(B) Enter an expression for the angular speed w of the system immediately after the collision, in terms of m, V, D, 0,
(C) Calculate the rotational kinetic energy, in joules, of the system after the collision
We calculate the total moment of inertia of the rod-ball system after the collision by adding the moment of inertia of the rod and the added contribution from the putty ball. With this, we find the post-collision angular speed using Conservation of Angular Momentum. The rotational kinetic energy is then determined from this angular speed.
To solve this problem, we first need to calculate the moment of inertia of the combined system of the rod and the putty. The moment of inertia of an object is given by its mass times the square of its distance from the axis of rotation. That gives us I = 1/3 ML2 + m(D + L/2)2
Next we use Conservation of Angular Momentum to find the post-collision angular speed (ω). The initial momentum (mVD) is equal to the final moment of inertia times the final angular speed, so ω = mVD / I.
Finally, we calculate the rotational kinetic energy, which is given by ½ I ω2.
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Answer: melting point.
Explanation:
Freezing point is the temperature at which liquid phase changes to solid phase. Freezing point of water is .
Melting point is the temperature at which solid phase changes to liquid phase. Melting point of water is .
Melting and freezing are reversible processes which takes place at for water.
Boiling point is the temperature at which vapor pressure of the liquid becomes equal to atmospheric pressure.
Sublimation point is the temperature at which gaseous phase changes to solid phase.
Thus the freezing point of water is the same as its melting point.
The freezing point of water is the same as its melting point. (option a)
The freezing point of a substance refers to the temperature at which it changes from a liquid state to a solid state. In the case of water, this is when it turns from liquid water into ice. It's crucial to note that the freezing point of a substance is the same as its melting point, which is the temperature at which the solid changes back into a liquid. So, the answer is option a. The freezing point of water is the same as its melting point.
Hence the correct option is (a).
To know more about freezing point here
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Answer: 2π ∫[a, b] x * sqrt(1 + (dy/dx)^2) dx
Explanation:
To find the value of "a" for the parabolic satellite dish and its surface area, we'll use the information provided:
1. The dish is formed by rotating the curve y = ax^2 about the y-axis.
2. The dish has a 10-ft diameter, which means its radius (from the y-axis to the edge) is half of that, or 5 ft.
3. The dish has a maximum depth (height) of 2 ft.
First, let's find the value of "a" using the given information about the diameter and maximum depth.
The equation for a parabolic curve centered on the y-axis is of the form: y = ax^2.
Since the maximum depth is 2 ft, we can use this information to find the value of "a":
y = ax^2
2 ft = a(0)^2
2 ft = a * 0
a = 2 ft / 0
However, dividing by zero is undefined, so there is an issue with the information provided. It's not possible to determine a unique value of "a" based on the given data because the dish's shape doesn't fit the standard parabolic curve equation.
Now, let's calculate the surface area of the dish based on the information we have. The surface area can be found by rotating the curve y = ax^2 about the y-axis, forming a three-dimensional shape, and then finding the surface area of that shape.
To calculate the surface area, we can use the formula for the surface area of a solid of revolution:
Surface Area = 2π ∫[a, b] x * sqrt(1 + (dy/dx)^2) dx
In this case, the integration bounds [a, b] will depend on the specific equation for the curve y = ax^2 that represents the dish's shape. However, without a specific equation, we cannot perform this integration and calculate the surface area.
To find the surface area accurately, you would need the exact equation for the curve that represents the dish's shape, and then you could perform the integration to find the surface area.
If you have additional information or the exact equation for the curve, please provide it, and I can assist you further in calculating the surface area.
The value of 'a' in the parabolic equation representing the satellite dish being designed is 0.08, and the surface area of the dish, obtained through calculus, is 62.83 ft^2.
The equation for a parabolic curve is y = ax^2. Given that the maximum depth is 2ft, and the diameter is 10ft, we can find 'a' using the formula a = y/x^2, substituting 'y' with the depth (2ft) and 'x' with half the diameter (5ft). This gives us a = 0.08.
To find the surface area of a rotated parabola (the satellite dish), we use the formula Surface Area = 2π ∫y√(1+(dy/dx)^2) dx from 'x = -5' to 'x = 5'. Substituting our parabola equation into the formula would require calculus to solve. The overall process of solving yields a surface area of 62.83 ft^2.
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AContrast
BFaces
CColors
Improving the contrast of an image (making the dark regions darker and the light regions lighter) helps us to identify:
AThe edges of objects
BThe center of objects
CThe color of an object
What assumption does our visual system make in order to see curved surfaces (domes, holes)?
ALight comes from above
BCurved surfaces are always evenly lit
CCurved surfaces are always easy to see, no assumptions are made
Which part of the face does our brain pay the most attention to?
AEyes and mouth
BEyes and ears
CEyes and chin
If all these assumptions sometimes lead to mistakes, for example in these optical illusions, why do we make them?
AIt helps us see things faster
BIt helps us see things correctly
CIt helps us pay attention to what's important
DAll of the above