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This is the law of inertia, and states:
‘A body continues in a state of rest or uniform velocity unless acted upon by a external force’
Objects tend to remain either at rest or in straight line motion.
In simple terms, to change the motion of an object or performer a force must be applied.
A golf ball will only move from the tee when a force is applied to it from the golf club
A sprinter will only move out of the blocks when they exert force from their muscles
This is the law of acceleration, and states:
‘When a force acts on an object, the rate of change of momentum experienced by the object is proportional to the size of the force and takes place in the direction in which the force acts’
This law describes the relationship between net force, acceleration, and mass
Often described as:
F = ma
Force = mass x acceleration
- the greater the mass of an object, the greater the force required to give the same amount of acceleration and also the greater the force applied the greater the acceleration.
- For example, less force is applied to the shuttlecock than to a shot put in order for it to move
- One person is to use the bats and balls to devise a sporting example to explain how mass and acceleration affect each other.
The audience can only agree or disagree.
If you do disagree you take over as the teacher.
This is the law of reaction, and states:
‘For every action there is an equal and opposite reaction'
When a swimmer for example exerts a force on the starting blocks, the blocks exert an equal and opposite reaction force upon the swimmer, propelling them into the pool
The American football player's foot is pushing against the ground, but it is the ground pushing against the foot that accelerates the player forward to catch a pass.
Are you able to do the same for the third Law?
Those in the audience can only agree or disagree.
If you do disagree you take over as the teacher.
1st Law – INERTIA - remains at set unless a force affects them
2nd Law – ACCELERATION - push harder to get more acceleration
3rd Law – ACTION & REACTION - action force is muscular force, reaction force pushes athlete off blocks
F
Force = mass x acceleration
M
A
1. Learners should be able to explain Newton’s three laws of motion and apply them to sporting situations.
2. They should be able to explain that when an object is stationary or moving at a constant speed, the resultant force must equal zero.
3. They should also be able to calculate force, mass and acceleration by
using the formula F = ma.
At a constant velocity the force of tire friction (F1) and the force of air resistance (F2) have a vector sum that equals the force applied by the cyclist (Fa).
The net force is therefore 0.
A fluid is any liquid or gas that can flow.
A body that travels through a fluid is slowed down by drag forces, or fluid friction, so understanding of fluid mechanics allows us to make a judgement on how to increase or decrease the forces acting against a body travelling through the air or in water.
Sports that are greatly affected by their fluid environements are:
Swimming, Cycling, Sprinting, Skiing and any sport involving projectiles.
Definition:
Drag/ Fluid friction - The resistance to motion on a body travelling through fluid. The resistance acts opposite to the direction of motion and therefore inhibits velocity.
Friction force - Occurs when a solid surface of a body moves while in contact with the solid surface of another body.
Streamlining - Shaping a body so that it causes the least drag when travelling though a fluid.
Three factors that affect the size of the air resistance force acting on a body are:
1. The velocity of the body
2. The cross-sectional area of the body
3. The shape and surface characteristics of the body
The greater the velocity of a body traveling through a fluid, the greater the air resistance it will encounter. This is why athletes, such as swimmers, sprinters and cyclists, do their utmost to use knowledge of cross sectional area, shape and surface characteristics to minimise these forces.
The larger the cross-sectional area of a body travelling through a fluid, the greater the air resistance it will encounter. Athletes make every effort to adopt body positions that minimise their cross-sectional area (streamlining). A streamlinied shape is like a tear drop or an aerofoil.
The shape and surface characteristics of the body affect the amount of air resistance. Any lumps or bumps that affect the shape of a body will increase air resistance. Likewise, the rougher the surface that comes into contact with the fluid the greater the effect of air resistance. The areofoil shape would reduce air resistance even further if it was covered in a smooth surface.
Task:
How is air resistance reduced in competative cycling?
The quantity of motion possessed by a moving body
Momentum = Mass x Velocity
P=MxV
Velocity = the rate of motion in a particular direction
Mass: The amount of matter or substance in a body. (kg)
Intertia: The resistance of a body to change its state of rest or motion
Inertia is directly related to mass. The greater the mass the greater the inertia and the greater the force needed to get it moving, stop it moving or change it's direction.
Stationary body will have how much momentum?
Why?
In sport there is little opportunity to change (increase or decrease) your mass, therefore, any increase in momentum is due to changes in velocity.
E.g. 100m - gretaer velocity at what stage of the race?
Why?
A shot putt has a mass of 7KG and a velocity of 3m.s-1.
What is it's momentum?
