When a force is applied to an object, movement will result—unless there is some other force also present to prevent movement. The response of objects to applied forces was described in detail by Isaac Newton. In the seventeenth century, Newton developed three laws that governed the motion of objects in response to applied forces. His fi rst law of motion, the law of inertia, explains that a stationary object will remain stationary until a force causes it to accelerate. Similarly, once it is moving, it will tend to keep moving in a straight line unless a force causes it to slow down or change direction.
The amount of acceleration experienced in response to an applied force is determined by the amount of force applied, and by the mass of the object.
This is Newton’s second law of motion. If twice as much force is applied, then twice as much acceleration will result. Mass has an inverse relationship with acceleration; if the amount of mass is doubled, the acceleration will be halved. Mass, therefore, is a measure of the object’s inertia. Objects with a large mass have a large amount of inertia, meaning they are diffi cult to accelerate; while objects with a small mass need only a small force to be accelerated. Newton’s second law is often written as a formula:
a = F m
This formula allows us to easily quantify the amount of acceleration resulting from an applied force. If a force of 120 Newtons is applied to a person of mass 60 kilograms, the resulting acceleration will be 2 m/s2. If a ball of mass 0.2 kilograms has the same 120 Newtons force applied, its acceleration will be 600 m/s2. Clearly, a smaller object will have much higher acceleration for a given amount of force.
When more than one force acts on an object simultaneously, we can add the forces together to get a total force. Figure 6.19 illustrates a person jumping into the air by applying a force to the ground of 1000 Newtons. The person has a mass of 60 kilograms, and consequently a weight of 588 Newtons. When we consider the total force acting on the body, the 1000 Newtons upwards is partially balanced by 588 Newtons of weight pulling down, leaving a total force of just 412 Newtons upwards. It is this force that would determine the amount of acceleration:
The following illustration shows us two ways in which body mass infl uences our acceleration while jumping. Firstly, a larger mass means increased inertia, resulting in a smaller acceleration for any given force. The second point compounds this, because a larger mass means that more weight is pulling the body downwards. This means that not only would there be less acceleration for a given amount of force, but there would also be less total
Newton’s fi rst law of motion(also known as the law of inertia) states that a body will maintain a state of rest or constant velocity in a straight line unless acted on by an unbalanced external force.
Newton’s second law of motion states that when a force is applied to an object, the object experiences an acceleration in the direction of that force that is directly proportional to the force applied and inversely proportional to the mass of the object. Known as the law of acceleration, this law is usually expressed mathematically as acceleration equals force divided by mass.
Inertiathe resistance of an object to acceleration. If an object has a large inertia, then it is diffi cult to accelerate. That is, a stationary object with large inertia will be diffi cult to start moving, while a moving object with large inertia will be diffi cult to stop. The inertia of an object is determined by its mass, measured in kilograms.
force because more weight is pulling the body down. This is a very great problem for jumping athletes. On one hand, they need to develop strong muscles to apply large forces to the ground while jumping. On the other hand, if they strengthen their muscles through excessive hypertrophy (i.e. enlarging muscle tissue), then the weight of those muscles may actually retard performance. Jumpers must therefore aim to strengthen their muscles in such a way that the benefi ts of increased force outweigh the disadvantages of increased mass.
The example in fi gure 6.19 applies to forces that are both aligned vertically. If the two forces were not parallel, they could still be added or subtracted, but this addition would require considering the direction of those forces, rather than just a adding the numbers. Consideration of this is beyond our scope, but will not be a problem for our current discussion provided we only consider forces in one direction at a time. If you want to consider the effect of forces on vertical acceleration, use only vertical forces in your consideration.
Similarly, only horizontal forces determine horizontal acceleration. Having more than two forces does not have any different effect. You can add as many forces as you like to get a total.
