![]() If the problem is one-dimensional-that is, if all forces are parallel-then the forces can be handled algebraically. In general, once external forces are clearly identified in free-body diagrams, it should be a straightforward task to put them into equation form and solve for the unknown, as done in all previous examples. This is done in Figure 6.2(d) for a particular situation. Once a free-body diagram is drawn, we apply Newton’s second law. Note that no internal forces are shown in a free-body diagram. Figure 6.2(c) shows a free-body diagram for the system of interest. We have drawn several free-body diagrams in previous worked examples. Only forces are shown in free-body diagrams, not acceleration or velocity. As illustrated in Newton’s Laws of Motion, the system of interest depends on the question we need to answer. (See Figure 6.2(c).) Newton’s third law may be used to identify whether forces are exerted between components of a system (internal) or between the system and something outside (external). We can then determine which forces are external and which are internal, a necessary step to employ Newton’s second law. It is particularly crucial to identify the system of interest, since Newton’s second law involves only external forces. It is apparent that if the piano is stationary, T → = − w → T → = − w →.Īs with most problems, we next need to identify what needs to be determined and what is known or can be inferred from the problem as stated, that is, make a list of knowns and unknowns. (d) Showing only the arrows, the head-to-tail method of addition is used. Now F → T F → T is no longer shown, because it is not a force acting on the system of interest rather, F → T F → T acts on the outside world. We then define the system of interest as shown and draw a free-body diagram. ![]() (c) Suppose we are given the piano’s mass and asked to find the tension in the rope. All other forces, such as the nudge of a breeze, are assumed to be negligible. (b) Arrows are used to represent all forces: T → T → is the tension in the rope above the piano, F → T F → T is the force that the piano exerts on the rope, and w → w → is the weight of the piano. 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.įigure 6.2 (a) A grand piano is being lifted to a second-story apartment. Then, as in Figure 6.2(b), we can represent all forces with arrows. 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. ![]() Let’s apply this problem-solving strategy to the challenge of lifting a grand piano into a second-story apartment. Check the solution to see whether it is reasonable.If necessary, apply appropriate kinematic equations from the chapter on motion along a straight line. Apply Newton’s second law to solve the problem.The result is a free-body diagram that is essential to solving the problem. Sketch the situation, using arrows to represent all forces.Identify the physical principles involved by listing the givens and the quantities to be calculated.Many problem-solving strategies are stated outright in the worked examples, so the following techniques should reinforce skills you have already begun to develop. These techniques also reinforce concepts that are useful in many other areas of physics. 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. 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. 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. Success in problem solving is necessary to understand and apply physical principles. Apply calculus to more advanced dynamics problems. ![]()
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