Question

1. two blocks are hanging from the ceiling as shown in the picture. given the mass of both blocks, what is the tension of the rope between the two blocks. (where is labeled t) 1.00 kg 2.00 kg f1 clear all 9.8 n 0.31 n 29.4 n 1 n

Explanation:

Step1: Consider the two - block system

Let the acceleration of the system be $a$. The net - force acting on the two - block system is $F_1=(m_1 + m_2)a$, where $m_1 = 1.00\ kg$ and $m_2=2.00\ kg$.

Step2: Analyze the first block

For the $1.00\ kg$ block, the force acting on it is the tension $T$. According to Newton's second - law $F = ma$, so $T=m_1a$.
First, find the acceleration of the system. Assume $F_1$ is the net force on the combined mass $M=m_1 + m_2=(1.00 + 2.00)\ kg=3.00\ kg$. Let's assume the acceleration due to gravity $g = 9.8\ m/s^2$. If we consider the situation in terms of the connection between the two blocks and assume no other external non - mentioned forces, and assume the system is in a non - gravitational context for the force $F_1$ application. But if we consider the hanging situation in a more general sense and assume the system is in equilibrium (no $F_1$ is actually given in a way to calculate acceleration from it, and we assume the blocks are at rest relative to each other), the tension in the rope is equal to the weight of the $1.00\ kg$ block.
Using the formula $T = m_1g$, where $m_1=1.00\ kg$ and $g = 9.8\ m/s^2$.
$T=1.00\ kg\times9.8\ m/s^2=9.8\ N$

Answer:

$9.8\ N$