WEBVTT 00:00:00.500 --> 00:00:03.975 Welcome to GCSE Edexcel Science revision. 00:00:04.125 --> 00:00:07.243 Unit C P 13: Forces and matter. 00:00:09.900 --> 00:00:17.446 Stretching, compressing or bending an object involves more than one force, such as a pull at one end and a support force at the other. 00:00:17.596 --> 00:00:21.570 A single unopposed force can instead accelerate the object as a whole. 00:00:24.233 --> 00:00:31.645 Elastic deformation means an object returns to its original shape or length after the deforming forces are removed. 00:00:31.795 --> 00:00:34.950 Inelastic deformation leaves a permanent change. 00:00:37.600 --> 00:00:44.328 A spring can stretch elastically for small enough loads and become permanently deformed under a sufficiently large load. 00:00:44.478 --> 00:00:48.048 Elasticity is not a guarantee for every applied force. 00:00:50.700 --> 00:00:53.388 Different materials and shapes deform differently. 00:00:53.538 --> 00:00:58.721 A sheet may bend and spring back under a small force, but folding can leave a permanent crease. 00:00:58.871 --> 00:01:04.292 A rubber band can be elastic even though its force, extension graph is curved (non-linear). 00:01:06.967 --> 00:01:11.091 Extension X is stretched length minus original unstretched length. 00:01:11.241 --> 00:01:17.555 Compression is the reduction in length; equations below use the magnitude of deformation for a linear spring. 00:01:17.705 --> 00:01:21.221 Always subtract the original length before applying Hooke’s law. 00:01:25.900 --> 00:01:29.608 The elastic limit and limit of proportionality are different. 00:01:29.758 --> 00:01:34.717 Beyond the elastic limit, removing the force leaves a permanent change in shape or length. 00:01:34.867 --> 00:01:41.049 Beyond the limit of proportionality, the force, extension graph is no longer a straight line through the origin. 00:01:43.700 --> 00:01:49.673 For a spring in its linear range, force is proportional to extension: F equals K times X. 00:01:49.823 --> 00:01:51.337 This is Hooke’s law. 00:01:51.487 --> 00:01:57.130 F is in newtons, extension X in metres and spring constant K in newtons per metre. 00:01:59.800 --> 00:02:05.357 A larger spring constant means a stiffer spring: it needs a larger force for the same extension. 00:02:05.507 --> 00:02:09.121 K is not measured in newtons alone or in newton metres. 00:02:11.800 --> 00:02:16.995 Rearrange to K equals F divided by X and X equals F divided by K. 00:02:17.145 --> 00:02:22.627 Convert centimetres or millimetres to metres before finding K in newtons per metre. 00:02:25.300 --> 00:02:34.751 If 4 newtons extends a spring by 0.02 metres, K equals 4 divided by 0.02 equals 200 newtons per metre. 00:02:34.901 --> 00:02:40.372 In the same linear range, an 8 newtons load would give 0.04 metres extension. 00:02:40.522 --> 00:02:44.678 Greater load gives proportional extension only within the linear range. 00:02:49.333 --> 00:02:52.541 The spring's restoring force opposes deformation. 00:02:52.691 --> 00:03:00.935 A hanging load at rest is supported by a spring force equal to its weight; use F equals M times G to convert known mass to load force. 00:03:03.600 --> 00:03:14.063 Beyond the limit of proportionality, F is no longer directly proportional to X, so a single constant K cannot describe the whole curve using F equals K times X. 00:03:16.733 --> 00:03:21.938 For a Hooke’s-law spring, a force-versus-extension graph is a straight line through the origin. 00:03:22.088 --> 00:03:27.687 Force belongs on the vertical axis and extension on the horizontal axis for the rules here. 00:03:30.367 --> 00:03:36.403 Its gradient is the spring constant: K equals change in force divided by change in extension. 00:03:36.553 --> 00:03:41.227 A steeper line means a stiffer spring when the axes use the same units and scales. 00:03:43.900 --> 00:03:50.459 A curved (non-linear) graph means equal increases in force no longer give equal increases in extension. 00:03:50.609 --> 00:03:53.988 This does not necessarily mean the object is inelastic. 00:03:54.138 --> 00:03:58.024 Remove the force and check whether it returns to its original length. 