4.7 Further applications of newton’s laws of motion  (Page 5/6)

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Solution for (a)

We are given the initial and final velocities (zero and 8.00 m/s forward); thus, the change in velocity is $\Delta v=8.00 m/s$ . We are given the elapsed time, and so $\Delta t=2.50 s$ . The unknown is acceleration, which can be found from its definition:

$a=\frac{\Delta v}{\Delta t}.$

Substituting the known values yields

$\begin{array}{lll}a& =& \frac{8.00 m/s}{2\text{.}50 s}\\ & =& 3\text{.}{\text{20 m/s}}^{2}.\end{array}$

Discussion for (a)

This is an attainable acceleration for an athlete in good condition.

Solution for (b)

Here we are asked to find the average force the player exerts backward to achieve this forward acceleration. Neglecting air resistance, this would be equal in magnitude to the net external force on the player, since this force causes his acceleration. Since we now know the player’s acceleration and are given his mass, we can use Newton’s second law to find the force exerted. That is,

${F}_{\text{net}}=\text{ma}.$

Substituting the known values of $m$ and $a$ gives

$\begin{array}{lll}{F}_{\text{net}}& =& \left(\text{70.0 kg}\right)\left(3\text{.}{\text{20 m/s}}^{2}\right)\\ & =& \text{224 N}.\end{array}$

Discussion for (b)

This is about 50 pounds, a reasonable average force.

This worked example illustrates how to apply problem-solving strategies to situations that include topics from different chapters. The first step is to identify the physical principles involved in the problem. The second step is to solve for the unknown using familiar problem-solving strategies. These strategies are found throughout the text, and many worked examples show how to use them for single topics. You will find these techniques for integrated concept problems useful in applications of physics outside of a physics course, such as in your profession, in other science disciplines, and in everyday life. The following problems will build your skills in the broad application of physical principles.

Summary

• Newton’s laws of motion can be applied in numerous situations to solve problems of motion.
• Some problems will contain multiple force vectors acting in different directions on an object. Be sure to draw diagrams, resolve all force vectors into horizontal and vertical components, and draw a free-body diagram. Always analyze the direction in which an object accelerates so that you can determine whether ${F}_{\text{net}}=\text{ma}$ or ${F}_{\text{net}}=0$ .
• The normal force on an object is not always equal in magnitude to the weight of the object. If an object is accelerating, the normal force will be less than or greater than the weight of the object. Also, if the object is on an inclined plane, the normal force will always be less than the full weight of the object.
• Some problems will contain various physical quantities, such as forces, acceleration, velocity, or position. You can apply concepts from kinematics and dynamics in order to solve these problems of motion.

Conceptual questions

To simulate the apparent weightlessness of space orbit, astronauts are trained in the hold of a cargo aircraft that is accelerating downward at $g$ . Why will they appear to be weightless, as measured by standing on a bathroom scale, in this accelerated frame of reference? Is there any difference between their apparent weightlessness in orbit and in the aircraft?

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