Chapter 4.3, Problem 36SSC

To determine

The tension in each rope

Answer to Problem 36SSC

Tension in the top rope is $T_1 =98\text{ N}$

Tension in the bottom rope is $T_2 =49\text{ N}$

Explanation of Solution

Given:

The masses of each block is 5 kg

The acceleration due to gravity g =9.8m/s²

Formula Used:

Weight is given as,

  $W=mg$

Calculation:

The free body diagram of the system is as shown below.

The net force on M₂ is zero

  $M_{2}g=T_2$

Tension in the second rope

$$

  $\begin{array}{l}{T}_2=5\times 9.8\\ T_2=49\text{N}\end{array}$

The net force on the first mass is also zero. From the free body diagram

  $\begin{array}{c}{T}_1=M_{1}g+M_{2}g\\ =\left(M_1+M_2\right)g\\ =\left(5+5\right)\times 9.8\\ =10\times 9.8\\ =98\text{N}\end{array}$

Conclusion:

The tension in the ropes are

T₁ = 98 N

T₂ = 49 N