# Forces and pulley systems

## 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)?

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
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## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
hi dorkymichelle!
… 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

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...

tiny-tim
Science Advisor
Homework Helper
hi dorkymichelle!
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!

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