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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Explanation:
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Answers
Answer:
a) The i-component of 7 is (7.61 + 2.5) - 3.4k = 7.61 + 2.5 - 3.4k
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f) The component of d that is perpendicular to the direction of d2 and in the plane of d and d2 is given by the vector subtracting the component of d along the direction of d2 from the original vector d
a) The i-component of 7 is (7.61 + 2.5) - 3.4k = 7.61 + 2.5 - 3.4k
b) The j-component of 7 is -1.01 + 2.0 + 3.0k = -1.01 + 2.0 + 3.0k
c) The k-component of 7 is 4.01 + 3.0 + 2.0k = 4.01 + 3.0 + 2.0k
d) To find the angle between 7 and the positive z-axis, we need the dot product of 7 and the unit vector along the positive z-axis (0,0,1). The dot product is given by:
(7.61 + 2.5 - 3.4k)(0) + (-1.01 + 2.0 + 3.0k)(0) + (4.01 + 3.0 + 2.0k)(1)
And the angle between 7 and the positive z-axis is given by the following formula:
cos(theta) = (7.dot.unit_vector_z_axis) / (||7||.||unit_vector_z_axis||)
e) To find the component of d along the direction of d2, we need to find the projection of d on d2. The projection is given by the dot product of d and d2 divided by the square of the magnitude of d2.
f) The component of d that is perpendicular to the direction of d2 and in the plane of d and d2 is given by the vector subtracting the component of d along the direction of d2 from the original vector d
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Answer:
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list add value
to end
A. To insert the first value in an array
B. To remove the last value from an array
C. To change a value at a certain index.
D. To add a value to the end of an array
Answers
The purpose of a block to add a value to the end of an array.
What is the function that adds an element to the end of an array?The push() is known to be often used to add an element to the end of your array.
The end() function is known to be one that transmit the internal pointer to, and also the outputs, the last factor in the array.
A null or zero value is known to be that which marks the end of an array and it is said to be the very equivalent of the null char for any kind of string
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Answer: The answers is C. To change a value at a certain index
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Answer:
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Explanation:
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For example, with regard to Receptacles, section (210-21(b)) of the Article 100 indicates that a "Receptacle" is a contact device provided at an outlet for the connecting of an attachment plug.
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Compressed gas cylinders shall be secured in an upright position at all times except, if necessary, for short periods of time while cylinders are actually being hoisted or carried.
Why do gas cylinders need to be upright?All gas cylinders must be stored upright and restrained with safety chains or other secure devices, as stated in AS4332-2004 - The storage and handling of gases in cylinders.
Acetylene cylinders should be stored upright in order to avoid the gas from separating from the acetone. All compressed gas cylinders, whether filled, half filled, or empty, must comply with the standard.
The cylinders are designed exclusively for use in the gas phase, which emerges when the cylinder is held upright. Liquid leakage occurs when the cylinder is used horizontally, which has negative effects. Gas cylinders should never be used horizontally. They might leak, which might be extremely dangerous.
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A b c or d?????? Please help
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Answer:
Explanation:
D Stationary measurement
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: