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  4. Newton’s second law of motion:

4.4 Newton’s second law of motion: concept of a system  (Page 6/14)

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Newton’s second law of motion is more than a definition; it is a relationship among acceleration, force, and mass. It can help us make predictions. Each of those physical quantities can be defined independently, so the second law tells us something basic and universal about nature. The next section introduces the third and final law of motion.

Section summary

  • Acceleration, a size 12{ { {a}} sup { ' }>a} {} , is defined as a change in velocity, meaning a change in its magnitude or direction, or both.
  • An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system.
  • Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
  • In equation form, Newton’s second law of motion is a = F net m size 12{a= { {F rSub { size 8{"net"} } } over {m} } } {} .
  • This is often written in the more familiar form: F net = m a size 12{F rSub { size 8{"net"} } =ma} {} .
  • The weight w size 12{w} {} of an object is defined as the force of gravity acting on an object of mass m size 12{m} {} . The object experiences an acceleration due to gravity g size 12{g} {} :

    w = m g size 12{w=mg} {} .

  • If the only force acting on an object is due to gravity, the object is in free fall.
  • Friction is a force that opposes the motion past each other of objects that are touching.

Conceptual questions

Which statement is correct? (a) Net force causes motion. (b) Net force causes change in motion. Explain your answer and give an example.

Why can we neglect forces such as those holding a body together when we apply Newton’s second law of motion?

Explain how the choice of the “system of interest” affects which forces must be considered when applying Newton’s second law of motion.

Describe a situation in which the net external force on a system is not zero, yet its speed remains constant.

A system can have a nonzero velocity while the net external force on it is zero. Describe such a situation.

A rock is thrown straight up. What is the net external force acting on the rock when it is at the top of its trajectory?

(a) Give an example of different net external forces acting on the same system to produce different accelerations. (b) Give an example of the same net external force acting on systems of different masses, producing different accelerations. (c) What law accurately describes both effects? State it in words and as an equation.

If the acceleration of a system is zero, are no external forces acting on it? What about internal forces? Explain your answers.

If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?

The gravitational force on the basketball in [link] is ignored. When gravity is taken into account, what is the direction of the net external force on the basketball—above horizontal, below horizontal, or still horizontal?

Problem exercises

You may assume data taken from illustrations is accurate to three digits.

A 63.0-kg sprinter starts a race with an acceleration of 4 . 20 m /s 2 size 12{4 "." "20"" m/s" rSup { size 8{2} } } {} . What is the net external force on him?

265 N

If the sprinter from the previous problem accelerates at that rate for 20 m, and then maintains that velocity for the remainder of the 100-m dash, what will be his time for the race?
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Source:  OpenStax, Introduction to applied math and physics. OpenStax CNX. Oct 04, 2012 Download for free at http://cnx.org/content/col11426/1.3
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