Question

1. a block hangs from the ceiling by a massless rope. a second block is attached to the first and hangs below it on another piece of massless rope. if each of the two blocks has a mass of 5.0 kg, what is the tension in each rope?

Explanation:

Step1: Analyze the forces on the upper - block

Let the mass of each block be $m = 5.0\ kg$ and the acceleration due to gravity $g=9.8\ m/s^{2}$. For the upper - block, the forces acting on it are the tension in the upper rope $T_1$ pulling it up and the tension in the lower rope $T_2$ and the weight of the upper - block $mg$ pulling it down. Since the system is in equilibrium (assuming no acceleration), from Newton's second law $F = ma$, and $a = 0$, so $T_1=T_2 + mg$.

Step2: Analyze the forces on the lower - block

For the lower - block, the only forces acting on it are the tension in the lower rope $T_2$ pulling it up and its weight $mg$ pulling it down. In equilibrium, $T_2=mg$.
Substitute $m = 5.0\ kg$ and $g = 9.8\ m/s^{2}$ into the formula for $T_2$: $T_2=5.0\times9.8=49\ N$.
Then substitute $T_2 = 49\ N$ and $mg = 49\ N$ into the formula for $T_1$: $T_1=T_2+mg=49 + 49=98\ N$.

Answer:

The tension in the lower rope is $49\ N$ and the tension in the upper rope is $98\ N$.