Forces and pulley systems

  • #1

Homework Statement




In the figure here three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are m1 = 28 kg, m2 = 45 kg, and m3 = 12 kg. When the assembly is released from rest, (a) what is the tension in the cord connecting 2 and 3, and (b) how far does 1 move in the first 0.300 s (assuming it does not reach the pulley)?

Homework Equations



F= ma
d= vit+1/2at^2


The Attempt at a Solution




first I got Ft = m1a
Ft - (m2g+m3g) = (m2+m3)a
subtracted those 2 equations and got
-(m2g+m3g)=-(m2+m3)a-m1a
solved for a,
a = (m2g+m3g)/(m2+m3+m1)
a = 6.57176 m/s^2
I did b correctly using the kinematics equation but didn't get A correct.
I thought tension in string is equal for all parts so i did Ft = ma = 184.0 N, but that's wrong.
Is there a connection between block 2 and 3 that I'm missing?

The figure is in the attatchments
 

Attachments

  • fig_5_E.gif
    fig_5_E.gif
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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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251
hi dorkymichelle! :smile:
… first I got Ft = m1a
Ft - (m2g+m3g) = (m2+m3)a
subtracted those 2 equations and got
-(m2g+m3g)=-(m2+m3)a-m1a
solved for a,
a = (m2g+m3g)/(m2+m3+m1)

you got a minus sign wrong near the start, so i'm not sure how you got the right result!
I thought tension in string is equal for all parts …

no, the tension is only the same along a continuous piece of string, not one with a mass in the way (or a frictional surface) …

do F = ma on the lowest block :wink:
 
  • #3
Hmm.. I did F=ma
F = (12)(6.57176) = 78.86 N
but that's the total forces which includes both tension and gravity. Since the block is not in freefall, then tension is bigger than gravity
Ft - mg = 78.86N
Ft-(12)(9.8)=78.86N
Ft-117.6=78.86N
Ft = 196.46 N
which is wrong...
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,836
251
hi dorkymichelle! :smile:
but that's the total forces which includes both tension and gravity. Since the block is not in freefall, then tension is bigger than gravity

rubbish! :rolleyes:

if tension is bigger than gravity, then the block will accelerate up, won't it? :wink:
 

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