10) A roller coaster has a circular loop of radius 5.0 m. You go around at the minimum speed.
How fast will you be moving at the bottom?
What is your acceleration? (in m/s2, in g’s)
How does this feel? Where else have you felt this effect?
Draw a Force Diagram at the bottom.
This is dangerous. What should the radius be at the bottom, so that you only feel 2 g’s?
.
Explain why these loops have the shape that they do.
Answers
Answer:
1) The speed of the roller coaster at the bottom is approximately 15.65 m/s
2) The acceleration of the roller coaster at the bottom is 6·g's
3) The high acceleration is 6 times the force of the weight of the passengers
The high acceleration can cause gravity induced loss of consciousness
4) Please find attached a force diagram of the forces at the bottom of the roller coaster created with Microsoft Visio
5) For the acceleration at the bottom to be 2·g's the radius of the rollercoaster at the bottom should be 25 meters
5) The radius at the bottom of roller coasters are increased to reduce the normal force felt by the passengers as they pass the bottom of a circular roller coaster
Explanation:
1) The given parameters are;
The radius of the roller coaster, r = 5.0 m
The speed of the roller coaster = Minimum = 0 m/s
The shape of the roller coaster's path = Circular loop
Therefore, the maximum height of the roller coaster, h = The diameter of the of a circular path of the roller coaster, d = 2 × r = 2 × 5.0 m = 10.0 m
∴ h = 10.0 m
The minimum speed is f=given by the following equation;
\(F_N = \dfrac{m \cdot v^2}{R} - m \cdot g = 0 \ (At \ the \ top \ of \ the \ roller \ coaster's \ path)\)
Therefore, we have;
\(\dfrac{m \cdot v^2}{R} = m \cdot g\)
From which we have;
v = √(R × g)
Where;
R = The radius of the path of the roller coaster = 5.0 m
g = The acceleration due to gravity = 9.8 m/s² = constant
By plugging in the values of the variable, 'R', and the constant, 'g', we get;
v = √(5.0 m × 9.8 m/s²) = 7 m/s
The minimum speed of the roller coaster, v = 7 m/s
The speed of the roller coaster at the bottom is given by the conservation of energy formula as follows;
The energy at the top of the roller coaster = The energy at the bottom of the roller coaster
∴ The total mechanical energy of the roller coaster, M.E., is constant and at the top, \(M.E._{top}\), is given as follows;
\(M.E._{top}\) = 1/2·m·v₁² + m·g·h₁
At the bottom, the total mechanical energy is given as follows;
\(M.E._{bottom}\) = 1/2·m·v₂² + m·g·h₂
Where;
v₁ = The velocity of the roller coaster at the top = 7 m/s
h₁ = The height of the roller coaster at the top = 10 m
v₂ = The speed of the roller coaster at the bottom
h₂ = The height of the roller coaster at the bottom = 0 m
g = The acceleration due to gravity = 9.8 m/s² = Constant
By plugging in the values, we get;
M.E. = \(M.E._{top}\) = \(M.E._{bottom}\)
∴ 1/2·m·v₁² + m·g·h₁ = 1/2·m·v₂² + m·g·h₂
1/2 × (7 m/s)² + 9.8 m/s² × 10.0 m = 1/2 × v₂² + 9.8 m/s² × 0 m
122.5 m²/s² = 1/2 × v₂²
∴ v₂² = 2 × 122.5 m²/s² = 245 m²/s²
v₂ = √(245 m²/s²) = 7·√5 m/s ≈ 15.65 m/s
The speed of the roller coaster at the bottom, v₂ ≈ 15.65 m/s
2) The normal force on the car at the bottom of the roller coaster is given as follows;
\(F_N = \dfrac{m \cdot v_2^2}{R} + m \cdot g = m \times \left(\dfrac{ v_2^2}{R} + g \right )\)
Force, F = Mass, m × Acceleration, a
∴ F = m×a
Therefore, the acceleration at the bottom, 'a' by comparison of the general equation for force, 'F', and the normal force, \(F_N\), is given as follows;
\(a = \left(\dfrac{ v_2^2}{R} + g \right )\)
Plugging in the values for 'v₂²', 'R', ang 'g', gives;
\(a = \left(\dfrac{ v_2^2}{R} + g \right ) = \left(\dfrac{ 245}{5} + 9.8 \right ) = \left(49+ 9.8 \right ) = (5 + 1) \times 9.8 = 6 \times 9.8 = 6 \times g\)
