The voltage across the compressor is 12 V.
Power of the power source, P = 54 W
Current utilized, I = 4.5 A
The equation for power of a circuit is given by,
P = VI
Therefore, voltage across the compressor,
V = P/I
V = 54/4.5
V = 12 V
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Calculate the average time for the tablet pieces to dissolve in room temperature water. Record the average time in Table D. Trial 141.00Trial 244.00Trial 341.00 What is the average time it took for the tablet pieces to dissolve in room temperature water? seconds
The average time it took for the tablet pieces to dissolve in room-temperature water is 42.00 seconds.
Room temperature refers to the typical temperature range that is comfortable for humans in an indoor environment. It is generally considered to be between 68°F (20°C) and 77°F (25°C). However, the exact definition of room temperature can vary depending on the context and the standards of a particular region or industry. In scientific experiments or industrial settings, room temperature may be defined more precisely and may range from 20°C to 25°C, or even narrower ranges such as 22°C to 24°C.
To calculate the average time it took for the tablet pieces to dissolve in room temperature water, we need to add up the times from all three trials and divide by the number of trials (3):
(41.00 + 44.00 + 41.00) / 3 = 42.00 seconds
Therefore, the average time it took for the tablet pieces to dissolve in room-temperature water is 42.00 seconds.
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Which sentence best describes what happens when you turn on a light? (1 point)
A. Potential energy is changed into kinetic energy.
B. Electrical energy is changed into light energy and thermal energy.
C. Light energy is created.
D. Chemical energy is changed into electrical energy and light energy.
Which statement describes a limitation of scientific models?
O they require no future improvement
O they can predict what will occur next
O they can be shown on maps, graphs and other displays
O they are simplified versions of the systems they represent
Answer:
"They are simplified versions of the systems they represent."
Explanation:
A limitation of scientific models is that they are simplified versions of the systems they represent. This means that there may be some aspects of the real world that the model cannot accurately capture or predict, which can limit its usefulness. Additionally, models can always be improved upon as new data or technology becomes available, so they are never perfect or final.
You are pushing your old dishwasher of mass 35.0 kg up the ramp into the truck bed. You are applying a force of 225 N along the ramp which is inclined at 22.0 degrees. There is a frictional force of 45.0 N between the ramp and the dishwasher. can you please help with b?
The acceleration of the dish washer is obtained as 5.1 m/s^2.
What is a free body diagram?A free body diagram is a type of image that physicists use to illustrate the forces operating on an item in a certain circumstance.
By dissecting the motion of the object into its component forces and displaying the direction and amount of each force acting on the object, the diagram may be used to study the motion of the object.
We know that;
Net force =Applied force - Frictional force
35a = 225 - 45
a = 225 - 45/35
a = 5.1 m/s^2
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A/An breaks down a complicated goal into daily action to make it more manageable?
A routine breaks down a complicated goal into daily action to make it more manageable.
What is a routine?A routine can be described as the sequence of actions regularly followed which do help individuals as well as the organization so they can acheive their goals.
It should be noted that a routine is neccessary in an organization because it will help help them to breakdown the task as well as the activities and this will help to achive the goals as well as the neccessary things on time because allcomplicated goals woud have been included as well as how it will be carried out.
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A voltage of 32 V generates a work done of 2.10x10^-7 J. Calculate the charge.
Determine the stopping location of the prize wheel. At this moment it is centered on the number 31. It is spinning at a rate of 27.50 rpm. It is slowing at a rate of 0.110 rad/s/s. quantity of spaces is 36.
Predict the time the wheel will remain spinning, the angular displacement it will go through, and then use this to predict the number on which the wheel will stop. To be safe, you will also get one number the right and to the left of the number you chose.
The wheel will spin clockwise.
30 pts
Since the wheel stops between 32 and 33, we can predict that the wheel will stop on either 32 or 33. As a safe bet, we can choose the two numbers on either side of these, so the predicted numbers are 31, 32, and 33.
A prize wheel is a wheel-shaped device used for games and promotions, where participants spin the wheel to win a prize or determine an outcome. The wheel is typically divided into sections, each with a different prize or outcome.
To determine the stopping location of the prize wheel, we need to consider the following:
The initial angular velocity of the wheel is 27.50 rpm, or 2.88 rad/s.
The angular acceleration of the wheel is -0.110 rad/s^2 (negative because the wheel is slowing down).
