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stunner5000pt

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have a look at the diagram. Mass on top is called Mass 1 and the mass below is caled Mass 2. The spring has spring constant k. At time t=0 the string is cut and the system falls freely. Neglect air resistance

Nothing spciel about this. Imagin the whole thing as a big body and the mass falls.

[tex] d_{CM} = v_{1} t + \frac{1}{2} g t^2 [/tex]

and since v1 =0

[tex] d_{CM} = \frac{1}{2} gt^2 [/tex]

to start with for mass 2

kx = mg (1)

for mass 1 T = kx + mg

but once the string is cut T = 0

kx + mg = 0

mg + mg = 0 from 1

2mg = 0

this is the net force 2mg = ma, thus a = 2g

(is there a flaw in this logic?)

for the mass 2

kx = mg but once string is cut kx = 0 since nothing pulls up

thus mg = ma = 0 a = 0??

once again what's the flaw with this logic??

[B} determine z as a function 0of t. Consider for values of t such that 2 has not hit the floor. [/B]

Now for the this part I am a bit confused.

Certainly z = L/2 + something

what is this something

the text gives the something to be mg/2k cos(root 2k/m) t

not quite sure how they got that part

Thank you in advance for ANY help!

**1) Determine the position of the centre of mass at time t>0. The position should be given as distance Ycm froim the CM position at t=0**Nothing spciel about this. Imagin the whole thing as a big body and the mass falls.

[tex] d_{CM} = v_{1} t + \frac{1}{2} g t^2 [/tex]

and since v1 =0

[tex] d_{CM} = \frac{1}{2} gt^2 [/tex]

**2) Determine the acceleration on mass 1 and mass 2 immediately after the string has just been cut**to start with for mass 2

kx = mg (1)

for mass 1 T = kx + mg

but once the string is cut T = 0

kx + mg = 0

mg + mg = 0 from 1

2mg = 0

this is the net force 2mg = ma, thus a = 2g

(is there a flaw in this logic?)

for the mass 2

kx = mg but once string is cut kx = 0 since nothing pulls up

thus mg = ma = 0 a = 0??

once again what's the flaw with this logic??

**We now refer to the motion for t>0 to a reference frame that has origin in the CM. Denote this frame the position of the lower mass 2 by z.**[B} determine z as a function 0of t. Consider for values of t such that 2 has not hit the floor. [/B]

Now for the this part I am a bit confused.

Certainly z = L/2 + something

what is this something

the text gives the something to be mg/2k cos(root 2k/m) t

not quite sure how they got that part

Thank you in advance for ANY help!

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