Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 7 - Newton's Third Law - Conceptual Questions - Page 185: 6

Answer

Larger than.

Work Step by Step

According to Newton's third law, the force exerted by the car on the mosquito is equal to the force exerted by the mosquito on the car but two forces are opposing each other. Thus, $$F_{\rm on\;mosquito}=m_{\rm mosquito}a_{x,\rm mosquito}$$ And $$F_{\rm on\;car}=m_{\rm car}a_{x,\rm car}$$ We know, from Newton's third law, that $$F_{\rm on\;car}=-F_{\rm on\;mosquito} $$ From both equations, $$m_{\rm car}a_{x,\rm car}=-m_{\rm mosquito}a_{x,\rm mosquito} $$ Thus, $$a_{x,\rm mosquito}=-\dfrac{m_{\rm car}a_{x,\rm car}}{m_{\rm mosquito}}$$ Now it is obvious that the acceleration of the mosquito will be enormous and fatal to it, while the acceleration of the car $$a_{x,\rm car}=-\dfrac{m_{\rm mosquito}a_{x,\rm mosquito} }{m_{\rm car}}$$ is negligible. Therefore, the acceleration of the mosquito must be larger than the acceleration of the car.
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