TNW2 = m2gTW1 = m1gFigure 4.1: Free body diagrams of the forces acting on (a) m2and (b) m1As shown in Figure 2 (a), there are three forces acting on m2; the force from the contact ofthe frictionless surface pushing up on m2 labelled T. The contact (normal) force and thegravitational force cancel each other, meaning the total force acting on along verticaldirection on m2is equal to zero. This leaves the tension in the string as the total force actingon m2. Newton’s second law said that m2will accelerate and give the equation:T=m2aFigure 2 (b) shows that there are only two forces acting on m1namely the gravitational force,W = m1g in downward direction and the tension that pulls m1upward. By using Newton’ssecond law;Ftotal=T−m1g=−m1aEliminating T from equation by substituting equation 2 into equation 3, a single equation forthe acceleration is written as:m2a−m1g=−m1aWhich is Newton’s Second Law for a system of mass (m2+m1) with net force applied to it isthe equation of a straight line with a slope equal to the mass of the system, (m2+m1). So, ifyou vary the mass of m1, keeping the gravitational force acting on the system and theacceleration system. Notice that the tension has been eliminated from the final equation andis not needed in the analysis since we are only concerned with forces acting on the system,not acting between objects within the system.
Acceleration, (a) can be determined using equation:x=v0t+12at2