Problem 55535. Magnitude of Balancing Force

Created by Tanya Kuruvilla

Solve Later

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Find the magnitude of the balancing force to the nearest hundredth of a pound.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"141\"/><w:attr w:name=\"width\" w:val=\"347\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" 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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 218.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 109.25px; transform-origin: 407px 109.25px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">A box weighing W1 pounds is placed where its center of mass is located d1 ft from the fulcrum. A balancing force is placed at the opposite end of an L ft plank, d2 ft from the fulcrum. The plank has a weight of W2. Find the magnitude of the balancing force to the nearest hundredth of a pound.</span></span></div><div style="block-size: 146.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 73.25px; text-align: left; transform-origin: 384px 73.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 347px;height: 141px" 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" 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Last Solution submitted on Mar 23, 2023

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David Hill on 9 Sep 2022

Need more tests

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Solution 9676813

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Arvind Mishra on 3 Nov 2022

Nice Problem.

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Problem 55535. Magnitude of Balancing Force

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Problem 55535. Magnitude of Balancing Force

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