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valentinak56 [21]
3 years ago
7

When matter and energy change forms within a closed system, A. The total amount of energy changes, but the total amount of matte

r does not. B. The total amount of both matter and energy changes. C. The total amount of matter changes, but the total amount of energy does not. D. The total amount of both matter and energy does not change.
Physics
2 answers:
maw [93]3 years ago
7 0

Answer: the total amount of both matter and energy does not change (d)

Explanation:

i just got this question on Study Island

Sphinxa [80]3 years ago
4 0

Answer: Option D. The total amount of both matter and energy does not change.

Explanation:

From Law of conservation of energy and Einstein's mass-energy relation, we know that, energy neither is formed not is destroyed. It converts from one form to another. Einstein's mass-energy relation: E = mc². It means, Matter is a form of energy i.e. matter holds energy equivalent to product of its mass and square of speed of light. Matter and energy can change forms but the total amount does not change in a closed system. Thus, correct option is D.

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Answer:

Approximately 3.1 \times 10^4 \; \rm N (assuming that the acceleration due to gravity is g = 9.81\; \rm kg \cdot N^{-1}.)

Explanation:

Let A_1 denote the first piston's contact area with the fluid. Let A_2 denote the second piston's contact area with the fluid.

Similarly, let F_1 and F_2 denote the size of the force on the two pistons. Since the person is placing all her weight on the first piston:

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Since both pistons fit into cylinders, the two contact surfaces must be circles. Keep in mind that the area of a square is equal to \pi times its radius, squared:

  • \displaystyle A_1 = \pi \times \left(\frac{1}{2} \times 3.0\right)^2 = 2.25\, \pi\;\rm cm^{2}.
  • \displaystyle A_2 = \pi \times \left(\frac{1}{2} \times 24\right)^2 = 144\, \pi\;\rm cm^{2}.

By Pascal's Law, the pressure on the two pistons should be the same. Pressure is the size of normal force per unit area:

\displaystyle P = \frac{F}{A}.

For the pressures on the two pistons to match:

\displaystyle \frac{F_1}{A_1} = \frac{F_2}{A_2}.

F_1, A_1, and A_2 have all been found. The question is asking for F_2. Rearrange this equation to obtain:

\displaystyle F_2 = \frac{F_1}{A_1} \cdot A_2 = F_1 \cdot \frac{A_2}{A_1}.

Evaluate this expression to obtain the value of F_2, which represents the force on the piston with the larger diameter:

\begin{aligned}F_2 &= F_1 \cdot \frac{A_2}{A_1} \\ &= 495\; \rm N \times \frac{2.25\, \pi\; \rm cm^2}{144\, \pi \; \rm cm^2} \approx 3.1 \times 10^4\; \rm N\end{aligned}.

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