Answer:
Approximately [tex]0.21\; {\rm m}[/tex].
(Assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
As the bottle cap slows down, it lost kinetic energy [tex](\text{KE})[/tex]: [tex]\Delta \text{KE} = (1/2)\, m\, (u^{2} - v^{2})[/tex], where [tex]m[/tex] is the mass of the cap, [tex]v = 1.0\; {\rm m\cdot s^{-1}}[/tex], and [tex]u = 2.0\; {\rm m\cdot s^{-1}}[/tex].
The amount of kinetic energy lost should also be equal to the sum of:
gain in gravitational potential energy ([tex]\text{GPE}[/tex]), andwork that friction has done on the cap.Let [tex]d[/tex] denote the distance that the cap has travelled along the ramp. The height of the cap would have increased by:
[tex]\Delta h = d\, \sin(\theta)[/tex], where [tex]\theta = 20^{\circ}[/tex] is the angle of elevation of the ramp.
The [tex]\text{GPE}[/tex] of the cap would have increased by:
[tex]\Delta \text{GPE} = m\, g\, \Delta h = m\, g\, d\, \sin(\theta)[/tex].
To find the friction on the cap, it will be necessary to find the normal force that the ramp exerts on the cap.
Let [tex]\theta = 20^{\circ}[/tex] denote the angle of elevation of this ramp. Decompose the weight of the cap [tex]m\, g[/tex] (where [tex]m[/tex] is the mass of the cap) into two directions:
Along the ramp: [tex]m\, g\, \sin(\theta)[/tex],Tangential to the ramp: [tex]m\, g\, \cos(\theta)[/tex].The normal force on the cap is entirely within the tangential direction.
Since the cap is moving along the ramp, there would be no motion in the tangential direction. Forces in the tangential direction should be balanced. Hence, the normal force on the cap will be equal in magnitude to the weight of the cap in the tangential direction: [tex]F_{\text{normal}} = m\, g\, \cos(\theta)[/tex].
Since the cap is moving, multiply the normal force on the cap by the coefficient of kinetic friction [tex]\mu_{\text{k}}[/tex] to find the friction [tex]f[/tex] between the ramp and the cap:
[tex]f = \mu_{\text{k}}\, F_{\text{normal}}[/tex].
After a distance of [tex]x[/tex] along the ramp, friction would have done work of magnitude:
[tex]\begin{aligned} (\text{work}) &= f\, s \\ &= (\mu_{\text{k}}\, F_{\text{normal}})\, (d) \\ &= \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d\end{aligned}[/tex].
Overall:
[tex]\begin{aligned} \Delta \text{KE} &= \Delta \text{GPE} + \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d \\ &= m\, g\, \sin(\theta)\, d + \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d \\ &= m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))\, d\end{aligned}[/tex].
At the same time:
[tex]\Delta \text{KE} = (1/2)\, m\, (v^{2} - u^{2})[/tex].
Therefore:
[tex]\displaystyle \frac{1}{2}\, m\, (v^{2} - u^{2}) = m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))\, d[/tex].
[tex]\begin{aligned}d &= \frac{m\, (u^{2} - v^{2})}{2\, m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))} \\ &= \frac{u^{2} - v^{2}}{2\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))} \\ &= \frac{(2.0)^{2} - (1.0)^{2}}{2\, (9.81)\, (\sin(20^{\circ}) + 0.40\, \cos(20^{\circ}))}\; {\rm m} \\ &\approx0.21\; {\rm m}\end{aligned}[/tex].
Horticulture (HURRY) 120 pts
Specialized technology works well in
, where the uniformity of the crop encourages tight-focused machines rather than unspecialized machines that can be adapted for multiple tasks
Horticulture is a field that greatly benefits from specialized technology. This is because the uniformity of crops in horticulture allows for machines that are tightly focused on specific tasks.
These machines are designed to perform specialized functions such as planting, pruning, and harvesting. This specialized equipment ensures that the crops are tended to with precision and care, which results in higher yields and better quality produce.
In contrast, unspecialized machines that can be adapted for multiple tasks may not perform as well in horticulture because they lack the precision and efficiency required for these specialized tasks.
So, in horticulture, specialized technology works well because it allows for precise and efficient handling of crops, which ultimately leads to better yields and higher-quality produce.
To learn more about horticulture, refer below:
https://brainly.com/question/28991945
#SPJ11
A typical color television draws about 2. 5 A
when connected to an 89 V source.
What is the effective resistance of the T. V.
set?
Answer in units of Ω
The effective resistance of the TV set is 35.6 ohms (Ω).
