PhysicsBowl 2019 Q23

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PhysicsBowl 2019

23) A block falls 10 meters to the ground accumulating a given speed. We want to find what was the air frictional force that acts on the object. Let's visualize this problem with a force diagram.

Where h is height, v is velocity, f is frictional force, and F[g] is gravitational force

The work done by the nonconservative force will account for the change in mechanical energy. When looking at the forces, we see that the frictional force is the only nonconservative force; therefore, the change in mechanical energy will be the work done by the frictional force.

Where W[nc] is work done by the nonconservative force, U is mechanical energy, f is air frictional force, and h is height

By expanding mechanical energy into the sum of kinetic energy and potential energy, we can further simplify this equation

Where f is frictional force, h is height, K is kinetic energy, P is potential energy, m is mass, v is velocity, F[g] is gravitational force, and g is acceleration due to gravity

Finally, by expanding the kinetic energy and potential energy, our only unknown will be frictional force, and we can plug our given values into the calculator.

Where f is air frictional force, K is kinetic energy, P is potential energy, h is height, F[g] is gravitational force, g is acceleration due to gravity, and v is velocity

Answer: A