# ROPE TENSION IN PULLEYS II

## Physics lesson, the subject of tension force in ropes. Finding of rope tension in the systems that consists of fixed and movable pulleys. The questions and its solutions related to pulleys.

Systems Consisting Of Fixed And Movable Pulleys

Example: In the system in the figure, mass of the K object is 30 kg. The pulleys are frictionless and weightless.

The system is in balance.

Find the magnitude of the F force.

(g = 10 m/s2)

Solution:

Relationship between forces is as follows.

F = T1 = T2

T3 = T1 + T2

T3 = T4

T = T3 + T4

T = GK

Let we write the value, starting from the last equality.

T = GK

GK = 30 • 10 = 300 N

T = 300 N

T3 + T4 = T

2T3 = 300 N

T3 = 150 N

T3 = T4  because of

T4 = 150 N

T3 = T1 + T2

150 = T1 + T2

T1 = T2  because of

2T1 = 150

T1 = 75 N

T2 = 75 N

F = T

F = 75 N

Example: In the system in the figure, the tension force at the T4 rope is 20 N.

Find the mass of the K object and the magnitude of the F force.

(g = 10 m/s2)

Solution:

We can start solving the question, using the equalities below.

T4 = T3

T3 + T4 = GK

T4 = 20 N and T3 = 20 N

GK = 20 + 20 = 40 N

T1 = T2

T1 + T2 = T3

2T1 = 20 N

T1 = 10 N

F = T1 because of

F = 10 N

Example: The system in the figure is balanced with the K and M masses and ropes. The mass of the M object is 20 N.

Find the T1, T2, T3, T4 rope tensions and the mass of the K object.

(g = 10 m/s2)

Solution: The forces that balance the weight of the K are T1 and T2 forces.

GK = T2 + T3

T2 = T because of

GK = 2T2

GM = 20 • 10 = 200 N

T1 = 200 N

T2 = 200 N

T3 = 200 N

GK = T2 + T3

GK = 200 + 200 = 400 N

T4 = T1 + T2

T4 = 400 N

Example: The system in the figure is in balance. The weight of the K objects is 200 N.

Find the T1, T2, T3, T4 rope tensions and magnitude of the F force.

Solution: Let we start to solving the question from most bottom pulley.

T1 = 2F

T2 = 2T1

T3 = T2

T4 = T2 + T3 = 2T3

The weight of the K object is balanced by T3 force.

GK = 2T3

200 = 2T3

T3 = 100 N

T3 = T because of

T2 = 100 N

T4 = 2T3

T4 = 200 N

T2 = 2T1 because of

100 = 2T1

T1 = 50 N

T1 = 2F because of

50 = 2F

F = 25 N

Rope Tension In Pulleys. Part -1

Tension Force On Rope

RISE KNOWLEDGE

11/07/2018

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