Question

1. a 1000 kg car collides with a 1 mg mosquito. by what factor will the acceleration of the mosquito be greater than the acceleration of the car when they collide?

Explanation:

Step1: Use Newton's third law

According to Newton's third law, the force \(F\) exerted by the car on the mosquito is equal in magnitude and opposite in direction to the force exerted by the mosquito on the car. So \(F_{car - mosquito}=F_{mosquito - car}\).

Step2: Use Newton's second law \(F = ma\)

For the car, \(F = m_{car}a_{car}\), so \(a_{car}=\frac{F}{m_{car}}\). For the mosquito, \(F = m_{mosquito}a_{mosquito}\), so \(a_{mosquito}=\frac{F}{m_{mosquito}}\).

Step3: Find the ratio of accelerations

\(\frac{a_{mosquito}}{a_{car}}=\frac{\frac{F}{m_{mosquito}}}{\frac{F}{m_{car}}}=\frac{m_{car}}{m_{mosquito}}\). Given \(m_{car} = 1000\space kg=10^{6}\space g\) and \(m_{mosquito}=1\space mg = 10^{- 3}\space g\). Then \(\frac{a_{mosquito}}{a_{car}}=\frac{10^{6}}{10^{-3}} = 10^{9}\).

Answer:

The acceleration of the mosquito is \(10^{9}\) times greater than the acceleration of the car.