a = 6·g = 58.8 m/s²
3) The high acceleration will lead to a very high normal force (equal to 6 times each of their weight) experienced by the passengers with a force
The high acceleration is dangerous and can lead to gravity induced loss of consciousness since it is more than 3·g's
4) Please find attached the force diagram at the bottom of the roller coaster created with Microsoft Visio
5) For the acceleration at the bottom to be 2·g's, we have;
\(a = \left(\dfrac{ v_2^2}{R} + g \right )\)
At a = 2·g, we have;
\(2 \cdot g = \left(\dfrac{ v_2^2}{R} + g \right )\)
\(\therefore 2 \cdot g - g = g = \dfrac{ v_2^2}{R}\)
\(R = \dfrac{ v_2^2}{g} = \dfrac{245}{9.8} = 25\)
R = 25 m
The radius at the bottom of the roller coaster should be 25 meters so that only 2·g's is felt
5) The shape of the roller coaster has an increases the radius at the bottom so as to reduce the acceleration of the car
Related Questions
Find Tpi, D and angle
Tpf = 6.65
d = 3 3/16
LT = 6in
Answers
Answer:
Find Tpi, D and angle
Tpf = 6.65
d = 3 3/16
LT = 6in
Please help !! TJI joists are stronger than 2x10’s True or false
Answers
Answer:
false this joists are stronger that 2×10s because it is not strong enough
Select the correct answer.
What Is a trade-off?
A
decreasing the amount of resources spent on all wants to reduce the total costs In future
O B.
replacing one resource with another resource to satisfy a want
c.
organizing the use of a resource in a manner that fulfills all wants
D.
reducing the amount of resources
spent on one want to spend more on another want
Answers
Answer:
d. reducing the amount of recourses spent on one want to spend more on another want
brainliest? plz!
Answer:
the answer is B. replacing one resource with another resource to satisfy a want
pls answer my question i need now
Answers
Answer:
Do it?
Explanation:
You're going to have to follow the instructions shown and do it yourself. We're not going to be able to send it to you through mail that fast... sorry you're by yourself here.
WHO IS SUPER COOL PLEASE RESPOND FOR 48 PTS
Answers
You're super cool!
We all are!
One integrated circuit design calls for the diffusion of arsenic into silicon wafers; the background concentration of As in Si is 2.5 x 1020 atoms/m. The predeposition heat treatment is to be conducted at 1000°C for 45 minutes, with a constant surface concentration of 8x 10^26 As atoms/m³. At a drive in temperature of 1100°C, determine the diffusion time required for a junction depth of 1.21m. For this system, values of Q and Do are 4.10 eV and 2.29x10^3m/s, respectively.
Answers
The diffusion time that is needed for the junction depth of 1.21 m is given as 13875 seconds
How to solve for the diffusion timebackground concentration of As in Si is 2.5 x 10²⁰ atoms/m
tp = 1000°c
tp = 45 minutes
= 45 x 60 seconds
surface concentration = 8x 10^26
Td = 1100°c
Junction depth = 1.2
= 1.2 x 10⁻⁶m
qd = 4.10ev
Do = 2.29 x 10⁻³
We have to use the equation
\(Dp = Doexp(-\frac{qd}{kTP} )\\\\= (2.23 * 10^-^1^3 m^2/s) exp [-\frac{4.10}{8.62*10^-^5 *(1000+273)} ]\)
= 1.36 x 10⁻¹³
From the relation that we have here
\(Qo = 2cs\sqrt{\frac{Dpte}{pi} } \\\\= 2 * 8* 10^2^6*\sqrt{\frac{1.36*10^-^1^3(45*60)}{pi} }\)
Qo = 1.73 x 10¹³
Dd at 1100
\(Dd = 2.29*10^-^3exp(\frac{-4.10}{8.62x10^-^5)(1100 + 273)}\)
Dd = 2.06 x 10⁻¹⁸m²/s
From the relation we have
\(exp[\frac{(1.2 * 10^-^6)^2}{4*(2.06x10^-^1^8)+d} ]=\frac{1.73*10^1^9}{2.5x10^2^0*\sqrt{pi*2.06*10^-^1^8x+d} }\)
\(ln\frac{2.72*10^7}{\sqrt{+d} } =\frac{1.75*10^5}{+d}\)
Using heat and trial, we would have the value of +d = 13875 seconds
The diffusion time is 13875 seconds
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1.
