Problem solving of Newton’s second law through a system of total mass motion

Problem solving is an important element as well as an integral part of physics. The core of physics matter is logic. Principle and theory in physics describe in logical mathematics in the form of formulation. As an example, Newton second law is expressed as follows:

a=(∑F)/m

(1)

This equation describes the relationship between acceleration (a) with force (F), while mass (m) is the object in which both quantities are applied. Force is a cause factor and acceleration is the effect, so that an object will be accelerated when a force act upon it. This indicates that equation (1) describes logical thinking about the movement of an object. Based on this view, physics problem is built on the basis of logical thinking. As a consequence, problem solving requires a certain procedure.

In teaching physics, problem solving is an important part of teaching strategy (Ibrahim and Rebello, 2013). This is because problem solving helps students to comprehend concepts, principles, laws and formulations. Problem solving is a tool to train thinking process. Therefore, many researchers recommend problem solving strategy to be applied in teaching physics (Hull, Kuo, Gupta, and Elby, 2013).

A number of physics university text books such as Serwey & Jewett (2004), Kerr & Ruth (2008), Bauer & Westfall (2011) describe problem solving procedures. The most popular one is by using “Free body diagrams (FBD)”. FBD is used particularly to solve problems related to Newton’s second law. The strategy used is to use free diagram (Savinainem, Mȁkynem, Nieminem, and Viiri, 2013) As an example a movement of an object on the surface of a table and pull by another object (Figure 1 and 2),

Figure 1.

Figure 2.

Figure 3. FBD problem for Fig-1

If the mass of the string and the pulley as well as the friction is neglected, the acceleration of the system can be determined by using the following procedure: (1) drawing force components (2) separating motion system for each object or creating, (3) using Newton’s second law to formulate each object, and (4) executing by using mathematical operation. For a problem in Fig-1, the solution stages is pictured in Fig-3.

Stage 4 is executing equations in Fig-3 by substituting both expressions to find the acceleration. The result is,

a=Mg/(M+m₁)

For a problem in Fig-2, the solution procedure is similar to problem in Fig-1, except that there is m2 behind m1. The solution of stage 1 is shown in Fig-4. The result of this stage is:

a=Mg/(M+m₁+m₂)

From both problems, it appears that if the system consists of two objects, the number of equation is 2, and 3 equations for 3 objects. Hence, if the system consists of n objects, the number of equation is also n. If this strategy is used, the main difficulties are the number of equation increase with the number of object. In order to overcome this problem, we propose a strategy to solve Newton’s law by using “System of Total Mass”.

Figure 4. FBD for problem fig-2