The Interplay of Work and Kinetic Energy

We’ve been discussing the different forms energy takes, delving deeply into de Coriolis’ claim that energy doesn’t ever die or disappear, it simply changes forms depending on the tasks it’s performing.   here we’ll combine mathematical formulas to derive an equation specific to our needs, an activity my work as an engineer frequently requires of me.   Our task today is to find a means to calculate the amount of kinetic energy contained within a piece of ceramic skidding across a concrete floor.   To do so we’ll combine the frictional force and Work-Energy Theorem formulas to observe the interplay between work and kinetic energy.

As we learned studying the math behind the Work-Energy Theorem, it takes work to slow a moving object.   Work is present in our example due to the friction that’s created when the broken piece moves across the floor.   The formula to calculate the amount of work being performed in this situation is written as,

W = F_F ×d              (1)

where, d is the distance the piece travels before it stops, and F_F is the frictional force that stops it.

We established last time that our ceramic piece has a mass of 0.09 kilograms and the friction created between it and the floor was calculated to be 0.35 kilogram-meters/second².   We’ll use this information to calculate the amount of kinetic energy it contains.   Here again is the kinetic energy formula, as presented previously,

KE = ½ × m × v²      (2)

where m represents the broken piece’s mass and v its velocity when it first begins to move across the floor.

The Interplay of Work and Kinetic Energy

The Work-Energy Theorem states that the work, W, required to stop the piece’s travel is equal to its kinetic energy, KE, while in motion.   This relationship is expressed as,

KE = W            (3)

Substituting terms from equation (1) into equation (3), we derive a formula that allows us to calculate the kinetic energy of our broken piece if we know the frictional force, F_F, acting upon it which causes it to stop within a distance, d,

KE = F_F × d

   Next time we’ll use this newly derived formula, and the value we found for F_F in our previous article, to crunch numbers and calculate the exact amount of kinetic energy contained with our ceramic piece.