P2.3 - Forces in action

• Elastic and Plastic


  • When you apply forces to an object it can be stretched, compressed or bent this is deformation.
  • To deform an object, you need at least two forces. If you just pull one end of a spring, and there's no force at the other end, you'll just pull the spring along rather than stretching it.
  • If an object returns to its original shape after the forces are removed, it's an elastic deformation.
  • If the object doesn't return to its original shape when you remove the forces, it's a plastic deformation.
• If you have a vertical spring that is fixed at the top end and has a mass attached to the bottom then when the spring and mass are in equilibrium (i.e. the spring isn't stretching any further), the downwards force on the mass (its weight) is equal in size to the upwards force that the spring exerts on the mass. The extension of a spring (or any object that's deforming elastically) is directly proportional to the force that the spring exerts on the mass (up to a point).

  A) extention

  B) natural length

  
• Limit of proportionality

  There's a limit to the amount of force you can apply to an object for the extension to keep on increasing proportionally.

  The graph shows force against extension for an object being stretched.

  For small forces, force and extension have a linear relationship. So the first part of the graph shows a straight-line (up to point P). This is where Hooke's law applies to the object.

  The gradient of the straight line is equal to the spring constant of the object the larger the spring constant, the steeper the gradient. Beyond point P, the object no longer obeys Hooke's law.

  
• elastic limit:

  Most objects still deform elastically for a little bit after you reach the limit of proportionality.

  But if you continue to increase the deforming force, you'll reach a point where it starts to deform plastically the object won't spring back to its original shape after the stretching force has been removed.

  The elastic limit can sometimes be at the same point as the limit of proportionality.

  The maximum force that can be applied to a material before this happens is called its elastic limit.
• For the graph here the elastic limit will be somewhere after point P (P is where a material stops obeying Hooke's law). For some objects, the elastic limit is so low that you'll never normally see them deforming elastically you might see these called plastic materials. The relationship between force and extension for these materials is non-linear, so the force-extension graphs of these materials are curved.

  The maximum force that can be applied to a material before this happens is called its elastic limit.

  
• Spring constant:

  How much an elastically deforming object stretches for a given force depends on its spring constant. The spring constant depends on the material that you're stretching - the stiffer the material, the larger the spring constant.

  The relationship between the extension of a spring and the force is called Hooke's law: force exerted by a spring (N) = spring constant (N/m) × extension (m) or F = k x X
• Investigation for extension of a spring:

  Hang spring from clamp stand, then measure spring's length using ruler - this is spring's original length.

  Weigh masses and add them one at a time to hook, so the force on the spring increases. After, measure new length of spring then calculate extension: extension = new length - original length Plot graph of force (weight) against extension using results and draw line of best fit. A straight line of best fit is where spring obeys Hooke's law and gradient = spring constant. If you've loaded spring with enough masses, graph will start to curve.
• Safety/accuracy for investigation of spring

  You should be standing up so you can get out of the way quickly if the masses fall, and wearing safety goggles to protect your eyes in case the spring snaps.

  When measuring the length of the spring, you should move yourself so the pointer on the hook is at eye level. Otherwise it could look like it is next to a different marking on the ruler. You also need to make sure the ruler is exactly vertical to get an accurate measurement, and that the spring isn't moving.
• Investigation for extension of a spring:

  A) spring

  B) clamp

  C) clamp stand

  D) hook

  E) masses

  F) ruler

  
• Work done to deform object:

  When a force deforms an object, work is done to stretch, compress or bend the object.

  If the deformation is elastic, this transfers energy to the object's elastic potential energy store.

  The equation for the energy stored in an object's elastic potential energy store is: energy transferred in stretching (J) = 0.5 × spring constant (N/m) × (extension)2 (m)2 or E = 0.5 x k x X² This also works for objects that are being compressed elastically. Just use the compression instead of extension.
• force-extension graph:

  You can also find the energy transferred when an object deforms elastically from its force-extension graph. The energy transferred is equal to the area under the graph up to its current extension. You can find this area by counting squares, or if the graph is linear, by finding

  the area of the triangle.

  A) energy transferred

  B) elastic limit

  C) elastic limit

  D) past

  
• Gravity:

  Everything that is made of matter has a gravitational field around it and a gravitational field attracts other masses.

  The bigger the object is, the greater the strength of its gravitational field.

  Earth has got a gravitational field that pulls us and everything else towards it.

  The Moon is big enough that its gravitational field creates the tides on Earth.
• gravitational field strength, g:

  A planet's gravitational field makes all things accelerate towards the planet's surface, all with the same acceleration.

  g is called the gravitational field strength. It's also known as the acceleration due to gravity (it's the acceleration an object will have when falling to Earth). Its value is about 10 N/kg near the Earth's surface. Meaning that anything that falls/is dropped on Earth (an object in free fall) will have an acceleration of 10 m/s². g is different on other planets, so an object in free fall on another planet will have a different acceleration.
• Weight:

  The force acting on an object when it's in a gravitational field is called the weight, or gravitational force. It's measured in newtons (N). You can calculate this force using the equation: gravitational force (N) = mass (kg) × gravitational field strength, g (N/kg) Or in symbols, where W is the weight in N (i.e. the gravitational force): W = m x g
• Mass:

  Mass is not the same as weight.

  Mass is just the amount of 'stuff in an object.

