Question

What is the tension in the rope of the figure? Assume that m = 64 kg .

What is the tension in the rope of the figure? Assume that m = 64 kg .

Answer 1

Concepts and reason

The concept required to solve the problem is the equilibrium condition for force and Newton’s law of motion.

A person is hanging on the rope connected to the left end of the pulley and a mass greater than the person is lying on the ground connected to the right end of the pulley to the other end of the rope.

Since the person is less massive than the mass attached to the right end of the rope, the system remains in equilibrium condition. Neither the man nor the mass moves up or down. Use the equilibrium condition of force to calculate the tension in the rope.

Fundamentals

The weight of an object is:

$W = mg$

Here, $W$ is the weight of the object, $m$ is the mass of the object, and $g$ is the acceleration due to gravity.

According to Newton’s second law of motion, the net force acting is:

$F = ma$

The weight of the person is,

$W = mg$

Here, $W$ is the weight of the person, $m$ is the mass of the person and $g$ is the acceleration due to gravity.

Substitute $64\,{\rm{kg}}$ for $m$ and $9.8\,{\rm{m/}}{{\rm{s}}^2}$ for $g$ . The weight of the person is:

$\begin{array}{c}\\W = \left( {64\,{\rm{kg}}} \right)\left( {9.8\,{\rm{m/}}{{\rm{s}}^2}} \right)\\\\ = 628\,{\rm{N}}\\\end{array}$

The weight of the person is $628\,{\rm{N}}$ .

According to Newton’s second law of motion, the equilibrium force on the rope is,

$T - W = Ma$

Here, $T$ is the tension on the rope, $W$ is the weight of the person, $M$ is the mass of the block and $a$ is the acceleration of the block.

Both the man and the block are not moving. The acceleration is zero. The net force is zero. Then, the tension is equal to the weight of the person.

$T = W$

Substitute $628\,{\rm{N}}$ for $W$ . The tension on the rope is:

$T = 628\,{\rm{N}}$

The tension on the rope is $628\,{\rm{N}}$ .

Ans:

The tension on the rope is $628\,{\rm{N}}$ .