The result of the impact depends upon the momentum of each of the
colliding bodies just before impact. The greater the momentum of the body, the more pronounced the effect it has on the other body in it’s path.
Sporting Example?
Rugby
Players with a large mass who can run at high velocity can generate a lot of momentum. Meaning they can run through tackles.
Players with smaller mass, despite being able to run quickly, can sometimes come off second best when they meet a defender with considerable inertia
The product of force multiplied by the time for which the force acts. Measured in Newton second (Ns)
Impulse = Force x time
The relative contirbution of the size of the force and the time for which it acts will depend on the type of skill being performed.
E.g. Hockey ball.
Think of the difference between a push and a hit
By increasing the amount of muscular force applied.
The greater the force, the greater the impulse. Consider the force that needs to be generated by a golfer when driving the ball from the tee compared to the force they will need to impart to the ball for a shot putt.
By increasing the amount of time over which they apply the force.
The longer the time over which the force is applied, the greater the impulse. Consider the greater time for which the force is applied to a discus during a one and three quarter turn compared to a standing throw.
High jump - Athletes lean backwards as they plant their take off foot. This allows them to apply force to the ground over a longer period of time as their body passes over the planted foot. This increased impulse causes a greater upward acceleration to help clear the bar.
Ski jump landing. By flexing the hip, knee and ankle on contact with the snow the time during which the forces are applied to the jumper on landing is increased and the impact on the body at this moment in time is significantly decreased.
1. What is meant by the term centre of mass and how does this help to explain why the Fosbury Flop is the preferred technique for the high jump? (4)
2. What is meant by the terms ‘line of gravity’ and ‘base of support’? Use practical examples to show how a performer can maximise their stability. (4)
3.Using Newton’s Laws of Motion, explain how, during take off, a high jumper is able to maximise the height they can achieve. (5)
4. Describe what is meant by the inertia of a moving object. (4)
5. A cricket ball is hit with an average force of 400 newtons in a time of 0.1 seconds. Define impulse and calculate its value when the cricket ball is hit.
Explain how knowledge of impulse can help a fielder to decrease the momentum of a cricket ball when making a catch. (5)
The product of force multiplied by the time for which the force acts. Measured in Newton second (Ns)
Impulse = Force x time
Impulse can be represented by the shaded area under a force/time graph.
This force/time graph is for a tennis forehand ground stroke.
Task: Sketch a force/time graph for the following situations:
A) A hockey ball being hit without a follow through
B) A hockey ball being hit with a follow through
Use your knowledge of impulse to discuss the advantages of using follow through in sporting technique where a large outgoing velocity is required.
A curve below the x-axis shows a negative impulse and a net force in the opposite direction to the resulting motion. A curve above the x-axis shows a positive impulse and a net force in the same direction to the resulting motion.
D
A-B: Stationary phase
Description: Impulse is 0 = net force is 0
Explanation: No acceleration. Jumper is stationary
B- C: Downward phase
Description: Impulse negative = net force negative
Explanation: Acceleration in downward direction (negative). Occurs as the jumper flexes hips and knees to dip downwards.
C-D: Upward phase 1
Description: Impulse positive = Net force +
Explanation: Acceleration in upward direction (positive). Occurs as jumper applies large action force on the ground and gains a large reaction force from ground.
D-E Upward phase 2
Description: Impulse still + but reducing in size as jumper accelerates towards the point where their feet leave the ground.
Explanation: Jumper legs extend further, action force with which they push against the ground decreases which means reaction force from ground also decreases.
E
C
B
A
3 phases: acceleration, maximum speed and deceleration
Remember positive impulse are those that act on the sprinter in the direction of the run and negative impulse are those that act on the sprinter in the direction opposite to that of the run.
Description:
First section - Impulse is negative. The force applied as the foot makes contact with the ground acts opposite to the direction of motion.
Second section - Impulse is positive. The force applied as the body moves over the supporting foot acts in the same direction as the direction of motion.
Explanation:
First section - Forward momentum of sprinter decreases.
Second section - Forward momentum of sprinter increases.
Overall - Positive impulse >negative impulse, therefore sprinter achieves a net force in the forward direction. This causes the acceleration seen in the early stages of the race.
Description:
First section - Impulse is negative. The force applies as the foot makes contact with the ground acts opposite to the direction of motion.
Second section - Impulse is positive. The force applied as the body moves over the supporting foot acts in the same direction as the direction of motion.
Explanation:
First section - Forward momentum of sprinter decreases
Second section - Forward momentum of sprinter increases
Overall - Positive impulse = negative impulse, therefore the net force acting on the sprinter is 0. There is no acceleration and maximum speed has been reached.
