Answers
Since the rope is parallel to the table, the tension in the rope is also equal to the force acting on the cart. The acceleration of the cart will be obtained as 1.32 m/s².
What is the acceleration of the cart?Since the rope is parallel to the table, the forces acting on the system are the tension in the rope (T) and the weight of the hanging block (m1g). Since the rope is parallel to the table, the tension in the rope is also equal to the force acting on the cart.
The acceleration of the system can be found using Newton's second law:
ΣF = ma
where ΣF is the net force on the system, m is the total mass of the system, and a is the acceleration of the system.
The net force on the system is given by:
ΣF = T - m₁g
Substituting the given values, we get:
ΣF = T - m₁g = ma
To solve for the acceleration, we need to find the tension in the rope (T). We can do this by considering the torque on the pulley. The torque on the pulley is equal to the product of the force and the radius of the pulley (τ = Fr). The torque due to the weight of the hanging block is equal to m1g * r, and the torque due to the tension in the rope is equal to T * r. Since the pulley is not accelerating, the net torque on the pulley must be zero:
Στ = m₁g * r - T * r = I * α
where I is the moment of inertia of the pulley and α is the angular acceleration of the pulley. Since the pulley is not slipping, the linear acceleration of the cart is equal to the angular acceleration of the pulley divided by the radius of the pulley (a = α * r).
Substituting for α and a, we get:
m₁g * r - T * r = I * a / r
Solving for T, we get:
T = (m₁g + I * a / r)
Substituting this expression for T into the equation ΣF = T - m₁g, we get:
ma = (m₁g + I * a / r) - m₁g
Simplifying, we get:
a = g * m₁ / (m₂ + I / r²)
Substituting the given values, we get:
a = (9.81 m/s²) * 2.0 kg / (4.0 kg + 0.4 kg-m² / (0.2 m)²) = 1.32 m/s²
Therefore, the acceleration of the cart is 1.32 m/s².
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Related Questions
please help me in this exercise
Answers
a. We can actually see here that the girl have kinetic energy which is respect to the escalator.
b. The kinetic energy does not depend on the chosen reference.
What is kinetic energy?Kinetic energy is a form of energy that an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Kinetic energy is a scalar quantity, meaning it only has magnitude and no direction. The formula for calculating kinetic energy is:
KE = 1/2 × m × v²
Where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
The concept of kinetic energy was first introduced by the French mathematician Gaspard-Gustave de Coriolis in 1829. It was later developed by other scientists such as James Prescott Joule and Hermann von Helmholtz.
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40 POINTS!!!
A wave travels along a stretched horizontal rope. The vertical distance from crest to trough for this wave is 18 cm and the horizontal distance from crest to trough is 26cm.
Part A
What is the wavelength of this wave?
Express your answer using two significant figures
Part B
What is the amplitude of this wave?
Express your answer using two significant figures.
Answers
part a. the wavelength of this wave is 26 cm
part b. The amplitude (A) of a wave is 9 cm
What is wavelength?The wavelength (λ) of a wave is described as the distance between two consecutive points on the wave that are in phase.
In this scenario, the distance between two corresponding points on the wave will be equal to the horizontal distance from crest to trough, which is 26 cm.
Hence, the wavelength of the wave is: λ = 26 cm
The amplitude (A) of a wave is described as the maximum displacement of a particle from its rest position as the wave passes through it.
In this scenario, the vertical distance from crest to trough is 18 cm, which is equal to twice the amplitude.
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a wave has a frequency of 60 hertz and a wave speed of 20 m/s . what is the wavelength
Answers
Answer
the wavelength of the wave is approximately 0.333 meters.
Explanation:
I need help please thank you .:)
Answers
Protons, neutrons, and electrons are the three main subatomic particles that make up atoms.
What is mass number and what is the mass number, number of protons, neutrons, and electrons of the given elements?An oxygen atom has 8 protons, 8 electrons, and its number of neutrons may vary depending on the isotope of oxygen. The more frequently encountered isotope of oxygen is oxygen-16, with 8 neutrons.
