6.1 Solving problems with newton’s laws  (Page 8/12)

Newton’s laws of motion and kinematics

Physics is most interesting and most powerful when applied to general situations that involve more than a narrow set of physical principles. Newton’s laws of motion can also be integrated with other concepts that have been discussed previously in this text to solve problems of motion. For example, forces produce accelerations, a topic of kinematics    , and hence the relevance of earlier chapters.

When approaching problems that involve various types of forces, acceleration, velocity, and/or position, listing the givens and the quantities to be calculated will allow you to identify the principles involved. Then, you can refer to the chapters that deal with a particular topic and solve the problem using strategies outlined in the text. The following worked example illustrates how the problem-solving strategy given earlier in this chapter, as well as strategies presented in other chapters, is applied to an integrated concept problem.

What force must a soccer player exert to reach top speed?

Strategy

Solution

1. We are given the initial and final velocities (zero and 8.00 m/s forward); thus, the change in velocity is $\text{Δ}v=8.00\text{m/s}$ . We are given the elapsed time, so $\text{Δ}t=2.50\text{s}\text{.}$ The unknown is acceleration, which can be found from its definition:
   
   $a=\frac{\text{Δ}v}{\text{Δ}t}.$
   
   Substituting the known values yields
   
   $a=\frac{8.00\text{m/s}}{2.50\text{s}}=3.20{\text{m/s}}^2.$
2. Here we are asked to find the average force the ground exerts on the runner to produce this acceleration. (Remember that we are dealing with the force or forces acting on the object of interest.) This is the reaction force to that exerted by the player backward against the ground, by Newton’s third law. Neglecting air resistance, this would be equal in magnitude to the net external force on the player, since this force causes her acceleration. Since we now know the player’s acceleration and are given her mass, we can use Newton’s second law to find the force exerted. That is,
   
   $F_{\text{net}}=ma.$
   
   Substituting the known values of m and a gives
   
   $F_{\text{net}}=(70.0\text{kg})(3.20{\text{m/s}}^2)=224\text{N}\text{.}$

This is a reasonable result: The acceleration is attainable for an athlete in good condition. The force is about 50 pounds, a reasonable average force.