affects the straight-line motion of a flying object by pulling it
down toward the ground.
A Buoyancy
B. Density
C. Gravity
D. Pressure
Answers
Explanation:
-Gravity is the force that attracts a body toward the center of the earth, or toward any other physical body having mass.
-Gravity does not affect horizontal motion, it only affects vertical motion and it acceleration going downward. Air resistance is what’s going to affect your projectiles horizontal motion going forward.
After adjusting your seat, your___ should be as closest possible to the back rest.
Answers
Answer:
ans would be back as back is the thing that needs rest by getting closest to seat
An electric kettle is used to boil some water. The kettle holds 1.5 litres of water when full and operates from a 230V, 13 amp supply. If all the electrical energy supplied is converted to heat energy, how long will it take the kettle to boil from an initial temperature of 15°C? (The specific heat capacity of water is 4190J/kgK.)
Answers
The time taken to heat the water is 1.79 * 10^5 s.
What is the time taken?We know that in this case, the principle of energy transformation holds true. The electrical energy is converted to the heat energy that causes the water to boil.
We then have;
IVt = mcdT
I = current
V = voltage
t = time taken
m = Mass of water
c = heat capacity of water
dT = temperature change
Thus;
230 * 13 * t = 1500 Kg * 4190 * (100 - 15)
t = 1500 * 4190 * (100 - 15)/230 * 13
t = 1.79 * 10^5 s
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Help me with sudoku have fun with it. It is a brain stretcher
Answers
Answer:
I think you should do it yourself because it will help your brain please mark me as brainlist please
In her first job out of college, Riki sometimes felt embarrassed by her mistakes. As she gained experience in technological problem solving, she began to like her mistakes more. Why?
Answers
Answer:
Explanation:There are many definitions of problem-solving – but at a basic level, it focuses on the ability to accurately assess a situation and arrive at a positive solution.
Solving problems is an analytical skill that many employers look for when reviewing candidate application forms.
This particular skill isn’t restricted to a single sector, industry or role, though employers in the engineering and legal industries, in particular, tend to look for proficiency.
Consequently, questions about your problem-solving ability are commonplace in interviews.
a life cycle assessment (LCA) determines the environmental impact at all stages of a product's life cycle, including production, usage, and disposal;
the LCA process includes procedures that gather and evaluate the inputs and outputs of materials, energy, and the related impact that can be directly assigned to the product or process at any point in its life cycle;
the main purpose of an LCA is to assess potential environmental impact in order to address issues before hazardous or irreversible effects are created;
LCAs include goal definitions, inventories, impact analyses, and improvement analyses, which enable companies to identify environmental issues and explore possible solutions to problems; and
inherency is the property of a life cycle that may hide hazardous or energy-consuming processes, creating a net total product that appears to be benign or efficient but in actuality does have negative impacts.
Answers
Devices thay are made magnetic by an electric current?
Answers
Answer:
Microphones, speakers, headphones, telephones and loudspeakers. Electric motors and generators. Doorbells and electric buzzers.
Explanation:
what is the fastest motorcycle in the world ?
