The orbital speed of the satellite orbiting around a planet of radius 34 Km is found to be 2.59 km/s.
To find the orbital speed (v) of the satellite, we can use the formula,
v = √(GM/r), gravitational constant (6.674 x 10⁻¹¹ N(m/kg)²) is G, mass of the planet is M, and orbital radius of the satellite is r. To calculate M, we can use the formula,
g = GM/r², rearranging this formula, we get,
M = gr²/G
Substituting the values, we get,
M = 3.3(34,000)²/(6.674 x 10⁻¹¹)
M = 6.06 x 10²⁰ kg
Now, substituting the values of G, M, and r into the formula for orbital speed, we get,
v = √((6.674 x 10⁻¹¹)(6.06 x 10²⁰)/(34,000))
v = 2.59 x 10³ m/s
Therefore, the satellite's orbital speed is approximately 2.59 km/s.
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1. Choose one from the following countries:
o United States
o United Kingdom
o Australia
o Nepal
o Russia
o Spain
o India
2. Then make research of some laws supporting sexuality and gender in your
chosen country.
uk
because they have a Sexuality law
Please answer the correct question and I will give you 50 points
1) Consider a ring, sphere and solid cyclinder all with the same mass. They are all held at the top of an inclined plane which is at 20° to the horizontal. The top of the inclined plane is 1 m high. The shapes are released simultaneously and allowed to roll down the inclined plane. Assume the objects roll without slipping and that they are all made from the same material. Assume the coefficient of static friction between the objects and plane to be 0.3.
A ) calculate the tangential (linear) Velocity of each shapes-
B) determine the linear acceleration(a)
C) which shapes have the greater moment of inertia ?
D) How long will it take each shape to reach the bottom of the Slope ?
E) workout what order they would get to the bottom of the Slope.
A) The tangential (linear) velocity of each shape is:
For the ring: v = rω = 2.41 m/s.
For the sphere: v = rω = 1.57 m/s.
For the solid cylinder: v = rω = 2.41 m/s.
B) The linear acceleration of each shape is:
For the ring: α = 2gsinθ/(3r(1 + 0.3) + 2R) = 1.191 m/s^2.
For the sphere: α = 2gsinθ/(5r(1 + 0.3)) = 1.176 m/s^2.
For the solid cylinder: α = 2gsinθ/(3r(1 + 0.3) + 2R) = 1.228 m/s^2.
C) The solid cylinder has the greatest moment of inertia.
D) The time taken for each shape to reach the bottom of the slope is:
For the ring: t = 0.576 s.
For the sphere: t = 0.197 s.
For the solid cylinder: t = 0.576 s.
E) The sphere will reach the bottom of the slope first, followed by the ring and the solid cylinder.
You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of o=2.45 km/s
. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth.
With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is E=6370000 m
, the mass of the Earth is E=5.98×1024 kg
, the acceleration due to gravity on the surface of the Earth is =9.81 m/s2
and the universal gravitational constant is =6.67×10−11 N·m2/kg2
.
Answer:
To calculate the minimum total speed required for the projectile to escape the Earth's gravitational pull, we can use the equation for escape velocity:
v_escape = sqrt(2GM/R)
where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.
Plugging in the given values, we get:
v_escape = sqrt(26.67e-115.98e24/6370000)
v_escape = 11186.4 m/s
This is the minimum total speed required for the projectile to escape the Earth's gravitational pull. In order to achieve this speed, the projectile would need to be launched with a velocity of 11186.4 m/s relative to the Earth.
Explanation:
A proton, moving with a velocity of viî, collides elastically with another proton that is initially at rest. If the speed of the initially moving proton is 1.90 times the speed of the initially at rest proton, find the following.
(a) the speed of each proton after the collision in terms of vi
(b) the direction of the velocity vectors after the collision
Answer:
We can approach this problem using the conservation of momentum and the conservation of kinetic energy.
Conservation of momentum:
The momentum before the collision is given by:
p1 = m1v1 = m1viî
where m1 is the mass of each proton (which we assume to be the same) and v1 is the velocity of the initially moving proton.
