`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`
${elem} `); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`
${book_segment.title} `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`
${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "OX5CUqdf6SPubaypNRzxPtZNvczau6AyL5soki4OfE1IS7kUlyjtFD6BqGf6w6am"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j
Solutions
Textbooks
`); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(` Solutions ${viewAllHTML} `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+" "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(` Textbooks View All `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "OX5CUqdf6SPubaypNRzxPtZNvczau6AyL5soki4OfE1IS7kUlyjtFD6BqGf6w6am"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "OX5CUqdf6SPubaypNRzxPtZNvczau6AyL5soki4OfE1IS7kUlyjtFD6BqGf6w6am", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
FAQs
Newton's law of gravitation gives a relation between the strength of the force F between two objects with masses M and m and the distance between them, r units and is defined as F=GMmr2.
What is the Cavendish method? ›
Cavendish experiment, measurement of the force of gravitational attraction between pairs of lead spheres, which allows the calculation of the value of the gravitational constant, G.
What is the torsion balance of gravity? ›
The gravitation torsion balance according to Cavendish is a light transverse beam, horizontally suspended by a thin torsion fiber, which supports a small lead ball with the mass m2 at each end at a distance d from the suspension point. These two balls are attracted by two large lead spheres with the mass m1.
What was the original Cavendish experiment? ›
The Cavendish experiment was the first to allow a calculation of the gravitational constant (G) by measuring the force of gravity between two masses in a laboratory framework. The original experiment was proposed by John Michell (1724-1793), who first constructed a torsion balance apparatus.
What is the gravitational force between a point mass m and m separated by a distance F? ›
Total force on the body of mass M is F, i.e., F=GM×(m+3m)r2=4GMmr2=4F.
What is force of gravitation between two bodies of masses m1 and m2? ›
The gravitational force between two point masses m1 and m2 at separation r is given by F=km1m2/r2 The constant k.
What was the conclusion of the Cavendish experiment? ›
His major project, now known as “the Cavendish experiment,” was a meticulous measurement of the gravitational attraction between lead balls in his laboratory carried out with extreme precision (6). The results allowed him to calculate the average density of the world, which he gave as 5.45 times that of water.
What was the torsion balance experiment by Henry Cavendish? ›
The experiment measured the faint gravitational attraction between the small and large balls, which deflected the torsion balance rod by about 0.16" (or only 0.03" with a stiffer suspending wire). Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed.
What important value did the Cavendish experiment determine? ›
The objective of Cavendish's experiment was to measure the density of Earth, or, in his own words, to '' weigh the Earth'~. ' Cavendish's result enabled the first calculation of the value of G. The value of G=6.673 X 10-11 N m2/kg2. G is also known as big G.
What is the formula for torsion balance? ›
T = (r · F1 x F2) /(F1 + F2). So, the torque on the fiber depends on the angle between the two forces. There is no torque unless there is a non-zero angle between the forces, so torsion balance experiments are null experiments that detect any non-parallelism of the forces on the test bodies.
K = T / θ = GJ / L. Torsion, if defined in simple terms, can be explained as the amount of twist that we give to a particular object at one end when the other end of the object is fixed and doesn't move with the twist applied at the other end of the object.
What is torsion balance method? ›
The torsion balance consists essentially of two small masses at different elevations that are supported at opposite ends of a beam. The latter is suspended from a wire that undergoes torsion because the masses are affected differently by the force of gravity.
Was Cavendish autistic? ›
He said that he is wary of recent claims of Asperger's syndrome for historical figures, but he considers Cavendish an exceptional case, finding the evidence for his autism “almost overwhelming.” 99 Upon rereading Wilson's biography of Cavendish, he wrote in his memoir Uncle Tungsten the same year that Cavendish was a “ ...
What did Henry Cavendish discover in physics? ›
He is noted for his discovery of hydrogen, which he termed "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper, On Factitious Airs. Antoine Lavoisier later reproduced Cavendish's experiment and gave the element its name.
Did Henry Cavendish have a wife? ›
In 1652 he married Frances Pierrepont (1630-1695), the daughter of William Pierrepont and sister of Grace Pierrepont, who became Countess of Clare as the wife of Gilbert Holles, the 3rd Earl (1633-1689).
What is the gravitational force between two objects with masses m and m? ›
The gravitational force of attraction between two objects of masses m1andm2 seperated by a distance d is given by F=Gm1m2d2.
How do you calculate the gravitational force between two masses? ›
Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)2.
What is the equation for the gravitational force between two bodies? ›
Find out how to calculate gravitational forces
We can do this quite simply by using Newton's equation: forcegravity = G × M × mseparation2 .
What is the formula for the gravitational force of mass? ›
The force of gravity measures the intensity of the attraction between two massive bodies. It can be calculate as F = (G * m1 * m2) / d^2. Where G is the gravitational constant, m1 and m2 are the masses of the bodies, and d is the distance between them.
