force

The diagram shows how the parallelogram of forces can be used to calculate the resultant (combined effect) of two different forces acting together on an object. The two forces are represented by two lines drawn at an angle to each other. By completing the parallelogram (of which the two lines are sides), a diagonal may be drawn from the original angle to the opposite corner to represent the resultant force vector.

Any influence that tends to change a body's state of rest or of uniform motion in a straight line. A force is a push or a pull on an object. It will cause a stationary object to move or a moving object to change direction, slow down, or speed up. It may, if the body is unable to move freely, result in the body's deformation (see Hooke's law). Force is a vector quantity, possessing both magnitude and direction; its SI unit is the newton.

Forces that make contact with an object are called contact forces. Examples are normal push/pull force, surface tension, air resistance, and frictional forces. Forces that are able to cause a push/pull without making contact with an object are called non-contact forces. Examples are magnetic force, gravity, and electric force. The force of gravity on an object is the weight of the object. A mass of 1 kg has a weight of 9.8 newtons (N). A newton is defined as the amount of force needed to move an object of 1 kg so that it accelerates at 1 metre per second per second.

Speed and distance

In order to understand movement and what causes it, we need to be able to describe it. Speed is a measure of how fast something is moving. Speed is measured by dividing the distance travelled by the time taken to travel that distance. Hence speed is distance moved in unit time. Speed is a scalar quantity in which the direction of travel is not important, only the rate of travel. It is often useful to represent motion using a graph. Plotting distance against time in a distance–time graph enables one to calculate the total distance travelled. The gradient of the graph represents the speed at a particular point, the instantaneous speed. A straight line on the distance–time graph corresponds to a constant speed. A form of this graph that shows the stages on the journey is called a travel graph. A speed–time graph plots speed against time. It shows the instantaneous speed at each point. A horizontal line on the speed–time graph corresponds to a constant speed.

Velocity and acceleration

Velocity is the speed of an object in a given direction. Velocity is therefore a vector quantity, in which both magnitude and direction of movement must be taken into account. Acceleration is the rate of change of velocity with time. This is also a vector quantity. Acceleration happens when there is a change in speed, or a change in direction, or a change in speed and direction.

Forces and motion

Galileo discovered that a body moving on a perfectly smooth horizontal surface would neither speed up nor slow down. All moving bodies continue moving with the same velocity unless a force is applied to cause an acceleration. The reason we appear to have to push something to keep it moving with constant velocity is because of frictional forces acting on all moving objects on Earth. Friction occurs when two solid surfaces rub on each other; for example, a car tyre in contact with the ground. Friction opposes the relative motion of the two objects in contact and acts to slow the velocity of the moving object. A force is required to push the moving object and to cancel out the frictional force. If the forces combine to give a net force of zero, the object will not accelerate but will continue moving at constant velocity. A resultant force is a single force acting on a particle or body whose effect is equivalent to the combined effects of two or more separate forces. Galileo's work was developed by Isaac Newton. According to Newton's second law of motion, the magnitude of a resultant force is equal to the rate of change of momentum of the body on which it acts; the force F producing an acceleration a metres per second per second on a body of mass m kilograms is therefore given by: F = ma. Thus Newton's second law states that change of momentum is proportional to the size of the external force and takes place in the direction in which the force acts. Momentum is a function both of the mass of a body and of its velocity. This agrees with our experience, because the idea of force is derived from muscular effort, and we know that we have to exert more strength to stop the motion of a heavy body than a light one, just as we have to exert more strength to stop a rapidly moving body than a slowly moving one. Force, then, is measured by change of momentum, momentum being equal to mass multiplied by velocity. (See also Newton's laws of motion.) Newton's third law of motion states that if a body A exerts a force on a body B, then body B exerts an equal force on body A but in the opposite direction. This equal and opposite force is called a reaction force.

Free fall and terminal velocity

Galileo also established that freely falling bodies, heavy or light, have the same, constant acceleration and that this acceleration is due to gravity. This acceleration, due to the gravitational force exerted by the Earth, is also known as the acceleration of free fall. It has a value of 9.806 metres per second per second/32.174 feet per second per second. However, air resistance acts when an object falls through the air. This increases greatly as the object's velocity increases, so the object tends to reach a terminal velocity. It then continues to fall with this same velocity (it has stopped accelerating because its weight is cancelled out by air resistance) until it reaches the ground. The acceleration due to gravity can be measured using a pendulum.

Statics

Statics is the branch of mechanics concerned with the behaviour of bodies at rest or moving with constant velocity. The forces acting on the body under these circumstances cancel each other out; that is, the forces are in equilibrium.