To find the effective resistance of the TV set, we can use Ohm's Law, which states that Voltage (V) = Current (I) × Resistance (R). We need to rearrange the formula to solve for resistance: R = V / I.
Given the information in your question:
Current (I) = 2.5 A
Voltage (V) = 89 V
Now we can calculate the resistance (R):
R = V / I
R = 89 V / 2.5 A
R = 35.6 Ω
The effective resistance of the TV set is 35.6 ohms (Ω).
To learn more about current, refer below:
https://brainly.com/question/13076734
#SPJ11
Do the Pressure vs. Depth Lab (record Describe how the distance the water
your activity)
•When will the water flow out the farthest: when the water is nearly full, half-full, or nearly empty?
•Hold the bottle over the bucket so that the water will flow out the hole into the bucket and loosen the bottle cap.
Observe the flow of water. PUT THE CAP BACK ON!
•Describe how the distance the water flowed out changed as the depth of the water changed.
fill in the blanks
•The pressure of a fluid _____ as depth increases. So pressure and depth are _____ proportional.
This can be written as _____
Pressure vs. Depth Lab:
The water will flow out the farthest when the bottle is nearly full.As the depth of the water increased, the distance the water flowed out also increased.The pressure of a fluid increases as depth increases. So pressure and depth are directly proportional.This can be written as P ∝ d, where P is pressure and d is depth.What is pressure?Pressure is defined as the force per unit area applied on an object. It is a scalar quantity, which means it only has magnitude and no specific direction.
It is often measured in units of Pascals (Pa), which is equivalent to one Newton of force per square meter of area. Pressure can be caused by the weight of an object, the force applied by a fluid, or the collision of particles with a surface.
Find out more on pressure here: https://brainly.com/question/28012687
#SPJ1
in the diagram below are shown snapshots of the changing electric and magnetic field that make up a beam of light. each frame has a time stamp, given in terms of the period of oscillation of the fields. in what direction is the beam of light moving?
Answer:
yes
Explanation:
27. A bicycle wheel on a repair bench can be
accelerated either by pulling on the chain that
is on the gear or by pulling on a string wrapped
around the tire. The tire's radius is 0. 38 m, while
the radius of the gear is 0. 14 m. What force would
you need to pull on the string to produce the
same acceleration you obtained with a force of
15 N on the chain?
You would need to pull on the string with a force of 5.76 N to produce the same acceleration you obtained with a force of 15 N on the chain.
To calculate the force needed to produce the same acceleration as a force of 15 N on the chain, we need to use the formula:
force = mass × acceleration
First, we need to calculate the acceleration of the bicycle wheel when a force of 15 N is applied to the chain. We can use the formula:
acceleration = [tex]\frac{acceleration}{mass}[/tex]
Assuming the mass of the wheel is negligible, we can simplify this to:
acceleration = [tex]=\frac{force}{0.38}[/tex] = [tex]\frac{15N}{0.38}[/tex]=39.47 N/m
Now we can calculate the force needed to produce the same acceleration when pulling on the string wrapped around the tire. We can use the formula:
force = mass × acceleration
The mass of the wheel does not change, so we can use the same acceleration value we calculated earlier. However, the radius of the tire is different from the radius of the gear, so we need to take this into account.
The circumference of the tire is 2π(0.38 m) = 2.39 m, while the circumference of the gear is 2π(0.14 m) = 0.88 m.
This means that the force needed to produce the same acceleration when pulling on the string is:
force = mass × acceleration × [tex](\frac{radius of the gear}{radius of the tire} )[/tex]
= 0.38 kg x 39.47 N/m x [tex](\frac{0.14 m}{0.38 m} )[/tex]
= 5.76 N
To know more about the different types of forces visit:
https://brainly.com/question/13191643
#SPJ11
Explain how meteorologists use weather data to predict the probability of a catastrophic wildfire.
Meteorologists use weather data to predict the probability of a catastrophic wildfire by analyzing several factors that contribute to fire risk. Here are some of the ways they do this:
1. Temperature: High temperatures can increase the risk of wildfires as they cause vegetation to dry out and become more flammable. Meteorologists track temperature changes to identify periods of high risk.
2. Humidity: Low humidity levels also contribute to an increased risk of wildfires. This is because dry air can cause vegetation to dry out more quickly. Meteorologists monitor humidity levels to help predict fire risk.
3. Wind speed and direction: Strong winds can rapidly spread wildfires, and wind direction can also influence the direction in which a fire spreads.
