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A box-shaped metal can has dimensions 5 in. by 19 in. by 4 in. high. All of the air inside the can is removed with a vacuum pump. Assuming n
Question
A box-shaped metal can has dimensions 5 in. by 19 in. by 4 in. high. All of the air inside the can is removed with a vacuum pump. Assuming normal atmospheric pressure outside the can, find the total force (in lb) on one of the 5-by-19 in. sides. (Enter the magnitude.)
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Physics
3 years
2021-08-31T02:57:01+00:00
2021-08-31T02:57:01+00:00 1 Answers
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Answer:
The force is![Rendered by QuickLaTeX.com F = 1397 lb](https://documen.tv/wp-content/ql-cache/quicklatex.com-640025ecec30c4886c253dfd0af21b9d_l3.png)
Explanation:
From the question we are told that
The length of the box is![Rendered by QuickLaTeX.com l = 19 \ in](https://documen.tv/wp-content/ql-cache/quicklatex.com-1e0200b39db09b895edea11ab6954dd1_l3.png)
The width of the box is![Rendered by QuickLaTeX.com w = 5 \ in](https://documen.tv/wp-content/ql-cache/quicklatex.com-1a883617b40c2ebf9f4baba8893ccb37_l3.png)
The height is![Rendered by QuickLaTeX.com h = 4\ in](https://documen.tv/wp-content/ql-cache/quicklatex.com-1b1ea17a18e18b8969ba01b7fefd0842_l3.png)
The pressure experience on one of the sides is mathematically represented as
Where A is the area of the box which is mathematically evaluated as
substituting values
This pressure is equivalent to the atmospheric pressure which has a constant value of![Rendered by QuickLaTeX.com p = 14.7 pi](https://documen.tv/wp-content/ql-cache/quicklatex.com-ce998a4438d3c617d2235cfe38929ee6_l3.png)
This implies that
=>![Rendered by QuickLaTeX.com F = 14.7 *95](https://documen.tv/wp-content/ql-cache/quicklatex.com-fa4560a34a4e81d6cba3a6e3a44380a1_l3.png)
=>![Rendered by QuickLaTeX.com F = 1397 lb](https://documen.tv/wp-content/ql-cache/quicklatex.com-640025ecec30c4886c253dfd0af21b9d_l3.png)