A 2kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.15m, to a hanging book with mass 3kg. The system is released from rest, and the books are observed to move 1.2m in 0.8s.

My solution so far:

using constant acceleration formula

$\displaystyle s = ut+\frac{1}{2}at^2 $

$\displaystyle 1.2 = 0 +\frac{1}{2}(a)(0.8)^2$

$\displaystyle a = 3.75$

For the hanging part:

$\displaystyle 3g - T_1 = ma$

$\displaystyle T_1 = 3g-ma$

$\displaystyle T_1 = 3g-3(3.75) = 18.2$(rounded) This agrees with my textbook

however for the horizontal tension in the cord

I make it

$\displaystyle T_1 - T_2 = ma$

$\displaystyle T_2 = T_1 - ma$

$\displaystyle T_2 = 18.2 - 2(3.75)$

$\displaystyle T_2 = 10.7N $

however the answer in my textbook is 7.5 which would suggest

$\displaystyle T_2=2(3.75)$

where has the $\displaystyle T_1$ force gone?

Have I missed out a force

Also how can you have different tensions in the cord surely it would snap?