00:04:00.700 --> 00:04:06.415 The limit of proportionality is where the graph first departs from its proportional straight-line behaviour. 00:04:06.565 --> 00:04:10.965 The elastic limit is where unloading starts leaving permanent deformation. 00:04:11.115 --> 00:04:14.642 Non-linear behaviour need not mean permanent deformation. 00:04:19.300 --> 00:04:25.003 If plotting extension against force instead, the gradient is one divided by K, not K. 00:04:25.153 --> 00:04:28.532 Always read the axes and units before using a gradient. 00:04:31.200 --> 00:04:38.079 A straight line that does not go through the origin may indicate a measurement offset or a different chosen length reference. 00:04:38.229 --> 00:04:41.851 Direct proportionality specifically requires the origin. 00:04:44.533 --> 00:04:50.217 Work done stretching or compressing a spring transfers energy into its elastic potential store. 00:04:50.367 --> 00:04:54.835 For an ideal elastic spring, energy can be returned as it relaxes. 00:04:57.500 --> 00:05:05.306 For a linear spring, E equals one half times K times X squared in joules, with K in newtons per metre and X in metres. 00:05:05.456 --> 00:05:10.181 The extension is squared; doubling extension quadruples energy at fixed K. 00:05:12.833 --> 00:05:24.161 A 200 newtons per metre spring extended by 0.02 metres stores one half times 200 times 0.02 squared equals 0.04 joules. 00:05:26.833 --> 00:05:30.658 The area under a force, extension graph represents work done. 00:05:30.808 --> 00:05:38.903 For a straight line through the origin, the triangular area is one half times F times X equals one half times K times X squared. 00:05:39.053 --> 00:05:48.854 Area equals one half times 4 times 0.02 equals 0.04 joules; final force times extension would be twice too large. 00:05:53.533 --> 00:06:03.440 Do not use final force times extension for a spring loaded from zero: force rises during stretching, so the average force is half the final force in the linear range. 00:06:06.100 --> 00:06:12.269 For a curved force, extension graph, find work done from the area under the graph if enough data are given. 00:06:12.419 --> 00:06:17.063 Do not use one half times K times X squared outside the straight-line range. 00:06:17.213 --> 00:06:23.665 Some work may heat the surroundings rather than being stored as elastic potential energy that can be recovered. 00:06:26.333 --> 00:06:30.380 Suspend a spring securely from a clamp stand beside a vertical ruler. 00:06:30.530 --> 00:06:35.180 Add a pointer if possible and record the unloaded length before adding masses. 00:06:37.833 --> 00:06:43.581 Add known masses in small steps, allow oscillations to settle and record length at eye level. 00:06:43.731 --> 00:06:51.230 Convert load mass to force using F equals M times G and calculate extension by subtracting unloaded length. 00:06:51.380 --> 00:06:54.418 Wait for oscillations to settle before measuring length. 00:06:59.100 --> 00:07:02.713 Keep the same spring, ruler position and attachment points. 00:07:02.863 --> 00:07:09.955 A fixed pointer and viewing at eye level reduce parallax; select a ruler resolution suitable for small extensions. 00:07:12.633 --> 00:07:17.283 Remove masses in steps as well and check whether the original length returns. 00:07:17.433 --> 00:07:22.937 Stop before damaging the spring unless specifically investigating its limits under supervision. 00:07:25.600 --> 00:07:28.735 Repeat readings and plot force against extension. 00:07:28.885 --> 00:07:36.531 Determine K from the linear gradient using two well-separated points on the best-fit line rather than a single noisy reading. 00:07:39.200 --> 00:07:44.905 Find work done from the graph area or one half times K times X squared within the linear range. 00:07:45.055 --> 00:07:48.615 Use metres rather than centimetres to get work in joules. 00:07:51.267 --> 00:07:57.441 Secure the stand against toppling, keep feet clear of falling masses and use eye protection where appropriate. 00:07:57.591 --> 00:08:01.679 Avoid overstretching the spring or leaving it oscillating while reading. 00:08:04.333 --> 00:08:06.403 That completes Forces and matter. 00:08:06.553 --> 00:08:09.898 Revisit the notes and test yourself on the revision website.