Explanation:
Newton's second law of motion says that the net force is equal to the mass times acceleration:
F = ma
If the net force is halved, and the mass stays the same, the acceleration will be halved as well.
F/2 = m a/2
The work performed on the spring is
W = 1/2 k x²
so that
4 J = 1/2 k (0.11 m)² ⇒ k ≈ 660 N/m
Then by Hooke's law, the force required to hold the spring in this position is
F = k x = (660 N/m) (0.11 m) ≈ 73 N
Answer:
It's best to also include the options since this is a multiple choice question! But the best answer would be D.
Explanation:
It flows through and is used by ecosystems.
b. left block.
c. justified block.
d. modified block.
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.
#SPJ2
The baseball will undergo 16 revolutions on its way to home plate.
Explanation:
As the parameters which are given are speed at which the baseball is thrown, (v = 90 mi/h) and the distance between the home plate and the ball thrown is 60 ft. Also the spin is said to 1950 rev/min, it indicates that the ball will undergo 1950 revolution in every single minute. So in order to determine the number of revolutions the baseball will make in its way to home plate, we have to first determine the time taken for the baseball to reach its home plate with the given speed.
As we know that speed can be obtained by the ratio of distance with time, in the present case, we know the speed and distance, then time can be obtained by ratio of distance with speed.
At first, we have to convert the speed from mi/h to ft/min
1 mi/hr = 5280/ 60 ft/min = 88 ft/min.
Then, Time = Distance/Speed = 60/(90×80)=60/7200=8.33 × 10⁻³ min
Since the ball undergoes 1950 revolutions in 1 min, then in 8.33 × 10⁻³ min, the number of revolutions will be 1950×8.33 × 10⁻³ = 16 rev
Thus, the baseball will undergo 16 revolutions on its way to home plate.
A moving ball primarily has kinetic energy (motion).
Elastic energy comes into effect if the ball is compressed or stretched, like in the case of a bouncing ball.
Theoretical problems usually have perfect pr controlled conditions, but a moving ball in real life would be compressed or changing with its contact with the ground.
If you want more help or could provide more context, feel free to ask.
If this is a question on a test or quiz and its asking what type of energy a 'moving' ball has, generally they want you to think about what causes the movement (in this case, kinetic), because there is always a lot of other energy being transferred and happening at the same time (i.e., thermal, sound).