# ROPE TENSION IN PULLEYS I

## The physics lesson, rope tension calculations. Tension calculatiıons of a rope in a pulley system. Calculation the rope tension in fixed and moved pulleys.

**1- Rope Tension In Fixed Pulleys**

In a system created with fixed pulley or pulleys, Only there are fixed pulleys that can rotating about their axis. The pulleys are fixed a point. A rope was passed over the pulleys.

In a system formed with fixed pulleys, the tension force is equal at all point of the same rope.

These systems are used to change the direction of a force. There is not force gain in these systems.

**Example:**

The mass of the K object in the figure above is 25 kg.

The system is in equilibrium.

Find the magnitude of the T_{1} and T_{2} rope tensions and the force F that keep the system in balance.

(g = 9.8 m/s^{2})

**Solution:**

The weight of the K object.

_{Gk }= m_{K}• g

_{Gk }= 25 • 9.8

= 245 N

Must be F = 245 N, because of the system in balanced.

Also, T1 and T2 rope tensions are 245 N too.

**Example:**

In the system in the figure, the K and L objects are hang on the ends of the T1 and T2 ropes and released.

The mass of the L object is 20 kg and the mass of the K object is 15 kg.

What is the acceleration of the system?

(g = 9.8 m/s^{2})

**Solution:**

The acceleration of the system is found by using the below equality.

Fnet = m•a

The force acting on object K is the downward F force. This force is equal to the gravity force that acting on the object K.

GK = mk•g

GK = 147 N

In the same way F_{L},

G_{L} = m_{L}•g

G_{L} = 196 N

F_{net} = 196 – 147

F_{net} = 49 N

Total mass,

m_{tot} = m_{K} + m_{L}

m_{tot} = 15 + 20

= 35 kg

F_{net} = m•a

49 = 35 • a

a = | 49 | |

35 |

= 1.4 m/s^{2}

**2. System Consisting Of Only One Movable Pulley**

In this system, one pulley can move freely. If there are other pulleys are fixed. The rope is fixed from one end.

**Example:**

In the figüre above, the mass of the K object is 10 kg.

The pulley is weightless and frictionless.

Find, the magnitude of the T, T_{1}, T_{2} and F forces.

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

**Solution:**

**Rule – 1 **

The same tension force is occurs at all points of the same rope.

According to this rule,

T_{1} = T_{2}

Also, T_{2} = F

In this case, T_{1} = T_{2} = F

T rope tension is equal to the weight of the K object.

T = 10 • 10 = 100 N

T_{1} + T_{2} = T

2T_{1} = T

2T_{1} = 100 N

T_{1} = 50 N

T_{1} = T_{2} = F

F = 50 N

RISE KNOWLEDGE

08/07/2018

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