Answers
Top Speed: 300-420 mph (480-680 km/h)
Year: 2003–2006 (9 units total)
Engine: 8.3 L V10 (500 hp)
Price: $555,000
30 points have a good day
Answers
Answer:
thank you :)
Explanation:
which of the time periods below corresponds to a recession
Answers
A recession is a period of economic downturn, typically characterized by a decline in the gross domestic product (GDP), high unemployment, and a decrease in business activity. Recessions are generally considered to be a normal part of the economic cycle, and they can occur at various times and for various reasons.
It is not possible to determine which of the time periods listed below corresponds to a recession without more information. To determine whether a particular time period experienced a recession, it is necessary to consider a range of economic indicators, such as GDP, unemployment, business activity, and other factors.
The use of seat belts in cars has significantly reduced the number of crash
fatalities. Which statement best explains how societal demand guided the
development of seat-belt technology?
A. Engineers improved the design of seat belts because consumers
wanted them to be easier to use.
B. Car manufacturers recognized the dangers of not wearing seat
belts in cars and then lobbied the government to make laws that
required their use.
C. Engineers developed seat-belt technology and then began a public
awareness campaign to educate people on how they could be
used to make cars safer.
D. When new seat-belt technology became available, consumers
began to demand their inclusion in all new cars.
Answers
Answer:
A. Engineers improved the design of seat belts because consumers wanted them to be easier to use
The statement best explains how societal demand guided the development of seat-belt technology is A. Engineers improved the design of seat belts because consumers wanted them to be easier to use.
Seat-belts are important in order to reduce the impact of a person getting injured in case there's an accident.It should be noted that when seatbelts were first introduced, they were not easy to use and this was challenging for consumers.Due to the advances and new innovations by engineers, the design of seat belts has become easier to use. Even children can use seatbelts easily now.Therefore, engineers improved the design of seat belts because consumers wanted them to be easier to use.
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17.) A customer complains that a vehicle has an off-center steering wheel.
Technician A says that an incorrect toe adjustment could be the cause.
Technician B says that an incorrect camber setting could be the cause.
Who is right?
OA. A only
OB. B only
OC. Both A and B
OD. Neither A nor B
Answers
Answer:
C
Explanation:
An incorrect Camber can affect the wheel alignment
An incorrect toe adjustment can also be the cause ie C
Expresa cada proposición mediante la gráfica, conjunto, desigualdad y la notación de
intervalo.
a. La estatura de los jugadores de un equipo de baloncesto es menor a 1,98 m y mayor o
igual a 1,82 m.
b. Los niveles normales de glucosa en ayunas en un ser humano deben ser mayores o
iguales a 70 mg/dl y menores que 100 mg/dl.
c. El tiempo que tarda una persona en llegar a su trabajo es mayor a 5/6 hora y menor o
igual a 3/2 hora.
d. La categoría juvenil es para personas mayores a 15 años y menores o iguales a 18
años.
e. La temperatura de la ciudad de Cali regularmente es menor a 31° C y mayor o igual a
19°C.
Answers
a. The height of the players of a basketball team is less than 1.98 m and greater than or equal to 1.82 m.
The Graph:Draw a number line with 1.82 and 1.98 marked on it. Shade the region between the two points, including the point at 1.82, but not 1.98.
Set:
H = {h | 1.82 ≤ h < 1.98}
Inequality:
1.82 ≤ h < 1.98
Interval Notation:
[1.82, 1.98)
b. Normal fasting glucose levels in a human should be greater than or equal to 70 mg/dl and less than 100 mg/dl.
Graph:
Draw a number line with 70 and 100 marked on it. Shade the region between the two points, including both endpoints.
Set:
G = {g | 70 ≤ g < 100}
Inequality:
70 ≤ g < 100
Interval Notation:
[70, 100)
c. The time it takes a person to get to work is greater than 5/6 hours and less than or equal to 3/2 hour.
Graph:
Draw a number line with 5/6 and 3/2 marked on it. Shade the region between the two points, not including 5/6, but including 3/2.
Set:
T = {t | 5/6 < t ≤ 3/2}
Inequality:
5/6 < t ≤ 3/2
Interval Notation:
(5/6, 3/2]
d. The youth category is for people over 15 years of age and under or equal to 18 years.
