 1. Types of forces
2. Free-body diagrams
3. Calculating resultant force

A force is a push or pull acting on an object due to its interaction with another object. It is a vector quantity and is measured in newtons (N). A force can be either a contact or a non-contact one, depending on whether the interacting objects are touching. A contact force is a force that requires objects to be touching to be exerted. A non-contact force is a force that can be exerted without objects touching.

Normal reaction force arises for objects placed on a surface and is perpendicular to a surface. Tension is a force that commonly exists in ropes and pulls objects in the direction of the side the rope is attached to. Friction is a force that opposes the motion of an object, usually due to interaction with a medium. Friction in a liquid is called drag, while in air it is called air resistance.

Gravitational force is a force between two objects that have mass. Usually gravitational forces between two objects is going to be significant when at least one of them is heavy, like the Earth or the Sun. Gravitational force near the surface of such heavy object is called weight. An electrical force is an attraction or repulsion between two charged particles. A magnetic force is an attraction or repulsion between two poles. A free-body force diagram is a diagram which shows the relative magnitude and direction of all the forces acting on an object. The object is drawn as a dot and all forces acting on it are drawn as arrows pointing away from it. Each force must be labelled with the name of the force. Both normal reaction force and friction arise from a surface, thus their vectors start from where an object touches the surface. Weight is caused by the mass of the object, thus an arrow representing weight starts at the centre of mass.

Forces can be split into two or more vectors as long as they add up to the original vector. To find the resultant force between two vectors, we can draw the two vectors one after the other, that is the second starts where the first ends. To get an accurate answer, the lengths of the vectors have to be proportional to the sizes of the forces. The resultant force is the vector that joins the start and the finish points. You can determine whether an object is in equilibrium, by drawing all the forces acting on it one after the other. If the last vector ends where the first started, then the object is in equilibrium. A resultant force is the force obtained when two or more forces are acting on a body. To find the resultant force in one direction, sum forces acting in the same direction and subtract forces acting in an opposite direction. When forces are acting perpendicularly to each other, the Pythagoras' theorem can be used to find the resultant force. # 1

A ball is being pulled towards the left across a table as in the free-body diagram provided. Name forces A, B, C, D.

Horizontally towards the left there is going to be a pull (D) and towards the right - friction (B). Vertically the weight of the ball (C) is going to be balanced by the normal reaction force (A).

A = normal reaction force
B = friction
C = weight
D = pull # 2

Jane tries to push a box forward horizontally by exerting a force of 45 N on it. The box does not move, thus she calls her friend, Mary, to help her. Jane pushes again with a force of 45 N and Mary pushes with a force of 38 N, both horizontally. If the frictional force exerted on the box by the ground is 47 N, what is the magnitude of the resultant force acting on the box?

The direction in which they are pushing can be considered to be positive.
resultant force = 45 N + 38 N − 47 N = 36 N in the direction they are pushing in

36 N # 3

A mass is placed on an inclined plane. Provide names and the directions of the forces that would you represent in a free-body diagram for the mass.

Normal reaction force would be acting perpendicular to the inclined plane. Friction arising from the surface wold be acting parallel to the surface. Weight would be acting on the climber downwards.

normal reaction force perpendicular to the surface, friction parallel to the surface, downwards weight # 4

The diagram provided shows a free-body force diagram of an object. Calculate the magnitude of the resultant force acting on the object.

resolving vertically: 5 N − 3 N = 2 N
resolving horizontally: 8 N − 6 N = 2 N
magnitude of resultant force = √(2² + 2²) = 2.8 N (2 s. f.)

2.8 N # 5

A board is placed on a support at one end as shown in the image. A box is put at the other end of the board. State the names and types of forces acting on the board.

A contact normal reaction force is exerted by the support on the board. A non-contact weight of the board is exerted on the board by the Earth. A contact push force exerted by the box on the board.

contact normal reaction from the support, non-contact weight from the Earth, contact push force from the box End of page