Q1.1 Thinking exercises (T)
- A large bowl contains a mouse and a ball-bearing. The mouse has to get the ball-bearing out of the bowl, but the ball is too heavy and the sides too steep for the mouse to support the ball’s weight. Is it possible (without levers, divine intervention or quantum tunnelling)?
- An elephant and a feather are dropped from the top of the Appleton Tower. Which encounters the greatest drag force due to air-resistance?
- A film is made of a falling object; it shows the object with a velocity and an acceleration that are directed downwards. The film is run backwards. How will the velocity and acceleration appear now?
[Acknowledgement: ‘Thinking Physics’, author L.C. Epstein ]
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Solution
The mouse can do the job by rolling the ball back and forth, feeding in a little extra energy on each oscillation, by pushing at appropriate times and in appropriate directions (‘in phase’ with the ball’s motion, in effect exploiting the phenomenon of resonance).
[Aside: What is ‘quantum tunnelling’? ...you can find out in Physics 1B: the Stuff of the Universe.... ]
- Experience tells us that drag forces like this increase with the volume and/or the surface area of the body so the elephant must experience the larger force. Not much thought required there. The thinking comes when we have to reconcile this conclusion with the fact that the effects of the drag force are surely smaller for the elephant, which will certainly ‘splat’ first and more satisfyingly. There is no contradiction here. The effects of the drag force, Fd, on the observed motion depend on the contribution, Δa, it makes to the acceleration. By Newton’s second law (we’ll be coming to it soon!) this contribution is Δa=Fd/m, where m is the mass of the body. Thus the greater drag force experienced by the elephant can be offset by its larger mass to give a smaller change in its acceleration.
- When the film is shown backwards the velocity of the
particle will be reversed: thus, for example, our elephant will sail
gracefully up to the top of the Tower. However, the acceleration
will not be reversed: the elephant leaves the ground at high
upward velocity
and reaches the top with zero velocity. The change
in its velocity is directed downwards; so the acceleration
must still be directed downwards too.