The element with 13 protons is aluminum (Al). To find the mass number, we add the number of protons and neutrons in the nucleus. Therefore, the mass number of this aluminum isotope would be 13 + 14 = 27.
If an atom has 7 electrons, it must be nitrogen (N), which has an atomic number of 7.
Number of neutrons = Mass number - Atomic number
Thus, we obtain the number of neutrons by the equation: 14 - 7 = 7
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101. A propeller is accelerated from rest to an angular velocity of 1000 rev/min over a period of 6.0 seconds by a constant torque of 2.0×103N⋅m . (a) What is the moment of inertia of the propeller? (b) What power is being provided to the propeller 3.0 s after it starts rotating?
Answers
The power being provided to the propeller 3.0 seconds after it starts rotating is approximately 21.8 MW and the moment of inertia of the propeller is approximately 0.55 kg⋅m².
What kind of forces do hydraulic systems produce?In hydraulic systems, forces are transferred from one area to another inside an incompressible fluid, such as water or oil. Most aircraft's landing gear and braking systems are hydraulic. In order to function, pneumatic systems need a compressible fluid like air.
I = (τt²) / (2πΔθ)
Substituting the given values, we get:
I = (2.0×10³ N⋅m × (6.0 s)²) / (2π × (1000 rev/min) × (1 min/60 s) × 2π)
I ≈ 0.55 kg⋅m²
P = τω
ω = ω₀ + αt
where ω₀ is the initial angular velocity (0 in this case), α is the angular acceleration, and t is the time.
ω = 0 + (τ/I)t
ω = (2.0×10³ N⋅m) / (0.55 kg⋅m²) × (3.0 s)
ω ≈ 10,909 rad/s
P = (2.0×10³ N⋅m) × (10,909 rad/s)
P ≈ 2.18×10⁷ W
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Why are there spikes in fragmentation debris between the years of 2006 and 2010? Why can this be considered a problem?
Answers
Answer: This is a problem because it can kill.
Explanation: There is no answer to this.
Which is more dense, a cubic meter of water at 2 degrees Celsius or a cubic meter of water at 3 degrees Celsius?
A. 2 Degrees
B. 3 Degrees
C. The Density is the same
Answers
Would you expect the smallest guitar string to produce waves in the glass of water at a higher or lower frequency?
Answers
Answer:
Explanation:
The frequency of the waves produced in the glass of water will depend on the frequency of the sound wave produced by the guitar string.
The frequency of a guitar string is inversely proportional to its length, thickness, and tension. Therefore, the thinnest string on a guitar will have the highest frequency, assuming that all other variables are kept constant.
Since the frequency of the sound wave produced by the thinnest guitar string is higher, we would expect the waves produced in the glass of water to also have a higher frequency than those produced by a thicker guitar string.
The following graph shows the kinetic energy of a roller coaster car as it passes through a loop.
Roller Coaster Car's Kinetic Energy
O B.
Kinetic Energy (kilojoules)
OC.
300
250
200
150
100
50
0
1
What was the most likely cause for the rise in kinetic energy after 2.5 seconds?
A. The roller coaster was pulled with decreasing gravitational force.
The roller coaster began slowing down.
The roller coaster started gaining elevation.
O D. The roller coaster began speeding up.
2
3
Time (s)
Reset
Next Question
5
6
Answers
Both the object's speed and mass affect how much kinetic energy it contains. Motional energy is produced while the roller coaster descends. The roller coaster's bottom of the track position is where the most kinetic energy is produced. Kinetic energy changes to potential energy when it starts to rise.