The momentum after the collision is given by:
p2 = m1v1' + m1v2'
where v1' and v2' are the velocities of the two protons after the collision.
Since the collision is elastic, the total momentum is conserved:
p1 = p2
m1viî = m1v1' + m1v2'
We can simplify this equation by dividing both sides by m1:
viî = v1' + v2'
Conservation of kinetic energy:
The kinetic energy before the collision is given by:
K1 = (1/2)m1 We need the value of the velocity v1, which is not given in the problem statement.
creation
Design a device to minimize impact from a collision.
Design a device to convert one form of energy to another.
In 2-3 paragraphs explain your design, the materials that would be used to construct it, its function, and the relative efficiency of your design compared to something that already exists and performs a similar function
The device I would design to minimize impact from a collision would be a shock absorber made from a combination of rubber and metal. The device would be installed between the two colliding objects, and its function would be to absorb and dissipate the energy of the collision, thereby reducing the impact forces on the objects.
CONSTRUCTION:
Compared to existing shock-absorbing devices such as airbags and crumple zones, this design would be more efficient in reducing the impact forces on the colliding objects. Unlike airbags and crumple zones, which are designed to absorb the impact forces by deforming, the shock absorber would absorb the impact energy through compression and dissipation of the energy as heat.
Designing a device to convert one form of energy to another:The device I would design to convert one form of energy to another would be a piezoelectric generator. The function of this device would be to convert mechanical energy into electrical energy through the use of piezoelectric materials.The piezoelectric generator would consist of a piezoelectric material such as quartz or lead zirconate titanate (PZT) sandwiched between two metal plates. When mechanical stress is applied to the piezoelectric material, it generates an electrical voltage across the metal plates.Compared to existing devices such as generators and batteries, the piezoelectric generator would be more efficient in converting mechanical energy into electrical energy. This is because the piezoelectric effect is a direct conversion of mechanical energy into electrical energy, without the need for any intermediate steps such as the conversion of mechanical energy into rotational energy in a generator. Additionally, the piezoelectric generator would be smaller and more lightweight than traditional generators, making it ideal for use in portable electronic devices.
What type of circuit is shown
=When three resistors are connected in parallel, they form a parallel circuit. In a parallel circuit, each resistor is connected across the same two points, with the current split between the resistors.
In this configuration, the voltage across each resistor is the same, but the current through each resistor can be different. The total resistance of the circuit is calculated using the equation:
1/R_total = 1/R1 + 1/R2 + 1/R3
where R1, R2, and R3 are the resistance values of the individual resistors.
The total current in the circuit is equal to the sum of the currents through each resistor:
I_total = I1 + I2 + I3
where I1, I2, and I3 are the currents through each resistor.
The total power dissipated in the circuit can be calculated using the equation:
P_total = V² / R_total
where V is the voltage across the resistors.
In summary, when three resistors are connected in parallel, they form a parallel circuit, with each resistor connected across the same two points, and the current split between them. The total resistance, current, and power dissipated in the circuit can be calculated using the equations provided.
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A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond and push each other apart. The girl moves in a negative direction with a speed of 3 m/s. What must be the final momentum of the boy?
A. 100 kgm/s
B. 120 kgm/s
C. -120 kgm/s
D. 40 kgm/s
Answer:
B. 120 kgm/s
Explanation:
The initial momentum of the system is zero since the boy and the girl are at rest. When they push each other apart, the total momentum of the system remains conserved. Since the girl moves in a negative direction, the boy must move in the positive direction with the same momentum to keep the total momentum of the system zero.
Let's assume the final momentum of the boy is p. According to the law of conservation of momentum,
(initial momentum) = (final momentum)
0 = p + (-40 kg)(-3 m/s)
0 = p + 120 kg m/s
p = -120 kg m/s
Therefore, the final momentum of the boy must be 120 kg m/s in the positive direction, which is answer choice B.
Ans
According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal. Initially, the momentum of the system is zero since the boy and the girl are at rest. When they push each other, the girl moves in the negative direction with a speed of 3 m/s. Let's assume that the boy moves in the positive direction with a speed of v m/s.
