Answer : (D) " all of the above "
Explanation :
The forces acting on a satellite are Earth's gravitational force and centripetal force. The properties of centripetal force acting on a satellite in orbit are as follows :
(1) It acts as an unbalanced force on the satellite. This is due to the reason that there is no same force present which pulls the satellite away from the earth.
(2) It changes the direction of the satellite. The satellite is revolving with a constant speed while the direction is kept on changing (in a circular motion).
(3) Centripetal force always acts towards the center.
So, the correct option is (D) " all of the above "
b. 20 km
c. 200 km
d. 2,000 km
Answer:
number 2!
Explanation:
Answer:
2s to 4s
Explanation:
Since the graph measures acceleration over time, when the line does not move up or down is when you can see a constant velocity.
Answer:
The speed of the object is increasing.
F = M a as long as the magnitude of the acceleration is acting towards the right there will be an acceleration towards the right
Answer:
D) When you increase the distance over which effort is expended, you don't have to work as hard.
Explanation:
This statement reflects one of the principles of mechanical advantage. When you increase the distance over which effort is applied (in situations like using a lever or a simple machine), it allows you to achieve the same work with less force. It's the concept of trading off force for distance, which is a fundamental principle in physics and mechanics.
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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