Meteorologists track wind speed and direction to help predict the potential spread of a wildfire.
4. Precipitation: Rain and other forms of precipitation can reduce the risk of wildfires by providing moisture to vegetation.
Meteorologists monitor precipitation patterns to predict how dry or moist the vegetation will be, which can affect fire risk.
5. Drought: Long periods of drought can increase the risk of wildfires by creating dry conditions. Meteorologists monitor drought conditions to predict fire risk.
By analyzing these weather factors, meteorologists can create models to predict the probability of a catastrophic wildfire.
They can also issue warnings and alerts to help people prepare for and respond to these events.
To know more about Meteorologists refer here
https://brainly.com/question/2542007#
#SPJ11
How far can you get away from your little brother (in meters) who has a squirt gun if you can travel at a speed of 3.0 m/s and you have 10.0 s before he sees you?
You can get 30.0 meters away from your little brother if you travel at a speed of 3.0 m/s for 10.0 seconds.
To solve this problem, we can use the formula:
distance = speed x time
Given, your speed is 3.0 m/s and you have 10.0 s to get away from your little brother. Using the formula, we get:
distance = 3.0 m/s x 10.0 s = 30.0 m
Therefore, you can get 30.0 meters away from your little brother if you travel at a speed of 3.0 m/s for 10.0 seconds. However, keep in mind that your little brother may also be able to run or move at a certain speed, so this distance may not guarantee complete safety.
To know more about speed, refer here:
https://brainly.com/question/17661499#
#SPJ11
A 10.0 cm object is 5.0 cm from a concave mirror that has a focal length of 12 cm. what is the distance between the image and the mirror? 3.5 cm –3.5 cm 8.6 cm –8.6 cm
Concave mirrors in The Mirror Equation. When objects are positioned at a specific location in front of a concave mirror, ray diagrams can be used to establish the image location, size, orientation, and type of image created. Here the distance between the image and the mirror is -8.6 cm. The correct option is D.
In order to retrieve the numerical data on image size and distance that ray diagrams are unable to offer, the Mirror formula is applied. The link between the object distance (v), image distance (u), and focal length (f) is also established by the Mirror formula.
The mirror formula is given as:
1/v + 1/u = 1/f
Based on the distance it is:
1 / f = 1 / d₂ - 1 / d₁
1 / 12 = 1 / v + 1 / 5.0
1 / v = - 7 / 60
d₂ = -8.6 cm
Thus the correct option is D.
To know more about mirror formula, visit;
https://brainly.com/question/30242207
#SPJ12
a computer to be used in a satellite must be able to withstand accelerations of up to 22 times the acceleration due to gravity. in a test to see whether it meets this specification, the computer is bolted to a frame that is vibrated back and forth in simple harmonic motion at a frequency of 8.30 hz. what is the minimum amplitude of vibration that must be used in this test?
The minimum amplitude of vibration that must be used in the test is 0.0312 m.
The maximum acceleration experienced by the computer will occur at the maximum displacement from the equilibrium position, which is equal to the amplitude of vibration (A). The maximum acceleration (a) is given by:
a = -4π²f²A
where f is the frequency of vibration.
To withstand 22 times the acceleration due to gravity (g), the amplitude of vibration must satisfy:
A >= 22g / (4π²f²)
Substituting g = 9.8 m/s² and f = 8.30 Hz, we get:
A >= 22(9.8) / (4π²(8.30)²) = 0.0312 m
As a result, the minimum amplitude of vibration required for the test is 0.0312 m.
To know more about the Harmonic motion, here
https://brainly.com/question/14449991
#SPJ4
a 193-v battery, an inductor, and a resistor are connected in series as shown in the diagram below. a two-way switch makes it possible to include or exclude the battery. the switch that had been in position 1 for a long time is suddenly moved to position 2. (enter your answers to at least two decimal places.) (a) what is the voltage across the resistor at the end of four time constants? 3.53 correct: your answer is correct. v (b) at this time, what is the voltage across the inductor? .107 incorrect: your answer is incorrect.
As for the Voltage across the inductor, it is equal to zero after four time constants because the current in the circuit has decreased to zero. Therefore, the correct answer for part (b) is zero, not 0.107.
When the switch is in position 1, the circuit is closed and the battery is connected in series with the inductor and resistor. This means that current flows through the circuit, causing a magnetic field to be generated by the inductor. However, when the switch is suddenly moved to position 2, the circuit is opened and the battery is no longer connected.