Newton’s third law of motion states that when one object exerts a force on a second object, the second object must also exert an equal-sized force back onto the fi rst object, in the opposite direction. This sounds complicated, but need not be when we consider some examples. Figure 6.19 shows a vertical force acting upwards under the foot. In practice, we jump by pushing down onto the Earth with our feet. The force in fi gure 6.19 is the oppositional force resulting from Newton’s third law as the ground pushes back at us. When we catch a ball by applying a force to slow it down, the ball will exert an equal and opposite force back onto our hands—this is a force equal in size, but opposite in direction. The force on the ball causes it to slow down (fi gure 6.20b); while the force on our hands may cause pain and will certainly cause our hands to accelerate in the direction of the ball (fi gure 6.20c). To avoid confusion, we should use diagrams that show only the forces acting directly onto the object, and not include the paired force from Newton’s third law that would act on another object. For example, fi gure 6.19 shows only the force of the ground pushing up onto the feet. If I also tried to illustrate the force pushing down onto the ground, then this might cause confusion about which direction the body would accelerate, or whether I should have added or subtracted the ground force in my acceleration equation.
Newton’s third law of motionthe law of reaction.
When one object exerts a force on a second, another force is applied back onto the fi rst object, which is equal in magnitude and opposite in direction to the original force.
This law is often stated as
‘every action has an equal and opposite reaction’.
Figure 6.20
The force applied to a ball during a catch is equal and opposite to that applied to the hand
Figure 6.19 Forces during a vertical jump
Weight = 588 N
Force = 1000 N
a b c
Only forces coming from outside a body are able to cause acceleration of that body. For example, you can squeeze your fi st as tight as you like, but it will not propel you anywhere. Only when your hand pushes against some external object, and that object pushes back against your hand through Newton’s third law, can we produce acceleration. The diagrams we draw to analyse movement therefore only ever show forces coming from outside the body. Our muscles initiate much of the force that causes us to move, but only when the muscles push our limbs against some external object can they be effective in causing acceleration.
Once an external force is applied to an object, then acceleration occurs in the direction of that applied force. If a sprinter needs to accelerate forward at the beginning of a race, then he must push backwards against the ground, so that the ground will push him forward. Sprinters lean forward so they can better direct the forces backward against the ground. Similarly, if a shot putter needs to direct his put higher into the air to increase the fl ight distance, then he needs to get his shoulder below the shot so that extending his arm will direct it upward as well as forwards. The use of diagrams can be invaluable in imagining what direction forces need to be applied for effective performance in any sport. By illustrating all the forces acting on an object, you can then visualise the acceleration that would result from those forces.
Newton’s laws tell us about acceleration. His second law tells us how much acceleration will occur as a result of a force being applied. The total velocity change in response to an applied force, however, is determined by how long the acceleration continues, as well as by how much acceleration there is. The longer a force is applied, the longer the body will spend accelerating and, therefore, the more the total velocity will change. We have already considered the effect of force and time multiplied together, and called this impulse. Impulse is not only important for stopping moving objects, but also for increasing speed, if that is desired. The greater the combination of force and time, the more momentum, and hence velocity, will increase.
When children fi rst learn to perform a shot put, they stand in one position and forcefully extend the knees and elbows to put the shot forward and upward.
This technique produces large acceleration of the put, but there is a limit to the amount of time the force can be applied because the arm very quickly reaches full extension and the put leaves the hand. The next stage of the technique involves performers starting at the very back of the circle and gliding forward to the front before release (fi gure 6.21).
This technique allows force to be applied to the put for a longer time, increasing the impulse applied to the shot, and consequently
Figure 6.21 Path of movement during shot put release
Understand and apply
1 High jumpers must generate a large acceleration during takeoff and require large forces to achieve this acceleration. Identify the training methods that might enable a jumper to produce larger forces and discuss why increasing strength to improve jumping force may not necessarily result in greater acceleration during the takeoff.
2 Imagine a force of 30 Newtons is applied to a golf ball and a table-tennis ball. Which ball will experience more acceleration during impact and why?
3 The above acceleration would be present only while the balls were in contact with the bat or club. If you said that the table-tennis ball had higher acceleration, why then would it not necessarily fl y through the air further than a golf ball? Hint: consider forces acting on the ball during fl ight.
4 You can throw a cricket ball much faster than you could propel it by striking it like a volleyball serve. Use the concept of impulse to explain why the larger force from striking does not necessarily result in larger velocity.
