# What is the tension in the rope of the figure? (figure 1)

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 .

General guidance

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:

Here, is the weight of the object, is the mass of the object, and is the acceleration due to gravity.
According to Newton’s second law of motion, the net force acting is:

Step-by-step

Step 1 of 2

The weight of the person is,

Here, is the weight of the person, is the mass of the person and is the acceleration due to gravity.
Substitute for and for. The weight of the person is:

The weight of the person is .

The weight of the person is the product of his mass and acceleration due to gravity.

The incorrect expression to calculate the weight of the person is because the correct expression is.

Determine the equilibrium force acting on the rope and use the force to find the tension.

Step 2 of 2

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

Here, is the tension on the rope, is the weight of the person, is the mass of the block and 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.

Substitute for. The tension on the rope is:

The tension on the rope is.

The tension on the rope is.

The tension on the rope will be equal to the weight of the hanging object if there is no acceleration of the object.

The tension on the rope is.

The tension on the rope is.

W = mg
F=ma
W = mg
W = mg
9.8m/s2
W =(64 kg) (9.8 m/s) = 628N
628N
W = ”
W = mg
T-W = Ma
T=W
628N
T = 628 N
628N
628N
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