Pulley Tension and Normal Force: Understanding the Relationship

[vaishakh]

When two objects are tied to some two ends of a string on a pulley hung on a surface, the normal force applied by the surface on the pulley is twice the tension of the string. Why is this so?
In fact one of the questions had such a pulley hung on a pulley with the help of a string whose other end is tied to a object. The question was to find the acceleration of all the three objects and I found the relative (to pulley) acceleration of first two objects. Now this pulley was given to be massless. So I thought the mass on this side should be taken as the sum of the two masses tied while finding the acceleration of pulley. This resulted in approaching a wrong answer. However when the mass was taken to be 2T/g where t is the tension on the string and g is the acceleration due to gravity my answer was perfect. I didn't understand the concept behind this. I mean what about those masses

 

[dx]

When two objects are tied to some two ends of a string on a pulley hung on a surface, the normal force applied by the surface on the pulley is twice the tension of the string. Why is this so?

The strings are pulling the pulley down with a force with contributions from each string. But since the pulley is not accelerating downward, there must be a compensating force of the same magnitude and opposite direction coming from the place where it is hung.

 

[quicknote]

?I can explain the relationship between pulley tension and normal force in this scenario. First, it is important to understand that tension is a force that is transmitted through a string or rope when it is pulled tight. In this case, the tension in the string is caused by the weight of the two objects hanging from it.

Now, when these two objects are tied to opposite ends of the string and hung on a pulley, the pulley experiences two forces - the tension in the string pulling it upwards and the normal force from the surface it is hung on pushing it upwards. These two forces are equal in magnitude and opposite in direction, resulting in a net force of zero on the pulley.

The normal force from the surface is equal to the weight of the two objects combined, as they are resting on the surface. This means that the tension in the string must also be equal to the weight of the two objects combined, as it is supporting their weight. Therefore, the normal force applied by the surface on the pulley is twice the tension in the string, as stated in the content.

In regards to the question of finding the acceleration of all three objects, it is important to consider the pulley as a separate object with its own acceleration. The mass of the pulley itself is not relevant in this scenario, as it does not contribute to the overall forces acting on the system. The acceleration of the pulley can be found by considering the net forces acting on it, which in this case would be the tension in the string and the normal force from the surface. This acceleration can then be used to calculate the acceleration of the other two objects.

In conclusion, the relationship between pulley tension and normal force is a result of the equal and opposite forces acting on the pulley in this scenario. Understanding this relationship is important in accurately analyzing the forces and accelerations in systems involving pulleys.