The number of spaces on the wheel is 36, so the angular displacement for each space is 2*pi/36 = pi/18 radians.
Using these values, we can use the following equations of motion to determine the time it takes for the wheel to stop and the angular displacement it goes through:
1. Angular displacement:
theta = theta_0 + omega_0*t + (1/2)alphat^2
where
theta_0 = 31*(pi/18) (initial angular position of the wheel)
omega_0 = 2.88 rad/s (initial angular velocity of the wheel)
alpha = -0.110 rad/s^2 (angular acceleration of the wheel)
t = time
Plugging in the values, we get:
theta = (31*pi/18) + (2.88)*t - (0.055)*t^2
2. Time is taken for the wheel to stop:
omega = omega_0 + alpha*t
where
omega_0 = 2.88 rad/s (initial angular velocity of the wheel)
alpha = -0.110 rad/s^2 (angular acceleration of the wheel)
t = time
Setting omega to zero (since the wheel stops when it reaches zero angular velocity), we get:
t = -omega_0/alpha
Plugging in the values, we get:
t = 26.18 seconds
So it takes 26.18 seconds for the wheel to stop.
Using the equation for angular displacement, we can find the angular displacement of the wheel during this time:
theta = (31pi/18) + (2.88)(26.18) - (0.055)*(26.18)^2
theta = 89.36 radians
To find the number on which the wheel will stop, we need to divide the angular displacement by the angular displacement for each space:
number of spaces = theta/(pi/18)
number of spaces = 32.4
Therefore, We may anticipate that the wheel will stop on either 32 or 33 because it pauses between 32 and 33. The projected numbers are 31, 32, and 33 since we can choose the two numbers on either side of these as a safe bet.
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3
Extremist groups typically mix radical beliefs or values with anger over some aspect of society.
OA. True
OB. False
We studied various patterns in the periodic table. 1) The pattern involving atomic number 2) The pattern involving valence electrons 3) The pattern of families.
Describe ONE of these patterns in the space below. Write at least one full sentence.
Answer:
The pattern of families in the periodic table refers to the grouping of elements with similar properties into vertical columns, also known as groups.
1. A material emits electrons when the electromagnetic radiation with a frequency equal to or less than the material's threshold frequency strikes the material.
True
False
2. In a particle model to show energy transfer, which of the following is correct?
a. Energy jumps are best described of electrons in packages known as photons
b. In energy transfers, electrons can absorb or emit energy
c. Photons carry energy from one location or object to another
d. All of the above are correct of particle models
1) The photoelectric effect is the phenomena by which, the metals release electrons when they are exposed to electromagnetic radiation with the suitable frequency. The photoelectrons are the electrons that are released in this process.
So, the statement is true.
2) In a particle model, energy transfer can be done through many ways such as:
The energy jumps between the particles in the form of photons.
Electrons can absorb or emit energy during energy transfer.
The energy is transferred between different objects in the form of photons.
So, all of them are true.
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1. How might race and cohort factors affect your work with older adults?
2. What is common ageist microaggressions? What type of communication patterns can you keep watch for and try to avoid when working with older adults?
3. What are common factors to consider when working with an older adult identifying as LGBT?
4. What resiliencies might you look for when working with older adults ?
Always make an effort to understand what the older people are thinking or feeling by placing yourself in their position.
1) Practitioners must take multicultural competency into account when evaluating older persons. This takes into account not only the older adult's ethnic, racial, and cultural background but also other cohort factors including their level of health literacy and previous interactions with mental health professionals.
2) Communication abilities deteriorate subtly with regular ageing, at least in part as a result of changes in physical health, depression, and cognitive loss. Physiologic modifications in the voice, speaking, and hearing functions are brought on by ageing.
3) The primary concerns of older LGBT individuals include chronic health care, caregiving, financial security for long-term care, social isolation, resilience development, and knowing where to turn for reliable assistance.
4) Be compassionate. Always make an effort to understand what they are thinking or feeling by placing yourself in their position. According to my observations, seniors' fear of falling is the main barrier to exercise.
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Complete the ray diagram below:
A convex lens is shown centered at 7 on a ruler that goes from 0 to 14 centimeters. The object is located at 4.5, and the focal points are at 5.5 and 8.5.
Describe the image characteristics (real or virtual, orientation, size).
Submit your completed ray tracing diagram as an image attachment to this question. Ensure your name and today's date are visible in the image capture.
