{"product_id":"hemisphera-magdeburg","title":"Hemisphera – The Magdeburg Hemispheres \/ F = πr²Δp Physics Sticker","description":"\u003cp\u003eHemisphera, a wide-hatted burgomaster, guards a sealed metal sphere crackling with sparks.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eOtto von Guericke, mayor of Magdeburg, invented an air pump and in 1654 demonstrated it at Regensburg before the Imperial Diet. He fitted two copper hemispheres together and pumped the air out. With the inside nearly empty, the outside air pressed them together so hard that teams of horses could not pull them apart. Let the air back in, and they fell apart by hand.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eF = πr²Δp\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eF: force needed to pull the hemispheres apart (N)\u003c\/li\u003e\n\u003cli\u003er: radius of the hemispheres (m)\u003c\/li\u003e\n\u003cli\u003eΔp: pressure difference, outside minus inside (Pa)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eNothing sucks: the vacuum pulls nothing. The force is the outside air pushing on the area of the seal's circle. At r = 0.25 m and full vacuum that is about 20 kN.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e His pump never made a perfect vacuum, so the real force was less than the full-vacuum figure; he repeated the show at Magdeburg and elsewhere in later years.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eHemisphera stands over a glowing sealed sphere with sparks bursting around its seam. Printed text: \u003cstrong\u003eHEMISPHERA\u003c\/strong\u003e with the line \u003cstrong\u003eF = πr²Δp\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50964083408999,"sku":"25293704709214953683","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50964083441767,"sku":"15867207896812776224","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50964083474535,"sku":"30954154532395303851","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50964083507303,"sku":"22297007003867539830","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/13653298730817691918_1200.jpg?v=1793659841","url":"https:\/\/pixelatedphysics.com\/pt\/products\/hemisphera-magdeburg","provider":"Pixelated Physics","version":"1.0","type":"link"}