![]() ![]() Later, Magellan became involved in an insular conflict in the Philippines and was killed in a tribal battle. During those long days at sea, many of Magellan’s men died of starvation and disease. ![]() Those who remained crossed the meridian now known as the International Date Line in the early spring of 1521 after 98 days on the Pacific Ocean. One ship deserted while in this passage and returned to Spain, so fewer sailors were privileged to gaze at that first panorama of the Pacific Ocean. Magellan named this passage the Strait of All Saints, but today it is known as the Strait of Magellan. Finally they found the passage they sought near 50 degrees S latitude. This ship sank, but the remaining four ships searched along the southern peninsula of South America. More than a year later, one of these ships was exploring the topography of South America in search of a water route across the continent. On September 20, 1519, Magellan set sail from Spain with five ships. Magellan offered to prove that the East Indies fell under Spanish authority. After he was dismissed from service by the king of Portugal, he offered to serve the future Emperor Charles V of Spain.Ī papal decree of 1493 had assigned all land in the New World west of 50 degrees W longitude to Spain and all the land east of that line to Portugal. As a young Portuguese noble, he served the king of Portugal, but he became involved in the quagmire of political intrigue at court and lost the king’s favor. In the 16th century, an age of great marine and terrestrial exploration, Ferdinand Magellan led the first expedition to sail around the world. The integral of impulse is written F xdt, where the integral sign is a distorted "S" meaning "sum" and the " dt " stands for "extremely small (infinitesimal) time interval.Questions 1 through 7 refer to the following passage: More generally, an "integral" is the sum of a large (infinite) number of very small (infinitesimal) quantities. This is an example of an "integral," which can often be thought of as the area under a curve. We're approximating the area under the curve by a bunch of rectangles, but if the little Δ t 's are small enough that the force isn't changing much during that short time interval, the total area of our rectangles is approximately equal to the area under the curve. We can continue through the entire collision with the spring, and we see that the total area under the curve is equal to the total impulse (and the total change in the momentum, which is the sum of all the changes to the momentum). In the next time interval Δ t 2, we can again represent the impulse (and the change in momentum) as the area of the next rectangle shown on the diagram. So the area of the rectangle is equal to the impulse during Δ t 1 and also equal to the change in momentum Δ p x1 during that short time interval. But F x1 Δ t 1 can be thought of as the area of a rectangle shown on the diagram, whose base is Δ t 1 and height is F x1. The small impulse F x1 Δ t 1 makes a small change Δ p x1 in the momentum. In the first short time interval Δ t 1, the spring is only slightly compressed, and the force F x1 on the cart is small. F How would you expect these values to compare?įinding Impulse Using Area Under the Curve There is a more accurate way to determine the actual impulse on the cart. ![]()
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