The image will be formed where the refracted rays intersect. In this case, the image is located above the principal axis and is therefore a virtual image. The image is also upright and smaller than the object.
The principal axis is an imaginary line passing through the center of a lens or a mirror that is perpendicular to the surface of the lens or mirror at its center. It is an important reference line in optics as it helps determine the direction in which light rays will be refracted or reflected by the lens or mirror. The principal axis is used as a reference line for constructing ray diagrams and for determining the position and characteristics of images formed by lenses or mirrors.
To complete the ray tracing diagram, follow these steps:
1. Draw a horizontal line to represent the principal axis of the lens.
2. Mark the center of the lens at 7 on the ruler.
3. Draw a vertical line to represent the object at 4.5, below the principal axis.
4. Draw a ray from the top of the object parallel to the principal axis. When it hits the lens, refract it through the focal point on the opposite side of the lens.
5. Draw a ray from the top of the object through the focal point on the left side of the lens. When it hits the lens, refract it parallel to the principal axis.
6. Draw a ray from the top of the object through the center of the lens. This ray will continue in a straight line.
7. Repeat steps 4-6 for the bottom of the object.
Therefore, the image will be created where the refracted rays intersect. Since the image in this instance is above the principal axis, it is a virtual image. Additionally upright and smaller than the object, the image.
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2. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then, it travels 210 km south with an average velocity of 75 km/h to the south. a. How long does the total trip last? b. What is the average velocity for the total trip?
Answer:76.78 km/h To calculate the average velocity for the total trip, you need to first determine the total distance travelled and the total time taken. First, let's calculate the total distance travelled. The trip consists of 2 legs. The 1st leg is 280 km and the 2nd leg is 210 km. So the total distance is 280 km + 210 km = 490 km. Now you need to calculate the total time taken. For this problem, there are 3 intervals that need to be accounted for. The travel time for the 1st leg, the duration of the rest stop in the middle, and the travel time for the 2nd leg. The travel time for both legs is calculated by dividing the distance travelled by the average speed. So for the first leg we have 280 km / (88 km / h) = 3.181818 h The 2nd leg is 210 km / (75 km/h) = 2.8 h The rest stop in hours is 24 min / (60 min/h) = 0.4 h The total time is 3.181818 h + 2.8 h + 0.4 h = 6.381818 h The average velocity is the distance divided by the time, giving: 490 km / (6.381818 h) = 76.78 km/h
Explanation: I am middle school genius and I spell diff bc I am british-english
CAN ANYONE PLEASE HELP!
One long wire lies along an x axis and carries a current of 36 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0,5.8 m, 0), and carries a current of 73 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0)?
The resultant magnetic field magnitude at the position (0, 2.0 m, 0) is 1.9 x 10⁻⁵ T.
How to find resulting magnetic field?The magnetic field due to each wire at point P will be:
B₁ = μ₀I₁/2πr₁ and B₂ = μ₀I₂/2πr₂
Where,
μ₀ = 4π x 10⁻⁷ T m/A is the permeability of free space,
I₁ = 36 A is the current in the first wire,
I₂ = 73 A is the current in the second wire,
r₁ = distance between point P and the first wire,
r₂ = distance between point P and the second wire.
As the first wire is along the x-axis, its magnetic field at point P will be purely in the y-direction. The magnitude of B₁:
B₁ = μ₀I₁/2πr₁ = (4π x 10⁻⁷ T m/A)(36 A)/(2π(2.0 m)) = 1.8 x 10⁻⁵ T
The second wire is perpendicular to the xy-plane, so its magnetic field at point P will be purely in the x-direction. The distance r₂ using the Pythagorean theorem:
r₂ = √(5.8 m)² + (2.0 m)² = 6.1 m
The magnitude of B₂:
B₂ = μ₀I₂/2πr₂ = (4π x 10⁻⁷ T m/A)(73 A)/(2π(6.1 m)) = 6.0 x 10⁻⁶ T
The resulting magnetic field at point P will be the vector sum of the magnetic fields due to each wire:
B = √(B₁² + B₂²) = √((1.8 x 10⁻⁵ T)² + (6.0 x 10⁻⁶ T)²) = 1.9 x 10⁻⁵ T
Therefore, the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0) is 1.9 x 10⁻⁵ T.
