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:

PulleySys_K1I1


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

The system is in equilibrium.

Find the magnitude of the T1 and T2 rope tensions and the force F that keep the system in balance.

(g = 9.8 m/s2)


Solution:

The weight of the K object.

Gk = mK• 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:

PulleySys_K1I2


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/s2)


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 FL,

GL = mL•g

GL = 196 N

Fnet = 196 – 147

Fnet = 49 N

PulleySys_K1I3


Total mass,

mtot = mK + mL

mtot = 15 + 20

= 35 kg

Fnet = m•a

49 = 35 • a

a = 49
35



= 1.4 m/s2


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:

PulleySys_K1I4


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, T1, T2 and F forces.

(g = 10 m/s2)


Solution:

Rule – 1 

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

According to this rule,

T1 = T2

Also, T2 = F 

In this case, T1 = T2 = F 

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

T = 10 • 10 = 100 N

PulleySys_K1I5



T1 + T2 = T

2T1 = T

2T1 = 100 N

T1 = 50 N

T1 = T2 = F

F = 50 N


Tension Force On Rope I

Tension Force On Rope II

Rope Tension In Pulleys


RISE KNOWLEDGE

08/07/2018

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