Question

If m=5 kg and M=8 kg, find the acceleration of the masses and the tension of the rope

Answer 1

$8g-T=8a\\ T-g=5a$

Adding the two equations gives

$3g=13a\\ a=\frac{3g}{13}\\ g=9.8m/s^2\\ a=\frac{3\times 9.8}{13}\\ a=2.26m/s^2\\$

To get the Tension T

$T=5(g+a)\\ T=5(9.8+2.26)\\ T=60.3N$