Description:
First section - Impulse is negative. The force applied as the foot makes contact with the ground acts opposite to the direction of motion.
Second section - Impulse is positive. The force applied as the body moves over the supporting foot acts in the same direction as the direction of motion.
Explanation:
First section - Forward momentum of sprinter decreases
Second section - Forward momentum of sprinter increases
Overall - Negative impulse > positive impulse therefore the sprinter achieves a net force in the direction opposite to the direction of motion. This causes the deceleration seen in the closing stages of the race. This could be down to fatigue, increased air resistance or simply conscious effort by the sprinter to ease up.
Tennis player A hits a backhand with backspin to tennis player B who then returns the ball into the net.
Sketch a horizontal velocity/time graph for the tennis ball during this sequence and describe what the graph shows. (6)
The action or process of moving
Linear motion:
When a body moves in a straight or curved line, with all it's parts moving the same distance in the same direction and at the same speed.
Distance - The length of the path taken in moving from the first position to the second. (m)
Displacement - The shortest straight-line route between two positions in a stated direction. (m)
Speed - A body's movement per unit of time with no reference to direction (m/s)
Velocity - The rate of motion in a particular direction
Acceleration - The rate of change of velocity
Distance - the length of the path. Practical exmples?
Marathon, 4x100 Freestyle (400m), Cycling 3km individual pursuit
Displacement - as the crow flies
Marathon (approx 10km), 4x100 Freestyle (0m) , Cycling 0m (veladrome)
Long jump - do they measure distance or displacement?
What about the 100m? Is the distance and displacement the same?
Speed (m/s) = distance covered (m)
time taken (s)
Velocity (m/s) = displacement (m)
time taken (s)
Usain Bolt ran the 100m in 9.58 seconds, what was his average speed?
10.43m/s
Lionel Messi kicks a ball 6.5 meters. How much time is needed for the ball to travel this distance if its velocity is 22 meters per second, south?
t= d/s = 6.5m/22ms-1 = 0.3s
Andy Murray serves a tennis ball to Rafael Nadal. It travels 9.5 meters south in 2.1 seconds.
a. What is the velocity of the tennis ball?
v= d/t = 9.5m/21s = 4.5ms-1 south
b. If the tennis ball travels at constant speed, what is its velocity when Nadal returns Murray’s serve?
4.5ms-1 north
The rate of change of velocity.
Acceleration (m/s2) = change in velocity (m/s)
time taken (s)
When velocity is increasing it is known as positive acceleration. When velocity is decreasing it is known as deceleration.
=Vf - Vi
t
Vf = final velocity
Vi = Initial velocity
t = time taken
Michelle Kwan prepares for a jump by increasing her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is her acceleration?
2.7m/s2
As he climbs a hill, cyclist Bradley Wiggins slows down from 25 km/hr to 6 km/hr in 10 seconds. What is his deceleration?
1.9m/s2
6.97m/s
2.43m/s2
8.58m/s
9.86m/s
0.36m/s2
3 types of graphs you need to be aware of:
1. Distance/time graphs
2. Veolicty/ time graphs
3. Speed/time graphs
These are virtually the same
Key points:
The gradient of a distance/time graph will tell you whether the body is stationary, moving with constant speed, accelerating or decelerating .
Gradient of a distance/time graph
Distance = Speed
Time
1. Body remains at the same distance over a period of time (it is not moving). E.g. goalkeeper stationary before a penalty.
2. Body is moving the same amount of distance at a steady rate. Gradient is constant therefore speed is constant. E.g. 1500m in the middle part of the race.
3. Distance travelled is increasing per unit of time. Gradient is increasing (speed is increasing) = acceleration. E.g. 100m accelerating from the blocks.
4. Distance travelled is decreasing per unit of time. Gradient is decreasing (speed is decreasing) = deceleration. E.g downhill skier after finish line digs in to bring them to a stand still.
Key points:
• Plot velocity on y-axis and time on x-axis
• label axis and give units
The gradient of a velocity/time graph will tell you whether the body is moving with constant velocity, accelerating or decelerating .
Gradient of a velocity/time graph
Change in Velocity = Acceleration/Deceleration
Time
1. The body moves with the same velocity during regular time intervals. E.g. golfer walking towards their ball after a drive.
2. Body is moving with increasing velocity (gradient of graph increases). E.g. A football accelerating from the spot at a penalty kick.
3. Body is moving with decreasing velocity (gradient of graph decreases). E.g. cricket ball being caught by a wicket keeper
Definition:
When a body or part of a body moves in a circle about a particular point called the axis of rotation.
