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Dynamics: Force and Newton’s Laws of Motion and Applications: Friction, Drag and Elasticity

23 Development of Force Concept

Learning Objectives

  • Understand the definition of force.

Motion is everywhere in biological systems: from the beating of your heart pumping blood, to muscles pulling on bones, to cells moving within tissues. To understand why things move, we study dynamics, the branch of physics that focuses on forces and their effects on motion.

What is Force?

At its simplest, force is a push or a pull. It has two important features:

  • Magnitude (how strong the force is)

  • Direction (which way the force acts)

Because force has both magnitude and direction, it is classified as a vector quantity.

For example:

  • A cannon exerts a very strong force to launch a cannonball.

  • Earth exerts a very weak downward pull on a tiny flea.

Forces can act in many directions and can be combined. When two people push a third person from different directions, the total force on that person is the vector sum of the individual forces (see Figure 23.1).

Visualizing Forces: Free-Body Diagrams

A useful tool in analyzing forces is the free-body diagram (Figure 23.1b). In these diagrams:

  • The object or system is represented by a dot.

  • All the external forces acting on the object are shown as arrows (vectors) pointing away from the dot.

Internal forces inside the object don’t affect its overall motion and are therefore ignored in free-body diagrams.

Free-body diagrams are essential for solving problems in dynamics and will be used frequently.

(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.
Figure 23.1: 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.

Measuring Force: Standard Units

Just like measuring length requires a standard unit (meters, feet, etc.), measuring force requires a standard force.

One common standard is the force exerted by a stretched spring (Figure 23.2). When you stretch a spring, it pulls back with a force called a restoring force. By measuring how much the spring stretches, we get a reproducible unit of force.

Devices like spring scales use this principle to measure forces, including weights.

 

(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.
Figure 23.2: The force exerted by a stretched spring can be used as a standard unit of force. (a) This spring has a length [latex]x[/latex] when undistorted. (b) When stretched a distance [latex]\Delta x[/latex], the spring exerts a restoring force, [latex]{\mathbf{\text{F}}}_{\text{restore}}[/latex], which is reproducible. (c) A spring scale is one device that uses a spring to measure force. The force [latex]{\mathbf{\text{F}}}_{\text{restore}}[/latex] is exerted on whatever is attached to the hook. Here [latex]{\mathbf{\text{F}}}_{\text{restore}}[/latex] has a magnitude of 6 units in the force standard being employed.

Take-Home Experiment: Force Standards

Try this simple experiment:

  • Hang one rubber band vertically.

  • Attach small weights (like paper clips with household items) and measure how much the rubber band stretches.

  • Increase the weights and observe how the stretch changes.

  • Try using two rubber bands and compare the stretch.

  • What happens if you push the weights sideways?

This hands-on activity demonstrates how forces can be measured and combined.

Section Summary

  • Dynamics studies how forces affect motion.

  • A force is a vector push or pull with magnitude and direction.

  • External forces come from outside the object and affect its motion.

  • A free-body diagram shows all external forces acting on an object.

Conceptual Questions

  1. 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.
  2. What properties do forces have that allow us to classify them as vectors?

Glossary

dynamics
the study of how forces affect the motion of objects and systems
external force
a force acting on an object or system that originates outside of the object or system
free-body diagram
a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces are represented by vectors extending outward from the dot
force
a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force
definition

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College Physics 1 Copyright © 2012 by OSCRiceUniversity is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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