What energy is propelling these teenagers into the air? Forces and energy in springs Quick Starter What energy is propelling these teenagers into the air? show hint show answer

What energy is propelling these teenagers into the air? Forces and energy in springs Quick Starter What energy is propelling these teenagers into the air? The trampoline is an elastic canvas suspended from a frame by lots of springs Hint X show hint show answer

What energy is propelling these teenagers into the air? Forces and energy in springs Quick Starter What energy is propelling these teenagers into the air? show hint show answer

Elastic potential energy Forces and energy in springs Quick Starter Elastic potential energy The teenagers supply the original energy by jumping from a standing start As they fall back they push the trampoline down, the springs extend and the energy is transferred into elastic potential energy, ready to propel them back up as the springs return This group of teenagers need to co-ordinate their jumping, however, so that they get a bigger spring back back to question

Stretching Materials and Storing Elastic Energy

extension force

Elastic limit for springs If a spring is stretched far enough, it reaches the limit of proportionality and then the elastic limit. The limit of proportionality is a point beyond which behaviour no longer conforms to Hooke’s law. The elastic limit is a point beyond which the spring will no longer return to its original shape when the force is removed. force Elasticity is the ability to regain shape after deforming forces are removed. extension

Stretching Materials and Storing Elastic Energy Learning Objectives: Calculate work done in stretching (or, the amount of elastic potential energy stored in a stretched object). Describe the difference between a linear and nonlinear relationship for force and extension.

E = F x d Calculating Work Done How do we calculate the work done while moving an object? Remember: Work Done is equal to Energy Transferred E = F x d E = energy transferred / work done (J) F = force (N) D = distance (m) Why can’t we use this equation for calculating the energy used to stretch a spring? The force from a spring changes as we extend it.

Applying the Work Done equation to a spring. Imagine you apply a constant force of 5N to a box an object and you move it a distance of 3m. On a graph it would look like this….. Distance Force 5N 3m Work done = force x distance 15J = 5N x 3m This is the same as the area under the graph. So, work done is equal to the area under the line of a force-distance graph. This is the same for force-extension graph for a spring.

Applying the Work Done Equation to a Spring. The area under the line of a force-extension for a spring is a triangle which is half the area of the previous graph, so: Work done on a spring = 0.5 x F x e Extension Force 5N 3m How much energy is stored in the spring in this graph? E = 0.5 x 5N x 3m = 7.5J

E = 0.5 x F x e E = energy/work done (J), F = force (N), e = extension (m) E = 0.5 x F x e A spring is extended by 0.8m at which point it pulls back with 6N. How much energy is stored in the spring? What is the minimum amount of work that must be done to stretch the spring to this point? Explain your answer. 50J of energy is used to pull a spring 4m. What force will the spring pull back with at this point? Extension What is the spring constant in Q1? What is the spring constant in Q2? 0.5 x 6N x 0.8m = 2.4J 2.4J Work done = energy transferred. 50J (0.5 x 4m) = 25N 6N 0.8m = 7.5N/m 25N 4m = 6.25N/m

Using the Spring Constant to calculate the Energy in Spring Work done on a spring = 0.5 x F x e But Hooke’s Law tells us that force is equal to spring constant multiplied by extension F = k x e So, if we replace (substitute) F with k x e we get…... Work done on a spring = 0.5 x k x e x e Which simplifies to…. Work done on a spring = 0.5 x k x e2

E = 0.5 x k x e2 k = spring constant (N/m) e = extension (m) E = energy/work done (J), k = spring constant (N/m) e = extension (m) E = 0.5 x k x e2 A spring has a spring constant of 3.5N/m. It is extended by 0.7m. How much energy is stored in the spring? A 0.1m spring with a spring constant of 8.1 N/m is stretched to 0.6m. How much energy is stored in the spring? A spring is stretched to 3m, it’s original length is 0.5m and it has a spring constant of 24N/m. How much work must be done to stretch the spring to this point? Extension 4. How much would you need to extend a spring with spring constant 6.4N/m for it to store 4.6 J 0.5 x 3.5 x 0.72 = 0.875 J 0.5 x 8.1 x 0.52 = 1.0125 J 0.5 x 24 x 2.52 = 75 J √(4.6 (0.5 x 6.4)) = 1.2m