5.3 Newton's second law  (Page 6/8)

Check Your Understanding A car has forces acting on it, as shown below. The mass of the car is 1000.0 kg. The road is slick, so friction can be ignored. (a) What is the net force on the car? (b) What is the acceleration of the car?

a. $159.0\widehat{i}+770.0\widehat{j}\text{N}$ ; b. $0.1590\widehat{i}+0.7700\widehat{j}\text{N}$

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Newton’s second law and momentum

Newton actually stated his second law in terms of momentum: “The instantaneous rate at which a body’s momentum changes is equal to the net force acting on the body.” (“Instantaneous rate” implies that the derivative is involved.) This can be given by the vector equation

This means that Newton’s second law addresses the central question of motion: What causes a change in motion of an object? Momentum was described by Newton as “quantity of motion,” a way of combining both the velocity of an object and its mass. We devote Linear Momentum and Collisions to the study of momentum .

For now, it is sufficient to define momentum $\overrightarrow{p}$ as the product of the mass of the object m and its velocity $\overrightarrow{v}$ :

Since velocity is a vector, so is momentum.

It is easy to visualize momentum. A train moving at 10 m/s has more momentum than one that moves at 2 m/s. In everyday life, we speak of one sports team as “having momentum” when they score points against the opposing team.

If we substitute [link] into [link] , we obtain

When m is constant, we have

Thus, we see that the momentum form of Newton’s second law reduces to the form given earlier in this section.

Summary

• An external force acts 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 says that the net external force on an object with a certain mass is directly proportional to and in the same direction as the acceleration of the object.
• Newton’s second law can also describe net force as the instantaneous rate of change of momentum. Thus, a net external force causes nonzero acceleration.

Conceptual questions

Problems