Physics Problem set

1. Oct 30, 2005

candyman86

those are my problems:
ok for the first one:
Xcm=(1/M)[(5)(m/6)+(15)(m/6)+(5)(m/6)+(5)(m/6)+(15)(m/6)+(25)(m/6)]
Xcm=(35/3)=11.667
Ycm=(1/M)[(25)(m/6)+(25)(m/6)+(15)(m/6)+(5)(m/6)+(5)(m/6)+(5)(m/6)]
Ycm=(40/3)=13.333
so the CM of mass is (11.667,13.33), which is not even on the surface, so i think its wrong. Any suggestions?

Second one:
45kg woman is in a 60kg canoe of length 5m. They are initially at rest. she walks from a point 1m from the end to a point 1m from the other end where she stops. If resistance and the motion of the canoe in the water are ignored, how far does the canoe move during the process.

Im totally lost on this problem, i dont know how to start. I have a feeling the C of M doesnt change, but im not sure. Know a way to start me off? Conservation of Momentum?

Since she moves 3m, was thinking something like this:

(3m)(45kg)=(Xm)(60kg)
X=2.25

but not sure.

Thank you for your time and patience!

Last edited: Oct 31, 2005
2. Oct 30, 2005

Pyrrhus

3. Oct 30, 2005

candyman86

Last edited: Oct 30, 2005
4. Oct 31, 2005

mathmike

for the first one

v = volume of part

x_cm = x_cm1*v1 + x_cm2*v2 + x_cm3*v3 / m1 + v2 + v3

so u have

[(15)(300) + (5)(200) + (5)(200)] / (300+100+200) =

4500 + 1000 + 1000 / 600 = 10.8333

can you do the y_cm now?

5. Oct 31, 2005

Staff: Mentor

The CM doesn't have to be on the surface itself. Suppose you have a uniform circular disk, whose CM is at the center, of course. Cut out a circular hole whose center is the same as the center of the original disk. The CM is still at the same location as before, even though there's nothing there now.

Yes, that is correct. In the absence of external forces, the CM remains stationary if it was stationary to begin with.

She walks 3m with respect to the canoe, but not with respect to the ground, because the canoe also moves. Using 3 and X, you can write an expression for how far she walks with respect to the ground. (Assuming X is the distance the canoe moves with respect to the ground.)