Question

use the information below to answer the two questions that follow.
a block hangs from the ceiling by a light - weight string. a second block is attached to the first block and hangs below it on another piece of light string. the bottom block has a mass of 5.31 kg. the tension in the top rope is 117 n. all blocks are at rest (at least for now).

1. what is the tension in the bottom rope?

this bottom block is at rest too
tension in the bottom rope equals the weight of the bottom block
w = mg
g = 9.8 m/s²
tension in the bottom rope?
m = 5.31 and g = 9.8 m/s²
t = 5.31×9.8 = 52.038 n

1. what is the mass of the top block?

Explanation:

Step1: Calculate bottom rope tension

The tension in the bottom rope equals the weight of the bottom block, so use $T_{bottom} = m_{bottom}g$.
$T_{bottom} = 5.31\ \text{kg} \times 9.8\ \text{m/s}^2 = 52.038\ \text{N}$

Step2: Find total mass from top tension

Top tension supports total weight, so $m_{total} = \frac{T_{top}}{g}$.
$m_{total} = \frac{117\ \text{N}}{9.8\ \text{m/s}^2} \approx 11.939\ \text{kg}$

Step3: Calculate top block mass

Subtract bottom mass from total mass: $m_{top} = m_{total} - m_{bottom}$.
$m_{top} = 11.939\ \text{kg} - 5.31\ \text{kg} \approx 6.63\ \text{kg}$

Answer:

1. Tension in the bottom rope: $\boldsymbol{52.04\ \text{N}}$ (rounded to two decimal places)
2. Mass of the top block: $\boldsymbol{6.63\ \text{kg}}$ (rounded to two decimal places)