The total initial momentum of the system is:
P_initial = m_boy * 0 + m_girl * 0 = 0
The total final momentum of the system must also be zero since there are no external forces acting on the system. Therefore:
P_final = m_boy * v + m_girl * (-3) = 0
where m_boy = 60 kg, m_girl = 40 kg, and v is the final speed of the boy in m/s.
Solving for v, we get:
60v - 120 = 0
v = 2 m/s
Therefore, the total final momentum of the boy must be:
P_final = m_boy * v = 60 kg * 2 m/s = 120 kg m/s.
So, the total final momentum of the boy must be 120 kg m/s.
The short-term effects of marijuana can include __________.
Answer:
Explanation:
Increased heart rate
list 5 importance of energy
Answer:
1. Energy powers our homes and businesses.
2. Energy is necessary for transportation.
3. Energy is required for manufacturing and industrial processes.
4. Energy is essential for agriculture and food production.
5. Energy is needed for healthcare and medical equipment.
6. Energy is critical for national defense and security.
7. Energy is required for communication and technology.
8. Energy is vital for education and research.
9. Energy is necessary for entertainment and leisure activities.
10. Energy is fundamental for maintaining a high standard of living.
11. Energy is necessary for economic growth and development.
12. Energy is essential for reducing poverty and improving quality of life.
13. Energy is required for environmental protection and sustainability.
14. Energy is critical for disaster relief and emergency response.
15. Energy is needed for space exploration and research.
16. Energy is important for cultural preservation and heritage.
17. Energy is necessary for water treatment and distribution.
18. Energy is required for waste management and recycling.
19. Energy is vital for public safety and law enforcement.
20. Energy is necessary for aviation and air travel.
21. Energy is essential for shipping and transportation of goods.
22. Energy is required for mining and natural resource extraction.
23. Energy is critical for oil and gas production.
24. Energy is needed for renewable energy research and development.
25. Energy is important for alternative fuel sources and technology.
26. Energy is necessary for energy storage and distribution.
27. Energy is essential for energy efficiency and conservation.
28. Energy is required for climate change mitigation and adaptation.
29. Energy is vital for international cooperation and diplomacy.
30. Energy is necessary for transportation infrastructure development.
31. Energy is required for public transportation systems.
32. Energy is critical for rural and remote communities.
33. Energy is needed for urban development and growth.
34. Energy is important for public health and sanitation.
35. Energy is necessary for disaster preparedness and response.
36. Energy is essential for emergency services and first responders.
37. Energy is required for military operations and equipment.
38. Energy is critical for scientific research and innovation.
39. Energy is needed for space heating and cooling.
40. Energy is important for water heating and distribution.
41. Energy is necessary for appliance and electronic usage.
42. Energy is essential for lighting and electricity.
43. Energy is required for cooking and food preparation.
44. Energy is critical for refrigeration and food storage.
45. Energy is needed for laundry and cleaning.
46. Energy is important for personal hygiene and grooming.
47. Energy is necessary for entertainment and leisure activities.
48. Energy is essential for sports and recreation.
49. Energy is required for tourism and travel.
50. Energy is critical for the arts and culture.
51. Energy is needed for social and community events.
52. Energy is important for festivals and celebrations.
53. Energy is necessary for religious and spiritual practices.
54. Energy is essential for personal communication and relationships.
55. Energy is required for social media and online interactions.
56. Energy is critical for telecommuting and remote work.
57. Energy is needed for internet connectivity and usage.
58. Energy is important for e-commerce and online shopping.
59. Energy is necessary for financial transactions and banking.
60. Energy is essential for education and online learning.
61. Energy is required for healthcare and telemedicine.
62. Energy is critical for legal and government services.
63. Energy is needed for transportation and delivery services.
64. Energy is important for customer service and support.
65. Energy is necessary for manufacturing and supply chain management.
66. Energy is essential for research and development.
67. Energy is required for data centers and cloud computing.
68. Energy is critical for cybersecurity and privacy protection.
69. Energy is needed for artificial intelligence and machine learning.
70. Energy is important for autonomous vehicles and drones.
71. Energy is necessary for robotics and automation.
72. Energy is essential for virtual and augmented reality.
convert 750W into kilowatts
Ans. 0.75
To convert watts into kilowatts we must divide it by 1000
so dividing 750W by 1000
we get,
750/1000 = 0.75
hence 750W in kilowatts equals to 0.75
A car travels 200 km in the first 2.5 hour then stop for half hour then travels the final speed of 200 km in 2 hours find the average speed of a car
A car travels 200 km in the first 2.5 hour then stop for half hour then travels the final speed of 200 km in 2 hours. The average speed of the car is 80 km/hour.
