# 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/s^{2})

**Solution:**

Relationship between forces is as follows.

F = T_{1} = T_{2}

T3 = T1 + T2

T3 = T4

T = T3 + T4

T = GK

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

T = G_{K}

G_{K} = 30 • 10 = 300 N

T = 300 N

T_{3} + T_{4} = T

2T_{3} = 300 N

T_{3} = 150 N

T_{3} = T4 because of

T4 = 150 N

T3 = T1 + T2

150 = T1 + T2

T1 = T2 because of

2T_{1} = 150

T_{1} = 75 N

T_{2} = 75 N

F = T_{1 }

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/s^{2})

**Solution:**

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

T4 = T3

T3 + T4 = G_{K}

T_{4} = 20 N and T_{3} = 20 N

G_{K} = 20 + 20 = 40 N

T_{1} = T_{2}

T_{1} + T_{2} = T_{3}

2T_{1} = 20 N

T_{1} = 10 N

F = T_{1} 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 T_{1}, T_{2}, T_{3}, T_{4} rope tensions and the mass of the K object.

(g = 10 m/s^{2})

**Solution:**

The forces that balance the weight of the K are T_{1} and T_{2} forces.

G_{K} = T_{2} + T_{3}

T_{2} = T_{3 } because of

G_{K} = 2T_{2}

G_{M} = 20 • 10 = 200 N

T_{1} = 200 N

T_{2} = 200 N

T_{3} = 200 N

G_{K} = T_{2} + T_{3}

G_{K} = 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 T_{1}, T_{2}, T_{3}, T_{4} 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 T_{3} force.

G_{K} = 2T_{3}

200 = 2T_{3}

T_{3} = 100 N

T_{3} = T_{2 } because of

_{}

T_{2} = 100 N

T_{4} = 2T_{3}

T_{4} = 200 N

T_{2} = 2T_{1} because of

100 = 2T_{1}

T_{1} = 50 N

T_{1} = 2F because of

50 = 2F

F = 25 N

**Rope Tension In Pulleys. Part -1**

RISE KNOWLEDGE

11/07/2018

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