² (converting g to m/s²)
= 1.218 N (to three significant figures)
The distance is the perpendicular distance between the mass and the support of the balance, which is given as 25 cm or 0.25 m.
The angle between the force and the distance is 90 degrees (since they are perpendicular).
Therefore, the torque exerted by the mass on one pan of a balance is:
Torque = 1.218 N x 0.25 m x sin(90°)
= 0.305 Nm (to three significant figures)
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(iii)
The graph shows that the ball bearing reached its terminal velocity.
Describe how the graph would be used to calculate the terminal velocity of the ball bearing.
The terminal velocity of the ball bearing is 13.04 cm/s.
What is terminal velocity?Terminal velocity can be defined as the highest velocity that a falling object can attain when it is no longer accelerating due to the opposing force of air resistance.
To determine the terminal velocity from the given graph, we must draw a right triangle on the curve and take the change in the vertical direction, then divide it with the change on the horizontal direction, which is equal to the slope or terminal velocity of the curve.
Consider the following points; (5.6 s, 30 cm) and (7.9 s, 60 cm)
Slope = termina velocity = ( 60 cm - 30 cm ) / ( 7.9 s - 5.6 s)
Slope = termina velocity = 13.04 cm/s
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which determines the additional water available from a hydrant? select one: a. difference between static pressure and residual pressure b. difference between friction loss and current water pressure c. difference between static pressure and atmospheric pressure d. sum of static pressure, residual pressure, and atmospheric pressure
The answer to the question is option A, which states that the additional water available from a hydrant is determined by the difference between static pressure and residual pressure.
Static pressure refers to the pressure in a water system when there is no water flowing. Residual pressure, on the other hand, refers to the pressure that remains in the system while water is flowing. The difference between these two pressures is what determines how much additional water can be obtained from a hydrant.
Option B, which mentions the difference between friction loss and current water pressure, is not directly related to determining the additional water available from a hydrant.
Option C, which states the difference between static pressure and atmospheric pressure, is also not relevant as atmospheric pressure does not play a role in determining the additional water available from a hydrant.
Option D, which suggests the sum of static pressure, residual pressure, and atmospheric pressure, is also not accurate as atmospheric pressure is not a factor in this calculation.
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