Week 2 - Spring and pulley systems

Springs

Springs are elastic members that exert a force or a torque and absorb energy which is usually stored for later release.

Springs are usually but not necessarily made from metal.

Linear springs handle compression and extension (tensile) loads.


There are many different types of springs including:

  • compression - ballpoint pens, mattresses, shock absorbers.

  • extension - found in weight scales and trampolines

  • torsion

  • disc

  • leaf

  • balloon


Hooke’s law

Linear springs are governed by Hooke’s law, which states that the deformation (x) of a spring over the elastic range is directly proportional to the applied force (F) via a spring constant/stiffness (k):

F = kx

The value of the spring constant is dependent on the type of material used and its shape, which can be measured experimentally.

Only valid in the elastic region of the material, if enough deformation occurs it will be in the plastic region and will not longer follow Hooke’s law.

Series and parallel springs

Multiple springs may be connected in series and in parallel.

Springs in series experience the same force. The total defamation is equal to the sum of all the spring deformations.

Springs in parallel experience the same deformation.

Pulleys

A pulley system is a mechanical device that uses a wheel with a grooved rim and a rope or cable to transmit force and motion.

The wheel is called a pulley and can either be fixed or moveable.

A fix pulley is attached to a stationary object, while a moveable pulley is attached to a load that needs to be lifted or moved.

Pulley systems are used in a variety of applications such as elevators, cranes, fitness equipment and are used in some types of machinery to transmit force and motion. They are also used in simple machines to lift heavy objects with less effort.

A pulley system is typically designed to make the work feel easier by changing the direction and/or magnitude of the input force required to achieve the output force.

Mechanical advantage

The mechanical advantage of the pulley can be defined as the ratio of the load (Foutput) to the input force (Finput). There is a tradeoff between force and the distance it is applied over (d).

Since work is conserved in this system there is a trade off between force and distance.

Assumptions

Cables are often assumed to have uniform tension throughout since they:

  • Only support tension loads

  • Have negligible weight

  • Are rigid/inextensible (cannot stretch)


Pulleys are often assumed to:

  • Be weightless

  • Be frictionless