Write down the equation for the Velocity of centre of mass of a system of n-particles and
derive the Newton’s Second Law of Motion for it.
Answers
Explanation:
Newton’s second law of motion is closely related to Newton’s first law of motion. It mathematically states the cause and effect relationship between force and changes in motion. Newton’s second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force. Before we can write down Newton’s second law as a simple equation giving the exact relationship of force, mass, and acceleration, we need to sharpen some ideas that have already been mentioned.
First, what do we mean by a change in motion? The answer is that a change in motion is equivalent to a change in velocity. A change in velocity means, by definition, that there is an acceleration. Newton’s first law says that a net external force causes a change in motion; thus, we see that a net external force causes acceleration.
Another question immediately arises. What do we mean by an external force? An intuitive notion of external is correct—an external force acts from outside the system of interest. For example, in Figure 1(a) the system of interest is the wagon plus the child in it. The two forces exerted by the other children are external forces. An internal force acts between elements of the system. Again looking at Figure 1(a), the force the child in the wagon exerts to hang onto the wagon is an internal force between elements of the system of interest. Only external forces affect the motion of a system, according to Newton’s first law. (The internal forces actually cancel, as we shall see in the next section.) You must define the boundaries of the system before you can determine which forces are external. Sometimes the system is obvious, whereas other times identifying the boundaries of a system is more subtle. The concept of a system is fundamental to many areas of physics, as is the correct application of Newton’s laws. This concept will be revisited many times on our journey through physics.
(a) A boy in a wagon is pushed by two girls toward the right. The force on the boy is represented by vector F one toward the right, and the force on the wagon is represented by vector F two in the same direction. Acceleration a is shown by a vector a toward the right and a friction force f is acting in the opposite direction, represented by a vector pointing toward the left. The weight W of the wagon is shown by a vector acting downward, and the normal force acting upward on the wagon is represented by a vector N. A free-body diagram is also shown, with F one and F two represented by arrows in the same direction toward the right and f represented by an arrow toward the left, so the resultant force F net is represented by an arrow toward the right. W is represented by an arrow downward and N is represented by an arrow upward; both the arrows have same length. (b) A boy in a wagon is pushed by a woman with a force F adult, represented by an arrow pointing toward the right. A vector a-prime, represented by an arrow, depicts acceleration toward the right. Friction force, represented by a vector f, acts toward the left. The weight of the wagon W is shown by a vector pointing downward, and the Normal force, represented by a vector N having same length as W, acts upward. A free-body diagram for this situation shows force F represented by an arrow pointing to the right having a large length; a friction force vector represented by an arrow f pointing left has a small length. The weight W is represented by an arrow pointing downward, and the normal force N, is represented by an arrow pointing upward, having the same length as W.
