Lewin introduced into psychology the concept of psychological force but was unable to specify an equation of motion, relating force to behavior. Physical analogs prove helpful in developing Lewin's ideas. The effort exerted by a hungry rat seeking food at the end of a linear runway can be defined as proportional to the gradient of a maximally smooth scalar field, whose source is the food in the goal box. This assumption leads to a direct analog between potential energy and utility in psychology. If a Newtonian equation of motion is used with this definition of force, the results compare favorably with Hull's data on rats' running behavior.
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