M1 question regarding two connected particles, a pulley, etc Watch

Skycat
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Hey all,

Struggling with question 14 from Heinemann M1, Exercise 5D. I've drawn a force diagram and whatnot and I'm sure it's right, I'm just trying to figure out what the heck I'm doing wrong to keep getting the mass as around 0.33kg.

I've done the following:

For A (using F=ma):

T - 0.5gsin[alpha] = 0.5a

For B (using F=ma):

mg - T = ma

Adding the two equations yields [the T's cancel]

mg - 0.5gsin[alpha] = 0.5a + ma

We're given the fact that the system starts from rest and B travels 1m in 1 second, hence the average velocity = 1m/s. I then find the acceleration to be 1m/s/s using a = (v-u)/t. I think I might be doing something wrong here by using "average" values and so getting incorrect acceleration and whatnot?

I then go on to substitute in g = 9.8 and a = 1:

9.8m - 0.5*4.9*(3/5) = 0.5*1 + m*1
9.8m -1.47 = 0.5 + m
-1.47 - 0.5 = m - 9.8m
-1.47 - 0.5 = m (1 - 9.8)
Therefore:

m = (-1.47 - 0.5) / (1-9.8)
=0.22kg (and now I get yet another new but wrong answer, great).

The answer in the back of the book is 0.505kg. What am I doing wrong?

Thanks so much,
-Gabor
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DKer
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The only things I can think it could be atm are:
Use S=ut+0.5at^2 to find a.
And in this line
9.8m - 0.5*4.9*(3/5) = 0.5*1 + m*1
I don't see where the 4.9 came from, maybe 9.8?
I haven't acctually done it so these may not help.
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