Graph:
Draw a number line with 15 and 18 marked on it. Shade the region between the two points, not including 15, but including 18.
Set:
Y = {y | 15 < y ≤ 18}
Inequality:
15 < y ≤ 18
Interval Notation:
(15, 18]
e. The temperature in the city of Cali is regularly less than 31° C and greater than or equal to 19°C.
Graph:
Draw a number line with 19 and 31 marked on it. Shade the region between the two points, including 19, but not 31.
Set:
T_Cali = {t | 19 ≤ t < 31}
Inequality:
19 ≤ t < 31
Interval Notation:
[19, 31)
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The question in English is:
Express each statement using the graph, set, inequality, and the notation of
interval.
to. The height of the players of a basketball team is less than 1.98 m and greater than or
equal to 1.82 m.
b. Normal fasting glucose levels in a human should be greater than or
equal to 70 mg/dl and less than 100 mg/dl.
c. The time it takes a person to get to work is greater than 5/6 hours and less than or
equal to 3/2 hour.
d. The youth category is for people over 15 years of age and under or equal to 18
years.
and. The temperature in the city of Cali is regularly less than 31° C and greater than or equal to
19°C.
QUESTION 1: Different Line Types Look at the drawing of a different bicycle pump below. This drawing is accurate, so we call it a scale draw It is four times smaller than a real pump. We say it is drawn to a scale of 1:4. That means that if you meas the length of the outer tube of this drawing, it will be four times smaller than the outer tube of the real pu F + 320 Figure 9: Bicycle pump. Scale 1:4 Why is the outer tube of this pump drawn with solid lines?
Answers
Answer:
The outer tube of the pump is drawn with solid lines because it represents the visible edges of the object, which are the most important and prominent features of the drawing. Solid lines are used to indicate visible edges, while other types of lines such as dashed or dotted lines are used for hidden or construction lines that are not meant to be seen in the final drawing.
Explanation:
When drawing an object, it's important to distinguish between the visible edges and the hidden or construction lines. The visible edges are the lines that represent the outer contour or silhouette of the object, which define its shape and form. In the case of the bicycle pump, the outer tube is the most prominent and recognizable feature of the pump, so it's drawn with solid lines to emphasize its importance and to make it stand out from the other parts of the pump.
On the other hand, the hidden or construction lines are used to guide the drawing process, to show the internal structure or components of the object, or to indicate the position of other features that are not visible from the current viewpoint. These lines are usually drawn with dashed or dotted lines to distinguish them from the visible edges and to avoid confusion.
By using different types of lines, the artist can create a clear and accurate representation of the object, with all the relevant information conveyed in a concise and understandable way. This is especially important in technical or scientific drawings, where precision and clarity are essential for conveying complex ideas or designs.
You want to park uphill on a two-way road and there is no curb. Which direction do you turn your front wheels?.
Answers
Answer:
hi
Explanation:
I don't know sorry
I really jjust needed to anwer something
Which quantity measures the rate at which a machine performs work?
A. Efficiency
B. Power
C. Power
D. Acceleration
E. Torque
Answers
Answer:
I believe B or D
Explanation:
Answer:
Power
Explanation:
Correct on Edmentum
Advances in vehicle manufacturing technology have decreased the need for:
Select one:
a. large-scale parts manufacturers.
b. high-volume production lines.
c. large-scale investments.
d. large amounts of labor.
Answers
Answer:
D large amounts of labor
Explanation:
The Engineering Design Process is used to:
Answers
Answer:
to find a solution to a problem.
Explanation:
The engineering design process, by definition, is a series of steps that engineers use to find a solution to a problem. These steps include: defining the problem, brainstorming solutions, designing and building a prototype of the solution, testing the solution, and improving it.
