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Toy cars go down a sloped lane (inclined plane). Over three hundred years ago, Galileo Galilei claimed that such a slide is the same as a fall, with the exception of being slower. As if the force of gravity was weaker (distributed into components). |
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At the end of the inclined plane they turn upside down, like a swimmer at the end of a lane, and they by no means slow down. It seems they bounce off. |
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The last car is charged by a piece of lead but this does not make it go faster. If a bike goes down a slope, it accelerates like a car. It was also noticed by Galileo. |
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Although toy cars going down a sloped plane should accelerate, it does not look so. As is the case with the other toys, the longitudinal component of the gravitation force is (approximately) equal to the friction force. Theoretically, the force of friction should not depend on the acceleration, according to Leonardo da Vinci's equation T = ηG, where G stands for the body's weight and η stands for the friction coefficient. Apparently, other forces are also involved - the resistance of air, the friction between the wheels and axes etc. |
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The observation that the velocity of the motion on the slope does not depend on the mass is essential. Galileo discovered that acceleration a of a body going down inclined plane increases with the angle of the slope, but does not depend on the mass of the body, in accordance with the well-known equation: a = g sin(α), where α stands for the angle at which the slope is inclined and g is Earth's acceleration. |
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The original Galileo's slide (or better: inclined plane) is exceptionally educational. It consists of an inclined beam with a groove in which a heave metal sphere rolls along. Five bells are fitted alongside the beam so that the sphere hits them when sliding. Galileo, a son of violin maker, was sensitive to the sounds and arranged the bells in such a manner that the sphere hits them at regular intervals (within the distance of 1:3:5:7 among them, as described by s = at2, equation, i.e. within the distance of 0,1,4,9,16 counting from the starting point.) |
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