Additional Physics Topic 1  Resultant Forces
Forces
You will know that forces are pushes, pulls, or twists. In this section we will only think about pushes and pulls. Some key concepts in forces are essential to understand before we explain the effects of forces. You will remember from previous work that:
Forces are vectors with a direction as well as a value (or magnitude);
Forces are measured in Newtons;
Forces act in pairs. If you push on something, it will push on you.
The blue force (from right to left) is the applied force. The red force (from left to right) is the reaction force. Physicists call this Newton's Third Law.
Balanced Forces
When forces are balanced, they are of equal size, but opposite in direction.
What will be the total value of the forces above? 
Note that this does NOT mean there is no force. It simply means that the total of the forces add up to the value in the answer above.
When forces are balanced, it means that:
If an object is stationary, it will continue to be stationary. If you are sitting on a chair, your weight is balanced by an upwards force from the chair.
If an object is moving, it will move at constant speed. If you are pedalling a bicycle at a constant speed, the force you put into the pedals is balanced by the air resistance and friction.
Physicists call these observations Newton's First Law. This explains why a car has a maximum speed. The engine has only a limited force it can provide. Eventually the air resistance (and the friction) balance out the force the engine can provide, and the car cannot go any faster.
What would happen if your weight was more than the upwards force from the chair? 
This cyclist is riding at maximum speed. The force that he puts on the pedals is balanced out by the air resistance from the wind.
Photo by Cruzcaray, Wikimedia Commons
Why is it harder to cycle into the wind than cycle at the same speed in still air? 
In an aeroplane in level flight at a constant speed there are two pairs of forces acting:
thrust from the engine (forwards force) and drag from the air resistance (backwards);
weight acting downwards and lift from the wings acting upwards. The lift comes from the wings moving through the air.
What will happen if the pilot increases the power to the engine? 
Architects designing buildings want to ensure that all forces are balanced. All forces add up to zero. That does not mean that there are no forces at all; all forces add up to zero. If they did not, there would be movement (strictly speaking, acceleration). The building would collapse.
Photo by Nigel Davies, Wikimedia Commons
Unbalanced Forces
Forces sum to a resultant force:
If the forces are in the same direction, they add up;
If the forces are in the opposite direction, they subtract.
If the forces are in the same direction, they add up to make a resultant force. In this picture the resultant force is shown in black:
If the forces are in opposite directions they take away. The resultant is in the direction of the bigger of the two forces.
Note that in this case the bigger force is from right to left, so the resultant force is from right to left.
The resultant force is the single force that would have the same effect as all the forces acting on the object. We can have as many forces as we like, but they would all sum to a single resultant force.
The forces above have a resultant force, which will result in acceleration in the direction of the resultant force.
Work out the resultant of these forces and state the direction of the resultant. (a) 25 N from left to right and 20 N from left to right; (b) 25 N from left to right and 20 N from right to left. 
These forces are unbalanced; one is bigger than the other. Wherever there are unbalanced forces on an object, the object will move (accelerate) in the direction of the bigger force.
If the object is stationary, it will accelerate. Therefore it will move.
If the object is moving at a constant speed, it will accelerate to a higher speed.
Uses of Resultant Forces
When a rocket is accelerating upwards, it exerts a force on each cosmonaut in it. They in turn exert an equal and opposite force. This force may be five times their weight, so they feel very heavy. They are trained in various machines like a centrifuge in order to know what to expect.
They sit in the capsule and are spun round on the giant machine. It is not a pleasant ride.
People also pay large sums of money to go on fairground rides that do similar things. As does a baby bouncer:
Extension only
Although this is NOT on the syllabus, it will help you if you are going on to do Alevel Physics.
If we have two forces that are not in the same direction, or in opposite direction, we can't simply add or take away. We have to do a vector sum to find the resultant. This aeroplane is flying with a wind blowing across its path. It will actually move along the grey arrow, the resultant of the two vectors.
We can show this as a triangle of forces:
Let's suppose the aeroplane is flying at 150 m/s and the wind is 20 m/s at 70^{o} to the direction of the flight.
We can work out the resultant by accurate drawing on graph paper. Choose a scale of 1 cm = 10 m/s. Draw the horizontal vector velocity as a line exactly 15 cm long. Draw the wind velocity as a vector exactly 2 cm long, and use a protractor to draw an angle of 70 ^{o}.
On measuring the resultant, we see that the line is 14.4 cm. Since 1 cm = 10 m/s, the speed of the aeroplane relative to the ground is 144 m/s.
We can resolve any force vector going in any direction as the resultant of two perpendicular force vectors. We resolve the force into its components.
If an object is going down a slope, there are two components, but they are NOT horizontal or vertical, because the weight always acts vertically downwards. The weight is the resultant of two force vectors:
When objects are moving, the idea of forces acting in pairs still applies. If a car pulls a trailer with a force of 1500 N, the trailer is pulling on the car with a force of 1500 N. When the car accelerates, the force on the trailer might increase to 2000 N. The pulling force on the car from the trailer is 2000 N as well.
Guns recoil because forces act in pairs. Since F = ma, the force that acts on the bullet is the same force acting on the gun (and the hunter). The hunter and gun have a much bigger mass so a lower acceleration. We can also use the concept of momentum to describe the recoil.
We can resolve forces without needing to do accurate drawing (which might not be all that accurate). Instead we use trigonometry. Let us go back to the object on a slope:
The weight is W. Weight is a force worked out by multiplying the mass (kg) by the acceleration due to gravity ( = 10 m/s^{2}).
W = mg Therefore the two components are:
The strange looking symbol q is "theta", a Greek letter 'th', which is often used to show an angle.