After the switch is moved, the current in the circuit begins to decrease due to the inductor's opposition to changes in current. The time it takes for the current to decrease to 36.8% of its original value is known as the time constant, which is calculated by dividing the inductance of the inductor by the resistance of the resistor.
After four time constants, the voltage across the resistor can be calculated using the equation V = V0 * e^(-t/RC), where V0 is the initial voltage, t is the time elapsed, R is the resistance, and C is the capacitance. Plugging in the values given, we get V = 193 * e^(-4/RC) = 3.53 volts.
As for the voltage across the inductor, it is equal to zero after four time constants because the current in the circuit has decreased to zero. Therefore, the correct answer for part (b) is zero, not 0.107.
To Learn More About Voltage
https://brainly.com/question/1176850
SPJ11
A small truck is moving at 20 m/s. A large truck, with twice the mass, is traveling at half the speed. How does the momentum of the larger truck compare to the smaller truck?
The momentum of an object is directly proportional to its mass and velocity. Therefore, the momentum of the larger truck can be calculated as follows:
Momentum of larger truck = (2 x mass of smaller truck) x (1/2 x velocity of smaller truck)
Momentum of larger truck = (2 x m) x (0.5 x 20)
Momentum of larger truck = m x 20
This shows that the momentum of the larger truck is equal to the momentum of the smaller truck, as the increased mass is balanced by the decreased velocity.
In other words, the momentum of an object depends on both its mass and velocity, and changes in one factor can be compensated by changes in the other factor to maintain the same momentum.
To know more about Momentum, refer here:
https://brainly.com/question/30677308#
#SPJ11
when traveling at 55mph, how many feet do you need to stop?
When traveling at 55mph, it takes approximately 211 feet to stop.
To determine how many feet you need to stop when traveling at 55 mph, you'll need to consider the following terms:
1. Speed: In this case, it's 55 mph.
2. Conversion factor: To convert mph to feet per second (fps), you need to multiply by 1.467.
3. Braking distance: The distance required to come to a complete stop from a certain speed, which is affected by factors such as the road conditions and vehicle's braking system.
Now, let's calculate the stopping distance:
Step 1: Convert the speed to feet per second.
55 mph × 1.467 = 80.685 fps
Step 2: Calculate the braking distance using the general rule of thumb (which assumes good road conditions and properly functioning brakes) that it takes 1.5 feet to stop for every 1 fps of speed.
80.685 fps × 1.5 = 121.028 feet
So, when traveling at 55 mph, you would need approximately 121 feet to stop. Please note that this is a rough estimate and can vary depending on factors such as road conditions and the efficiency of the vehicle's braking system.
Learn more about Braking distance: https://brainly.com/question/13666022
#SPJ11
a weight lifter must expert of force to lift a set of barbells off the ground
It should be noted that the statement regarding the weightlifter is true.
How to explain the informationA weightlifter must apply a certain amount of force to lift a set of barbells off the ground. This force is known as the lifting force and it must be greater than the weight of the barbells in order to overcome the force of gravity and lift the barbells.
The amount of lifting force required will depend on the weight of the barbells and the strength of the weightlifter's muscles. The weightlifter can increase their lifting force by improving their strength and technique through training and practice.
Learn more about weight on
https://brainly.com/question/27855042
#SPJ1
A weight lifter must be expert of force to lift a set of barbells off the ground
true or false
imagine that you have a vehicle traveling on mars. the shortest distance between earth and mars is 56 * 106 km; the longest is 400 * 106 km. what is the delay time for the signal that you send to mars from earth? can you use radio signals to give commands to the vehicle?
The delay time for the signal that you send to mars from earth is 22.4 minutes.
The delay time for a signal sent from Earth to Mars depends on the distance between the two planets and the speed of light, which is approximately 299,792 km/s. Using the shortest distance of 56 * 10⁶km, the delay time would be approximately 187 seconds, or just over 3 minutes. Using the longest distance of 400 * 10⁶ km, the delay time would be approximately 22.4 minutes. Radio signals can be used to send commands to the vehicle on Mars, but the delay time must be taken into account.
This delay can make real-time communication with the vehicle difficult, so some form of autonomous or pre-programmed control may be necessary. Additionally, the distance between Earth and Mars can vary depending on the relative positions of the two planets, so the delay time can also vary. However, despite these challenges, radio communication remains a vital tool for sending commands and receiving data from spacecraft on Mars and other distant locations in the solar system.
To know more about the Distance, here
https://brainly.com/question/13046933
#SPJ4
Describe the ways the reading addresses how some people use ""uncertainty"" as a way to undermine science:
The reading addresses how some people use "uncertainty" as a way to undermine science: by pointing out that these individuals often exploit the inherent limitations and ambiguities present in scientific research.
