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As a little kid, I used to be fascinated by that until my senior secondary school, then I realized it wasn't rocket science. It is a combination of physical and chemical activities. 

The match head contains powder glass, potassium chlorate and sulphur while the striking surface is made of powder glass, red phosphorus and sand. When a match stick is struck against the surface, the sand and powder glass cause friction and heat. This further converts the red phosphorus to white phosphorus - a volatile chemical that ignites. 

The heat produced also breaks down the potassium chlorate thereby releasing oxygen. This reaction fuels It and keeps the fire burning a some moment. 
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Today match's fire due to simple chemical reaction. When a match is struck, friction creates a heat and a flammable compound that ignites in the air. 
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A matchstick starts burning on rubbing it on the one side of the matchbox because the heat produced by friction heats the chemical at the head of the matchstick to their ignition temperature and makes it to catch fire.
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The matchbox is manufactured with a capability of starting up a fire when it is struck on the matchbox. Friction force causes the fire to be lit.
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A match stick lights when the tip of the matchstick is rubbed against a rough surface, such as a matchbox, which causes friction and produces heat. This heat is transferred to the match stick's phosphorus-sulfur coating, which ignites, producing a small flame.
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Friction produce heat, when a match stick is scratch on a rough surface , surface  the friction is produce that cause it to light up and is supported by the oxygen gas
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striking a match against the powdered glass on the matchbox creates friction. Heat from this friction converts the red phosphorus into white phosphorus. That white phosphorus is extremely volatile and reacts with oxygen in the air, causing it to ignite.
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