To find the average speed of the car, we need to calculate the total distance traveled and the total time taken.
In the first 2.5 hours, the car travels 200 km.
Then, it stops for half an hour.
After that, the car travels another 200 km in 2 hours.
So the total distance traveled is 200 km + 200 km = 400 km.
The total time taken is 2.5 hours + 0.5 hours + 2 hours = 5 hours.
Therefore, the average speed of the car is:
Average speed = total distance / total time
= 400 km / 5 hours
= 80 km/hour.
So the average speed of the car is 80 km/hour.
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graph
shows a variety of moving objects and how their distance is related to time what do these objects have in common
What is common among all the graphs is that they all show an object that is moving.
What is a graph?In the distance time graph, we have the distance on the vertical axis and we have the time on the horizontal axis and the shape of the plots may differ depending on the nature of the motion of the objects.
Graphs of distance vs time help us to examine motion by showing how an object has moved over time. All objects shown on a distance vs. time graph are shifting positions over time, regardless of the graph's specific shape or slope, and the graph reveals information about the direction and speed of their motion.
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what is the net charge when you rub a plastic ruler with fur
The net charge when you rub a plastic ruler with fur would be infinitesimal or zero
How to detect the net chargeThe effect of friction between a plastic ruler and fur is evident when electrons are transferred from the hairy surface to the ruler's plane, ending with the ruler possessing a negative charge while the fur taking on a positive one.
As a result, the whole system presents with a net charge that is negative it converges due to the excess electrons now found on the ruler. However, occasionally, the magnitude of this charge is very small, consequently making it difficult to probe without reliable technology or instruments.
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A 0.530-kg cart moving at 0.572 m/s to the right collides elastically with a 0.25-kg cart initially at rest. The 0.25-kg cart then moves off rapidly and compresses a spring before the 0.530-kg cart can catch it again.
To solve this problem, we can use the conservation of momentum and the conservation of kinetic energy.First, let's find the velocity of the 0.530-kg cart after the collision. We can use the conservation of momentum:m1v1 + m2v2 = m1v1' + m2v2'where m1 and v1 are the mass and velocity of the 0.530-kg cart before the collision, m2 and v2 are the mass and velocity of the 0.25-kg cart before the collision, and v1' and v2' are the velocities of the carts after the collision.Plugging in the numbers, we get:(0.530 kg)(0.572 m/s) + (0.25 kg)(0 m/s) = (0.530 kg)v1' + (0.25 kg)v2'Solving for v1', we get:v1' = [(0.530 kg)(0.572 m/s) + (0.25 kg)(0 m/s)] / (0.530 kg + 0.25 kg) = 0.378 m/s to the rightSo the 0.530-kg cart moves off to the right at 0.378 m/s after the collision.Next, let's find the maximum compression of the spring. We can use the conservation of kinetic energy:(1/2)m2v2^2 = (1/2)kx^2where k is the spring constant and x is the maximum compression of the spring.We know the mass and velocity of the 0.25-kg cart before the collision (v2 = 0 m/s), so we can solve for k:k = 2(1/2)m2v2^2 / x^2 = m2v2^2 / x^2Plugging in the numbers, we get:k = (0.25 kg)(0 m/s)^2 / x^2 = 0This means that the spring constant is 0, which is not physically possible. Therefore, there must be an error in the problem statement or some missing information that would allow us to calculate the maximum compression of the spring.
Price $15 12 9 6 3 Quantity Demanded per Month 1 2 3 5 7 Price $15 12 9 6 3 In the BOX what you would expect to see if you plotted the numbers on the graph. The quantit demand pe month dec 0 1 2 3 4 5 6 7 Quantity b. It costs Charlene $2.00 to ride to bus to the dog owners house each time she goes. What number of dog walks will give her the most profit?
