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;
[tex]F_N = \dfrac{m \cdot v^2}{R} - m \cdot g = 0 \ (At \ the \ top \ of \ the \ roller \ coaster's \ path)[/tex]
Therefore, we have;
[tex]\dfrac{m \cdot v^2}{R} = m \cdot g[/tex]
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, [tex]M.E._{top}[/tex], is given as follows;
[tex]M.E._{top}[/tex] = 1/2·m·v₁² + m·g·h₁
At the bottom, the total mechanical energy is given as follows;
[tex]M.E._{bottom}[/tex] = 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. = [tex]M.E._{top}[/tex] = [tex]M.E._{bottom}[/tex]
∴ 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;
[tex]F_N = \dfrac{m \cdot v_2^2}{R} + m \cdot g = m \times \left(\dfrac{ v_2^2}{R} + g \right )[/tex]
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, [tex]F_N[/tex], is given as follows;
[tex]a = \left(\dfrac{ v_2^2}{R} + g \right )[/tex]
Plugging in the values for 'v₂²', 'R', ang 'g', gives;
[tex]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[/tex]
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;
[tex]a = \left(\dfrac{ v_2^2}{R} + g \right )[/tex]
At a = 2·g, we have;
[tex]2 \cdot g = \left(\dfrac{ v_2^2}{R} + g \right )[/tex]
[tex]\therefore 2 \cdot g - g = g = \dfrac{ v_2^2}{R}[/tex]
[tex]R = \dfrac{ v_2^2}{g} = \dfrac{245}{9.8} = 25[/tex]
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
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Answer:
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Answer:
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Answer:
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Answers
The purpose of a block to add a value to the end of an array.
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Answers
Answer:
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Explanation:
Answer:
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Have a nice day!
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Answers
Answer:
I. Inclined plane: GPE to KE.
II. Screw: KE to GPE.
III. Wheel and axle: GPE to KE.
IV. Lever: GPE to KE.
V. Wedge: GPE to KE.
VI. Pulley: GPE to KE.
Explanation:
A simple machine can be defined as a type of machine with no moving parts but can be used to perform work.
Basically, a simple machine allows for the transformation of energy into work. The six simple machines are;
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V. Wedge: gravitational potential energy to mechanical energy (kinetic energy). It can be used to split objects into halves.
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The three major types of wire ferrules are as follows:
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Answers
I feel that the developer or team of developers who built the code should not be held accountable; rather, the organization that approved its use should be held accountable.
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Summarize key
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Your employer is paying you to serve the needs of his or her
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Explanation:
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Answers
If an electric dryer has a nameplate rating of 5.6kva, Kilovolt-amperes (kVA) is often used for the service calculation.
What is a service calculation?A service calculation is known to be the NEC given way or procedure that is used for sizing service conductors, service equipment, and others so that they can be able to meet the needed electrical demands of a home and office
Note that for a person to calculate dryer load, the use of Kilovolt-amperes (kVA) is often considered as it is equivalent to kilowatts (kW).
Hence, If an electric dryer has a nameplate rating of 5.6kva, Kilovolt-amperes (kVA) is often used for the service calculation.
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Research and find out whether any laws or guidelines exist for robotics. Describe these guidelines.
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Answer:
1.A robot may not injure a human being or, through inaction, allow a human being to come to harm.
2.A robot must obey the orders given it by human beings except where such orders would conflict with the First Law.
3.A robot must protect its own existence as long as such protection does not conflict with the First or Second Laws.
Explanation: