EDUH 1017 Sports Mechanics L12Sem 2, 2014 1

EDUH 1017Sports Mechanics

Lecture 12Jumping

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Centre of mass

• A body acts as though all its mass were concentrated at a single point: the centre of mass. It takes energy to raise the centre of mass.

• However, the centre of mass of a person depends on posture and limb position.

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EDUH 1017 Sports Mechanics L12Sem 2, 2014

Centre of mass

• In jumping, the energy required depends on how far the centre of gravity is raised, but athletes can re-arrange their limbs to clear greater heights e.g. the Fosbury Flop

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centre of mass1.0 m

diagrams from http://coachr.org/rotation.htm

2.0 m

EDUH 1017 Sports Mechanics L12Sem 2, 2014

Elastic potential energy

Objects that are bent or stretched can store elastic potential energy. When the object is released, it can turn this energy into kinetic energy.

Examples: trampoline, bow string

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Jumping

• In a running jump, the height achieved is determined by the jumper’s vertical velocity. Why?

• Pole vaulters can jump much higher. How?• The pole provides a means of transforming almost all the

jumper’s initial KE from his run-up, into gravitational PE – i.e. into height.

• Once the jumper is off the ground, his run-up KE is converted into both gravitational PE and elastic PE of the pole. As the pole straightens again it gives up its elastic PE and hurls him even higher.

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Example Hecht Example 6.10

• A pole vaulter carrying a graphite-fibreglass pole (a thin walled tube weighing about 2kg) is about to make a jump.

• At what speed must he run in order to clear the 6.00 m mark?

• Neglect all possible energy losses. Assume his “centre of mass” is 1.00 m above the floor while standing, and that it just clears the bar.

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PoleVault

The height the pole vaulter clears may be regarded as the sum of 4 separate parts

• The height H1 of the vaulter’s centre of mass at the instant of take-off

• The height H2 that the centre of mass is raised while he is on the pole

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PoleVault

• The height H3 that the centre of mass is raised once the vaulter has released the pole

• The difference between the height of the cross bar and the maximum height reached by the centre of mass – the clearance height H4

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PoleVault

For example, Serge Bubka (USSR) jumping 5.85 m

Height(m)

% of barheight

H1 1.30 22H2 4.45 76H3 0.37 6H4 -0.27 5

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Long Jump

The distance the long jumper covers may be regarded as the sum of 3 separate parts

• The horizontal distance L1 from the front edge of the take-off board to the athlete’s centre of mass

• The horizontal distance L2 the centre of mass travels while the athlete is in the air

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Long Jump

• The horizontal distance L3 between the centre of mass when the heels hit the sand and the mark in the sand from which the distance of the jump is ultimately measured

• Contributions to distance in the Long JumpDistance

(m)% oftotal

L1 0.41 5L2 7.22 90L3 0.39 5

Total 8.02

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Projectile Motion

• The long jumper has two motions at take-off – one vertical and one horizontal – which can be treated separately.

Once in the air: • There is an initial component of velocity in the vertical

direction, but acceleration due to gravity is downward and the jumper’s upward motion is slowed and then reversed.

• The initial horizontal velocity component is unaffected because (neglecting air resistance) there is no net force in the horizontal direction.

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Summary

• Jumps may be broken into several phases• Most easily considered in terms of energy• One in the air, the jumper is subject to gravity only and

traces out a projectile path

• NEXT: Projectile Motion