From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.
How to solve
Based on the provided data, we can create a demand schedule for the prices and the quantity demanded per month.
Let's first organize the data in a table:
Price ($) Quantity Demanded per Month
15 1
12 2
9 3
6 5
3 7
If you plotted these numbers on a graph, you would expect to see a downward-sloping curve, illustrating the inverse relationship between price and quantity demanded. As the price decreases, the quantity demanded per month increases.
Now let's consider Charlene's costs and profits from walking dogs. It costs her $2.00 for each bus ride to the dog owner's house.
To calculate her profit, we need to find her total revenue at each price point, then subtract her total costs.
Price ($) Quantity Demanded per Month Total Revenue ($) Total Costs ($) Profit ($)
15 1 15 2 13
12 2 24 4 20
9 3 27 6 21
6 5 30 10 20
3 7 21 14 7
From the table, we can see that Charlene will have the most profit ($21) when she walks 3 dogs per month, charging $9 per walk.
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b) A motorcycle moving at 75 mph starts to slow down at a constant rate of 0.25 m/s^2 for 15 seconds. Find its final velocity (in both m/s and mph) and the total distance (in meters) that it traveled during this 15 s timeframe.
The final velocity of the motorcycle is
29.78 m/s (66.7083 mph),the total distance traveled during the 15-second timeframe is
516.98 meters.How to find the final velocityConvert the initial velocity from mph to m/s:
75 mph = 75 x 0.44704 m/s = 33.528 m/s
Using vf = vi + at
where
vf is the final velocity,
vi is the initial velocity
a is the acceleration, and
t is the time interval.
Plugging in the given values, we get:
vf = 33.528 m/s - (0.25 m/s^2)(15 s) = 32.59 m/s
convert the final velocity back to mph
32.59 m/s = 32.59 x 2.237 mph/m = 72.9 mph
distance traveled, d
d = vi*t + (1/2)at^2
d = 32.59 m/s * 15 s + (1/2)(-0.25 m/s^2)(15 s)^2
d = 516.98 m
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The figure below shows electrons moving along an electric current towards and away from the light bulb.
Electrons traveling along an electric current. Arrow under electrons points right and left both towards and away from the light bulb.
Does this figure show a direct or alternating current? Explain your response.
Based on the information provided, it is likely that the figure shows an alternating current (AC). The arrows under the electrons pointing right and left, both towards and away from the light bulb, indicate that the direction of the electron flow is changing periodically. This is a characteristic of alternating current, where the flow of electric charge reverses direction periodically, typically in a sinusoidal manner.
In an AC circuit, the voltage also changes direction periodically, which is consistent with the changing direction of the electron flow shown in the figure.
In an alternating current, the flow of electrons periodically reverses direction, causing the current to switch between positive and negative values. This is different from direct current (DC), where electrons flow in a single, constant direction.
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Two children setup a “telephone” by placing a long, slender aluminum (Y = 6.9 × 1010 N/m2) rod that has a length of 6.1-m between their two houses. To communicate, a child taps a coded message on one end. How long do the sound waves take to reach the other end? Note: the density of aluminum is 2700 kg/m3.
The time takes is 1.19 ms for the sound waves to travel the length of the aluminum rod between the two houses.
The speed of sound in aluminum can be determined utilizing the condition
v = sqrt(Y/ρ),
where Y is the Youthful's modulus and ρ is the thickness of the material. Connecting the qualities for aluminum, we get
v = [tex]sqrt(6.9x10^10 N/m^2/2700 kg/m^3) = 5110 m/s[/tex].
The time it takes for the sound waves to venture to every part of the length of the aluminum pole can be determined utilizing the condition
t = d/v,
where d is the distance and v is the speed of sound. Connecting the qualities, we get
t = 6.1 m/5110 m/s = 0.00119 s or 1.19 ms.
Subsequently, it takes 1.19 ms for the sound waves to venture to every part of the length of the aluminum bar between the two houses.
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What is the inertia of motion?
Answer:
The ability of a body to resist changes to its uniform motion condition is known as inertia of motion.