Energy changeThrough the transformation of potential energy into kinetic energy, roller coasters are propelled forward. As they are propelled to the peak of the first hill, the roller coaster vehicles accumulate potential energy. The cars drop as the potential energy is transformed into kinetic energy.Kinetic energy is produced by converting potential energy. As the car navigates hills, loops, twists, and turns, this process keeps happening. With height, it increases potential energy, but as it slows down, it loses kinetic energy. Energy only changes from one form to another; it never creates or destroys itself.For more information on kinetic energy of roller coaster kindly visit to
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7. How do paragraphs 12-13 contribute to the development of ideas in the text? The Monroe Doctrine and American Imperialism
Answers
INTERTEXTUALITY is described as the modeling of a text's meaning by another text.
it can also be defined as the connections between language, images, characters, themes, or subjects depending on their similarities in language, genre or discourse. This view recognizes that the text is always influenced by previous texts.''
What does the text contain?A text contains many layers of accumulated, cultural, historical, and social knowledge, which continually adds to and affects one another. The function and effectiveness of intertextuality can often depend quite a bit on the reader’s prior knowledge and understanding before reading the secondary text; parodies and allusions depend on the reader knowing what is being parodied or alluded to.
11. Julia Kristeva, a French semiotician, coined the term "intertextuality" in the 1960s. The term was coined by her using the Latin verb intertexto, which means "to intermingle while weaving." According to Kristeva, every piece of contemporary literature is intertextual with literature from the past.
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103. A uniform rod of length L and mass M is held vertically with one end resting on the floor as shown below. When the rod is released, it rotates around its lower end until it hits the floor. Assuming the lower end of the rod does not slip, what is the linear velocity of the upper end when it hits the floor?
Answers
When the rod is released, it begins to rotate around its lower end, and its potential energy is gradually converted into kinetic energy. At the instant just before it hits the floor.
What is energy ?Energy is the ability of a system to perform work. It is a scalar physical quantity that is associated with objects and systems and can come in many different forms, such as mechanical, thermal, electrical, chemical, and nuclear energy. Energy can be transferred from one object to another, or from one form to another, but it cannot be created or destroyed according to the law of conservation of energy. The SI unit of energy is the joule (J), but other common units include the calorie, kilowatt-hour, and electronvolt.
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WILL MARK BRAIN THING HURRY PLS
Imagine that you are an extraterrestrial creature who lives in the extrasolar planetary system where Proxima-b resides. You are studying the Sun, which to you appears to be an exceptionally bright star. You do not know it, but your optical technology is almost identical to humanity’s optical technology. What evidence might indicate to you that (a) planets orbit that star (the Sun) and (b) that at least one of those planets appears to lie within the habitable zone and would thus be a potentially habitable planetary body?
Answers
a.) The evidence for planets orbiting the Sun might be :
Periodic variations in the brightness of the SunChanges in the position of the starb. Evidence for potentially habitable planets might come in the form of
Transit observationsSpectral observationsWhat is meant by planets?A planet is described as a celestial body that is in orbit around the Sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and has cleared the neighborhood around its orbit.
There is a slight decrease in the brightness of the star as planets pass in front of it, blocking a fraction of its light.
The extraterrestrial being might notice periodic fluctuations that are consistent with a planet's orbital period if it can track the Sun's brightness over time.
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What would be the intensity of a sound wave produced by a 150 Watt speaker from a distance of 5.8 meters? (write your answer to two digits)
Answers
The relationship between a sound wave's intensity and pressure amplitude (also known as pressure variation p) is. I is equal to (p) 2 2 v w, where is the thickness of the substance that the sound is contained in.
Describe a sound wave.
Hence, a sound wave is made up of periodically occurring compressions and compression and rarefaction, or areas of high and low pressure, that are travelling at a specific pace. In other words, it consists of a regular (i.e., oscillating or vibrating) change in pressure that takes place around the optimum pressure that is present at a specific time and location.
A sound wave is created by a speaker in what way?
A speaker creates a sound by vibrating a cone, which causes air molecules to vibrate. A speaker in Figure 17.2. 2 vibrates with a consistent frequency and amplitude, causing motions in the molecules of the surrounding air. The speaker transfers power to the air as it vibrates back and forth, primarily as thermal energy.
