BIO Human Biomechanics. The fastest served tennis ball,...

BIO Human Biomechanics. The fastest served tennis ball, served by "Big Bill" Tilden in $1931,$ was measured at 73.14 $\mathrm{m} / \mathrm{s} .$ The mass of a tennis ball is $57 \mathrm{g},$ and the ball is typically in contact with the tennis racquet for $30.0 \mathrm{ms},$ with the ball starting from rest. Assuming constant acceleration, (a) what force did Big Bill's racquet exert on the tennis ball if he hit it essentially horizontally? (b) Draw free-body diagrams of the tennis ball during the serve and just after it moved free of the racquet.

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Key Concepts

Constant Acceleration

This concept involves motion where the acceleration remains constant over time. In such scenarios, simple kinematic equations can be applied, such as v = at when an object starts from rest. Constant acceleration is critical for estimating changes in velocity and computing subsequent motion variables, which is essential in analyzing dynamic systems in biomechanics.

Newton's Second Law

Newton's Second Law states that the net force acting on an object equals the mass of the object times its acceleration (F = ma). This fundamental principle connects the concepts of force and acceleration, allowing us to determine one if the other is known. It is widely used in biomechanics and other fields to analyze the forces involved during motion.

Free-Body Diagrams

Free-body diagrams are visual representations that isolate an object and depict all the external forces acting upon it. These diagrams help in understanding the interactions affecting an object, identifying forces such as gravity, friction, and applied forces, and are a crucial tool for applying Newton's laws in problem solving and biomechanical analysis.