___________________
Hope this helps!
The second law of thermodynamics states that
a change in a system's energy is equal to the energy
transferred to the system.
energy cannot be created or destroyed.
energy can flow from a colder object to a warmer object
only if something does work.
the only way to reduce an object's temperature is to
increase the entropy of the environment.
Answer: energy can flow from a colder object to a warmer object
only if something does work.
Explanation: Consider the flow of water from a higher level to a lower level. There is no need to use energy to make this process occur. This type of process which does not need the application of energy to take place is said to be spontaneous. But to make water go up to the water tank, a pump must be used to make the process take place. This type of process which needs the use of energy to make it happen is said to be nonspontaneous.
but why not the only way to reduce an object's temperature is to
increase the entropy of the environment.?
coz the motion of particles decreases and their velocity decreases so they have less entropy at a lower temperature.
hope it helped:)
Why is compound interest more advantageous than simple interest
Compound interest is more advantageous than simple interest because it allows for the accumulation of interest on both the principal amount and the interest earned over time. In simple interest, interest is only earned on the principal amount, while in compound interest, the interest earned is added to the principal amount and then interest is earned on the new, higher amount. This leads to a compounding effect where the interest earned increases over time, resulting in a larger total return on investment. Additionally, compound interest is commonly used for long-term investments such as retirement funds and savings accounts, where the power of compounding can significantly increase the final amount earned.
Brainliest for answer!! How does the light spectrum measured for a nearby star compare to the light spectrum of a distant galaxy that is moving rapidly away from the observer? Explain what causes the differences between the two spectra. Answer in 3-5 sentences please.
Answer:
The light spectrum measured for a nearby star can be used as a benchmark for more distant stars because two stars with identical spectra have the same intrinsic luminosity. Spectroscopy can be applied to light from a distant galaxy, but the dark lines in the solar spectrum give a unique pattern that can be used to identify the elements present in the star. The light spectrum of a distant galaxy that is moving rapidly away from the observer will be shifted towards the red end of the spectrum due to the Doppler effect, which causes the wavelengths of light to stretch out as the object moves away from the observer.
The softest sound a human ear can hear is at 0 dB (Io = 10-12 W/m2). Sounds above 130 dB cause pain. A particular student's eardrum has an area of A = 51 mm2. What is the most power, in watts, the ear can receive before the listener feels pain?
Im so confused on how to even start with this problem, my main question is how sound and power are related.
Answer:
Sound and power are related through intensity, which is the amount of power per unit area. The intensity of a sound wave is proportional to the square of its amplitude, which is a measure of how far the wave oscillates from its equilibrium position.
To solve this problem, you can use the formula for sound intensity:
I = P/A
where I is the intensity of the sound wave in watts per square meter (W/m^2), P is the power of the sound wave in watts (W), and A is the area of the eardrum in square meters (m^2).
You are given that the softest sound a human ear can hear is 0 dB, which corresponds to an intensity of 10^-12 W/m^2. You are also given that sounds above 130 dB cause pain. To find the maximum power the ear can receive before the listener feels pain, you can rearrange the formula for intensity to solve for power:
P = AI
where A is the area of the eardrum in square meters.
Substituting the given values, you get:
P = (51 x 10^-6 m^2)(10^-12 W/m^2 x 10^(130/10))
Simplifying this expression, you get:
P = 1.8 x 10^-3 W
Therefore, the most power the ear can receive before the listener feels pain is 1.8 x 10^-3 watts.
What is inertia of motion explain one example?
THE INABILITY OF A BODY TO CHANGE ITS STATE OF MOTION BY ITSELF
example : a passenger tends to fall forward when breaks are applied in a busThe tendency of an item to resist a change in its state of motion is referred to as inertia. It specifically refers to an object's resistance to any change in velocity, whether that change be in speed or direction.