5 Use Newton’s second law of motion to explain why all objects would fall with the same acceleration due to gravity, regardless of their weight, if we ignore the effects of air resistance.
6 Use Newton’s second law once again to explain why air resistance seems to have more effect on objects such as feathers and table tennis balls.
7 a Use Newton’s third law of motion to explain why catching a fast-moving ball can cause pain.
b Use the concept of momentum to explain why a ball that has a larger mass, or one that is moving faster, will cause more pain to your hand.
c Use the concept of impulse to explain why a harder ball will cause more pain to your hand. Hint: compare the time taken for a softer ball to come to a halt.
resulting in a higher release velocity. Many modern shot putters now use a rotational technique, like a discus wind up, where the body spins prior to release, allowing even more time for force to be applied and, therefore, producing an even greater impulse.
During a shot put, the athlete commences at the very back of the circle and glides towards the front as he accelerates the shot. The dotted line illustrates the path taken by the shot before release. By increasing the time over which force is applied, a greater impulse can be applied to the shot, resulting in a higher release velocity.
chapter review
Displacement, velocity and acceleration can be used to describe the position of an object, how fast its position is changing and how quickly the speed is changing.
Momentum is the product of mass times velocity. An object with more momentum will be more diffi cult to stop moving.
Adopting a stable posture requires the centre of gravity to be located above the base of support. Increasing stability involves strategies to ensure that the line of gravity does not move outside this base.
Bodies immersed in water experience an upwards force called buoyancy that is proportional to the weight of water displaced by the body’s volume underwater.
Adopting a horizontal fl oating position requires the centre of gravity and centre of buoyancy to be aligned at the same location in the body.
Objects moving through air or water experience a fl uid resistance force that increases with the square of velocity. Faster moving objects therefore have much more fl uid resistance than do slower objects.
Different causes of fl uid resistance are surface drag, caused by the amount of surface area and the smoothness of the object; form drag, caused by the shape of the object and its frontal area; and wave drag, caused by movements of the object at the interface between two different fl uids (for example, water and air).
Weight and mass are quite different concepts. Weight is the force of gravity measured in Newtons. Mass is a measure of a body’s inertia, determined by the amount of matter packed into the body and expressed in kilograms.
The body can apply force to other objects through weight, by contracting the muscles, or by using momentum.
When moving objects collide with the body (or vice versa), enough force needs to be applied over the time of contact in order to remove the momentum of the object.
Applying force over a longer time allows momentum to be removed without requiring as much force to be applied.
Newton’s laws of motion describe how an object will respond when a force is applied by telling us whether velocity changes, what the size of the acceleration will be, and how forces will be returned from one object to another.
Recap
Exam-style questions
1 View the velocity–time graph in fi gure 6.3 and answer the following questions:
a What was the maximum velocity reached during the race? (1 mark) b At what time was the maximum velocity reached? (1 mark) c What was the average acceleration from time zero up until maximum (2 marks)
velocity?
d Describe how velocity was changing over the last second of the race. (2 marks) 2 Describe the strategies that people use to hold a stable, balanced position.
For example, how they hold a balance position during a gymnastics routine. (4 marks) 3 Explain why people do not always fl oat in a horizontal position, and what
strategies can be used to make the body more horizontal. (4 marks) 4 Explain the difference between mass and weight. (2 marks) 5 What is Newton’s second law of motion? Use this law to explain why it
would be diffi cult to play table tennis with a normal tennis ball while still
using a table tennis bat. (4 marks)
chapter review
Useful websites for study
Organisation Current URL Useful for …
Coaches’ Information Service www.coachesinfo.com Articles about sport science and improving performance. Although not exclusively a biomechanics site, there are many articles describing the biomechanics of sports BioLab www.biolab.org.uk The downloads page from the BioLab web site
provides many practical activities that can be used for teaching biomechanics. Although designed primarily for university students, there are many activities that will be suitable for high school students
Teachers’ Information Service www.usfca.edu/ess/tis Again, a site designed more for university students, there are once again practical activities that can be used to teach principles of biomechanics