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$\bullet \mathrm{A} 0.100 \mu \mathrm{g}$ speck of dust is accelerated from rest to aspeed of 0.900$c$ by a constant $1.00 \times 10^{6} \mathrm{N}$ force. (a) If thenonrelativistic form of Newton's second law $\left(\sum F=m a\right)$ is used, how far does the object travel to reach its final speed? (b) Using the correct relativistic form of Equation $27.19,$ howfar does the object travel to reach its final speed? (c) Which distance is greater? Why?

$$=1.59 \mathrm{m}$$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Rutgers, The State University of New Jersey

McMaster University

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

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all right. In this problem, we want to know what distance it will take to accelerate an object up to 0.9 C. If its mass is 0.1 micrograms or 1/10 the negative 10 kilograms and the force that supply it is a constant 10 to the sixth Newtons. And in part a where to do the calculation. Non relativistic Lee. So the Catic energy is just 1/2 and b squared. So if we solve this free anti Oh, we have the d. A is equal toe m v squared over Teo where AM is 10 to the negative 10. The is 0.9 times three times 10 to the eight and we divide by two times 10 to the sixth and this comes out to 3.65 meters now in part B, we're to do with the correct on to use the relativistic expression was correct. Way to do it act and relativistic lee. The chaotic energy is M C squared gamma minus one x. And, um so again, just a matter of solving for tea and then plug in the numbers. So, um, is 10 to the negative 10. Ana multiplied by three times 10 to the eight squared Um Gammas won over the square root of one minus 0.9 squared in this case, and we subtract one divide by 10 to 6 and this comes out to 11.6 meters and the distance is longer and B because in the relativistic formula, as your speed gets greater on, it becomes harder and harder to accelerate.

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