Example 7.9 from College Physics, 7.5 Nonconservative Forces

Calculating Distance Traveled: How Far a Baseball Player Slides

Consider the situation shown in Figure 7.17, where a baseball player slides to a stop on level ground. Using energy considerations, calculate the distance the 65.0-kg baseball player slides, given that his initial speed is 6.00 m/s and the force of friction against him is a constant 450 N.

A baseball player slides to stop in a distance d. the displacement d is shown by a vector towards the left and frictional force f on the player is shown by a small vector pointing towards the right equal to four hundred and fifty newtons. K E is equal to half m v squared, which is equal to f times d.

Figure 7.17 The baseball player slides to a stop in a distance

d

. In the process, friction removes the player’s kinetic energy by doing an amount of work

fd

equal to the initial kinetic energy.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Friction stops the player by converting his kinetic energy into other forms, including thermal energy. In terms of the work-energy theorem, the work done by friction, which is negative, is added to the initial kinetic energy to reduce it to zero. The work done by friction is negative, because $f$ is in the opposite direction of the motion (that is, $θ = 180º$ , and so $cos θ = - 1$ ). Thus $W_{nc} = - fd$ . The equation simplifies to
$\frac{1}{2} {mv}_{i}^{2} - fd = 0$
7.59

or

$fd = \frac{1}{2} {mv}_{i}^{2} .$
7.60

This equation can now be solved for the distance $d$ .
Solution
Solving the previous equation for $d$ and substituting known values yields
$\begin{array}{l} d & = & \frac{{mv}_{i}^{2}}{2 f} \\ = & \frac{(65.0 kg) (6 . 00 m/s)^{2}}{(2) (450 N)} \\ = & 2.60 m. \end{array}$
7.61
Discussion
The most important point of this example is that the amount of nonconservative work equals the change in mechanical energy. For example, you must work harder to stop a truck, with its large mechanical energy, than to stop a mosquito.

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