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# Physics: terminal velocity of a sphere; stress in the bones of the arm during the swing

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1. Find an equation for the terminal velocity of a sphere falling through a viscous fluid (like water or blood). How does the terminal velocity scale with the size of the falling object? Assume that the density of that object is much larger than that of the fluid through which it falls (neglect buoyancy).
a. V ~ L^-3
b. V ~ L^0
c. V ~ L^1
d. V ~ L^2
e. V ~ L^3

2. A person is bowling with a 8 kg bowling ball. Their arm is 1 m long. If they pull the ball back 0.7 m (hint: call this A) and use no muscle effort to accelerate their bowl (gravity provides the driving force), what is the stress in the bones of their arm during the swing, just as the arm passes the straight up-and-down position. Treat the arm as a simple pendulum with one long bone, and assume that the cross-sectional area of this bone is 2 cm2. Neglect the mass of the arm itself.

a. 4.8 x 106 dyn/cm2
b. 2.7 x 106 dyn/cm2
c. 3.9 x 106 dyn/cm2
d. 6.0 x 105 dyn/cm2
e. 5.8 x 106 dyn/cm2.

##### Solution Summary

In the attached Word document, an equation is determined to find terminal velocity and its relation to size of the falling object, and stress in the bones is determined.

##### Solution Preview

1 Find an equation for the terminal velocity of a sphere falling through a viscous fluid (like water or blood). How does the terminal velocity scale with the size of the falling object? Assume that the density of that object is much larger than that of the fluid through which it falls (neglect buoyancy).

a. V ~ L-3
b. V ~ L0
c. V ~ L1
d. V ~ L2
e. V ~ L3

Solution:

Fd

mg

The sphere is subjected to two forces i) weight mg down wards and ii) viscous drag upwards (third force due to buoyancy has been neglected). As per Stoke's formula, viscous drag is given by : Fd = 6Πηrv where η = coefficient ...

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