# Forces In Action

## Newton's Laws of Motion

Newton's laws are only approximations. Newton's laws work pretty well. At everyday speeds they give really, really good approximations. But at very high speeds you have to take into account relativistic effects. According to the Special Theory of Relativity, as you increase the speed of an object its mass increases. So mass isn't constant and F=ma doesn't work any more. Newton's 1st law says that a force is needed to change velocity. Newton's 1st law states that the velocity of an object will not change unless a net force acts on it. If the forces aren't balanced, the overall net force will make the body accelerate. This could be a change in speed and/or direction. Newton's 2nd law says that acceleration is proportional to the force, which can be written as the well known equation: net force(N) = mass(kg) x acceleration(metres per second squared). F=m x a. It says that the more force you have acting on a certain mass, the more acceleration you get. It says that for a given force the more mass you have, the less acceleration you get. You can see why Galileo was right about saying all objects fall at the same rate if you ignore air resistance by a bit of ball dropping and newton's 2nd law. Remember: The net force is the vector sum of all forces. The force is always measured in newtons, the mass in kilograms and the acceleration is in the same direction as the net force. Acceleration is independent of mass. Imagine two balls dropping at the same time, ball 1 being havy and ball 2 being light. Then use F=ma to work out their acceleration. Mass of ball 1=m1. Resultant force=f1, acceleration= a1. Ignoring air resistance, the only force acting on the ball is weight, given by w1=m1g. So f1=m1a1 = w1=m1=a1. The m1 cancels out to give a1 =g. Do this for ball 2, and you will find that a2=g aswell. The acceleration is independent of the mass.

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## Drag and Terminal Velocity

Friction is a force that opposed motion. There are two main types of friction: contact friction between solid surfaces, and fluid friction (a.k.a drag or fluid resistance or air resistance). Fluid is a word that means liquid or gas - something that can flow. The force depends on the thickness (viscosity) of the fluid. It increases as the speed increases (directly proportional for simple situations). It also depends on the shape on the object moving through it - the larger the area pushing against the fluid, the greater the resistive force. Frictional forces always act in the opposite direction to the motion of the object. They can never speed things up or start something moving from rest. They convert kinetic energy into heat. Terminal velocity, when the friction force equals the driving force. You will reach a terminal velocity at some point if you have: a driving force that stays the same all the time, and a frictional force that increases with speed. There are three main stages to terminal velocity: The object accelerates from rest with a constant driving force. As the velocity increases the resistance forces increase. This reduces the resultant force on the object and reduces its acceleration. Eventually the object reaches a velocity at which the resistance forces are equal to the driving force. There is now no resultant force and no accleration, so the object moves on at a constant velocity. Sketching a graph for terminal velocity. You need to recognise and sketch the velocity-time and acceleration-time graphs for the terminal velocity. The velocity-time graph has a decreasing curve, that flattens out to a horizontal straight line. The accleration-time graph has a curve that starts at the left and decreases down to near the x-axis and flattens out, becoming zero eventually. Things falling through air or water reach a terminal velocity too. When something's falling through the air, the weight of the object is a constant force accelerating the object downwards. Air resistance is a frictional force opposing this motion, which increase with speed. E.g a skydiver leaves a plane and will accelerate until the air resistance equals his weight. He is then falling at a terminal velocity. But the terminal velocity is too high to survive landing. A parachute increases the air resistance on the person and slows him down to a terminal velocity low enough to survive landing. The v-t graph is a bit different, because you have a new terminal velocity after the parachute is opened. The graph starts with an decreasing curve to a terminal velocity (horizontal line), then drops after the parachute is opened to a new terminal velocity.

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## Mass, Weight and Centre of Gravity

The mass of a body makes it resist changes in motion. The mass of an object the amount of matter in it, measured in kg. The greater an objects mass the greater resistance to a change in velocity (called its inertia). The mass doesn't change if the strength of the gravitational field changes. Weight is the force experienced by a mass due to a gravitational field. The weight on an object does vary according to the size of the gravitational field acting on it. Weight = mass x gravitational field strength, where g=9.81 on Earth. Density is mass per unit volume. Density is a measure of the compactness of a substance. It relates the mass of a substance to how much space it takes up. Density = mass/volume, or rho = m/V. The symbol for densoity is the greek letter rho, which looks like a p but isn't. The density of an object depends on what it's made of. It doesn't vary with size or shape. The average density of an object determines whether it floats or sinks. A solid object will float on a fluid if it has a lower density than the fluid. Centre of gravity - assume all the mass is in one place. The centre of gravity of an object is the point that you can consider all the weight of the object to act through, also called centre of mass. The object will always balance around this point, but sometimes it falls outside the object. Find the centre of gravity either by symmetry or experiment. Hang the object freely from a point. Draw a vertical line downwards from the point of suspension - use a plumb-bob to get it exactly vertical. Hang the object from a different point. Draw another vertical line down. The centre of gravity is where the lines cross. For a regular object the centre of gravity is at the centre of it (using symmetry). How high the centre of gravity is tells you how stable the object is. An object will be stable if it has a low centre of gravity and a wide base area. The higher the centre of gravity, and the smaller the base area, the less stable the object will be. An object will topple over if a vertical line drawn downwards from its centre of gravity falls outside the base area.

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## Forces and Equilibrium

Resolving a force means splitting it into components. Forces are vector quantities and so when you draw the forces on an object, the arrow labels should show the size and direction of the forces. Forces can be in any direction, not just right angles. To deal with a force at an angle you can split it into two forces at right angles to each other. To find the size of a component you use trigonometry. Using trigonometry you get horizontal component =Fcos theta where theta is the angle. And for the vertical component you get Fsin theta. Three forces acting on a point in equilibrium form a triangle. When three forces all act on an object in equilibrium, there is no net force - the sum of the forces = 0. You can draw the forces as a triangle showing the magnitude and direction of the forces. The F3 on your triangle should oppose the other two forces i.e travel in the opposite way to F1 and F2. You can then use them to work out the magnitude or direction of a missing force. You add the components back together to get the resultant force. If two forces act on an object you find the resultant by adding the vectors together and creating a closed triangle, with the resultant force represented by the third side. You use vector addition - draw the forces as vector arrows put 'tail to top'. Then use trig to work out the angle and length of the missing side. Choose sensible axes for resolving. Use directions that make sense for the situation you're dealing with. If you have an object on a slope choose your directions along the slope and at right angles to it.

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## Moments and Torques

A moment is the turning effect of a force. The moment/torque of a force depends on the size of the force and how far the force is applied from the turining point. Moment of a force (in Nm) = force (in N) x perpendicular distance from pivot (in m), or M=Fxd. Moments must be balanced or the object will turn. The principle of moments states that for a body to be in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point. Muscles, bones and joints act as levers. In a lever an effort force acts against a load force by means of a rigid object rotating around a pivot. You can use the principle of moments to answer lever questions. Take moments about a point and put the clockwise and anticlockwise moments equal, and solve for what you want to find. A couple is a pair of forces of equal size which act parallel to each other but in opposite directions. A couple results in no resultant linear force, but does produce a turning force (usually called a torque). The size of this torque depends on the size of the forces and the distance between them. Torque of a couple (in Nm) = size of one of the forces (in N) x perpendicular distance between the forces (in m), or T=Fxd. E.g a cyclist turns a sharp right corner by applying equal but opposite forces of 20N to the ends of the handlebars. The length of the handlebars = 0.6m. The torque is 20x0.6=12 Nm.

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