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If the universe were to suddenly begin shrinking rather than continue expanding, how would it affect the cosmic microwave background radiation?
A. It would decrease in temperature.
B. It would blue-shift.
C. It would red-shift.
D. It would increase in temperature.
Answers
If the universe were to suddenly begin shrinking rather than continuing to expand, it would have a significant effect on the cosmic microwave background radiation (CMB).
The CMB is the afterglow of the Big Bang and is observed as a nearly uniform background radiation in all directions. It is thought to have been emitted when the universe was about 380,000 years old and had cooled enough for neutral atoms to form.
If the universe were to suddenly begin shrinking, the photons in the CMB would lose energy as they travel through the contracting space. This would cause the CMB radiation to shift to shorter wavelengths, which is known as blue-shifting.
Therefore, the correct answer is B. It would blue-shift.
In the Roman soldier model for refraction, a muddy stream crosses the road they are on walking on at 45°. Will the soldiers in the front row all hit the water at the same time?
A. Sometimes
B. Yes
C. No
D. Not enough info
Answers
Therefore, even if the soldiers in the front row are lined up perfectly and walk at the same speed, they may not all hit the water at the same time due to the uneven terrain and the resistance of the mud. Additionally, if the stream is flowing, the soldiers may be pushed in different directions by the current, further increasing the likelihood that they will not hit the water at the same time.
Therefore, the answer is C: No, the soldiers in the front row are unlikely to hit the water at the same time due to the uneven terrain and resistance of the mud.
C. No.
The Roman soldier model for refraction assumes that light travels faster in air than in water. When light passes from a medium of lower refractive index (air) to a medium of higher refractive index (water), it bends towards the normal (a line perpendicular to the surface of the water at the point of incidence).
In the case of the muddy stream crossing the road at an angle of 45 degrees, the soldiers in the front row will hit the water first, and then the soldiers behind them will hit the water progressively later. This is because the light from the front of the stream reaches the soldiers' eyes first, while the light from the back of the stream takes a longer path and reaches their eyes later.
Therefore, the soldiers in the front row will not hit the water at the same time.
The length of the river span of a bridge is 2799.0 ft. The total length of the bridge is 6998ft. Convert the length of the river span of the bridge to meters.
Answers
According to the question the length of the river span of the bridge in meters is 853.3232 m.
What is Length?Length is a physical quantity that measures the distance between two points. It is one of the fundamental units in the International System of Units (SI). It is usually measured in meters, although it can also be measured in other units such as centimeters, kilometers, feet, yards, miles, and so on.
The length of the river span of the bridge is 2799.0 ft. To convert this length to meters, we need to use a conversion factor. There are 0.3048 meters in one foot, so the conversion factor we will use is 1 ft
= 0.3048 m.
To convert 2799.0 ft to meters, we multiply by the conversion factor:
2799.0 ft * 0.3048 m/ft
= 853.3232 m
Therefore, the length of the river span of the bridge in meters is 853.3232 m.
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Raphael wants to test the effect of different food types on the growth rate of mice. He measures the mass of thirty mice and separates them into three groups. Each group is given a different type of feed. All of the mice are kept in identical environments and given access to clean water.
After three months, Raphael measures the mass of the mice again. The results of Raphael's experiment are shown below.
Food Type Average Growth (g)
oat grains 1.5 g
cereal flakes 0.3 g
sunflower seeds 2.1 g
Which of the following is a fact that Raphael can determine from his experiment?
A.
Mice do not like the taste of cereal flakes.
B.
Sunflower seeds are the best type of food to feed pet mice.
C.
Mice that ate sunflower seeds gained an average of 2.1 grams.
D.
Bigger mice are more desirable as pets than smaller mice.
Answers
Mice that ate sunflower seeds gained an average of 2.1 grams that Raphael can determine from his experiment. Each group is given a different type of feed.
