Newton’s Laws of Motion

Abstract

In this chapter, we will learn the Newton’s laws of motion, especially on the second law, where the motion equation for one particle can be given.

Exercises

• 10.1 As shown in Fig. 10.2, a small object with mass m is falling from point O in the liquid, and the resistant force of the liquid is F = Rv², where R is the resistant force factor, and v is the velocity of the object. Please give the governing equation and the solution of this problem.

  Fig. 10.2

  

  An object falling in the liquid

• 10.2 As shown in Fig. 10.3, an object is in oblique throwing. The initial velocity is v₀, and the initial angle is $\alpha$. The resistant force is ignored, and the gravity of the object is G. Please determine the orbit of this object.

  Fig. 10.3

  

  An oblique throwing object

Answers

• 10.1 $x = \frac{m}{2R}\ln \frac{{mg - Rv^{2} }}{mg}$

• 10.2 $y = x\,\tan \alpha - \frac{g}{{2v_{0}^{2} \cos^{2} \alpha }}x^{2}$