Chapter 3 Acceleration and free fall - Light and Matter

118 Chapter 3 Acceleration and free fall
22 You take a trip in your spaceship to another star. Setting off,
you increase your speed at a constant acceleration. Once you get
half-way there, you start decelerating, at the same rate, so that by
the time you get there, you have slowed down to zero speed. You see
the tourist attractions, and then head home by the same method.
(a) Find a formula for the time, T , required for the round trip, in
terms of d, the distance from our sun to the star, and a, the magnitude
of the acceleration. Note that the acceleration is not constant
over the whole trip, but the trip can be broken up into constantacceleration
parts.
(b) The nearest star to the Earth (other than our own sun) is Proxima
Centauri, at a distance of d = 4 × 1016 m. Suppose you use an
acceleration of a = 10 m/s2 , just enough to compensate for the lack
of true gravity and make you feel comfortable. How long does the
round trip take, in years?
(c) Using the same numbers for d and a, find your maximum speed.
Compare this to the speed of light, which is 3.0 × 108 m/s. (Later
in this course, you will learn that there are some new things going
on in physics when one gets close to the speed of light, and that it
is impossible to exceed the speed of light. For now, though, just use
√
the simpler ideas you’ve learned so far.)
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Problem 23. This spectacular series of photos from a 2011 paper by Burrows
and Sutton (“Biomechanics of jumping in the flea,” J. Exp. Biology
214:836) shows the flea jumping at about a 45-degree angle, but for the
sake of this estimate just consider the case of a flea jumping vertically.
23 Some fleas can jump as high as 30 cm. The flea only has a
short time to build up speed — the time during which its center of
mass is accelerating upward but its feet are still in contact with the
ground. Make an order-of-magnitude estimate of the acceleration
the flea needs to have while straightening its legs, and state your
answer in units of g, i.e., how many “g’s it pulls.” (For comparison,
fighter pilots black out or die if they exceed about 5 or 10 g’s.)