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  • Understand the definition of force.

Dynamics is the study of the forces that cause objects and systems to move. To understand this, we need a working definition of force. Our intuitive definition of force    —that is, a push or a pull—is a good place to start. We know that a push or pull has both magnitude and direction (therefore, it is a vector quantity) and can vary considerably in each regard. For example, a cannon exerts a strong force on a cannonball that is launched into the air. In contrast, Earth exerts only a tiny downward pull on a flea. Our everyday experiences also give us a good idea of how multiple forces add. If two people push in different directions on a third person, as illustrated in [link] , we might expect the total force to be in the direction shown. Since force is a vector, it adds just like other vectors, as illustrated in [link] (a) for two ice skaters. Forces, like other vectors, are represented by arrows and can be added using the familiar head-to-tail method or by trigonometric methods. These ideas were developed in Two-Dimensional Kinematics .

(a) Overhead view of two ice skaters pushing on a third. One skater pushes with a force F two, represented by an arrow pointing up, and a second skater pushes with a force F one, represented by an arrow pointing from left to right. Vector F one and vector F two are along the arms of the two skaters acting on the third skater. A vector diagram is shown in the form of a right triangle in which the base is vector F one pointing east and perpendicular is shown by vector F two pointing north. The resultant vector is shown by the hypotenuse pointing northeast. (b) Free-body diagram showing only the forces acting on the skater.
Part (a) shows an overhead view of two ice skaters pushing on a third. Forces are vectors and add like other vectors, so the total force on the third skater is in the direction shown. In part (b), we see a free-body diagram representing the forces acting on the third skater.

[link] (b) is our first example of a free-body diagram    , which is a technique used to illustrate all the external forces acting on a body. The body is represented by a single isolated point (or free body), and only those forces acting on the body from the outside (external forces) are shown. (These forces are the only ones shown, because only external forces acting on the body affect its motion. We can ignore any internal forces within the body.) Free-body diagrams are very useful in analyzing forces acting on a system and are employed extensively in the study and application of Newton’s laws of motion.

A more quantitative definition of force can be based on some standard force, just as distance is measured in units relative to a standard distance. One possibility is to stretch a spring a certain fixed distance, as illustrated in [link] , and use the force it exerts to pull itself back to its relaxed shape—called a restoring force —as a standard. The magnitude of all other forces can be stated as multiples of this standard unit of force. Many other possibilities exist for standard forces. (One that we will encounter in Magnetism is the magnetic force between two wires carrying electric current.) Some alternative definitions of force will be given later in this chapter.

(a) A spring of length x, fixed at one end, is shown in horizontal position. (b) The same spring is shown pulled by a person by a distance of delta x. The restoring force F restore is represented by an arrow pointing left toward the position where the spring is fixed. (c) A spring balance containing a spring stretched a distance delta x is shown. The restoring force is represented by an arrow F restore pointing toward the left in the direction opposite to the elongation of the spring.
The force exerted by a stretched spring can be used as a standard unit of force. (a) This spring has a length x size 12{x} {} when undistorted. (b) When stretched a distance Δ x size 12{Dx} {} , the spring exerts a restoring force, F restore size 12{F rSub { size 8{"restore"} } } {} , which is reproducible. (c) A spring scale is one device that uses a spring to measure force. The force F restore size 12{F rSub { size 8{"restore"} } } {} is exerted on whatever is attached to the hook. Here F restore size 12{F rSub { size 8{"restore"} } } {} has a magnitude of 6 units in the force standard being employed.

Take-home experiment: force standards

To investigate force standards and cause and effect, get two identical rubber bands. Hang one rubber band vertically on a hook. Find a small household item that could be attached to the rubber band using a paper clip, and use this item as a weight to investigate the stretch of the rubber band. Measure the amount of stretch produced in the rubber band with one, two, and four of these (identical) items suspended from the rubber band. What is the relationship between the number of items and the amount of stretch? How large a stretch would you expect for the same number of items suspended from two rubber bands? What happens to the amount of stretch of the rubber band (with the weights attached) if the weights are also pushed to the side with a pencil?

Section summary

  • Dynamics is the study of how forces affect the motion of objects.
  • Force is a push or pull that can be defined in terms of various standards, and it is a vector having both magnitude and direction.
  • External forces are any outside forces that act on a body. A free-body diagram    is a drawing of all external forces acting on a body.

Conceptual questions

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.

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What properties do forces have that allow us to classify them as vectors?

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Questions & Answers

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Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
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the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
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aliyu Reply
mass ×velocity
it is the product of mass ×velocity of an object
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Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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