While a person is walking, his arms swing through approximately a 45.0 angle in 0.590 . As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. A typical arm is 70.0 long, measured from the shoulder joint. What is the acceleration of a 1.90 gram drop of blood in the fingertips at the bottom of the swing? Find the force that the blood vessel must exert on the drop of blood in part (a). What force would the blood vessel exert if the arm were not swinging?

Question

While a person is walking, his arms swing through approximately a 45.0 angle in 0.590 . As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. A typical arm is 70.0  long, measured from the shoulder joint. What is the acceleration of a 1.90 gram drop of blood in the fingertips at the bottom of the swing? Find the force that the blood vessel must exert on the drop of blood in part (a). What force would the blood vessel exert if the arm were not swinging?

jamesj · Answer

...in 0.590 seconds?

anonymous · Answer

how'd did you get .590secs ?

jamesj · Answer

I'm trying first to understand your question: "his arms swing through approximately a 45.0 angle in 0.590 ."  What are the units?

anonymous · Answer

oh sorry...its .590 seconds, 45 degrees, 70 cm

jamesj · Answer

Yes.  Ok.  Now, at the bottom of the swing there are two forces acting, gravity and centripetal.  Write
$$ F = F_g + F_c $$

jamesj · Answer

F_g is easy to calculate.

For F_c the form easiest to use is
$$ F_c = m \omega^2 r $$
The thing you'll need to calculate here is the angular velocity $ \omega $.

jamesj · Answer

And that you can calculate from the fact that an angle in radians of $ \pi/4 $ is swept out in 0.590 seconds.

jamesj · Answer

Make sense?

jamesj · Answer

So the total force is
$$ F = F_g + F_c $$ $$ = mg + m\omega^2 r $$
$$ = m(g + \omega^2 r) $$

The acceleration therefore is the terms in brackets,
$$ a = g + \omega^2 r $$

jamesj · Answer

Making sense?

anonymous · Answer

its taking a while for me to understand...now how would i use the formula's ?

jamesj · Answer

You know g, you are given r, and you can calculate $ \omega $, as I indicated above.

anonymous · Answer

ok. im going to try and solve this....it may take a while. but thank you so much

anonymous · Answer

Sorry for cutting in, but seeing as I have a similar problem I can't seem to get it right, it led me here. I solved the Q that asked the force without swing pretty simply but can't seem to get the first question? I got 11.04 $$m/s^{2}$$ but it doesn't seem right

jamesj · Answer

See here: http://openstudy.com/study?login#/updates/4f3eaac4e4b0cf389e2a1cbe