Question 19.CE.10: Carrying a glass of juice Snehal is crossing a room while ca......
Carrying a glass of juice
Snehal is crossing a room while carrying a glass of cranberry juice. Estimate the stepping frequency that might cause the juice to splash onto the carpet. The natural frequency of vibrations of the juice sloshing in the nearly full glass is about 3 vibrations/s.
Sketch and translate Snehal’s arm is a vibrating object that interacts with the glass of juice as well as with his legs.
Simplify and diagram Assume that Snehal’s hand and arm oscillate at the same frequency at which his feet hit the ground. To avoid spilling the cranberry juice, he should try to walk so that his feet do not hit the ground 3 times per second (or 1.5 steps/s for each foot). That is a rapid pace, so it is unlikely that Snehal will cause resonant vibrations in the glass.
Try It Yourself: Do a follow-up investigation. First, determine the natural sloshing frequency in some container of liquid. Then walk with each of your legs swinging at the same frequency to see if the liquid spills. Think about what other factors affect the possibility of a coupled resonance between your stepping and the sloshing vibrations of liquid in a container. List the possible factors and then do experiments to determine the effect of changing those factors.