- Slides: 23
Hooke’s Law ?
Hooke’s Law In 1660, a scientist called Robert Hooke discovered a law for elastic materials. He was trying to improve the type of clocks that were used on ships (pendulum clocks) and theorized that a spring would work better on a pitching ship.
We are familiar with spring scales Not used in industry, b/c can’t be calibrated accurately and can become overstretched
Hooke's Law, elasticity • If a material returns to its original size and shape when you remove the forces stretching or deforming it (reversible deformation), we say that the material is demonstrating elastic behaviour. • If you apply too big a force a material will lose its elasticity. • Hooke discovered that the amount a spring stretches is proportional to the amount of force applied to it. This means if you double the force its extension will double, if you triple the force the extension will triple and so on.
The elastic limit can be seen on the graph. This is where it stops obeying Hookes law.
You can write Hooke's law as an equation: F = k∆x Where: • F is the applied force (in newtons, N), • x is the extension (in metres, m) and • k is the spring constant (in N/m). • ∆x = stretched length – original length.
Hooke's H______ Law: The compression or elongation x of an equilibrium ideal spring from its e________ position (x = 0) directly proportional is d______________to the applied force Fs. Fs = kx compression: stretching or elongation: x=0 x x Fs Fs More F more s______ or c_________. stretch compression
Hooke's Law is often written: Fs = - kx This is because it also describes the force that the itself object s spring _______ exerts on an o______ that is attached to it. The negative sign indicates that the direction of opposite the spring force is always o _______ to the displacement of the object
A weight of 8. 7 N is attached to a spring that has a spring constant of 190 N/m. How much will the spring stretch?
Ex. A weight of 8. 7 N is attached to a spring that has a spring constant of 190 N/m. How much will the spring stretch? w/ weight w/o weight Given: Fs = 8. 7 N k= 190 N/m x Unknown: x =? Equation: Fs = kx 8. 7 N = (190 N/m) x x = 4. 6 x 10 -2 m 8. 7 N
Fs = kx Ex: A force of 5. 0 N causes t 0. 015 m. How far will it stretch if the force is 10 N? he spring to stretch Fs direct 10 5 2 (0. 015 m) = 0. 030 m . 015 ? x What quantity does the slope represent? slope = Dy/Dx = Fs/x the spring constant, k. The slope represents ________________ k
Ex. Comparing two springs that stretch different amounts. spring B Fs spring A Applying the same force F to both springs x. B Which spring stretches more? Which is stiffer? B x. A x A greater larger stiffer spring _____ slope _____ k
Elastic ______ PE - the energy stored in a spring when work is done on it to stretch or compress it PEs = (½)kx 2 Ex. A spring with a spring constant of 370 N/m is stretched a distance 6. 4 x 10 -2 m. How much elastic PE will be stored in the spring? PEs = (½)kx 2 = (0. 5)( 370 N/m)(6. 4 x 10 -2 m)2 = 0. 76 (N/m)(m 2) = 0. 76 Nm = 0. 76 J How much work was done to stretch the spring by this amount? W = DPE = 0. 76 J
Hold on a minute, K? Spring Constant? ! • The spring constant measures how stiff the spring is. • The larger the spring constant the stiffer the spring. • You may be able to see this by looking at the graphs below: k is measured in units of newtons per metre (Nm -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 m – 0. 38 m = 0. 04 m F=k∆x 2. 0 N = k x 0. 04 m So, k = 2. 0 N 0. 04 m = 50 N m-1
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.
Key Definitions • Hooke’s Law = The amount a spring stretches is proportional to the amount of force applied to it. • The spring constant measures how stiff the spring is. The larger the spring constant the stiffer the spring. • A Diagram to show Hooke’s Law F=k∆x