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  4. Applications of newton's laws
  5. Solving problems with newton’s

6.1 Solving problems with newton’s laws

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By the end of the section, you will be able to:
  • Apply problem-solving techniques to solve for quantities in more complex systems of forces
  • Use concepts from kinematics to solve problems using Newton’s laws of motion
  • Solve more complex equilibrium problems
  • Solve more complex acceleration problems
  • Apply calculus to more advanced dynamics problems

Success in problem solving is necessary to understand and apply physical principles. We developed a pattern of analyzing and setting up the solutions to problems involving Newton’s laws in Newton’s Laws of Motion ; in this chapter, we continue to discuss these strategies and apply a step-by-step process.

Problem-solving strategies

We follow here the basics of problem solving presented earlier in this text, but we emphasize specific strategies that are useful in applying Newton’s laws of motion . Once you identify the physical principles involved in the problem and determine that they include Newton’s laws of motion, you can apply these steps to find a solution. These techniques also reinforce concepts that are useful in many other areas of physics. Many problem-solving strategies are stated outright in the worked examples, so the following techniques should reinforce skills you have already begun to develop.

Problem-solving strategy: applying newton’s laws of motion

  1. Identify the physical principles involved by listing the givens and the quantities to be calculated.
  2. Sketch the situation, using arrows to represent all forces.
  3. Determine the system of interest. The result is a free-body diagram    that is essential to solving the problem.
  4. Apply Newton’s second law to solve the problem. If necessary, apply appropriate kinematic equations from the chapter on motion along a straight line.
  5. Check the solution to see whether it is reasonable.

Let’s apply this problem-solving strategy to the challenge of lifting a grand piano into a second-story apartment. Once we have determined that Newton’s laws of motion are involved (if the problem involves forces), it is particularly important to draw a careful sketch of the situation. Such a sketch is shown in [link] (a). Then, as in [link] (b), we can represent all forces with arrows. Whenever sufficient information exists, it is best to label these arrows carefully and make the length and direction of each correspond to the represented force.

This figure shows the development of the free body diagram of a piano being lifted and passed through a window. Figure a is a sketch showing the piano hanging from a crane and part way through a window. Figure b identifies the forces. It shows the same sketch with the addition of the forces, represented as labeled vector arrows. Vector T points up, vector F sub T points down, vector w points down. Figure c defines the system of interest. The sketch is shown again with the piano circled and identified as the system of interest. Only vectors T up and w down are included in this diagram. The downward force F sub T is not a force on the system of interest since it is exerted on the outside world. It must be omitted from the free body diagram. The free body diagram is shown as well. It consists of a dot, representing the system of interest, and the vectors T pointing up and w pointing down, with their tails at the dot. Figure d shows the addition of the forces. Vectors T and w are shown. We are told that these forces must be equal and opposite since the net external force is zero. Thus T is equal to minus w.
(a) A grand piano is being lifted to a second-story apartment. (b) Arrows are used to represent all forces: T → is the tension in the rope above the piano, F → T is the force that the piano exerts on the rope, and w → is the weight of the piano. All other forces, such as the nudge of a breeze, are assumed to be negligible. (c) Suppose we are given the piano’s mass and asked to find the tension in the rope. We then define the system of interest as shown and draw a free-body diagram. Now F → T is no longer shown, because it is not a force acting on the system of interest; rather, F → T acts on the outside world. (d) Showing only the arrows, the head-to-tail method of addition is used. It is apparent that if the piano is stationary, T → = − w → .

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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