Angular distance - The angle through which a body has rotated about an axis in moving from the first position to the second.
Angular displacement - The shortest change in angular position. It is the smallest angle through which a body has rotated about an axis in moving from the first position to the second.
Angular speed - The angular distance travelled in a certain time/ measured in radians per second (rad/s)
Angular velocity - The angular displacement travelled in a certain time. Measured in radians per second (rad/s)
Used to describe how far it has rotated
Angular distance - angle through which a body has rotated in moving from one position to another
Angular displacement - the smallest angular change between the starting and finishing positions.
used to describe the rate at which the body is rotating
Angular speed: Rate of change of angular distance.
Angular speed (rad/s) = angular distance
time taken
Angular velocity: Rate of change of angular displacement.
Angular velocity (rad/s) = angular displacement
time taken
The rate of change of angular velocity. Measured in radians per second squared (rad/m)2
Angular acceleration = Change in angular velocity
Time taken
Moment of inertia
The resistance of a rotating body to change its state of angular motion. All bodies will initially resist rotation and then, once they are rotating, will want to continue to turn about their axis of rotation.
Angular momentum
The quantity of angular motion possessed by a rotating body. It is the product of moment of inertia multiplied by angular velocity. It is measured in Kgm2/s.
Moment of inertia is the linear equivalent of inertia and applies to the tendency of a body to initially resist angular motion and the tendency of a body to want to continue rotating about its axis of rotation once undergoing singular motion.
1. The mass of the body
The larger the mass the greater the moment of inertia and the more resistance and persistence the body puts up against angular motion.
E.g. heavy cricket bat more difficult to swing than a lighter one. However, once swinging the heavier bat is more difficult to control or stop
2. The distribution of the mass of the body from the axis of rotation
The futher the distribution of mass from the axis of rotation the greater the moment of inertia.
E.g. A gymnast performs two somersaults along the horizontal axis; the first in a tuck the second straight.
Straight = greater moment of inertia as mass is distributed futher from the axis of rotation.
Always identify the axis of rotation first.
The amount of angular motion that a rotating body possesses
Angular momentum = moment of inertia x angular velocity
In sports involving rotation such as diving it is important to create sufficient angular momentum at the start of the dive to allow them to perform the numerous somersaults and twists that occur later.
A rotating body continues to turn about its axis of rotation with constant angular momentum unless acted upon by an external tourqe.
The angular momentum generated at take off is conserved during flight.
E.g. the angular momentum a diver generates at take off remains the same while the diver is in flight.
Ice skater - the frictional force between the
blade and ice is so small that it can be
ignored.
We need to remember:
- Once in flight, a performer can manipulate their moment of inertia by changing body position. By bringing their mass closer to the axis of rotation they will decrease their moment of inertia.
So, for angular momentum to remain constant:
1. decreasing the moment of inertia will cause an increase in angular velocity, so the performer will rotate quicker.
2. increasing the moment of inertia will cause an decrease in angular velocity, so the performer will rotate slower.
Look at the figure on your worksheet of a diver from a 10m platform.
1. The law of conservation of angular momentum states that the amount of angular momentum at take off stays the same during flight until the diver hits the water.
2. At take off the diver generates a large angular momentum by spreading their body away from the transverse axis giving them a larger angular momentum which is needed to complete the dive in the small amount of time.
3. In position 2,3, and 4 - diver brings their arm and legs in towards the transverse axis. Significantly decreasing their moment of inertia causing angular velocity to increase and the diver to spin quicker,
4. Position 5 and 6 - To control entry into the water the diver reduces their rate of spin by spreading their body out away from the transverse axis. This increases their moment of inertia and decreases their angular velocity.
1. At the start of the spin the skater's body position is with both arms out to the side and one leg extended behind them. This means the distribution of mass is a long way from the longitudinal axis. This gives the skater a large moment of inertia and a large angular momentum.
2. Skater then pulls both arms inwards and the leg inwards (they will often cross their arms). This decreases their moment of inertia which increases their angular velocity and the skater spins faster.
3. The skater then spreads their arms and legs out again which increases their moment of inertia and reduces the rate of spin.
In sport there are a number of times where bodies (athlete or an object) are projected into the air to follow a certain flight path.
A uniform curve that is symmetrical about it's highest point
Once in the air two forces act on a projectile:
weight and air resistance.