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A source of sound with a frequency of 620 Hz is
placed on a moving platform that approache
s a physics student at speed v; the student h
ears sound with a frequency f1. Then the so
urce of sound is held stationary while the stu
dent approaches it at the same speed v; the
student hears sound with a frequency of f2. ch
oose the correct statement.
(A) f1 =f2 ;both are greater than 620 Hz
(B) #1-12,;both are less than 620 Hz
(c) M>12>620 H2
(D) 12311>620 H2
. Describe the five adjustments you made to the Rube Goldberg device in order to keep the flow of energy going.
The five changes I made to the Rube Goldberg apparatus to keep the energy flowing is 1) Reduced the height of the first ball platform 2) Attached the weight that has to be lifted. 3) The sling shot was attached to the pin. 4) Took a shot, I lowered the seesaw gadget. 5) A water-filled balloon. this is basically a machine.
A Rube Goldberg machine, named after American cartoonist Rube Goldberg, is a machine or device that is purposely constructed to do a basic task in an indirect and (impractically) too convoluted manner. Typically, these machines are made up of a sequence of basic unconnected devices; the action of one initiates the next, finally culminating in the achievement of a specified purpose. A similar device is known as a "Heath Robinson contraption" in the United Kingdom, after the cartoonist W. Heath Robinson.
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explanation of the 3 newtons laws? at least 2 paragraphs please
Share an experience you've had with the bureaucracy. In thinking about that experience, how would you describe the bureaucracy? What characteristics of the bureaucracy did you observe in that experience? Please explain. (Refer to Weber's theory of bureaucracy in the module.)
A bureaucracy is a collection of non-elected government authorities or a group that makes administrative policy. A bureaucracy was historically a government administration governed by departments manned by non-elected individuals.
In bureaucracy, there are two major quandaries. The first quandary is whether bureaucrats should be independent or directly answerable to their political masters. The second quandary concerns bureaucrats' responsibilities to follow process, regulation, and legislation, as well as the degree of leeway they may have in determining proper answers to conditions that look unaccounted for in advance. it is governed by non-elected individuals.
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A 7 ton utility truck comes over a blind hill and cannot stop when he sees an obsticle in the road. He travels to the left of the road across 127 feet of dry, grassy ditch, 75 feet of dry pavement, and 81 feet of deep clay. He hits a tree on his right hand bumper at 227 feet, totalling his truck, and then continues to travel an additional 57 feet through brush, and pulverizing a steel and metal mesh fence.
How fast was the truck traveling?
Answer:
80 mph using speed = mass / distance
Explanation:
truck traveled = 227 feet + 57 feet
truck traveled = 284 feet
truck weighs 7 tons
truck weighs 15,422 pounds
formula to calculate the speed of the truck =
speed = mass / distance
mass is 15,422 pounds
distance is 284 feet
speed = 15,422 pounds / 284 feet
speed = 54.1 feet per second
convert feet per second to miles per hour by multiplying by 1.4667.
speed = 54.1 feet per second * 1.4667
speed = 80.0 miles per hour
A research paper which has been turned in for credit is a final product.
Please select the best answer from the choices provided
О т
OF
False. A research paper which has been turned in for credit is not a final product.
What is a research paper?A research paper is a piece of academic writing that provides analysis, interpretation, and argument based on personal or assissted research in a thorough or detailed manner.
We can also define a research paper as a written document that gives the results of an individual or new research or study on a chosen subject.
This research paper is typically written by researchers, or academia. Which is usually a process or a way of contributing to new knownledge.
Researchers often use research papers to document their findings and sometimes earn some recognitions or award from these researchers.
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Complete the ray diagram below:
A convex lens is shown centered at 7 on a ruler that goes from 0 to 14 centimeters. The object is located at 4.5, and the focal points are at 5.5 and 8.5.
Describe the image characteristics (real or virtual, orientation, size).
Submit your completed ray tracing diagram as an image attachment to this question. Ensure your name and today's date are visible in the image capture.
The image is real, inverted, and smaller in size.
Based on the given information, we can use ray tracing to determine the characteristics of the image.
Draw the incident ray from the top of the object, parallel to the principal axis, that passes through the focal point on the opposite side of the lens.Draw the incident ray from the top of the object, passing through the center of the lens.Draw the refracted ray from the top of the object, passing through the focal point on the same side of the lens.Repeat the above steps for the bottom of the object.The image is formed by the intersection of the refracted rays. In this case, the image is located between the lens and the focal point on the opposite side of the lens. Therefore, the image is real.
