Sem 2 2014 EDUH 1017 Sports Mechanics L6 1

EDUH 1017Sports Mechanics

Lecture 6Describing motion

and

VectorsSem 2 2014 EDUH 1017 Sports Mechanics L6 2

Where are we?

• Distance/displacement, speed/velocity and acceleration are words you need in describing motion – you (hopefully!) now know what they mean.

• So now we have the concepts we need to describe a lot of motion (e.g. to say how long it will take to get from start to finish) – at least if the motion is simple or we can make the assumption that it nearly is.

• We can describe walking, running, throwing balls,…

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Can you interpret graphs of motion?

• The handout summarises what we’ve learned about interpreting graphs.

• The slope of the line between two points on a displacement-time graph gives the average velocity between the points

Sem 2, 2013 EDUH 1017 Sports Mechanics - GRAPHS SUMMARY 1

Velocity

• The slope of the line between two points on a velocity-time graph gives the average acceleration between the points

• The slope of the tangent at p1 is the instantaneous accelerationSem 2, 2013 EDUH 1017 Sports Mechanics - GRAPHS SUMMARY 3

Acceleration

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Acceleration due to gravity

• Motion of a ball thrown straight up (at t=0), reaching maximum height (at t=tp), and falling straight back down again, ending at t=2tp.

(Upwards is chosen to be positive)

Displacement-time Velocity-time Acceleration-time

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Can you interpret graphs of motion?

• The handout summarises what we’ve learned about interpreting graphs.

• Have a look at the detailed example on the back.

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Uniform acceleration

• Acceleration is rarely really constant, but it can sometimes be treated as if it were, at least over a limited time.

• Consider • constant acceleration over time t• only straight line motion, where the acceleration vector

must lie along the direction of motion. • The equation defining acceleration is then

a =v f − v it

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• Re-arranging

• There are two other equations for use when acceleration is constant:

(using symbols as in Hay’s book – however symbols vary widely)

vf = vi + at

d = vit + 12at2

vf2 = vi

2 + 2ad

Equations of constant acceleration

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Examples (Hecht Example 3.4)

• A bicyclist pedalling along a straight road at 25 km/h uniformly accelerates at +3.00 m/s2 for 3.00 s. Find her final speed.

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The fastest animal sprinter is the cheetah, reaching speeds in excess of 113 km/h. These animals have been observed to bound from a standing start to 72 km/h in 2.0 s.

What is the cheetah’s acceleration (assuming it is constant)Using this acceleration, what minimum distance is required for the cheetah to go from rest to 20 m/s?

Examples (Hecht Example 3.9)

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Examples (Hecht Example 3. 12)

• A ball is dropped from the roof of a building. If the building is 100 m high, ...

• At what speed will the ball hit the ground? • How long will the ball take to reach the ground?

• How would these results change if the ball is thrown downwards at 10.0 m/s?

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More on vectors :Adding vectors together

• A vector has magnitude AND direction – it is usually represented by an arrow

• Two vectors can be added by arranging them “tip-to-tail” – the sum is the resultant vector

• The order of the addition is irrelevant

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Vectors can be added in any order

A Treasure map was torn into six pieces. Find the treasure.

How?

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or

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“Breaking vectors apart”

• Any vector can be broken into two perpendicular components.

• e.g. the vector A can be broken into two components Ax and Ay

• Together the components are equivalent in every way to the original vector – and can be added together again to make the original vector.

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Components of a vector

• Any vector can be broken into two perpendicular components

• For example the velocity of a ball kicked at an angle can be broken into horizontal and vertical components.

17

!

v

vx

vy

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• Knowing how to

add two vectors makes it easy to add many vectors

• C = A + B• E = C + D• G = E + F• G = A + B + D + F

Adding vectors II

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Subtracting vectors

• Vectors can also be subtracted

• A – B = A + (–B)• What is –B?• Its just the same

magnitude (size) but the opposite direction to +B