# Finding forces acting on spring/pulley system

• uglies1992
In summary, the relationship between spring extension and weight of the block can be determined by considering the equilibrium of the spring and axle of the pulley and taking into account the third law pairs of forces involved. This includes the force of the rope on the block and the block on the rope, as well as the force of the spring on the block and the block on the spring. The force of the rope on the pulley and the pulley on the rope should also be considered.
uglies1992

## Homework Statement

There is a spring attached to a hanging block by a rope over a pulley, with a stop on the other end. Using basic physics principles, determine the relationship between spring extension and weight of the block.

F=-kd
w=mg

## The Attempt at a Solution

I know that if the system is in equilibrium, the sum of forces acting on the block/spring should be zero. Also, since the force of the rope on the block and the force of the rope on the spring are third law pairs, they should be equal in magnitude but in opposite directions. Not quite sure where to go from here though.

uglies1992 said:

## Homework Statement

There is a spring attached to a hanging block by a rope over a pulley, with a stop on the other end. Using basic physics principles, determine the relationship between spring extension and weight of the block.

F=-kd
w=mg

## The Attempt at a Solution

I know that if the system is in equilibrium, the sum of forces acting on the block/spring should be zero. Also, since the force of the rope on the block and the force of the rope on the spring are third law pairs, they should be equal in magnitude but in opposite directions. Not quite sure where to go from here though.

Not like this.

Hint: First consider the axle of the pulley as the system and not the whole pulley. Consider equilibrium of spring and axle of pulley. What equation can you make for this ?

uglies1992 said:

## Homework Statement

There is a spring attached to a hanging block by a rope over a pulley, with a stop on the other end. Using basic physics principles, determine the relationship between spring extension and weight of the block.

F=-kd
w=mg

## The Attempt at a Solution

I know that if the system is in equilibrium, the sum of forces acting on the block/spring should be zero. Also, since the force of the rope on the block and the force of the rope on the spring are third law pairs, they should be equal in magnitude but in opposite directions. Not quite sure where to go from here though.
Hello uglies1992 . Welcome to PF !

The force of the rope on the block and the force of the rope on the spring are not a third law pair .

The force of the rope on the block and the force of the block on the rope is a third law pair .

Similarly, the force of the spring on the block and the force of the spring on the rope is a third law pair .

There are also the force of the rope on the pulley and the force of the pulley on the rope to consider.

Last edited:

## 1. What are the main forces acting on a spring/pulley system?

The main forces acting on a spring/pulley system are tension, weight, and the force from the spring. Tension is the force that is transmitted through the rope or cable connecting the pulleys, weight is the force due to gravity acting on the objects attached to the system, and the force from the spring is the force exerted by the spring itself.

## 2. How do you calculate the tension in a spring/pulley system?

To calculate the tension in a spring/pulley system, you can use the equation T = kx, where T is the tension in the rope or cable, k is the spring constant, and x is the displacement of the spring from its equilibrium position. You can also use the principle of conservation of energy to calculate the tension by equating the potential energy of the spring to the kinetic energy of the objects attached to the system.

## 3. What factors can affect the forces in a spring/pulley system?

The forces in a spring/pulley system can be affected by factors such as the weight of the objects attached to the system, the stiffness of the spring, the angle of the ropes or cables, and any external forces acting on the system. Friction and air resistance can also affect the forces in the system.

## 4. How does the displacement of the spring affect the forces in a spring/pulley system?

The displacement of the spring directly affects the force exerted by the spring itself. As the spring is stretched or compressed, the force it exerts will change according to Hooke's Law (F = -kx). This change in force will also affect the tension in the ropes or cables and the weight of the objects attached to the system.

## 5. Can a spring/pulley system experience forces in multiple directions?

Yes, a spring/pulley system can experience forces in multiple directions. The tension in the ropes or cables can act in different directions depending on the configuration of the system, and the weight of the objects attached to the system can also act in different directions. The force from the spring, however, will always act in the opposite direction of the displacement of the spring.

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