The refracted rays converge at a point below the principal axis, which means that the image is inverted.
Finally, the height of the image is smaller than the height of the object, indicating that the image is smaller in size.
Please refer to the attached image for the ray tracing diagram.
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Calculate the potential difference to be maintain between two horizontal conducting plates separated by a distance of 10mm so that a small charged oil drop of mass 1.31x10-14 kg will remain in equilibrium. [charge on the oil drop = 6·4×10-¹⁹c] C
Answer:
Explanation:
The potential difference required to maintain the equilibrium of a charged oil drop in a uniform electric field can be calculated using the following equation:
V = (mg)/(qE)
where V is the potential difference, m is the mass of the oil drop, g is the acceleration due to gravity, q is the charge on the oil drop, and E is the electric field strength.
We are given the mass of the oil drop (m = 1.31x10^-14 kg), the charge on the oil drop (q = 6.4x10^-19 C), and the separation between the plates (d = 10 mm = 0.01 m).
The electric field strength between two parallel plates separated by a distance d and with a potential difference V applied between them is given by:
E = V/d
Substituting this expression for E into the equation for V, we get:
V = (mg)/(qE) = (mgd)/(qV)
Rearranging this equation, we obtain:
V^2 = (mgd)/q
Substituting the given values, we get:
V^2 = [(1.31x10^-14 kg)(9.81 m/s^2)(0.01 m)]/(6.4x10^-19 C)
V^2 = 2.02x10^-5 V^2
Taking the square root of both sides, we obtain:
V = 0.0045 V
Therefore, the potential difference required to maintain the equilibrium of the charged oil drop is approximately 0.0045 volts.
a) i) Calculate the change in length of a 1.5m long copper bar when its temp is raised from 303K to 353K . (3mks)
Answer:
the change in length of the copper bar is 1.26 x 10^-3 meters (or 1.26 millimeters).
Explanation:
The change in length of a copper bar can be calculated using the formula:
ΔL = L₀αΔT
where:
ΔL = change in length
L₀ = original length of the copper bar (1.5 m)
α = coefficient of linear expansion for copper (16.8 x 10^-6 K^-1)
ΔT = change in temperature (353 K - 303 K = 50 K)
Plugging in the values, we get:
ΔL = (1.5 m)(16.8 x 10^-6 K^-1)(50 K)
ΔL = 1.26 x 10^-3 m
A long jumper leaves the ground with an initial speed of 9.5m/s at an angle of 22degrees from the ground. Determine the time it takes for the long jumper to reach her maximum height of her jump.
The time it takes for the long jumper to reach her maximum height will be approximately 0.372 seconds .
To determine the time it takes for the long jumper to reach her maximum height, the vertical motion of the jumper separately.
The initial vertical velocity, v₀y, can be calculated by multiplying the initial speed, v₀, by the sine of the launch angle, θ:
v₀y = v₀sin(θ)
Plugging in the given values:
v₀ = 9.5 m/s (initial speed)
θ = 22° (launch angle)
We can convert the launch angle from degrees to radians, as the trigonometric functions in most programming languages (including Python, which we'll use later) take input in radians:
θ = 22° * (π/180) ≈ 0.384 radians
Substituting the values:
v₀y = 9.5 m/s * sin(0.384) ≈ 3.65 m/s
The maximum height of the jump occurs when the vertical velocity, vy, becomes zero. At that moment, the jumper is at the highest point of the jump before descending.
vy = v₀y + at
where a is the acceleration due to gravity, which is approximately 9.8 m/s² (assuming no air resistance).
Setting vy to zero and solving for t:
0 = v₀y + at
t = -v₀y / a
Substituting the values:
t = -3.65 m/s / 9.8 m/s² ≈ -0.372 seconds
Since time cannot be negative in this context, we discard the negative value and take the absolute value. Therefore, the time it takes for the long jumper to reach her maximum height is approximately 0.372 seconds .
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A work done of 25 J happen to a charge that is 8.33 μC. Calculate the voltage.
Betelgeuse has a surface temperature of 3500 k and is located 643 light-years away from Earth. The light intensity from betelgeuse at the ground is 9.88 times 10^-8 W/m^2. How large it radiates the effect of betelgeuse
Betelgeuse has a surface area of roughly 8.98 × 10²¹ square meters.
