Additionally, we can relate the acceleration of a ball down an incline with a = g sin θ, which is what Galileo did too.Ī 10 second fall necessitate dropping from a height of. We use g instead of a because g is a constant rather than a variable like a. Galileo was exactly right, though: the acceleration of gravity on planet Earth is indeed. He had to postulate it because, again, free fall times were difficult for him to measure accurately. The acceleration rate a changed with the angle of incline, but Galileo postulated that at a 90° angle, or free fall, the acceleration of gravity is a constant. The distance fallen (or rolled down an incline) consistently corresponded to. The velocity increased uniformly and predictably from a constant acceleration. This means the ball rolls the last of the incline in the same amount of time as the first quarter. When he rolled the ball down only a quarter of the incline, it would take half the time as rolling down the entire incline. Here’s what he found: the distance fallen down the incline was proportional to the time squared. His clock was a water clock, meaning the amount of water leaking from a container with a hole in it corresponded to the total time. The more data collected, the better the accuracy of the results, and accuracy is precisely what Galileo was going for. Then he rolled a lead ball down it, over and over. He kept the angle of incline of the ramp small so the times and distances would be easier to measure accurately. He made a grooved, smoothed, wooden track and marked distances on it. Galileo got around this by slowing the acceleration with a ramp. The initial speed of an object in free fall is always zero, but the final speed is super hard to measure. Not only that, but objects in free fall are innately hard to time because the of the acceleration: it’s all over so quickly. This was hard in his day: he had no reliable clock, no gadgets, nothing. The perfect song to study Galilleo’s work.Īfter verifying that objects fall at the same rate no matter their size or mass, Galileo designed an experiment to measure the position of a falling object as a function of time to calculate the speed, and thereby determine whether the constant acceleration he hypothesized was correct. While we could certainly investigate this matter by rigorous experimentation, we don’t have to. We’ve always wondered whether it’s possible to calculate the position of a dropped or thrown object.
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