WEBVTT 00:00:00.500 --> 00:00:03.975 Welcome to GCSE Edexcel Science revision. 00:00:04.125 --> 00:00:07.095 Unit S P 15: Forces and matter. 00:00:09.767 --> 00:00:17.313 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. 00:00:17.463 --> 00:00:21.437 A single unopposed force can instead accelerate the object as a whole. 00:00:24.100 --> 00:00:31.512 Elastic deformation means an object returns to its original shape or length after the deforming forces are removed. 00:00:31.662 --> 00:00:34.817 Inelastic deformation leaves a permanent change. 00:00:37.467 --> 00:00:44.195 A spring can stretch elastically for small enough loads and become permanently deformed under a sufficiently large load. 00:00:44.345 --> 00:00:47.915 Elasticity is not a guarantee for every applied force. 00:00:50.567 --> 00:00:53.255 Different materials and shapes deform differently. 00:00:53.405 --> 00:00:58.588 A sheet may bend and spring back under a small force, but folding can leave a permanent crease. 00:00:58.738 --> 00:01:04.159 A rubber band can be elastic even though its force, extension graph is curved (non-linear). 00:01:06.833 --> 00:01:10.958 Extension X is stretched length minus original unstretched length. 00:01:11.108 --> 00:01:17.422 Compression is the reduction in length; equations below use the magnitude of deformation for a linear spring. 00:01:17.572 --> 00:01:21.088 Always subtract the original length before applying Hooke’s law. 00:01:25.767 --> 00:01:29.475 The elastic limit and limit of proportionality are different. 00:01:29.625 --> 00:01:34.583 Beyond the elastic limit, removing the force leaves a permanent change in shape or length. 00:01:34.733 --> 00:01:40.915 Beyond the limit of proportionality, the force, extension graph is no longer a straight line through the origin. 00:01:43.567 --> 00:01:49.539 For a spring in its linear range, force is proportional to extension: F equals K times X. 00:01:49.689 --> 00:01:51.204 This is Hooke’s law. 00:01:51.354 --> 00:01:56.997 F is in newtons, extension X in metres and spring constant K in newtons per metre. 00:01:59.667 --> 00:02:05.224 A larger spring constant means a stiffer spring: it needs a larger force for the same extension. 00:02:05.374 --> 00:02:08.988 K is not measured in newtons alone or in newton metres. 00:02:11.667 --> 00:02:16.861 Rearrange to K equals F divided by X and X equals F divided by K. 00:02:17.011 --> 00:02:22.493 Convert centimetres or millimetres to metres before finding K in newtons per metre. 00:02:25.167 --> 00:02:34.617 If 4 newtons extends a spring by 0.02 metres, K equals 4 divided by 0.02 equals 200 newtons per metre. 00:02:34.767 --> 00:02:40.239 In the same linear range, an 8 newtons load would give 0.04 metres extension. 00:02:40.389 --> 00:02:44.545 Greater load gives proportional extension only within the linear range. 00:02:49.200 --> 00:02:52.407 The spring's restoring force opposes deformation. 00:02:52.557 --> 00:03:00.801 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. 00:03:03.467 --> 00:03:13.929 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. 00:03:16.600 --> 00:03:21.805 For a Hooke’s-law spring, a force-versus-extension graph is a straight line through the origin. 00:03:21.955 --> 00:03:27.553 Force belongs on the vertical axis and extension on the horizontal axis for the rules here. 00:03:30.233 --> 00:03:36.270 Its gradient is the spring constant: K equals change in force divided by change in extension. 00:03:36.420 --> 00:03:41.094 A steeper line means a stiffer spring when the axes use the same units and scales. 00:03:43.767 --> 00:03:50.325 A curved (non-linear) graph means equal increases in force no longer give equal increases in extension. 00:03:50.475 --> 00:03:53.855 This does not necessarily mean the object is inelastic. 00:03:54.005 --> 00:03:57.891 Remove the force and check whether it returns to its original length. 00:04:00.567 --> 00:04:06.282 The limit of proportionality is where the graph first departs from its proportional straight-line behaviour. 00:04:06.432 --> 00:04:10.831 The elastic limit is where unloading starts leaving permanent deformation. 00:04:10.981 --> 00:04:14.509 Non-linear behaviour need not mean permanent deformation. 00:04:19.167 --> 00:04:24.869 If plotting extension against force instead, the gradient is one divided by K, not K. 00:04:25.019 --> 00:04:28.399 Always read the axes and units before using a gradient. 00:04:31.067 --> 00:04:37.945 A straight line that does not go through the origin may indicate a measurement offset or a different chosen length reference. 00:04:38.095 --> 00:04:41.718 Direct proportionality specifically requires the origin. 00:04:44.400 --> 00:04:50.084 Work done stretching or compressing a spring transfers energy into its elastic potential store. 00:04:50.234 --> 00:04:54.702 For an ideal elastic spring, energy can be returned as it relaxes. 00:04:57.367 --> 00:05:05.173 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. 00:05:05.323 --> 00:05:10.048 The extension is squared; doubling extension quadruples energy at fixed K. 00:05:12.700 --> 00:05:24.028 A 200 newtons per metre spring extended by 0.02 metres stores one half times 200 times 0.02 squared equals 0.04 joules. 00:05:26.700 --> 00:05:30.525 The area under a force, extension graph represents work done. 00:05:30.675 --> 00:05:38.769 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. 00:05:38.919 --> 00:05:48.721 Area equals one half times 4 times 0.02 equals 0.04 joules; final force times extension would be twice too large. 00:05:53.400 --> 00:06:03.307 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. 00:06:05.967 --> 00:06:12.136 For a curved force, extension graph, find work done from the area under the graph if enough data are given. 