Problem 55555. Find the force required to support a lever

Created by Tanya Kuruvilla

Solve Later

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<div style = "text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 308.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.4px; transform-origin: 407px 154.4px; vertical-align: baseline; "><div style="block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">Students are designing a robot that will lift a block to the equilibrium position for transport to the scoring area. They have decided to use a lever to accomplish this. The lever below is composed of a W</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style="">P</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style="">lb. plank of length L hinged at the far-left end. The effort force F</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style="">E</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style="">is applied between the fulcrum and the W</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style="">L</span></span><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: 0px 0px; transform-origin: 0px 0px; "><span style=""> lb. load. Determine the force required to support the lever in the equilibrium position. Assume the center of gravity of the plank is at the mid-point. Round to the nearest hundreds.</span></span></div><div style="block-size: 164.8px; 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 82.4px; text-align: left; transform-origin: 384px 82.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATsAAACfCAMAAACx+I65AAABUFBMVEX//////v7r8PaVlqmfrMbYt6f6zK1EcsT4y63/AAD4y6z9/f1xcHFpaGkAAAC0tLRFdMj39/eAgIFEc8U/aLHg4OBIR0ZXV1e4uLjAv7/Pzs6urq6dnZ3rezB7e3vU1NTvfTCQkJEwMDDv7+/09PQ7XqDr6+t3dnb5za/Dw8PU2+dhYWG8vLz9z7Dbdzfy9vzb29uJiInKycm3loAbLU37+voBAgEDBQiOfoWko6OLMjKShI0+Pj7n5+cKDhexsbFPT0/GxsZEbbasra1Abr4iOWLj5OSXd3aXlpfoAAC/AgLPAACkkpL/29upqan/rKz/mpq3cU22wdbJdEFbfLbf5e7/ubn/7+99Sj+kb1reAABcYoaotMyNamb/x8d2kL7O1uSDiaOSnLaLoMWcp7/Dzd/2AACJcndxXFPsw6rEq6QiOmOsAADs4eHfxcX/8Klfg3wkAAALBUlEQVR42uyd+UObSBvHobZ1d5mRBUsggBAChbKkCrzL26YNhhhfmm3XtGrV19Ue9nh7vMf//+M7kEOSqDk2Gt3M105jeIY5Pj5zkgBBYGFhYWFhYWFhYWFhYV1fcRxmQE4GgWTZqy+qVkpfKbl+TeApyk1hR1W81qskXBd21s1hp7V+cV1K5WwhxOzGZ8dajJODOajfXHaUTQtcns6HKHACXUNBVGnadVEQUajRpRCFJEos0D46LHI0raqpWYhR4Gy6FJdoG53poyii2zb7NB37qTnPIXOIAtPHzmLUoth6i2InCYUocK3ExJhO81PFNDEhTSyf5lULhVaUtplrlVSIW5VI8vJRKTsVSaO0K4HqaaOEa8nhpCLUn2AXeBDYLGRFFGwLenkAZQlCiYaQliEsadASPWjZClRqFtQECGUbwHITwqoMQQ2FPDLXlPRMTQSwgaIkZkGDwG+kZgWdzaooit7HrkyYlVp7CGnFFNuxUR4NH8IGKka9jIrSaCfGtvJC+aQlrULYLKPDKCT52e1KiKikJZiaq9W0pGlFkFlR2TRxrYQqgVIoB5fUZskRkrjQSA5ps3KX3Wi5/YmC/jX6O15qqqiyCuhjh8eKoXmilgeS6UlVCso+YWgcZndzNSE7TcPoCG8yCIaB0WEIWFizUsCQg4eGn4TBIdlgoOeS2KA7MHI2dcZJZTzVSERHA/sKsnPqVlVwlotpDgaHJPC97IJQz7JjTJIxjLDPNxuY3RnsdDZy+Ay7vBMIDowcDvvdGW0WsdPjWE8CetvM+X7En7ITcoFUlNQomQobcWy2omG/6/pdk+fLKDTRWwBI1N8ZOpVhFwWEZ6EDNSfymnwkY7/L+B1yKB0Fo8uOY/UsO6bFjglj08B+d25/V67U8hXeBRl29Q473N+d4XfZsULJQYvluuxsGJRAQMgaicfZoXMUSjcCJu5OmAMj+UcwDB5nh7NLFTty/qJllwYxOCRTDAYPMnbVvogdp2JwWFjzIJKe8udpkitfUxcji9eRnTLlzSvDKU+/kAZfv47spn2NkbkEdsQ8sDM92ODny+8oiiL7whmHMqazoiSzeCVqWsUOuyHJDM+F7LxeY78LNGDVPOCpKNQUoNkWKFcBoAUABBmAfAOwogbYGgs8XwGNEgBlFKVeR1HKwPJlYOU1oMQEEeYkwkR+R6YkbZDGQUkkcRQbxfFZoKkK8GwFyEJqtvJNYJUaaQFYlU1z0dCZibmahDIAtWvMjspLNFeShLgklThayrtVSVQlSXVR8OtV15boOIkiSAIy28jscyiKWEdmqcqh4CIzWgy5uVLS3/lQoVHSbjcOjeLQbiuJfEinufgoB1FEpyahhpLJS0KY5ICioIwTs5oEUZK4m9ffjf+pLD3SglqxKXnMeFftyCG5zcU428w5TqVe5ZsxHmfHnBYfHNz5/r87//0d5s25GGenOTd++yrVMyU058LvprgmI4OtYOvgYMtXHlcDcpqlZOS//DYRmX66ONjff7W/H+C9gkkAbr1EPxgEFhYWFhYWFhYWFhYWFhYW1kyEv7Y0scSv+TOOkmNoftE9ef5kEJ6QG12QmVt0f/z42yA8eWl0FZn5RffjGfDkpUe/jqb1eWXXQncGPHlp/d7PI+nfc8qug24QXsJueXEE/fyP+WR3im4AHmY3Orp+eJjdGOj64GF246DrhYfZjYWuBx5mNx66LDzM7lz5T178C6kHXHLgjyclzO5Cka7zJNWLDLoXrUNfRczuQpkcx8Vc/Ph5lt2bmEsUYnaj6Pceds/w3Bizw+wwO8xuXtn5KmY3qXiA2WF2mB1mh9ldZ3bU3s7O+zXMbgIZx8+2tw8X9jC78b3u+HClUFjZbdzC7MbVL89WCghe4fB4bbgYzC6r420EDsFbPXo8XCfBtWM3y88FfNotpI63+mZ1Zager103dvdH06+Xwk7YLqTwVuHu6lCxe7cuRxFcO8ey9vQ/v53q+ZesSVtaejSilooXFH1SrO+fraRtdvvo6XCdLFySirlzTco/s7KyJmfp76Pq0fr5mZ/cnpBd8Gk7GSpWn558e/DDMP10Sbqb+/rwXNuDrLJFuHvnb2Po7rm53/k0ITvm48nh7u7h0/cfvv0wMyXsxj/rp7sPx9D5mU/Mbsf6cnS0sHOLmCW7BxOxG+/PM312aye7K2/uH6M58odvd2emh4jd7DKflN3nNyurR/de30Lsvt+ZnSr8DDP/Phm7tYXdwvb9xY0d1Hhvz1ALCzPM/NPnyWYoX1ZWwOby5rv5fsbUJF++oD5sJ263mDoe1ngbAYnbJcvpzXf4O0fjLma3C7v3N5Odho33mMZY2nu8uvKmtYuz+ZHCPMbpIY8PC7tHqdstbr7+BQMZQ7e81ULb7RaXN26TmMgY256HhdW22y0ub77ew0RGd7uT3cLhvc629PLG8awLFISUEd4I7yfT5dhmd79/8/WVXu3hymhWZFfRCCV07p2v8qHg3IhbDibLscP7mQsiVzs/FosqwfDFkDCizn24xYirRhcP95RLC+HQtA0/0P3L/CP0uV0yP77ChRlpRDLBVYo2Iebcjt8l7EI1JgnGVbOP3QlkHsJGSkUBfOT2JpX3GILUZIpgtPbz4tWKKVbMS+xcWrsAWW18vkrHUyBR4nmNKPPBKTu6CKNKKfCiKPsAbMbhBUFsIQ9M3utNqFZRCbOIWHEVv8MuFCv65RU93QXY6Lm6ufnuKjsbIRd6XplnrC4lMWFX0tmIq0im2cMui8vqe6qTnqsTtWJRJOiodRKZshPrgkHoQnP6Dw3p7gL0ON5VLsziiuAIYs6PbMKtuWSnzVJEvmh6kcf1sLPCznNPqZhv9DV/xSJk4GiEohCnflfkQYVlFB54014wUXudXYAex/t4hY4XABjFRgT40AAsqLXHilxA0BWDEmH2OWOMU+R5uvW7zIP+wULKmbDacExeyrLzCbro8po+9SqRt7u7AFl2Vzo/ltcdhmDXLUJXwnrScMUcarOezQNT8L3IzLIDHGfEZblGkg47AMPN0ZHq56oRF7QeQ9bu79yiW+Kd6rT9LrMLkNHyvatcmLnJ5MTO5QkdlNnk23WcYvosyyuxafHQ7mmzyX3TaWijpq3Rgx7s8I5h5hwYmNDssnMJuxgTulxxp78c6+wC9OhKHY9K/lDIK3To5ZEzHbx9m9xTen8/vbX02/2trT52VmwQZKM5mFDjkUJQyrpMZNgVnUZkmQ1Z4cPpFjq7C9A7WsxiYaazyRMbyODlq33087L70mUX1BO3FCJPJUiZPsODFTSY+izXZkeGDT0uS0ojPChbnhgQU+3ydjK7AH093gw+hkfFaeXI4IA8IA6CAP1H/r+9s1lBEIiicCOBq4h+oAcwjdpIryAuWqWo2aasjOj93yCzFpYzcw1EHTrfwtmJXI7DPZ65mC+fDNfknV6128exn/ix570WP0nq/gpgck+qtRhcUFvtcjbeEvu+MVhsjB7L333vvQVky75O2X3bsZaM2Y9NjWFRz8bmVv5rbZZto+y9PC81PoRYdk0bM+W43TPZOYLDpkjMpLJLw7Ida8mYqcaKZ8cKtUNi9ttXgIK3QGImxk6PoUR2SMxkurNvF9PVZcJDYiZsglgwlQ1ydCAx6y6jkysfg4k0FEnA2SFGiHCiTNjfXQnZ6f9+lFHS3znk7BqMmYA+XbtmEzN12EUuPTQJY8bl4FQYOG00MVMGLdInNDr6Y05jHEwrYfZRqxLWqho7mFqO8lACAAAAAACFeQDry7bQRozGbAAAAABJRU5ErkJggg==" data-image-state="image-loaded"></div><div style="block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 0px 0px; transform-origin: 0px 0px; "><span style=""></span></span></div></div></div>

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Problem 55555. Find the force required to support a lever

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Problem 55555. Find the force required to support a lever

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