They tend to focus on the fact that scientific findings are often provisional, and conclusions can change with the introduction of new evidence or advancements in methodologies. By emphasizing the uncertainty aspect, they attempt to discredit or cast doubt on the overall credibility of scientific results.
Furthermore, these individuals may cherry-pick data or studies that support their preconceived beliefs, while ignoring the broader consensus within the scientific community. This selective presentation of evidence contributes to misinformation and public confusion about scientific issues, such as climate change or vaccinations.
In some cases, those who use uncertainty to undermine science may have ulterior motives, such as protecting vested interests or promoting a specific political or ideological agenda. By sowing doubt and mistrust in scientific findings, they can manipulate public opinion and obstruct the development or implementation of evidence-based policies.
To counteract these attempts to undermine science, it is essential for the scientific community and the public to recognize and appreciate the inherent uncertainties within the scientific process.
By fostering critical thinking, encouraging open and transparent communication, and supporting continued research and education, we can help build resilience against misinformation and promote a better understanding of the role of uncertainty in scientific progress.
To know more about scientific research, refer here:
https://brainly.com/question/30336884#
#SPJ11
A force compresses a bone by 1. 0 mm. A second bone has the same cross-sectional area but twice the length as the first. By how much would the same force compress this second bone
The second bone has the same cross-sectional area and material as the first bone, the same force would create the same stress in both bones.
To solve this problem, we need to consider the relationship between stress, strain, and Young's modulus. Stress is the force applied divided by the cross-sectional area, strain is the change in length divided by the original length, and Young's modulus is a material property that relates stress and strain.
1. Calculate stress (σ) for the first bone:
σ = Force / Cross-sectional area
2. Calculate strain (ε) for the first bone:
ε = Compression / Original Length
ε = 1.0 mm / Original Length
3. Find Young's modulus (Y) for the bone material:
Y = σ / ε
4. Calculate the strain (ε') on the second bone, using the same force and Young's modulus:
ε' = σ / Y
5. Calculate the compression (ΔL) of the second bone, given that its length is twice the first bone:
ΔL = ε' * (2 * Original Length)
However, since the second bone is twice as long, it would experience a greater strain and, as a result, a larger compression. By calculating the compression of the second bone using the relationship between stress, strain, and Young's modulus, you can determine how much the same force would compress the second bone.
For more about cross-sectional area:
https://brainly.com/question/20532494
#SPJ11
Some machines will have a body constructed around a frame for_____
Some machines will have a body constructed around a frame for added structural support and stability.
This design approach ensures that the machine can withstand various forces, stresses, and vibrations that it may encounter during operation. The frame acts as a skeleton, providing a solid foundation for the machine's various components, such as motors, gears, and electronic systems, to be mounted securely.
By constructing the body around the frame, the machine's weight is evenly distributed, helping to prevent any undue strain on individual parts. This structural design can also facilitate easier maintenance, as components can be accessed and replaced more easily.
Additionally, the frame may be designed with specific materials, such as steel or aluminum, to enhance durability and resist corrosion. In summary, constructing a machine's body around a frame provides numerous benefits, including enhanced structural support, improved stability, and easier maintenance.
To know more about machines, refer here:
https://brainly.com/question/2555822#
#SPJ11
What is the absolute index of refraction of medium x?
The refractive index of the wave in medium X is 0.577.
What is the refractive index?The refractive index of a substance or medium measures how much light can bend through it. The difference between the speed of light in an object or medium and the speed of light in a vacuum (or in air) is how it is defined. Usually, the letter n is used to denote the refractive index.
The refractive index of a substance or medium is a critical property that determines how light will behave when it passes through it.
We know that the refractive index can be obtained as;
n = sin i/sinr
Thus we have that;
sin i = sin 30
sin r = sin 60
n = sin 30/sin 60
n = 0.577
Learn more about refractive index:https://brainly.com/question/23750645
#SPJ1
A. 149 kg baseball moving at 17. 7 m/s is caught by a 57 kg catcher at rest on an ice skating rink, wearing
frictionless skates. With what speed does the catcher slide on the ice?
Do NOT put in units or it will be marked wrong! The answer's value only! Please round each answer to 3 places.
MaVa + MbVb = (Ma+b)(Va+b)
The speed at which the catcher slides on the ice after catching the 149 kg baseball moving at 17.7 m/s is 12.80 m/s. it can be found using the conservation of momentum formula: MaVa + MbVb = (Ma + Mb)(Va+b).
