Untitled Document

In continuing the investigation of force it is necessary to introduce the concept of MOMENTUM. If the question "how much motion does an object have?" is asked, then the intuitive answer of the lay person often involves the concept of speed or velocity. However, this is an incomplete way of quantifying motion. Consider the following question. "If a 110 kg prop forward and a 65 kg fly half are both running with a ball at a speed of 6 m×s^-1 which has the greater quantity of motion?". For a player who had to tackle a prop forward or fly half, the question itself reveals that a consideration of speed or velocity alone is not sufficient to describe the quantity of motion but that the mass of the object must also be taken into account. The definition of momentum incorporates these two parameters in the following way:

Consideration of the formula shows that an arrow shot from an archers bow has a large momentum despite having a relatively small mass and similarly a set of eight rugby forwards pushing scrummaging machine, even slowly, have a large momentum.

The rate of change of momentum of an object (or acceleration of an object of fixed mass) is directly proportional to the force causing the change and the resulting change in momentum takes place in the direction in which the force was applied .

This is a fairly complicated definition and formula and needs to be considered carefully. Taking the previous discussion of the first law together with the definition above, it is now possible to state the following.

In fact, Newton's Second Law indicates, that the rate at which an object loses or gains momentum, is directly related to the applied force.

A stationary golf ball on a tee experiences a large force over a short period of time when struck by a golf club, and therefore the rate at which the momentum of the golf ball is changed is very high. However, this example tells only half the story, because the second law indicates that the change in momentum will take place in the direction of the applied force. In the case of the stationary golf ball this may be clear, but the situation where an object is already moving (i.e. already has some momentum) before the force is applied also should be considered.

TASK: Using your understanding of vectors, draw a diagram to represent the momentum possesed by a soccer ball as it leaves one player's foot and travels in a direct line to a second player. Develop the diagram, again using vector representation, to show the direction and magnitude of momentum that the second player must give to the ball if s/he wishes the ball to go directly to a third player who is standing directly at right angles to the original direction of the path followed by the ball (i.e. direction from the first to the second player). Discuss your solution on the Blackboard discussion forum which has already been set up. Remember you can attach a copy of your diagram to the posting or use the white board facility if you wish to share ideas about your diagram in real time.

The interpretation of Newton's Second Law can be considered from a different point of view if the mass of the object being investigated may be assumed to be constant. In most sport situations this is a reasonable assumption, and therefore the second law may be summarised by the formula:

An element of this equation inside is in fact the formula for acceleration and therefore the equation may further be simplified to:

This equation simply states that the acceleration an object experiences will be directly proportional to the force applied.

It is this form of the equation which is often used to define the unit of measurement for force - a newton (N). This is defined as:

the force required to give a mass of one kilogram an acceleration of one metre per second per second.

It is worth emphasising the direct relationship between force and acceleration, and it is also appropriate to briefly return to consider the effects of gravitational force.

It was noted earlier that for objects of fixed mass the gravitational force (weight) remains constant. According then to Newton's Second Law, the acceleration of an object when it is only under the influence of gravity will also be constant and this indeed is the case. In fact, because the gravitational force that an object experiences is directly proportional to its mass, all objects accelerate at approximately 9.8 m×s^-2when gravity is the only influencing force. This can be observed more clearly if the basic formula is rearranged in the following way.

In this case F represents gravitational force, m the mass of the object and a the acceleration due to gravity. The formula shows that if F and m are proportionally related, as is the case when considering gravity, then a will be a constant. This relationship therefore implies that, if two divers with different masses were to jump from a high diving position at the same time, they would both hit the water at the same instant (assuming the influence of air resistance is ignored).

Consider the acceleration that a ball experiences when it is thrown up into the air. If it is assumed that air resistance is negligible, then the only force that the ball experiences once it has left the thrower's hand is gravity.

Time from release (s)	Velocity m/s	Acceleration m/s/s
0.00	14.7
		-9.8
1.00	4.9
		-9.8
2.00	-4.9
		-9.8
3.00	-14.7

The table above shows how the velocity of the ball changes from the moment it leaves the thrower's hand to the moment it is caught. The data assumes that the ball is thrown vertically and is caught at the same height at which it was released.

The table also shows that during the period of flight, the ball experiences a constant acceleration, which is exactly what Newton's Second Law would predict. It is important to reflect on, and note that, the ball's speed and direction changed during the flight, but the acceleration remains constant.

Note that the upwards direction is taken to be positive and the fact that the acceleration is shown to be negative throughout the flight indicates that the force was acting in a downwards direction, which of course gravity does!!.

The key factor to note in the above example is that the observed acceleration of an object will be directly proportional to the net force acting on the object at any particular time. This is not just true for situations where the force is constant but applies to all force situations.

TASK: Imagine a situation where an object with a fixed mass is struck on three successive occasions by a force which doubled in magnitude for each application. Sketch a graph with force along the bottom axis and acceleration on the vertical axis. Verify your answer by using a search engine on the internet to find out how others have graphed this relationship. Tip: Remember Newton's Second Law is key to many physics problems and not just sport biomechanics.