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Harrizon [31]
3 years ago
12

When plug prongs are connected to the metal case of an appliance, a part that should always be placed next to the case is a

Physics
1 answer:
Zielflug [23.3K]3 years ago
6 0
The correct answer is (d.) mica washer. When a plug prongs are connected to the metal case of an appliance, a part that should always be placed next to the case is a mica washer. Mica washer are used as a window for any radiation detectors.
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A non uniform rod has mass
Doss [256]

Answer:

r_{cm} = L/3

Explanation:

Mass: M, Length: L.

\sigma (x) = b(L-x)

The formula that gives center of mass is

\vec{r}_{cm} = \frac{m_1\vec{r}_1 + m_2\vec{r}_2 + ...}{m_1 + m_2 + ...} = \frac{\Sigma m_i \vec{r}_i}{\Sigma m_i}

In the case of a non-uniform mass density, this formula converts to

\vec{r}_{cm} = \frac{\int\limits^L_0 {x\sigma(x)} \, dx }{\int\limits^L_0 {\sigma(x)} \, dx }

where the denominator is the total mass and the nominator is the mass times position of each point on the rod.

We have to integrate the mass density over the total rod in order to find the total mass. Likewise, we have to integrate the center of mass of each point (xσ(x)) over the total rod. And if we divide the integrated center of mass to the total mass, we find the center of mass of the rod:

\vec{r}_{cm} = \frac{\int\limits^L_0 {x\sigma(x)} \, dx }{\int\limits^L_0 {\sigma(x)} \, dx } = \frac{\int\limits^L_0 {xb(L-x)} \, dx }{\int\limits^L_0 {b(L-x)} \, dx } = \frac{b\int\limits^L_0{(xL - x^2)} \, dx }{b\int\limits^L_0 {(L-x)} \, dx } = \frac{\frac{x^2L}{2} - \frac{x^3}{3}}{Lx - \frac{x^2}{2}}\left \{ {{x=L} \atop {x=0}} \right.

Here x's are cancelled. Otherwise, the denominator would be zero.

r_{cm} = \frac{\frac{xL}{2}-\frac{x^2}{3}}{L-\frac{x}{2}}\left \{ {{x=L} \atop {x=0}} \right. = \frac{\frac{L^2}{2}-\frac{L^2}{3}}{L-\frac{L}{2}} = \frac{\frac{L^2}{6}}{\frac{L}{2}} = \frac{L}{3}

8 0
3 years ago
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