  For any given object this will have the same value anywhere in the Universe. The more massive an object is, the larger its weight. Similarly, the stronger the gravitational field an object is in (e.g. the more massive the planet it is on), the higher the gravitational field strength and so the larger the object's weight.
• Gravitational Potential Energy:

  When an object is at any height above the Earth's surface, it will have energy in its gravitational potential energy store.

  You can calculate the amount of energy in the gravitational potential energy store using the equation: gravitational potential energy (J) = mass (kg) x gravitational field strength, g (N/kg) × height (m) or E = m x g x h
• Moment:

  A moment is the turning effect of a force

  If a force acts on an object with a pivot, it can cause the object to rotate around the pivot like pushing open a door on a hinge. The size of the moment of the force is given by: moment of a force (Nm) = force (N) × distance (m) or M = F x d

  The distance here is the normal (perpendicular) distance between the pivot and the line of action of the force (the direction of the force).
• The force on the spanner causes a turning effect or moment on the nut (which acts as a pivot). A larger force would mean a larger moment.

  A) force

  B) distance

  C) x

  
• Using a longer spanner, the same force can exert a larger moment because the distance from the pivot is greater.

  A) pivot

  
• To get the maximum moment you need to push at right angles (perpendicular) to the spanner. Pushing at any other angle means a smaller moment because the perpendicular distance between the line of action and the pivot is smaller.

  A) line of action

  B) perpendicular distance

  
• A force can either cause an object with a pivot to rotate clockwise or anticlockwise. The direction of the rotation depends on the direction of the force and which side of the pivot the force is on. Just imagine the object is in front of you and you're applying the force to work out which direction the rotation is in.
• Principle of moments:

  If the anticlockwise moments are equal to the clockwise moments, an object won't turn. Balanced objects obey the principle of moments:

  Total anticlockwise moments = Total clockwise moments
• Force Multipliers:

  Levers transfer the turning effect of a force - push one end of a lever down and the rotation around the pivot causes the other end to rise.

  The moment due to a force depends on the distance of the force from the pivot.

  Levers increase the distance from the pivot that the force is applied, so less input force is needed to get the same moment. This moment provides an output force to a load.

  Levers are known as force multipliers - they reduce the force needed to get the same moment.
• Example of when levers act as force multipliers:

  A) output

  B) input

  C) load

  
• Example of when levers act as force multipliers:

  A) input

  B) output

  C) load

  
• Example of when levers act as force multipliers:

  A) output

  B) input

  C) input

  D) output

  
• The moment of the input force (the force you apply) equals the moment of the output force (which is applied to the load). Moment = force X distance, which means you can write: input force / output force = distance of output force from pivot / distance of input force from pivot
• Gears:

  Gears fit together to transfer turning effects, they are circular cogs with 'teeth' around their edge.

  The teeth of different gears can interlock so that turning one gear causes another to turn as well. Because of how they are linked together, a gear spinning clockwise will make the next gear spin anticlockwise. This then alternates as you go from gear to gear.

  
• Moment in gears:

  A force applied to a small gear creates a small moment. The small gear applies this force to the gear next to it. If this second gear is larger, the force is being applied further from the pivot (of the larger gear), so the moment of the second gear is larger.

  A series of gears that get bigger from gear to gear will multiply the moment of the first, smallest gear.

  Interlocked gears will rotate at different speeds, depending on their size - the larger the gear, the slower it spins. (For every complete turn of the small gear, the large gear has only turned a small amount.)
• Ratios in gears:

  You can work out how the speeds and moments will change between gears by looking at the gear ratios. E.g. A Large gear has 16 teeth and a medium gear has 8 teeth. The ratio of teeth between the largest and medium gear is 16: 8 = 2:1. This means that for every 1 turn the largest gear does, the medium gear will do 2 turns.
• Ratio in gears:

  Because moment = force x distance, and the forces applied to each gear are the same, the ratio of moments of two gears is equal to the ratio of the gears' radii, and therefore equal to the ratio of teeth. For the gears above, the moment of the largest gear to the medium gear is also 2:1 - so the moment gets doubled. A gear's radius is equal to the distance of the applied force from the pivot.
• Pressure:

  Pressure in a fluid (liquid or gas) is caused by the particles in the fluid moving around and bumping into the sides of its container.

  This pressure causes a net force at right-angles to all surfaces that the fluid is in contact with.

  You can calculate pressure from the force and the area of the surface that the force is being exerted on:

  pressure (Pa) = force normal to a surface (N) / area of that surface (m²)

  or P = F / A
• Liquids:

  Liquids are incompressible this means that if a force is applied to one point in a liquid, there will be a net force transmitted (passed) to other points in the liquid.

  Imagine a balloon full of water with a few holes in it. If you squeeze the top of the balloon, the water will squirt out of all the holes faster. This is because the force applied to the water at the top of the balloon is transmitted to the water in other parts of the balloon.

  
• Hydraulic system

  Hydraulic systems are used as force multipliers they use a small force to produce a bigger force.

  The system has two pistons, one with a smaller cross-sectional area than the other. Pressure is transmitted equally through a liquid so the pressure at both pistons is the same. P = F/A, so at the 1st piston, a pressure is exerted on the liquid using a small force over a small area.

  This pressure is transmitted to the 2nd piston.

  The 2nd piston has a larger area, and so as F = P x A, there will be a larger force.
• Hydraulic systems:

  A) small

  B) large

  C) small cross-sectional area

  D) cross-sectional

  E) same pressure