How to calculate size of star?The radiated power of a star is given by the Stefan-Boltzmann law:
P = σAT⁴
where P = power radiated,
A = surface area of the star,
T = surface temperature, and
σ = Stefan-Boltzmann constant.
To find the surface area of Betelgeuse, if the light intensity at a distance d from the star is I, the intensity at a distance 2d will be I/4.
Given that the intensity of light from Betelgeuse at a distance of 643 light-years is 9.88 × 10⁻⁸ W/m²:
I/4 = σAT⁴/(4πd²)
where d = distance to the star in meters.
Solving for A:
A = 4πd²I/(σT⁴)
Convert the distance to meters by multiplying by the number of meters in a light-year:
d = 643 light-years × (9.461 × 10¹⁵ meters/light-year) = 6.07 × 10¹⁸ meters
Substituting the given values into the equation:
A = 4π(6.07 × 10¹⁸ meters)²(9.88 × 10⁻⁸ W/m²)/(5.67 × 10⁻⁸ W/m²/K⁴)(3500 K)⁴
A ≈ 8.98 × 10²¹ m²
Therefore, the surface area of Betelgeuse is approximately 8.98 × 10²¹ square meters.
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A 2.02-kg particle has a velocity (2.03 î − 2.96 ĵ) m/s, and a 2.94-kg particle has a velocity (0.91 î + 5.94 ĵ) m/s.
(a) Find the velocity of the center of mass.
î +
ĵ
m/s
(b) Find the total momentum of the system.
î +
ĵ
kg · m/s
(a)The velocity of the center of mass is (0.829 î + 2.261 ĵ) m/s. and (b) the total momentum of the system is (6.79 î + 8.66 ĵ) kg · m/s.
Momentum is a measure of an object's motion and is the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.
(a) The velocity of the center of mass can be found using the formula:
v_cm = (m1v1 + m2v2) / (m1 + m2)
where m1 and v1 are the mass and velocity of the first particle, and m2 and v2 are the mass and velocity of the second particle. Substituting the given values:
v_cm = (2.02 kg)(2.03 î − 2.96 ĵ) m/s + (2.94 kg)(0.91 î + 5.94 ĵ) m/s / (2.02 kg + 2.94 kg)
v_cm = (4.115 î + 11.242 ĵ) / 4.96
v_cm = 0.829 î + 2.261 ĵ m/s
So, the velocity of the center of mass is (0.829 î + 2.261 ĵ) m/s.
(b) The total momentum of the system can be found by adding the momentum of the two particles:
p_total = m1v1 + m2v2
Substituting the given values:
p_total = (2.02 kg)(2.03 î − 2.96 ĵ) m/s + (2.94 kg)(0.91 î + 5.94 ĵ) m/s
p_total = (4.115 î − 8.798 ĵ) kg · m/s + (2.67494 î + 17.4636 ĵ) kg · m/s
p_total = 6.78994 î + 8.6646 ĵ kg · m/s
So, the total momentum of the system is (6.79 î + 8.66 ĵ) kg · m/s.
Therefore,(a)The velocity of the center of mass is (0.829 î + 2.261 ĵ) m/s. and (b) the total momentum of the system is (6.79 î + 8.66 ĵ) kg · m/s.
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a 60.0kg crate slides from rest at h(1)=1.46m down to a horizontal surface where it passes over a 1.60m patch .the rough patch has a kinetic friction coefficient of 0.34 an incline has 25.0 degrees .what is the maximum height the crate reach
The maximum height the crate reaches is 0.856 m.
To determine the maximum height the crate reaches, we need to use the conservation of mechanical energy:
Initial potential energy = final kinetic energy + final potential energy + work done by friction
Let's calculate each term:
Initial potential energy:
PE₁ = mgh₁ = 60.0 kg * 9.81 m/s² * 1.46 m = 868.98 J
Final kinetic energy:
KE₂ = (1/2)mv², where v is the final velocity of the crate after passing over the rough patch.
To find v, we can use the work-energy principle:
Work done by friction = change in kinetic energy
F * d = (1/2)mv² - 0
where F is the force of kinetic friction and d is the distance over which the force acts.
F = μ_k * N, where N is the normal force acting on the crate.