What is grams ?Grams (g) is a unit of measurement for mass in the International System of Units (SI). It is the base unit of mass in the SI, and is defined as being equal to the mass of a physical prototype, which is kept at the International Bureau of Weights and Measures. In practical terms, 1 gram is equal to 0.0352739619 ounces, or 0.00220462262 pounds. Grams are often used to measure the weight of food, medicines, and other small objects.
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What inductance must be put in series with a 100-kiloohm resistor at 1.0-MHz for a total impedance
of 150 kiloohm
Answers
An inductance of 0.0191 H (19.1 mH) must be put in series with the 100-kiloohm resistor to achieve a total impedance of 150 kiloohm at 1.0 MHz.
What is Induction?
Induction refers to the production of an electric or magnetic effect through the relative motion or change in magnitude of a magnetic field or electric current. This phenomenon is based on the principles of electromagnetism and is commonly used in various electrical and electronic devices, including transformers, motors, generators, and wireless charging systems.
The total impedance can be calculated using the following formula:
Z_total = sqrt([tex]R^{2}[/tex] X_[tex]L^{2}[/tex])
where R is the resistance (100 kiloohm) and X_L is the inductive reactance. We can rearrange this formula to solve for X_L:
At 1.0 MHz, the angular frequency is:
w = 2πf = 2π × 1.0 × [tex]10^{6}[/tex] = 6.28 × [tex]10^{6}[/tex]ad/s
The inductive reactance can be calculated using the following formula:
X_L = wL
where L is the inductance in henries. We can rearrange this formula to solve for L:
L = X_L / w
Now we can substitute the given values and solve for L:
X_L = sqrt((150 ×[tex]10^{3}[/tex]) - (100 ×[tex]10^{3}[/tex])) = 120 × [tex]10^{3}[/tex] ohm
L = X_L / w = 120 × [tex]10^{3}[/tex] ohm / 6.28 × [tex]10^{6}[/tex] rad/s = 0.0191 H
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The element of an electric fire with an output of 1.5kw is a cylinder 0.3m long and 0.04 in radius calculate temperature if it behave as black body
Answers
The temperature of the electric fire element is 18.3 K
How do we calculate?
We use the formula at:
P = σAT^4
where P= power radiated,
A = surface area of the black body,
σ =Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4),
T = temperature in Kelvin.
P = 1500 W
The surface area of a cylinder is gotten by:
A = 2πrh + 2πr^2
A = 2π(0.04 m)(0.3 m) + 2π(0.04 m)^2
A = 0.0902 m^2
Substituting the values into the Stefan-Boltzmann law, we have:
1500 W = (5.67 × 10^-8 W/m^2K^4)(0.0902 m^2)T^4
T^4 = 4196.9
T = 18.3 K
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which statement about magnets is correct
Answers
what are the options???????????
hot water is put into a refrigerator. if the refrigerator is power off, is that true that the more the water inside the refrigerator, the slower the temperature increase ?
Answers
No, that is not necessarily true. The temperature inside a refrigerator is regulated by a thermostat, which detects the temperature inside and turns the cooling system on or off as needed to maintain a consistent temperature. When hot water is put into a refrigerator, the temperature inside will initially increase as the refrigerator works to cool the water down to the desired temperature.
The amount of water inside the refrigerator can affect how long it takes to cool down to the desired temperature, but once the temperature has stabilized, the amount of water will not have a significant impact on the rate at which the temperature increases if the refrigerator is powered off. In fact, if the refrigerator is powered off, the temperature inside will gradually increase regardless of the amount of water inside.
1. A kid jumps straight up at 7.20 m/s. How long will he remain in the air?
Answers
The time takes the kid to remain in the air is 0.735 s.
What is time?Time is the duration of an events. The s.i unit of time is seconds.
To calculate how long the kid will be in the air, we use the formula below.
