Balanced and unbalanced forces

Up to this point we have concentrated on the idea of balanced forces and explained them using Newton's 1st Law of motion.

When an unbalance force is applied to an object it will begin to accelerate according to Newton's 2nd Law of motion.  This states that:

The acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma. 

Basically:

• The bigger the force, the larger the acceleration for a fixed mass, or 
• The bigger the mass, the lower the acceleration for a fixed force.

People intuitively know that Newton's second law is true when riding bikes, pushing objects or even driving cars.

Contact forces are when the object is in contact with the person or other object that is producing the force.. This includes cars pulling trailers etc.

Non-contact forces are those produced by electrostatic charges, magnetic fields or gravity.

Another example of unbalanced forces is where a car is on a slope.  We can show the forces are unbalance using a vector diagram.  However, we will ignore the frictional forces described here.  

The car has weight as determined by the formula F=mg where m is the mass of the car and g is acceleration due to gravity.  The direction of this force is directly down towards the center of the Earth.  However, the reaction force exerted by the road is at right angles to road surface.  If we do a vector addition of these 2 forces, we find that:

1. They don't cancel out, meaning that the forces are unbalanced.
2. The resultant is parallel to the road pointing downhill.

 As a result the car will begin rolling downhill.  The mathematical calculation of the force exerted on the car can be calculated by 

F = mg sinX

where m = mass of the car, g = acceleration due to gravity, X is the angle of the slope from the horizontal.