Question

While a person is walking, his arms swing through approximately a 45.0 angle in 0.520 . 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 0.700 gram drop of blood in the fingertips at the bottom of the swing?

Answer 1

I got a 11.396 \[m/s^{2}\] as an answer but it doesn't seem to be right?
I would really appreciate it if someone is willing to help~

Answer 2

I did
ω=θ/t
and got 1.51 rad/sec
then did a = g + Rω2 = 11.396

Answer 3

What's the 0.520? Seconds?

Answer 4

Yes it is seconds

Answer 5

Is the middle of his swing perpendicular to the ground?

Answer 6

I would presume so, yes, because the question has not stated otherwise~

Answer 7

Alright, give me some time to do it out. Do you just want me to corroborate your answer or give you hints? Because I'd prefer to not actually calculate. XD

Answer 8

Hints are fine and more preferable, I would like to work out the question without getting the answer so I can try to figure it out myself as well. Thank you~

Answer 9

Velocity is constant (thank God) and the velocity vector at the bottom of the swing is directly parallel to the ground. Assuming no drag, the only F=ma acting on the droplet of blood is vertical F=mg.

Answer 10

Unless I'm doing something wrong, no calculations are necessary. :o I sense a trick question.

Answer 11

Hmm...let me see what I get if your right

Answer 12

Well, it should be acceleration of gravity...

Answer 13

Aw...got it wrong apparently the answer seems to be 1.60\[m/s^{2}\]

Answer 14

Don't know where that came from...

Answer 15

Huh, that's interesting. I must've made a mistake or misread the question. My bad.

But I've no idea what I'm doing wrong. >.> Better wait for someone else to step in.

Answer 16

That's what happened to me as well, I thought I was right but...oh well

Answer 17

http://en.wikipedia.org/wiki/Pendulum Wikipedia agrees with me. ಠ_ಠ

Answer 18

Are you sure you typed out the full question?

Answer 19

Yes, the only thing I left out was the other 2 questions which I think I can get myself

Answer 20

http://upload.wikimedia.org/wikipedia/commons/2/24/Oscillating_pendulum.gif This makes it pretty clear that the velocity vector is parallel to the ground, and the acceleration vector is perpendicular--however, we're told that the arm swinging is at a constant velocity, so there's no acceleration.

Answer 21

I agree, but if that would hold true, either the answer is wrong or we're just missing something

Answer 22

So there are three forces acting: gravity, the normal force against the blood of the arm and the centripetal force. As the motion of the drop of blood shows, i.e., circular, the gravitational force plays no role; or rather, it is cancelled by the force of the blood vessel on it, the 'normal force'.

The acceleration due to the centripetal force is
\[ \omega^2 r = 1.51^2(0.7) = 1.6 \ m/s^2 \]
which is your answer.

This is a bit of a trick question, and to be honest, the last time a version of this question was asked, I missed the fact that the motion of the blood drop itself demonstrates that the net force is just the centripetal force.

Answer 23

This is true. I forget that parabolic motion where the object is never in free fall can be modeled as a part of a circle, hence centripedal force. XD

Answer 24

(You're making this slightly harder than it needs to be. There's no parabolic motion here. The blood drop is moving in a circle.)

Answer 25

I'm sorry, pendulum motion. >.> Not parabolic.

Answer 26

ah, I see.

Answer 27

They both start with p, don't judge me XD