00:06:12.286 --> 00:06:16.930 Do not use one half times K times X squared outside the straight-line range. 00:06:17.080 --> 00:06:23.532 Some work may heat the surroundings rather than being stored as elastic potential energy that can be recovered. 00:06:26.200 --> 00:06:30.247 Suspend a spring securely from a clamp stand beside a vertical ruler. 00:06:30.397 --> 00:06:35.047 Add a pointer if possible and record the unloaded length before adding masses. 00:06:37.700 --> 00:06:43.448 Add known masses in small steps, allow oscillations to settle and record length at eye level. 00:06:43.598 --> 00:06:51.097 Convert load mass to force using F equals M times G and calculate extension by subtracting unloaded length. 00:06:51.247 --> 00:06:54.285 Wait for oscillations to settle before measuring length. 00:06:58.967 --> 00:07:02.579 Keep the same spring, ruler position and attachment points. 00:07:02.729 --> 00:07:09.821 A fixed pointer and viewing at eye level reduce parallax; select a ruler resolution suitable for small extensions. 00:07:12.500 --> 00:07:17.150 Remove masses in steps as well and check whether the original length returns. 00:07:17.300 --> 00:07:22.803 Stop before damaging the spring unless specifically investigating its limits under supervision. 00:07:25.467 --> 00:07:28.601 Repeat readings and plot force against extension. 00:07:28.751 --> 00:07:36.398 Determine K from the linear gradient using two well-separated points on the best-fit line rather than a single noisy reading. 00:07:39.067 --> 00:07:44.772 Find work done from the graph area or one half times K times X squared within the linear range. 00:07:44.922 --> 00:07:48.482 Use metres rather than centimetres to get work in joules. 00:07:51.133 --> 00:07:57.308 Secure the stand against toppling, keep feet clear of falling masses and use eye protection where appropriate. 00:07:57.458 --> 00:08:01.546 Avoid overstretching the spring or leaving it oscillating while reading. 00:08:04.200 --> 00:08:09.693 Pressure equals force acting at right angles to a surface (normal force) divided by area. 00:08:09.843 --> 00:08:14.718 It is measured in pascals: 1 pascals equals 1 newtons per square metre. 00:08:14.868 --> 00:08:19.572 For the same force, a smaller area gives greater pressure, as with a sharp blade. 00:08:22.233 --> 00:08:28.718 Atmospheric pressure decreases with height because there is less air above and the air is generally less dense. 00:08:28.868 --> 00:08:34.626 Pressure arises from air-particle collisions and the weight of the atmosphere, not from a solid ceiling. 00:08:37.300 --> 00:08:41.031 Fluid pressure pushes at right angles (normal) to any surface. 00:08:41.181 --> 00:08:45.515 In a liquid at rest, pressure acts in all directions, not just downwards. 00:08:45.665 --> 00:08:51.521 Absolute liquid pressure also includes the atmospheric pressure acting on the liquid’s surface. 00:08:54.200 --> 00:09:05.687 (Higher tier) Pressure due to a liquid column increases with density and vertical depth: pressure difference equals density times gravitational field strength times vertical depth (Higher tier). 00:09:05.837 --> 00:09:14.689 Use kilograms per cubic metre, newtons per kilogram and metres to obtain pascals; h is vertical depth, not the length of a sloping tube. 00:09:17.367 --> 00:09:27.306 For water with density 1000 kilograms per cubic metre at depth 2 metres and G equals 10 newtons per kilogram, gauge pressure is 20000 pascals. 00:09:27.456 --> 00:09:31.511 Add atmospheric pressure only if absolute pressure is requested. 00:09:34.167 --> 00:09:41.183 (Higher tier) At the same vertical depth in a connected stationary liquid, pressure is the same regardless of container shape. 00:09:41.333 --> 00:09:45.339 A denser liquid produces a greater pressure difference for the same depth. 00:09:48.000 --> 00:09:53.758 (Higher tier) A submerged object experiences more pressure on its lower surface than its upper surface. 00:09:53.908 --> 00:09:59.976 The resulting upward force is upthrust; pressure forces from the sides balance in a symmetric simple model. 00:10:00.126 --> 00:10:05.234 The larger lower-surface pressure gives a net upward force; force arrows are schematic. 00:10:09.900 --> 00:10:14.375 (Higher tier) Upthrust equals the weight of fluid displaced by the object. 00:10:14.525 --> 00:10:22.949 An object partly immersed in a liquid displaces only the submerged volume; a fully immersed object displaces its full external volume. 00:10:25.600 --> 00:10:29.885 (Higher tier) An object floats in equilibrium when upthrust equals weight. 00:10:30.035 --> 00:10:38.002 If weight exceeds maximum available upthrust it sinks; if upthrust initially exceeds weight it rises until a new balance is reached. 00:10:40.667 --> 00:10:52.250 (Higher tier) Average density matters: a hollow boat can float even if its material is denser than water because its total mass divided by its displaced external volume can be low enough. 00:10:54.900 --> 00:10:59.915 (Higher tier) The same fully submerged object has greater upthrust in a denser fluid. 00:11:00.065 --> 00:11:09.909 In a liquid of uniform density, putting it deeper does not increase its upthrust: pressure rises on both its top and bottom, but the difference between them stays the same. 00:11:12.567 --> 00:11:16.556 (Higher tier) Calculate upthrust with displaced-fluid mass times G, 00:11:16.706 --> 00:11:24.033 or density times displaced volume times gravitational field strength when density and displaced volume are known. 00:11:24.183 --> 00:11:27.932 Do not substitute the object's mass for the displaced fluid’s mass. 00:11:30.600 --> 00:11:32.669 That completes Forces and matter. 00:11:32.819 --> 00:11:36.165 Revisit the notes and test yourself on the revision website.