NOT THIS ONE! Hooke’s Law

Robert Hooke 1635-1703 Researched and wrote papers on Geometry, Snowflakes, Heat, Astronomy, Fossils, Air Pumps, Light, Watches, Telescopes and Silkworms…..among other things…. Continually squabbled with Newton with whom he was miffed because Newton seemed to get all the attention and credit..Hookes Law was one of the few things he was popularly credited with A rather crabby individual but credited with the invention of universal joints, the balance wheel and the iris diaphragm

What did Hooke discover? The more force that was put on materials the more they extended With some materials they also extended in a regular way e.g., if the force was doubled so did the extension This was true as long as their elastic limit was not exceeded

What does this mean?

What does the graph show?

What is the elastic limit? The material no longer shows elastic behaviour i.e., does not return to original size when stretching force is removed The material is permanently deformed i.e., is larger or longer than originally The material is weaker as the above effects are caused by fracture of some atomic bonds

Since Force is proportional to extension Hooke’s Law could be put as: Where F is the applied force in Newtons x is the extension in metres Or if k is the proportionality constant F=kx

What does k mean in F=kx? k is called the spring constant and is a measure of the stiffness of the spring or material It has units of N m-1 (newtons per metre) The higher the k, the stiffer the spring Materials with a high k need a large force for a given extension

k is measured in units of newtons per metre (Nm -1). Spring Constants The spring constant k is measured in Nm-1 because it is the force per unit extension. The value of k does not change unless you change the shape of the spring or the material that the spring is made of. k is measured in units of newtons per metre (Nm -1).

Series and parallel springs k decreases by 2 Combined springs slacken compared with single spring extension doubles Series k increases by 2 Combined springs stiffen compared with single spring extension halves Parallel

Example F= kx 2.0 = k x 0.04 = 50 N m-1 A spring is 0.38 m long. When it is pulled by a force of 2.0 N, it stretches to 0.42 m. What is the spring constant? (Assume the spring behaves elastically.) Extension, x = Stretched length – Original length = 0.42 – 0.38 = 0.04 m F F= kx 2.0 = k x 0.04 k x So, k = 2.0 0.04 = 50 N m-1

So what? Understanding Hookes law is critical to the construction of any structure e.g., bridges buildings Deformation of materials is also critical in vehicle design though in practice the terms stress ( the force per square metre) strain (the extension per unit length) are more commonly used instead of simply force and extension http://www.youtube.com/watch?v=aNHStI-MDWU

Elastic behaviour – Car Safety Elastic behaviour is very important in car safety, as car seatbelts are made from elastic materials. However, after a crash they must be replaced as they will go past their elastic limit. Why have seat belts that are elastic? Why not just have very rigid seatbelts that would keep you firmly in place? The reason for this, is that it would be very dangerous and cause large injuries. This is because it would slow your body down too quickly. The quicker a collision, the bigger the force that is produced.

This can be seen very plainly by comparing the effect of kicking a football, which squashes as you kick it giving a big collision time

Andy O Brian with both the Ball and his nose showing elastic behaviour

followed by kicking a brick followed by kicking a brick. The brick doesn't squash, giving a very quick collision time and a very painful foot. This is why airbags and crumple zones can reduce injuries (these are both parts of a car designed to squash rather than be rigid). So to reduce injuries in a collision, always slow down in as long a time as possible. This is why you bend your legs when landing after a jump and why parachutists roll when they hit the ground.