What is Inertia ?When you are riding in a car and the driver abruptly stops, you are experiencing inertia of motion. Because of inertia, your body wants to continue going forward at the same pace and in the same direction as before the brakes were applied. You will lean forward as a result, and if you are not wearing a seatbelt, you may be flung forward. Similarly, while the automobile speeds, your body tries to remain at rest owing to inertia, causing you to be motionless. Despite being widely accepted, Aristotle's theory of motion was challenged by prominent philosophers multiple times over the course of roughly two thousand years. For instance, Lucretius claimed that mobility rather than stasis (stagnation) was the "default state" of the matter (following, presumably, Epicurus).
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What is the critical angle between polycarbonate (n1 = 1.58) and quartz (n2 = 1.41)?
24 degrees
46 degrees
63 degrees
75 degrees
Answer:
Approximately [tex]63.2^{\circ}[/tex].
Explanation:
The refractive index [tex]n[/tex] gives the ratio between the speed of light in vacuum and the speed of light in the given material. A larger refractive index means slower speed of light in the medium. In this question, the speed of light is slower in polycarbonate than in quartz.
When light travels from a material of low light speed to a material of higher light speed, the angle of refraction [tex]\theta_{r}[/tex] will exceed the angle of incidence [tex]\theta_{i}[/tex] (both with respect to the normal.)
The critical angle at this interface is the [tex]\theta_{i}[/tex] for which [tex]\theta_{r} = 90^{\circ}[/tex]. Note that since [tex]\theta_{i}\![/tex] cannot exceed [tex]90^{\circ}[/tex], [tex]\theta_{i} < \theta{r}[/tex] and light must be entering a faster medium from a slower medium. In this question, light would be entering quartz ([tex]n = 1.41[/tex], faster) from polycarbonate ([tex]n = 1.58[/tex], slower.)
By Snell's Law:
[tex]n_{i}\, \sin(\theta_{i}) = n_{r}\, \sin(\theta_{r})[/tex],
Where:
[tex]n_{i}[/tex] is the refractive index of the medium from which light enters, [tex]n_{r}[/tex] is the refractive index of the medium light enters into,[tex]\theta_{i}[/tex] is the angle of incidence at which light enters the interface (with respect to the normal), and[tex]\theta_{r}[/tex] is the angle of refraction at which light leaves the interface (also with respect to the normal.)Set [tex]n_{i} = 1.58[/tex] (polycarbonate), [tex]n_{r} = 1.41[/tex] (quartz), and [tex]\theta_{r} = 90^{\circ}[/tex]. Rearrange the equation and solve for [tex]\theta_{i}[/tex]:
[tex]\begin{aligned}\sin(\theta_{i}) &= \frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \end{aligned}[/tex].
[tex]\begin{aligned}\theta_{i} &= \arcsin\left (\frac{n_{r}\, \sin(\theta_{r})}{n_{i}} \right) \\ &= \arcsin \left(\frac{1.41\, \sin(90^{\circ})}{1.58}\right) \\ &\approx 63.2^{\circ}\end{aligned}[/tex].
Sean throws a baseball at an angle of 25 relative to the ground at a speed of 23m/s. What is the maximum height the ball will achieve? How long will it be in the air? How far away does Kelly need to be to catch the ball?
Answer:
To solve this problem, we can use the equations of motion for projectile motion:
- Vertical displacement: Δy = v₀sinθt - 1/2gt²
- Vertical velocity: v = v₀sinθ - gt
- Time of flight: T = 2v₀sinθ/g
- Horizontal displacement: Δx = v₀cosθt
where v₀ is the initial speed, θ is the angle of projection, g is the acceleration due to gravity (9.81 m/s²), t is the time of flight, and Δy and Δx are the vertical and horizontal displacements, respectively.
First, we can find the maximum height by using the equation for vertical displacement:
Δy = v₀sinθt - 1/2gt²
At the maximum height, the vertical velocity is zero, so we can find the time of flight by setting the vertical velocity equation to zero:
v = v₀sinθ - gt = 0
Solving for t, we get:
t = v₀sinθ/g
Substituting this into the equation for vertical displacement, we get:
Δy = v₀sinθ(v₀sinθ/g) - 1/2g(v₀sinθ/g)²
Simplifying, we get:
Δy = (v₀²sin²θ)/(2g)
Substituting the given values, we get:
Δy = (23²sin²25)/(2*9.81) ≈ 29.4 m
So the maximum height is approximately 29.4 meters.
