# Mechanics of Motion

In this assignment I am going to undertake calculations involving speed, velocity and acceleration. I will recall Newton’s laws and describe the factors which affect stability. I will also try to apply Newton’s laws to simple movement. I will also explain how angular motion can be applied to sporting performance.

Newton’s first law of Motion also sometimes known as the Law of Inertia, states that an object at rest stays at rest unless acted upon by an unbalanced force, and an object in motion stays motion at the same speed and in the same direction unless acted upon by an unbalanced force. If all forces acting upon an object are equal it is said that the acceleration will be 0 and the object described as in a state of equilibrium. An example of this can be seen on a Hockey pitch, a ball sat on a flat Astroturf will not move, it is held in place by the gravitational pull of the earth. However when a player comes along and hits the ball, it is acted on by an unbalanced force (as Newton says). Which causes it to move, the ball will carry on moving until one or a mixture of opposing forces stops it. If the ball hits a stable object i.e. the fence it will stop. This is because the fence does not move when acted on by a force. The ball could also stop from friction, the contact between the ball and the floor slows it down. To measure this first law we have several different things to consider.

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The first is distance or displacement they are measurements of how far a single body has traveled. Distance doesn’t take into account the direction of movement and is therefore a scalar quantity. Displacement however takes into account not only the distance traveled but in what direction also. So for a 400m runner the distance run will be 400m but the displacement is 0m because they finish in the same place that they started. For this reason the displacement is known as a vector quantity. For my example distance or displacement are measured in meters (m).

Speed is the second measurement we have to consider, it looks at how quickly the displacement or distance moved has occurred. It is measured in either speed or velocity. Speed is quite simply the rate of motion and is a scalar quantity whereas velocity is the rate of motion in a given direction. Velocity is a vector quantity. The unit used to measure speed is simply seconds. We can work out speed by dividing distance traveled by time taken to travel this distance. So if a sprinter runn100m in 10.5 seconds his speed would be 100/10.5 = 9.52, so his speed is 9.52. Average velocity is the speed averaged out over the whole race. The equation for average velocity is:

S = L/T

Where S = Average velocity, L = Distance and T = Time taken

Position (m)

Subject A: Ben Johnson

Subject B: Carl Lewis

0 m

0 s

0 s

10 m

1.83 s

1.89 s

20 m

2.87 s

2.96 s

30 m

3.80 s

3.90 s

40 m

4.66 s

4.79 s

50 m

5.50 s

5.65 s

60 m

6.33 s

6.48 s

70 m

7.17 s

7.33 s

80 m

8.02 s

8.18 s

90 m

8.89 s

9.04 s

100 m

9.79 s

9.92 s

This is the elapsed times for each 10 meter interval for Ben Johnson and Carl Lewis in the Men’s 100 m Final at the 1988 Olympic Games in Seoul, Korea. I am going to use each of the final times and the distance (100m) to calculate an average velocity for both of them.

Ben Johnson: 100 / 9.79 = 10.2ms-1

Average velocity = 10.2ms-1

Carl Lewis: 100 / 9.92 = 10.08ms-1

Average velocity = 10.08ms-1

Acceleration is the change in velocity over a period of time, if velocity goes down it is called deceleration. When you start running you accelerate until you reach a constant rate. The equation for this is:

a = (vf – vi) / t

Where a = average acceleration, vf = final velocity, vi = initial velocity and t = time taken.

A Graph showing 100m sprint time for Ben Johnson in the 1988 Olympics

Distance

Time at this distance

Time for previous 10m

Average distance at which

Speed at

Time at

measurements is taken (m) D

this point

point D

0

0s

10

1.83 s

1.83

0

0

0

20

2.87 s

1.04

5

5.46

0.91

30

3.80 s

0.93

15

9.61

2.36

40

4.66 s

0.86

25

10.75

3.35

50

5.50 s

0.84

35

11.62

4.23

60

6.33s

0.83

45

11.9

5.11

70

7.17 s

0.84

55

12.04

5.97

80

8.02 s

0.85

65

11.9

6.88

90

8.89 s

0.87

75

11.76

7.66

100

9.79 s

0.9

85

11.49

8.55

95

11.1

9.41

The graph was made from table above and this allows us to work out the acceleration which is 5.80ms-1.

Using my Graph I can refer to Newtons second law which states objects for which all existing forces are not equal. Newton says that the acceleration of an object is dependant on the sum of all the forces acting upon it and also the mass of the object. As the total forces increases as will the acceleration, however the greater the mass of the object the more its acceleration will decrease. To work out the total force acting upon the object we use the equation:

F = m x a

Where F = force m = mass and a = acceleration

The unit used to count force is Newtons (N) one Newton is defined as the amount of force required to move 1kg mass an acceleration of 1ms-2.