Recovery Assignment 3: Engineering ethics 1 1/2 page typed
paper 12 font double spaced. Research engineering ethics
and explain the following: Explain why engineering ethics is
so important. Explain why engineers are expected to practice
engineering using the highest standards of honesty and
integrity. List and explain one of the engineering canons. This
is a research project, please write what you have researched
and not what you think. Copied and pasted papers will not be
considered for grading.
Answers
Explanation:
Engineering is an important and learned profession. As members of this profession, engineers are expected to exhibit the highest standards of honesty and integrity. Engineering has a direct and vital impact on the quality of life for all people. Accordingly, the services provided by engineers require honesty, impartiality, fairness, and equity, and must be dedicated to the protection of the public health, safety, and welfare. Engineers must perform under a standard of professional behavior that requires adherence to the highest principles of ethical conduct.
Bright flowers were jewels gleaming in the sunlight meaning
Answers
Answer:This sentence is a metaphor to express that flowers were so beautiful and vibrant that they seemed to be jewels gleaming under the sun.Explanation:Let's remember that metaphors are used to make comparisons; a metaphor is a figure of speech in which a word or phrase is applied to an object to which it is not literally applicable. In this case, for example, flowers are not capable of gleaming, but the comparison with the shining jewels under the sun is made in order to express how beautiful, vibrant and shining they were.
The phrase "bright flowers were jewels gleaming in the sunlight" is a poetic metaphor that conveys the beauty and radiance of flowers when illuminated by the sun.
It suggests that the flowers are so vibrant and colorful that they resemble precious gemstones, sparkling and catching the light in a similar way. The metaphor emphasizes the brilliance and attractiveness of the flowers, highlighting their aesthetic appeal and the way they stand out in their natural environment.It captures the sense of wonder and admiration one might feel when observing flowers in full bloom under the warm glow of sunlight.
A metaphor is a figure of speech that compares two unrelated things by stating that one thing is another thing. It is a rhetorical device used to create vivid and imaginative descriptions or to convey abstract ideas in a more understandable and relatable manner. In a metaphor, the comparison is implied rather than explicitly stated, unlike a simile which uses "like" or "as" to make the comparison.
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A bicycle with 540mm wheel diameter passes over a segment arched culvert of radius 760mm. draw the locus of a point on the circumference of the wheel when it makes one complete revolution
Answers
In order to draw the locus, we can construct a circle with a radius of 1696.62mm centered at the center of the culvert.
How to calculate the valueThe diameter of the wheel is given as 540mm, so the radius of the wheel is half of that: 540mm / 2 = 270mm. The circumference of the wheel can be calculated as 2π times the radius: 2π × 270mm
≈ 1696.62mm.
Since the circumference of the wheel is approximately 1696.62mm and point P traces out a circle, the locus of point P will be a circle with a circumference of 1696.62mm.
Hence, to draw the locus, we can construct a circle with a radius of 1696.62mm centered at the center of the culvert.
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Which two muscles control breathing!
Answers
Answer: The work of breathing is done by the diaphragm, the muscles between the ribs (intercostal muscles), the muscles in the neck, and the abdominal muscles.
The symmetrical load below is connected to a three-phase network. A line current of 25A has been measured. The load resistors have a value of 18 Ω.
What is the line voltage of the three-phase network?
Answers
Answer:
The line voltage of the three phase network is 346.41 V
Explanation:
Star Connected Load
Resistance, R₁ = R₂ = R₃ = 18 Ω
For a star connected load, the line current = the phase current, that is we have
\(I_L = 25 \, A = I_{Ph}\)
Whereby the the voltage across each resistance = \(V_R\) is given by the relation;
\(V_R\) = \(I_{Ph}\) × R
Hence;
\(V_{Ph}\) = \(V_R\) = \(I_{Ph}\) × R = 25 × 8 = 200 V
Therefore we have;
The line voltage, \(V_{L}\) = √3 × \(V_{Ph}\) = √3 × 200 = 346.41 V.
Hence, the line voltage of the three phase network = 346.41 V.
What is the theory behind the individual approach to team performance?
Answers
Answer:
Trust and communication
Explanation:
You have you trust people and yourself and believe in yourself that you can do it and have faith in yourself.