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how did archimedes determine the purity of gold插图

Principle of buyoancy
Archimedes used theprinciple of buyoancyto find the purity of gold.

How did Archimedes determine that the gold was not pure?

The Archimedes principle. Archimedes was able to determine that the crown was not pure gold due to the volume of the displaced water, because even though the weight of the crown was identical to the weight of the gold that the king gave the crown maker, the volume was different due the various densities of the metals.

How did Archimedes determine if a crown was really made of gold?

According to the legend, Hiero II of Syracuse asked Archimedes to determine without damaging it if a crown he has ordered was really made of gold. He suspected it was made of a cheaper metal. Archimedes first measured the mass of the crown (m 0 = 0.44 kg) and then its apparent mass, when the crown was immersed in water (m’ = 0.409 kg).

What is the origin of the story of Archimedes?

in Greek. The story behind that event was that Archimedes was charged with proving that a new crown made for Hieron, the king of Syracuse, was not pure gold as the goldsmith had claimed. The story was first written down in the first century B.C. by Vitruvius, a Roman architect .

What is Archimedes’s principle?

This story is not found anywhere among the known works of Archimedes, though in his book, On Floating Bodies, he gives the principle known as Archimedes’ Principle, which states that a body partially or completely immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

Why is the buoyant force acting on both objects the same?

This is so because in this case both objects have the same volume and therefore they displace the same volume of water, so the buoyant force acting on both objects is the same. But if the balance tilts towards the mass of gold (right), the density of the crown will be smaller, its volume will be larger the buoyant force acting on it will be larger …

How did Archimedes determine the mass of the crown?

Archimedes first measured the mass of the crown (m 0 = 0.44 kg) and then its apparent mass, when the crown was immersed in water (m’ = 0.409 kg). Using both masses he determined the density of the crown and realized it wasn’t made of gold. How did he come to this conclusion?

What is the magnitude of apparent weight P?

The magnitude of the apparent weight P’ of the crown will be its weight minus the buoyant force F. And the latter equals the weight of the displaced water:

What is Archimedes’ principle?

Archimedes’ principle – The gold crown. According to the legend, Hiero II of Syracuse asked Archimedes to determine without damaging it if a crown he has ordered was really made of gold. He suspected it was made of a cheaper metal.

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What did Archimedes tell his soldiers to do?

When a soldier told him to accompany him to see the general, Archimedes told him to go away. The enraged soldier struck him down. Marcellus ordered that Archimedes be buried with honors. Archimedes’ tombstone was engraved with the image of a sphere within a cylinder, illustrating one of his geometrical treatises.

Why did Archimedes settle in Syracuse?

After studying geometry and astronomy in Alexandria, the "greatest intellectual center in the ancient world," according to Scientific American, Archimedes settled down in Syracuse to pursue a life of thought and invention.

Why did Marcellus send soldiers to get Archimedes?

Marcellus had respect for Archimedes and sent soldiers to get him so he could meet the famous mathematician. According to the Archimedes Palimpsest, he was so focused on solving a mathematical problem that he did not know the Romans had stormed the city. When a soldier told him to accompany him to see the general, Archimedes told him to go away. The enraged soldier struck him down. Marcellus ordered that Archimedes be buried with honors. Archimedes’ tombstone was engraved with the image of a sphere within a cylinder, illustrating one of his geometrical treatises.

What was Archimedes’ greatest achievement?

Many of his inventions, theories and concepts are still in use today. Perhaps his best-known achievement was his "Eureka" moment, when he discovered the principle of buoyancy.

What did Archimedes say about the power of leverage?

Archimedes famously said, "Give me a lever and a place to stand, and I’ll move the world." This boastful claim expresses the power of leverage, which, at least figuratively, moves the world. Archimedes realized that in order to accomplish the same amount or work, one could make a trade-off between force and distance using a lever. His Law of the Lever states, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights," according to "Archimedes in the 21st Century," a virtual book by Chris Rorres at New York University.

Why was Archimedes able to determine that the crown was not pure gold?

Archimedes was able to determine that the crown was not pure gold due to the volume of the displaced water , because even though the weight of the crown was identical to the weight of the gold that the king gave the crown maker, the volume was different due the various densities of the metals.

Why do bugs walk on water?

These dips can then be used to derive the water volume that was displaced leading to the force used to keep the water-bugs afloat. The authors said there is a great deal of interest in understanding the physics behind the water-walking bugs in order to create biomimetic water-walking robots.

What did Hiero do before the ceremony?

Hiero made preparations for the ceremony to place the wreath in the temple that he had chosen. But a few days before the ceremony, he heard rumours that the goldsmith had cheated him, and given him a crown not of pure gold, but of gold that had silver mixed in it. The goldsmith, said the rumours, had replaced some of the gold that Hiero had given him, with an equal weight of silver.

How did Archimedes solve Hiero’s problem?

Deep in thought, pondering how best to solve the king’s problem, Archimedes walked to the public baths for his daily bath. Still thinking about the golden crown, he went through the rituals of cleansing and washing, and stepped into a tub of cool water for his final dip. As he began to lower himself into the water, the water in the tub began to spill out over the sides. Curious, Archimedes continued to lower himself slowly into the water, and he noticed that the more his body sank into the water, the more water ran out over the sides of the tub. He realised that he had found the solution to Hiero’s problem.

What did the goldsmith deliver to the king?

The goldsmith did as he had been ordered, and on he appointed day, he delivered to the king an exquisitely wrought crown, shape d, as the king had ordered, like a laurel wreath. The wreath seemed to weight exactly as much as the gold that the king had given the goldsmith. Hiero was pleased, and paid the goldsmith handsomely. The goldsmith, receiving his payment, went away.

How did Archimedes balance the crown?

Instead of immersing the crown and an equal weight of gold in a vessel filled with water, Archimedes could have suspended the crown from one end of a pair of scales, balancing it with an equal amount of gold on the other end. Once equally balanced, he would have immersed the suspended crown and lump of gold into a vessel of water. Now, since a body immersed in water is buoyed up by a force equal to the weight of the water displayed by the body, the denser body, which has a smaller volume for the same weight, would sink lower in the water than the less dense one.

Why was Hiero furious?

Hiero was furious to learn that he might have been tricked. But he was a fair-minded man and wished to determine the truth before he punished the goldsmith.

Why was Galileo put under house arrest?

The Church forced Galileo to recant, and placed him under house arrest for the last eight years of his life, for having believed and taught Copernicus’ theory. It was only in 1992 that the Church formally acknowledged its error.

How to find the volume of a crown?

The simplest method of determining the volume of the crown would have been to melt it down, shape it into a cube and measure its volume. But Hiero had given strict instructions that the crown was not to be damaged in any way. So how was the volume to be determined? This is where Archimedes’ discovery came in useful.