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Help with #57 and #72

Posted: Mon Jan 22, 2007 1:27 pm
by rrr
Could anyone please explain the answers to #57 and #75 on the GRE 0177?

Posted: Mon Jan 22, 2007 1:37 pm
by rjharris
for those w/o the test in hand, could you post the questions? thanks.

Posted: Mon Jan 22, 2007 2:30 pm
by rrr
57. A stream of water of mass density, p (rho), cross-sectional area A, and speed, v, strikes a wall that is perpendicular to the direction of the stream, as shown in the firgue. The water then flows sideways across the walls. The force exerted by the stream on the wall is
The answer is pv^2A.

72. Two identical blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immeadiately after the string breaks, what is the downward acceleration of the upper block?
The answer is 2g.

There are diagrams with the problem, but I couldn't draw them. The link to the test is

Posted: Mon Jan 22, 2007 4:30 pm
by rjharris
on 57, (a) and (c) are the only ones with the correct units. and (c) contains an h, which is entirely irrelevant. so (a) must be the answer.

/ i dont feel like thinking about how to actually do the problem at the moment.

Posted: Tue Jan 23, 2007 10:02 pm
by CPT
Hey rrr,

I hope you've figured out the questions by now. If not here's a hint:

The volume of water hitting the slab in time dt is: A (v.dt), it's velocity changes from v to 0 in the direction of flow, and mass is just ρ time V, so that shouold do it for the first one.

The second question: Initially everything's at rest so, by writing the equations for the lower block you can see that the tension in the spring is : kx = mg. Now after the thread breaks, the upper block has a net force of: mg(gravity) + mg(spring) acting on it, so the net force is 2mg.

Hope that helps,

Almost get it...

Posted: Wed Jan 24, 2007 1:33 pm
by rrr
Thank you, but could you expand a little more on #57?

Posted: Wed Jan 24, 2007 4:35 pm
by CPT
Consider the situation like this:

Code: Select all


    /                      /    /|
   /<--------  x  ------->/ dx / |
  /                      /    /  |
 /______________________/____/   |
 |                      |    | A |   
 |                      |    |   /
 |                      |    |  /
 |                      |    | /


    /                      /|
   /<--------  x  ------->/ |
  /                      /  |
 /______________________/   |
 |                      | A |
 |                      |   /
 |                      |  /
 |                      | /

The ammount of water that has splashed past the wall is a volume of length dx = v.dt {v is the velocity and dt is the infinitesimal time}, and the cross section area is A.

Therefore mass of water = ρ (A v dt)
This much water had velocity v initially so its momentum would have been:
ρ (A v dt) v = ρ A v^2 dt

Its final momentum is zero as it stops moving in that direction, so change in momentum is: ρA(v^2) dt

Force = d(momentum)/dt = ρ A v^2

Thanks for all the help!!

Posted: Thu Jan 25, 2007 8:04 am
by rrr
I finally get it.

Posted: Thu Jan 25, 2007 10:48 am
by CPT
Hey, glad to be able to help. Just keep at it and things'll get familiar soon.

Good Luck! :D