Since the crate is on an incline, we need to find the components of the gravitational force and the normal force acting on it:
mgsinθ = 60.0 kg * 9.81 m/s² * sin(25.0°) = 243.2 N
mgcosθ = 60.0 kg * 9.81 m/s² * cos(25.0°) = 550.2 N
N = mgcosθ = 550.2 N
F = μ_k * N = 0.34 * 550.2 N = 187.07 N
Now we can solve for v:
187.07 N * 1.60 m = (1/2) * 60.0 kg * v² - 0
v = √(2 * 187.07 N * 1.60 m / 60.0 kg) = 2.47 m/s
Final kinetic energy:
KE₂ = (1/2)mv² = (1/2) * 60.0 kg * (2.47 m/s)² = 183.08 J
Final potential energy:
PE₂ = mgh₂
At the maximum height, the final velocity of the crate is zero, so all the final energy is potential energy. Therefore:
PE₂ = PE₁ - KE₂ - work done by friction
mgh₂ = 868.98 J - 183.08 J - 187.07 N * 1.60 m
Solving for h₂, we get:
h₂ = (868.98 J - 183.08 J - 187.07 N * 1.60 m) / (60.0 kg * 9.81 m/s²) = 0.856 m
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Two charges of Q coul each are placed at two opposite corners of a square. What additional charges q placed at each of the other two corners will reduce the resultant electric force on each of the charges Q to zero? Is it possible to choose these charges so that the resultant force on all the charges is zero?
Answer:
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Physics 2 FRQ, please explain the answers if you can!
(a)To determine the sign of the charge on sphere 1, the students can bring the charged conducting sphere close to it. If the spheres attract each other, then sphere 1 has a charge opposite to the one of the charged sphere. If they repel, then sphere 1 has the same charge as the charged sphere. They can also use the pair of parallel conducting plates to determine the sign of the charge on sphere 1 by observing the direction of the deflection of a charged object placed between the plates.(b) The net charge on spheres 1 and 2 after being touched together is the same due to electrical charge conservation and the angle of the string can be related to the charge on sphere 1 to determine if the same amount of charge is deposited on it each time it is rubbed.
A charge is a fundamental property of matter that describes the amount of electrical energy present in a system.
(a) The following procedure can be used by the students to determine the sign of the charge on sphere 1:
1. Suspend the sphere 1 from an insulating string so that it is isolated and does not touch any other object.
2. Rub the sphere 1 with the cloth to charge it.
3. Bring a conducting sphere of known charge near sphere 1. If the suspended sphere is attracted to the known charged sphere, it means that the charges on both spheres are opposite in nature. If the suspended sphere is repelled, it means that the charges on both spheres are of the same nature.
4. Repeat step 3 with conducting spheres of different sizes to ensure consistency of the observations.
5. Alternatively, the students can use the parallel conducting plates to determine the sign of the charge on sphere 1. They can charge the plates with opposite charges, and then bring the charged sphere near them. If the suspended sphere is attracted towards one of the plates, it means that the charge on the sphere is of the opposite nature. If the sphere is repelled, the charge on the sphere is of the same nature.
The students should observe the behavior of the suspended sphere carefully and take measurements of the distance between the charged sphere or plates and sphere 1 to draw conclusions about the sign of the charge on sphere 1.
(b) 1. . After sphere 1 and sphere 2 are touched together, they will have the same amount of charge. This is due to the property of electrical charge conservation, which states that the total amount of charge in a closed system remains constant.
2. The angle α that the string makes with the vertical can be related to the original charge Q on sphere 1 by the equation tanα = (nQ)/(4πεd^2mg), where ε is the permittivity of free space, m is the mass of sphere 1, and g is the acceleration due to gravity. This equation relates the angle α of the string to the charge on the sphere, allowing the students to determine if the same amount of charge is deposited on sphere 1 each time it is rubbed with the cloth.
3. By measuring the angle α and using the equation, the students can determine if the same amount of charge is deposited on sphere 1 each time it is rubbed with the cloth. If the angle remains constant after multiple rubs, then the same amount of charge is deposited on sphere 1 each time.
Hence,a) To determine the sign of the charge on sphere 1, the students can use a charged conducting sphere and observe if they attract or repel, or use a pair of parallel conducting plates to observe the direction of deflection of a charged object, and b) After being touched together, spheres 1 and 2 have the same net charge due to electrical charge conservation, and the angle of the string can be related to the charge on sphere 1 to determine if the same amount of charge is deposited on it each time it is rubbed.
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