## (Solved) Einstein's theory of special relativity predicts that an object's mass m changes as its velocity 1) increases according to the formula m=L (1)...

3. Einstein's theory of special relaticity predicts that an object's mass m changes as its velocity v increases according to the formula.

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3. Einsteinâ€™s theory of special relativity predicts that an objectâ€™s mass m changes as its velocity 1)
increases according to the formula m=L (1) â€˜/1â€”'02/c2 where c is the speed of light and m0 is the objectâ€™s mass when it is at rest (1) = 0). Additionally, the
theory predicts that the objectâ€™s kinetic energy, K, is given by K 2 mt:2 â€” mocz. (2) (a) Using (1), write down the ï¬rst two nonzero terms of the Taylor series for me2 about 1) = 0.
What is the radius of convergence of this Taylor series? (b) If v is very small compared to c, i.e. if v/c is close to 0, then we can get a good approximation for K using the ï¬rst two nonzero terms from (a). Show that this approximation gives the
1
classical expression for K, which is imovz.

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