With this equation I can look at the first 2 seconds of Ben Johnson’s race I can determine how much force he used to power himself this far. If I take into consideration that Ben Johnson weighed around 78kg.

8.5 – 0 / 2 = 4.25

Acceleration = 4.25ms-1

78 x 4.25 = 331.5

Force used to create amount of speed is 331.5 Newtons. The momentum of Ben Johnson as he was running is: Mass x velocity = 78 x 5.80 = 425.4. N

Stability is when an object experiences force and remains the same or returns to its original position. The more quickly it returns the more stable it is. The amount of stability an object has depends on the base, height and weight. If the centre of gravity is low and base area large and object will have high stability. This is like a F1 car. An object will have low stability if the centre of gravity is outside of the base or lies to the side of it. Taller objects also tend to have less stability, because the centre of gravity is higher off of the ground.

This is why short, heavy people succeed well in sports which require stability i.e. judo. To avoid disaster on the balance beam, which is only 4 inches wide, a gymnast’s center of mass must remain above the beam’s surface at all times, even during flips and spins. A deviation of more than 2 inches in either direction will leave her center of mass unsupported and cause her to fall. Once again, Smith says, short girls have the advantage. “Because her height is smaller in proportion to the width of the beam, she has an easier time keeping her center of mass over the beam, and keeping her balance.”

Equilibrium is a condition characterized by a balance of forces, if an object is at rest or moving in uniform velocity it is described as in a state of equilibrium. Static equilibrium is when all the combined force acting on the body are 0 and the body is at rest. In dynamic equilibrium the system is moving but the forces complement each other so that the movement is all predictable.

Newton’s third law of motion states that for every action there is an equal and opposite reaction. For example when swimming a human pushes the water backwards and therefore the body is pushed forward by the water. This can also be seen in a hockey game, when the player hits the ball with their stick they have to absorb the equal and opposite force which can be felt through the stick, when it is cold this tends to be painful. Many factors affect the movement of an object friction being one of them, it is because of friction that humans are able to walk without it we would be sliding all over the place as though attempting to walk on ice. Friction occurs between to surfaces, i.e. the feet and the ground.

The rougher the two surfaces the more friction that occurs. Friction is also a factor that affects acceleration, acceleration can be slowed by friction, like the way in which a cars breaks work, the feeling we get when a car brakes demonstrates Newton’s first law, as the car breaks our bodies carry on moving hence the need for a seatbelt (an opposing force) to prevent us from going straight out of the windscreen. Friction is also the reason that Ben Johnson can run because his shoes create friction between his feet and the floor.

The torque or moment of a force can be defined as the tendency of a force to produce rotation in a body about an axis. The turning affect of a force depends on the magnitude of force (F) and the moment arm (r). The moment arm is the product of force and moment arm gives the torque about any axis.

T = F x r T= torque

F = force

r = moment arm

If a body rotates about its axis in an anticlockwise direction then the torque is described as positive, however if it’s clockwise then the torque is negative.

A lever produces a moment, they comprise of a lever arm a pivot point (fulcrum) and a load force (the thing to be moved) and an effort force (the thing that does the moving). The effort force creates a turning effect (moment) around the pivot. The size of the turning effect is dependant on the size of the force and its distance from the pivot. The amount of load force magnification changes when you change the distance between the pivot and the load force. There are three main classes of levers; first, second and third. A first class lever has the fulcrum located between the effort force and the load force an example of this is the neck. A Second class lever has the load force in between the effort force and the fulcrum on the lever arm. An example of this is a standing toe raise. Third class levers have the effort force in between the fulcrum and load force on the lever arm. An example of this type of lever is the elbow performing a bicep curl.

During Hockey the movement and motions are not always linear, in a straight line. They can be in curves like the swinging of a hockey stick in order to strike a ball. However it is possible to use the same principles and concepts to describe angular motion, or motion in a circle. When measuring angular motion it differs from linear motion because of the units involved. Linear motion uses meters per second (ms-1). In angular motion changes in position are measured in degrees (?).

The position of the hockey stick at any given moment is its angular position; this is measured in relation to something else such as the ground or another object. When the stick swings the distance it travels is referred to as angular displacement. This is represented by the Greek letter theta (?). And the rate at which this happens is known as angular velocity. It is calculated by dividing angular displacement by time. This then means that the average angular velocity of a rotating stick is worked out by dividing the angular displacement by time taken to turn through this angle. The symbol for this is the Greek letter omega and is measured in ?s-1.

Conclusion

In this assignment I have learnt all three of Newton’s laws of motion and applied them to simple sporting movement. I have undertaken calculations and talked about angular motion as well as linear motion.