In this case, Ma represents the mass of the baseball (149 kg)
Va represents the initial velocity of the baseball (17.7 m/s)
Mb represents the mass of the catcher (57 kg), and Vb represents the initial velocity of the catcher (0 m/s, as he is at rest).
We need to solve for Va+b, which represents the final velocity of the catcher after catching the baseball.
Plugging in the given values, we have:
(149 kg)(17.7 m/s) + (57 kg)(0 m/s) = (149 kg + 57 kg)(Va+b)
2637.3 kg·m/s = (206 kg)(Va+b)
To find the final velocity of the catcher (Va+b), we can now divide both sides by the total mass (206 kg):
Va+b = 2637.3 kg·m/s / 206 kg = 12.80 m/s
Therefore, the catcher slides on the ice with a speed of approximately 12.80 m/s after catching the baseball. Please remember to round your answer to 3 decimal places as required.
Know more about conservation of momentum click here:
https://brainly.com/question/24989124
#SPJ11
which one of the following is the correct order of the electromagnetic spectrum from low to high frequencies? select one: a. radio waves, uv, x-rays, microwaves, infrared, visible, gamma rays b. radio waves, infrared, microwaves, uv, visible, x-rays, gamma rays c. radio waves, microwaves, infrared, visible, uv, x-rays, gamma rays d. radio waves, infrared, x-rays, microwaves, uv, visible, gamma rays
The correct order of the electromagnetic spectrum from low to high frequencies is: radio waves, microwaves, infrared, visible, UV, X-rays, gamma rays. Option C is correct.
The electromagnetic spectrum is the range of all types of electromagnetic radiation, from low-frequency radio waves to high-frequency gamma rays. Radio waves have the longest wavelengths and lowest frequencies, followed by microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays, which have the shortest wavelengths and highest frequencies.
This order is based on the different ways in which electromagnetic radiation interacts with matter, with longer wavelengths being less energetic and shorter wavelengths being more energetic. It is important to note that while this order is generally accepted, there can be some overlap and variation depending on context and source. Option C is correct.
To know more about the Electromagnetic, here
https://brainly.com/question/14876487
#SPJ4
A liquid (rho = 1.65 g/cm3 ) flows through two horizontal sections of tubing joined end to end. in the first section, the cross-sectional area is 10 cm2 , the flow speed is 275 cm/s, and the pressure is 1.20x105 pa. in the second section, the cross-sectional area is 2.50 cm2 . calculate the smaller section’s (i) flow speed and (ii) pressure.
(i). The flow speed in the smaller section is 11 m/s.
(ii). The pressure in the smaller section is 7,352.56 Pa.
To solve this problem, we can apply the principle of conservation of mass and the Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a steady flow.
Given:
Density of the liquid (ρ) = 1.65 g/cm³ = 1650 kg/m³ (since 1 g/cm³ = 1000 kg/m³)
First section:
Cross-sectional area (A1) = 10 cm² = 0.001 m²
Flow speed (v1) = 275 cm/s = 2.75 m/s
Pressure (P1) = 1.20 ×[tex]10^5[/tex] Pa
Second section:
Cross-sectional area (A2) = 2.50 cm² = 0.00025 m²
(i) To find the flow speed in the smaller section (v2), we can use the principle of conservation of mass:
A1v1 = A2v2
Solving for v2:
v2 = (A1v1) / A2
v2 = (0.001 m² × 2.75 m/s) / 0.00025 m²
v2 = 11 m/s
(ii) To find the pressure in the smaller section (P2), we can use Bernoulli's equation:
P1 + (1/2)ρv1² + ρgh1 = P2 + (1/2)ρv2² + ρgh2
Since the two sections are horizontal, the heights (h1 and h2) are the same, so the terms ρgh1 and ρgh2 cancel out. Additionally, the liquid is assumed to be at the same height, so we can disregard the gravitational term.
Simplifying the equation:
P1 + (1/2)ρv1² = P2 + (1/2)ρv2²
Solving for P2:
P2 = P1 + (1/2)ρv1² - (1/2)ρv2²
P2 = 1.20 × [tex]10^5[/tex] Pa + (1/2) × 1650 kg/m³ × (2.75 m/s)² - (1/2) × 1650 kg/m³ × (11 m/s)²
P2 = 1.20 × [tex]10^5[/tex] Pa + 9526.56 Pa - 45675 Pa
P2 = 7,352.56 Pa
To know more about Bernoulli's equation refer here
https://brainly.com/question/29865910#
#SPJ11
Help me!
in your own words, describe how the marble-jar experiment explains newton's law of inertia.