Formula:
t = (v-u)/g.................................... Equation 1Where:
t = Timev = Final Velocityu = Initial velocityg = Acceleration due to gravityFrom the question,
Given:
u = 7.20 m/sv = 0 m/sg = -9.8 m/s² (Going against the force of gravity)Substitute these values into equation 1
t = (0-7.20)/-9.8t = -7.20/-9.80t = 0.735 secondsHence, the time is 0.735 s.
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Question 15 of 32
A bungee jumper jumps off a bridge and bounces up and down several times.
She finally comes to rest 30 m below the bridge from which she just jumped.
If her mass is 50 kg and the spring constant of the bungee cord is 10 N/m,
how much energy was lost due to air resistance while she was bouncing?
(Recall that g = 9.8 m/s²)
A. 7330 N
B. 9200 N
C. 10,200 N
D. 8605 N
Answers
C. 10,200 N is how much energy was lost due to air resistance while she was bouncing
How much energy was lostThe energy lost due to air resistance while the bungee jumper was bouncing can be calculated by finding the total mechanical energy of the system at the beginning of the jump and comparing it to the total mechanical energy at the end of the jump.
At the beginning of the jump, the total mechanical energy is given by:
Ei = mgh
where m is the mass of the bungee jumper, g is the acceleration due to gravity, and h is the height of the bridge. Therefore, at the beginning of the jump:
50 x 30 x 10 - 1/2 x 30^2 x 10
= 15000 - 4500
= 10,200 N
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5) A Brachiosaurus moves with a momentum of 134,052 kgm / s What is the Brachiosaurus' mass it is moving at 3.9m / s ?
Answers
The mass of Brachiosaurus moves with a momentum of 134,054 kgm/s and the velocity is 3.9 m/s, which is 34.37 kg.
The momentum is the product of mass and velocity. The momentum is the vector quantity and the unit of momentum is Kgm/s.
Momentum = mass × velocity
mass = momentum/velocity
momentum = 134,052 kgm / s
velocity = 3.9 m/s
mass = 134052 / 3.9
= 34.37 kg
Thus, the mass of Brachiosaurus is 34.37 kg.
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The radius of the earth is 6.4 x 10^6 m . Calculate the angular and linear velocity of a participle at the earth's surface.
Answers
Answer: the angular velocity of a particle at the Earth's surface is approximately 7.27 x 10^-5 rad/s, and the linear velocity of the particle is approximately 464.1 m/s.
Explanation:
Look at each written description and equation. Determine if the solution to the equation answers the question by selecting Yes or No.
A
A long-distance athlete can run 12
kilometer in 3 minutes. How many kilometers can he run in an hour?
12 km360 hr=12×603
Yes No B
A search and rescue drone can scan 0.5 hectare in 2 minutes. How many hectares per minute can the drone scan?
510 ha2 min=510×21
Yes No C
In 15 minutes a crew of highway workers paved 110
mile. If they work at the same rate, what portion of a mile will they pave in 1 hour?
14 hr110 mi=14×101
Yes No D
A soup recipe uses 112
cups of water for every 14
teaspoon of seasoning. If a large batch of soup is made using 1 teaspoon of seasoning, how many cups of water is needed?
32 c14 tsp=32×41
Yes No
Answers
As you sit in a fishing boat, you notice that 12 waves pass the boat every 45 s. If the distance from one crest to the next is 9.0 m what is the speed of these waves?
Express your answer to two significant figures and include the appropriate units.
Answers
The frequency of the waves can be calculated as the number of waves passing a given point per unit of time. In this case, the frequency is:
f = (number of waves) / (time)
f = 12 waves / 45 s
f = 0.267 Hz
The wavelength is the distance between two adjacent wave crests, which is given as 9.0 m in the problem.
What is the speed of these waves?The speed of the wave can be calculated using the formula:
v = f × λ
where v is the wave speed, f is the frequency, and λ is the wavelength.