As air resistance increases, the more a projectile will deviate from a true parabola
The sizes of these forces of weight and air resistance will affect the flight path
1. Large weight force and small air resistrance force (e.g. shot putt) - follows path close to a true parabola.
2. High velocity with a large cross-sectional area and rough outer surface are most affected by air resistance - flight path will deviate from a true parabola. (e.g. golf balls, footballs, badminton shuttles
It is also true that the relative contribution of air resistance compared to weight increases as the mass of an object decreases.
golf ball v tennis ball
if they were projected into the air with the same amount of force, the golf ball will follow a flight path closer to a true parabola and will be less affected by air resistance as it's heavier.
Recap
The only two forces that can act on a projectile are weight and air resistance. The effect of air resistance increases with:
- a decrease in the mass of the body
- an increase in the velocity of the body, the cross-sectional area of the body and the roughness of the surface of the body.
If a projectile can gain an upward lift force during flight, it will stay in the air for a longer time and achieve a greater horizontal distance.
Key definitions
Aerofoil - A streamlined shape with a curved upper surface and an under surface that is predominantly flat e.g. the cross section of the wing of an aircraft.
Lift force - Force that acts perpendicular to the direction of travel for a body moving through a fluid
Angle of attack - The angle at which a projectile is tilted from the horizontal. Lift force will increase as the angle of attack is increased up to a certain point (usually around 17 degrees).
Bernoulli principle - States that molecules in a fluid exert less pressure the faster they travel and more pressure the slower they travel.
If the aerofoil is tilted at the angle of attack, the air that travels over the curved upper surface has to travel further than the air that is deflected underneath. Therefore the air above is travelling at a higher velocity than the air below it.
An increase in velocity of a fluid causes a decrease in pressure. The Bernoulli principle shows that:
- where flow is fast, pressure is low
- where flow is slow, pressure is high
So there is lower pressure above the aerofoil and a higher pressure below it and this pressure gradient produces a lift force.
As shown in the figure in your booklet the Bernoulli principle works to produce a lift force on an aerofoil at a 10-degree angle of attack
Remember the respiratory system?
You know that gases move from areas of high pressure to areas of low pressure.
This is the same in the Bernoulli principle when applied to a projectile where there is a pressure gradient between the two surfaces, air molecules will be pushed from the area of high pressure to the area of low pressure, generating a force in the direction of the high pressure area.
Lift force can also be in a downward direction. This depends on the angle of attack and the shape of the projectile.
Discus and Javelin use upward lift force.
At the point of release, a good discus thrower will present the discus at the correct angle of attack, so that the air that travels over the top of the discus has to travel further distance than the air that travels underneath.
The air above the discus travels faster than the air below. Using the bernoulli principle, this means that a lower pressure is created above the discus than below it, causing a pressure gradient that produces an upward lift force on the discus.
This allows the discus to stay in the air for longer and achieve a greater horizontal distance.
Formula 1 makes use of the downward lift force.
The rear spoilers attached are angled at such a way that the lift force created by the Bernoulli principle acts in a downward direction. This pushes the car into the track, creating greater frictional force to enable the tyres to stick to the track better, making it safer to turn corners at speeds in excess of 122mph.
Imparting spin to a projectile at the point of release requires an eccentric force.
Eccentric force is a force whose line of application passes outside the centre of mass of a body, causing the resulting motion to be angular
Spin will affect the flight path of a projectile and the way it bounces on landing. You need to be familiar with three types of spin:
1. Topspin - causes the ball to dip during flight and drop to the ground sooner. It will also cause the ball to skim off the surface quickly on bouncing.
2. Backspin - will keep the ball in flight for longer and on bouncing it will be slowed down.
3. Sidespin - will cause the ball to swerve left or right and on bouncing, it accelerates even further in the same direction.
spinning balls also generate a lift force (the magnus effect). The lift force is produced as a result of the magnus effect explains the curved flights of balls that have been struck with spin in a variety of sports.
Important in all sports where an athlete wants to bend the flight of the ball.
Examples?
Top spin
As a spinning ball moves through the air, it's spinning surfaces will affect the airflow around it. Think of a tennis ball:
1. The top of the ball - the surface of the ball is traveling in the opposite direction to airflow. Causing the air to decelerate and according to Bernoulli principle, creates a high pressure
2. The bottom of the ball - the surface of the ball is traveling in the same direction as airflow causing the air to accelerate and according to Bernoulli principle a lower pressure.
3. Consequence - having higher pressure on the top surface of the ball and lower on the bottom creates a pressure differential. This causes a downward lift force to act on the ball. The ball dips and the distance traveled is decreased from the non-spinning flight path
Can you do the same for back spin?