The marble-jar experiment is a classic demonstration of Newton's Law of Inertia. The experiment consists of a jar filled with marbles and a card covering the jar's opening.
When the jar is inverted quickly, the card falls, and the marbles remain in place.
According to Newton's Law of Inertia, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant velocity unless acted upon by an external force.
In this experiment, the marbles' inertia keeps them in place when the jar is inverted, while the card falls due to the external force of gravity.
This experiment provides a simple and tangible way to understand Newton's Law of Inertia.
To know more about Law of Inertia, refer here:
https://brainly.com/question/1830739#
#SPJ11
Which statement describes what the hand shows?
A-When the current flows down the wire, the magnetic
field flows out on the left side of the wire and in on the
right side of the wire.
B-When the current flows up the wire, the magnetic field
flows out on the left side of the wire and in on the right
side of the wire.
C-When the current flows down the wire, the magnetic
field flows in on the left side of the wire and out on the
right side of the wire.
D-When the current flows up the wire, the magnetic field
flows in on the left side of the wire and out on the right
side of the wire.
When the current flows up the wire, the magnetic field flows in on the left side of the wire and out on the right side of the wire.
Right hand ruleThe right-hand rule is a method for determining the direction of the force experienced by a current-carrying conductor in a magnetic field or the direction of the magnetic field created by the conductor.
The direction of the magnetic field created by the current is indicated by the way your fingers curl. This is the statement of the right hand rule as shown in the image.
Learn more about right hand rule:https://brainly.com/question/9750730
#SPJ1
A concrete column has a diameter of 350m and length of 2m. If the density (mass/volume) of the concrete is 2. 45mg/m^3 determine the weight of column in pounds
The weight of the concrete column with a diameter of 350mm and a length of 2m, having a density of 2.45 Mg/m³, is: approximately 1042 pounds.
To determine the weight of the concrete column with a diameter of 350mm and a length of 2m, we first need to calculate its volume. Since the column is cylindrical, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height.
The radius of the column is half of the diameter, so r = 350mm / 2 = 175mm, which is equivalent to 0.175m. The height is 2m. Plugging these values into the formula, we get:
V = π(0.175m)²(2m) ≈ 0.193m³
Now that we have the volume, we can use the given density of concrete, which is 2.45 Mg/m³, to determine the mass. The mass can be calculated using the formula: mass = density × volume.
Mass = 2.45 Mg/m³ × 0.193m³ ≈ 0.473 Mg
Next, we need to convert the mass from Mg (megagrams) to kg (kilograms) since 1 Mg = 1000 kg:
Mass = 0.473 Mg × 1000 kg/Mg = 473 kg
Now, to find the weight, we'll use the formula: weight = mass × gravity. The gravitational force is approximately 9.81 m/s².
Weight = 473 kg × 9.81 m/s² ≈ 4638.93 N (Newtons)
Finally, we'll convert the weight from Newtons to pounds using the given conversion factor: 1 pound = 4.4482 N.
Weight = 4638.93 N × (1 pound / 4.4482 N) ≈ 1042 pounds
To know more about density, refer here:
https://brainly.com/question/28929608
#SPJ11
Complete question:
A concrete column has a diameter of 350mm and a length of 2m. If the density (mass/volume) of concrete is 2.45 Mg/m3 determine the weight of the column in pounds. 1 pound = 4.4482 N
An electrically neutral balloon is rubbed on your hair. if your hair loses electrons, the balloon has what type of electric charge?
When a neutral balloon is rubbed on your hair, the balloon becomes negatively charged because it gains electrons from your hair. The process of triboelectric charging occurs because of the difference in the materials' ability to give up or gain electrons.
When you rub an electrically neutral balloon on your hair, some electrons are transferred from your hair to the surface of the balloon. As a result, the balloon becomes negatively charged, and your hair becomes positively charged.
This is because electrons are negatively charged particles, and when they move from one object to another, the object that loses electrons becomes positively charged, and the object that gains electrons becomes negatively charged.
The process of transferring electrons from one object to another through friction is called triboelectric charging, and it occurs because some materials have a stronger tendency to give up electrons, while others have a stronger tendency to gain electrons.
In summary, when a neutral balloon is rubbed on your hair, the balloon becomes negatively charged because it gains electrons from your hair. The process of triboelectric charging occurs because of the difference in the materials' ability to give up or gain electrons.
To know more about electrons refer here:
https://brainly.com/question/19448078#
#SPJ11
How to find Vdsq from Vdst? How did they find the value of 7 for Vdsq?
