Forces, Gravity and Resultant Forces
What Are Forces?
A force is a push or a pull that acts on an object. Forces are measured in newtons (N) and are vector quantities — they have both a magnitude (size) and a direction.
Forces can be contact forces or non-contact forces. Contact forces include friction, air resistance, tension, and normal contact force. Non-contact forces include gravitational, electrostatic, and magnetic forces.
A force is an interaction between two objects. When two objects interact, each exerts a force on the other — these are equal in size and opposite in direction (Newton’s third law).
Gravity and Weight
Gravity is a non-contact force that attracts any two objects with mass. The strength of gravity depends on the masses of the objects and the distance between them.
Weight is the force of gravity acting on an object. It depends on the mass and the gravitational field strength:
$$W = mg$$
Where \(W\) is weight in newtons, \(m\) is mass in kilograms, and \(g\) is gravitational field strength in N/kg. On Earth, \(g\) is about 9.8 N/kg. On the Moon, \(g\) is about 1.6 N/kg. The exam always gives you the value of \(g\), and the worked examples here round it to 10 N/kg to keep the numbers simple.
Mass is the amount of matter in an object, measured in kilograms. It is the same everywhere. Weight is a force and depends on the gravitational field strength at that location. An astronaut with a mass of 80 kg weighs 800 N on Earth (\(80 \times 10\)) but only 128 N on the Moon (\(80 \times 1.6\)).
Weight is measured using a Newton meter (spring balance). Mass is measured using a balance.
Resultant Forces
When multiple forces act on an object, they can be replaced by a single force that has the same effect. This is called the resultant force.
If forces act in the same direction, add them. If forces act in opposite directions, subtract the smaller from the larger. The resultant force acts in the direction of the larger force.
If the resultant force on an object is zero, the object is in equilibrium. This means it is either stationary or moving at a constant velocity. If the resultant force is not zero, the object will accelerate in the direction of the resultant force.
A free body diagram shows all the forces acting on a single object. Each force is drawn as an arrow starting from the object, with the length of the arrow representing the force’s magnitude and the direction showing which way it acts.
For example, a book on a table has two forces: weight acting downwards and the normal contact force acting upwards. If these are equal, the resultant force is zero and the book stays still.
When two forces do not act along the same line, you can find the resultant using a scale drawing. Draw the forces as arrows, tip-to-tail, to scale. The resultant is the arrow from the start of the first force to the end of the second. Measure its length and angle.