Substituting the values given, we get:
v = 0.267 Hz × 9.0 m
v = 2.40 m/s
Therefore, the speed of the waves is 2.40 m/s (to two significant figures).
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5. A risk factor is an aspect of the child or environment that increases the probability of poor outcomes.
Name at least two (2) risk factors of childhood and how these factors might affect their ability to learn in
school. (2 Points)
Anyone pls
Answers
The two risk factors that can affect the ability of a child to learn in school is poor parenting and malnutrition.
What is a risk factor?A risk factor can be defined as any predisposing factor that can expose an individual to harm.
A risk factor that affects a child is an aspect of the child or environment that increases the probability of poor outcomes.
The two risk factors that can affect the ability of a child to learn in school include the following:
Poor parenting: When there is lack of understanding and love between the couple is affects the emotions of the children.Malnutrition: The brain of the child is yet to fully develop and this can be help through adequate nutrition.Learn more about nutrition here:
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A 6.5kg ball with radius 8 cm rolls without Stopping down a Lone at 5m/s. calculate its kenetic energy (I= ² / 3 MR²)
Answers
KE = 1/2 mv^2 + 1/2 Iω^2
where KE is the total kinetic energy, m is the mass of the ball, v is its velocity, I is the moment of inertia of the ball, and ω is its angular velocity.
To calculate the moment of inertia I of the ball, we can use the formula you provided:
I = (2/3)MR^2
where M is the mass of the ball and R is its radius.
Substituting the given values, we have:
M = 6.5 kg
R = 0.08 m
So, the moment of inertia of the ball is:
I = (2/3)(6.5 kg)(0.08 m)^2 ≈ 0.027 kg m^2
Now we can calculate the translational kinetic energy of the ball:
KE_trans = 1/2 mv^2 = 1/2 (6.5 kg)(5 m/s)^2 = 81.25 J
Next, we need to calculate the angular velocity ω of the ball. For a rolling ball without slipping, the tangential velocity v and the angular velocity ω are related by:
v = Rω
So, we have:
ω = v/R = 5 m/s / 0.08 m = 62.5 rad/s
Finally, we can calculate the rotational kinetic energy of the ball:
KE_rot = 1/2 Iω^2 = 1/2 (0.027 kg m^2)(62.5 rad/s)^2 ≈ 52 J
Therefore, the total kinetic energy of the rolling ball is:
KE = KE_trans + KE_rot = 81.25 J + 52 J ≈ 133.25 J
So, the kinetic energy of the rolling ball is approximately 133.25 J.
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50 POINTS!!
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A wave oscillates 5.0 times a second and has a speed of 4.0 m/s
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What is the frequency of this wave?
Express your answer to two significant figures and include the appropriate units.
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What is the period of this wave?
Express your answer to two significant figures and include the appropriate units.
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What is the wavelength of this wave?
Express your answer to two significant figures and include the appropriate units.
Answers
The answers are:
Frequency = 5.0 HzPeriod = 0.20 sWavelength = 0.80 mHow to solve for the frequencyThe frequency (f) of a wave is the number of oscillations (or cycles) per second and is measured in Hertz (Hz). The period (T) of a wave is the time it takes for one complete oscillation and is measured in seconds (s). The wavelength (λ) of a wave is the distance between two consecutive peaks (or troughs) and is measured in meters (m).
Given:
Frequency (f) = 5.0 Hz
Speed (v) = 4.0 m/s
We can use the formula:
f = v/λ
to find the wavelength of the wave.
Solving for λ, we get:
λ = v/f = 4.0 m/s / 5.0 Hz = 0.80 m
Therefore, the wavelength of the wave is 0.80 m.
To find the period of the wave, we can use the formula:
T = 1/f
Substituting the given frequency value, we get:
T = 1/5.0 Hz = 0.20 s
Therefore, the period of the wave is 0.20 s.
So the answers are:
Frequency = 5.0 Hz
Period = 0.20 s
Wavelength = 0.80 m
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