10.8 Forces and elasticity Q1a. The limit of proportionality of a spring is where the extension is no longer proportional to the applied force. b. The spring constant of a spring is equal to the force per unit extension. The stiffer the spring the larger the spring constant and the steeper the gradient of the force vs extension graph. The extension of a stretched spring is equal to: the loaded ( new) length - the original length

Q2a. If polythene is stretched beyond its limit of proportionality ‘P’ less force is required to give the extension. ‘Plastic flow’ occurs as the polymer chains slide over each other. P

Q2b. If a rubber band is stretched and released it returns to its original length. Rubber is an example of an elastic material. force extension Stretching polythene leaves it elastically deformed. It does not return to its original shape. Rubber returns to its original length when stretched and released.

Q3.a i. For the steel spring at a weight = 4N , extension = 80mm ii. For the rubber band at a weight = 4N , extension = 53mm iii. For the polythene strip at a weight = 4N , extension = 10mm

Q3b. The extension of the steel spring when the weight is 3.0N = 60mm Spring constant k = ∆ force = 3 N = 0.5 N/cm ∆ extension 6 cm

Q4a. Hooke’s law says that ; ‘The extension of a spring is directly proportional to the force applied so long as its limit of proportionality is not exceeded.’ Q4bi. k= 25 N/m ; Force required to give an extension of 0.10m is; F = ke = 25 N/m x 0.1m = 2.5 N Q4bii. Calculate the extension of the spring with a 5N force applied: F = ke F = e k 5 N = e = 1/5 or 0.2m 25 N/m