Next, we can find the time of flight using the equation for time of flight:
T = 2v₀sinθ/g
Substituting the given values, we get:
T = 2*23*sin25/9.81 ≈ 3.5 s
So the time of flight is approximately 3.5 seconds.
Finally, we can find the horizontal displacement using the equation for horizontal displacement:
Δx = v₀cosθt
Substituting the given values, we get:
Δx = 23*cos25*3.5 ≈ 64.3 m
So Kelly needs to be approximately 64.3 meters away to catch the ball.
A flashlight bulb is connected to a dry cell of voltage 5.25 V. It draws 15 mA (1,000 mA = 1 A). Its resistance is
2.5 E2 ohms
3.0 E2 ohms
3.5 E2 ohms
4.0 E2 ohms
____________________________________
C) 3.5 ΩOhm's Law: R = V / I × 10= 5.25 ÷ 15mAh × 10= 3.5 Ω____________________________________
Question 11 of 25
In the circuit below, resistors R₁ and R₂ are in parallel. What is the equivalent
1
1
resistance? (R₁ = 30 22,R₂ = 20 2) (
A
+A)
Ptot R₁
S₁
S₂
R₁
S₂ S
ww
R₂
1
R₂₂k
Answer:
60 ohms
Explanation:
To find the equivalent resistance of two resistors R₁ and R₂ in parallel, we can use the formula:
1/Req = 1/R₁ + 1/R₂
where Req is the equivalent resistance.
Substituting the values given, we get:
1/Req = 1/30 + 1/20
Simplifying, we get:
1/Req = 1/60
Multiplying both sides by Req, we get:
Req = 60 ohms
Therefore, the equivalent resistance of the two resistors R₁ and R₂ in parallel is 60 ohms.
13. If the supply of gasoline rises, name a substitute that will increase in demand? 14. How do you think each of the following affected the world price of oil? List if it will effect supply or demand, and the price change if any. Use basic supply and demand analysis. a. Tax credits were offered for expenditures on home insulation. b. The Alaskan oil pipeline was completed. c. Oil was discovered in Mexico and the North Sea. d. Sport Utility Vehicles and minivans became popular. e. Natural oil reserves became depleted
13. If the supply of gasoline rises, a substitute that may increase in demand could be electric or hybrid vehicles.
14. Here is how each of the following events may have affected the world price of oil using basic supply and demand analysis:
a. Tax credits offered for expenditures on home insulation would likely decrease the demand for oil as people would use less energy to heat their homes. This would lead to a decrease in the price of oil.
b. The completion of the Alaskan oil pipeline would increase the supply of oil, leading to a decrease in the price of oil.
c. The discovery of oil in Mexico and the North Sea would increase the supply of oil, leading to a decrease in the price of oil.
d. The popularity of Sport Utility Vehicles and minivans would increase the demand for oil as these vehicles typically consume more gasoline than smaller cars. This would lead to an increase in the price of oil.
e. The depletion of natural oil reserves would decrease the supply of oil, leading to an increase in the price of oil.
13. List the general strengths and weaknesses of epidemiology for providing an answer to Mary Beth’s question.
14. List the specific strengths and weaknesses of this study.
15. List the general strengths and weaknesses of toxicology for providing an answer to Mary Beth’s question.
The general strengths of epidemiology for providing an answer to Mary Beth’s question.
epidemiology can study a large populationepidemiology can identify patterns and trends in health and diseaseepidemiology can be used to study different diseases and health conditionsThe general weaknesses of epidemiology for providing an answer to Mary Beth’s question:
epidemiology may not provide a definitive answer or explanationepidemiology results may be affected by biases and confounding variablesThe Specific strengths of a study:
Big sample sizeLengthy follow-up periodThe specific weaknesses of a study are :
Use of self-recorded data, which may be inaccurate or biasedBiased selection due to non-random samplingWhat is epidemiology?Epidemiology is described as the study and analysis of the distribution, patterns and determinants of health and disease conditions in a defined population.
The main objective of epidemiology has been said is to find out what causes different health outcomes in different groups of people.
Learn more about epidemiology at:
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