Hey, I am quite stuck on this question. I've worked on it for ages but can't find out how they got their answer. Here is the question:
A tape is wound round two smooth cylinders (in an tipped over S shape, 1 cylinder above the other; lower cylinder first then higher cylinder). The higher cylinder is fixed, but the lower cylinder sits in a loop formed by the tape. There is a 5kg block (attached to the bottom of the tape hanging from the higher cylinder) and the lower cylinder is 12 kg.
a/ Explain why the upward acceleration of the 5 kg block is twice the downward acceleration of the lower cylinder
b/ Find the acceleration of the 5kg block
| |o| <--higher cylinder
|o| |
......D <---5 Kg weight.
The answer is 1.225m/s²
I have no idea how they got that answer though. =S
Any suggestions?
I've let the acceleration of the weight be 2a and the acceleration of the cylinder be a. I also let T equal the tension in the tape.
So I got these two equations after resolving vertically on the two components.
5*9.8 - T = 5*2a
2T - 12*9.8 = 12a
However, solving this simultaneously gives me 0.3769m/s² which isn't the right answer.... What have I done wrong? =S
Thank you in advance.