Vdst and Vdsq are different measurements of the voltage drop across the drain-source terminals of a MOSFET transistor, and to find Vdsq from Vdst, we need to measure Vdst and use a formula that takes into account Vgs and Vth.
To understand how to find Vdsq from Vdst, we need to first understand what these terms represent.
Vdst is the voltage drop across the drain-source terminals of a MOSFET transistor when it is in its ON state. This voltage drop is caused by the current flowing through the transistor, and it is a dynamic value that changes as the current changes.
Vdsq, on the other hand, is the voltage drop across the drain-source terminals of a MOSFET transistor when it is in its steady-state or quiescent state. This voltage drop is caused by the biasing of the transistor and is a static value that remains constant as long as the biasing conditions remain the same.
To find Vdsq from Vdst, we need to first measure the value of Vdst while the transistor is in its ON state. This can be done using a multimeter or an oscilloscope. Once we have the value of Vdst, we can then calculate Vdsq using the following formula:
Vdsq = Vdst + Vgs - Vth
where Vgs is the voltage applied to the gate of the transistor and Vth is the threshold voltage of the transistor.
As for how the value of 7 for Vdsq was found, it is impossible to say without more context. It could have been calculated using the formula above, or it could have been measured using experimental methods.
To learn more about transistors
https://brainly.com/question/31052620
#SPJ4
Explain why the magnifying glasses made from transparent materials?
Transparent materials are preferred for magnifying glasses because they allow light to pass through, resulting in clear and accurate images with natural colors. The quality of the material used is also important for achieving clarity and preventing distortion.
Magnifying glasses are typically made from transparent materials such as glass or plastic because they need to allow light to pass through them to form an image. When light passes through a transparent material, it refracts or bends, which is what allows the lens to focus the light onto a small point.
The quality of the material used to make the magnifying glass is important as it affects the clarity and sharpness of the image produced. The material should be free from impurities and scratches to prevent distortion of the image.
Transparent materials are also preferred for magnifying glasses because they allow us to see the object being magnified in its natural colors. If the material were opaque, the colors would be distorted or blocked altogether, making it difficult to see the object clearly. Overall, using transparent materials for magnifying glasses allows for clear, sharp images with accurate colors, making them ideal for a wide range of applications.
To learn more about magnifying glasses
https://brainly.com/question/14961076
#SPJ4
A 1345-kg car moving east at 15. 7m/s is struck by a 1923-kg car moving north. They stick together and move with a velocity of 14. 5m / s at theta = 63. 5 degrees Was the north-moving car exceeding the 20. 1 m/s speed limit?
We need to first calculate the final velocity of the two cars after the collision. We can do this using the conservation of momentum principle, which states that the total momentum of a system remains constant if no external forces act on it.
Initially, the east-moving car has a momentum of (1345 kg) x (15.7 m/s) = 21136.5 kg m/s in the east direction, while the north-moving car has a momentum of (1923 kg) x (v) in the north direction, where v is the velocity of the north-moving car.
After the collision, the two cars stick together and move with a velocity of 14.5 m/s at an angle of 63.5 degrees. To find the velocity in the x-direction (east), we can use the cosine function:
cos(63.5 degrees) = x / 14.5 m/s
x = cos(63.5 degrees) x 14.5 m/s = 6.25 m/s
Similarly, to find the velocity in the y-direction (north), we can use the sine function:
sin(63.5 degrees) = y / 14.5 m/s
y = sin(63.5 degrees) x 14.5 m/s = 13.12 m/s
Therefore, the final velocity of the two cars is (6.25 m/s) east + (13.12 m/s) north = 14.5 m/s at 63.5 degrees.
To determine if the north-moving car exceeded the 20.1 m/s speed limit, we need to compare its initial velocity with the speed limit. The initial velocity of the north-moving car is not given in the problem, so we cannot determine whether it exceeded the speed limit or not.
In summary, the final velocity of the two cars after the collision is 14.5 m/s at 63.5 degrees. However, we cannot determine whether the north-moving car exceeded the 20.1 m/s speed limit without additional information.
To know more about conservation of momentum principle refer here
https://brainly.com/question/30582604#
#SPJ11
young's double-slit experiment is performed with 568-nm light and a distance of 2.00 m between the slits and the screen. the tenth interference minimum is observed 7.08 mm from the central maximum. determine the spacing of the slits.
Answer:
yes
Explanation:
A 0.050 kg bullet strikes a 5.0 wooden block and embeds itself