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$\cdot$ Relativistic baseball. Calculate the magnitude of the forcerequired to give a 0.145 kg baseball an acceleration of$a=1.00 \mathrm{m} / \mathrm{s}^{2}$ in the direction of the baseball's initial velocity,when this velocity has a magnitude of (a) $10.0 \mathrm{m} / \mathrm{s} ;$ (b) 0.900 $\mathrm{c}$ ;(c) 0.990 $\mathrm{c} .$

$=1.75 \mathrm{N}$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Simon Fraser University

Hope College

University of Sheffield

McMaster University

Lectures

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okay. And the first part of this problem, the baseball's only going at 10 meters per second. So we can safely ignore relativity. And in this case, the force required is just equal to the mass times the acceleration, which is 0.145 times one now in part B and C. The bull is initially traveling at a significant fraction of the speed of light. And so we have to use the relativistic formula f equals gamma cubed and they so it may well be the same as before. And we divide by the square root of one minus 0.9 squared. Excuse me. This this Ah, it's actually gamma cubed. So we take this and then, um, raise it to the third power and this comes out to 1.75 Newtons. Likewise in part C, we just adjust for the new velocity and we get 51.7 Newtons. So as you get closer to the speed of light, the force required to accelerate it grows dramatically

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