lecture 11 - university of sydney school of physicshelenj/spm/lecture11.pdf · lecture 11 energy...

EDUH 1017 Sports Mechanics L11Sem 2, 2014 1

EDUH 1017Sports Mechanics

Lecture 11Energy and Work


Energy and Work

• There is another way to think about jumping – as a change in Energy

• Energy derives from the Greek words en (meaning in) and ergon (meaning work). Energy is the capacity to do work.

• But what does work mean?• In mechanics, work is the change in energy resulting from the

application of a force to an object as the object moves through a distance in space.

• or more generally where θ is the angle between the direction of the force F and the displacement d

W = Fd W = Fd cosθ


Work

• At the heart of the concept of work is the idea of movement with some force or against some “resistance”

• In jumping, it is gravity that is resisting the attempt to jump up

• In lifting an object, your hand is doing work to lift the object “against gravity”


Work

• Say you lift with a constant velocity (i.e. acceleration = 0), then the upward force F = weight FW = mg

• The work done by your hand to raise an object a height h “against gravity” is

• What is the work done on the 1.0 kg object by the hand in raising it by 2.0 m?

• The SI unit of work (and energy) is the newton-meter, known as the Joule (J)

W = Fd

= mg( )h


Energy

• Energy is needed to do useful work.• Energy can move things, heat things up, cool them down, join

things, break things, cut things, make noise, make light, and power our electronics, etc.

• Energy can be changed from one form to another.

6

kinetic energy

gravitational potential energy

elastic potential energy

chemical energy


Kinetic Energy

• Under the influence of a net force, a body accelerates as (positive) work is done on it. It increases its speed and gains energy

• Energy associated with motion is called Kinetic Energy (KE)

• Example:• A Boeing 747 weighing 2.2 x 106 N at take-off cruises at

960 km/h. Calculate its KE.• Note that the units are Joules

KE =

12mv2


Kinetic Energy

• A force acting over a distance results in a change in KE• Your arm can do work on a cricket ball and increase the ball’s

KE. It travels some distance and then crashes into the stumps, doing work on them and losing a corresponding amount of KE.

• The ball transports energy in the form of KE from one place to another

EDUH 1017 Sports Mechanics L11Sem 2, 2014

How much KE?

A primary school child can throw a cricket ball (m=0.156 kg) at a speed of 40 km/h

Shoaib Akhtar hold the world record for the fastest bowl in cricket, with a speed of 161.3 km/h.

How much more energy does Akhtar’s ball have than a ball bowled by the school kid?

9 EDUH 1017 Sports Mechanics L11Sem 2, 2014 10

Gravitational Potential Energy

• An object lifted against gravity still experiences the downward force of gravity when it is held up, but at rest. When no longer held up, it will obviously fall.

• Energy will appear as KE as it falls, but what’s happening while the object is held motionless, high in the gravitational field?

• Apparently it is possible to do work on a system when lifting it and not have it appear as KE.

• Energy is stored, waiting to be let loose.


Gravitational Potential Energy

• This retrievable stored energy is called Gravitational Potential Energy (PE)

• The change in PE of an object in moving from one point to another equals the work done in overcoming the interaction that stores the energy.

• We have already calculated the work done in lifting an object a height h “against gravity”

• So Gravitational PE (sometimes GPE) is

W = Fd

= mg( )h

PE = mghEDUH 1017 Sports Mechanics L11Sem 2, 2014 12

Energy values

• PE is a relative quantity since the h is relative – from where are we measuring height?

• Thus the zero level of PE is arbitrary and chosen for convenience in any situation.

• Usually we are only concerned with changes in PE so where the zero value is doesn’t really matter.

• KE is also relative – any measured velocity depends on our velocity


Mechanical Energy

• Mechanical Energy of a system is defined as the sum of KE and gravitational PE of all its parts.

If no additional forces (except gravity) are applied to a system, no energy is transferred into or out of the system, and mechanical energy is conserved. This is a limited case of the more general concept of conservation of all forms of energy


A Pendulum

• Again, if we ignore air resistance, no forces other than gravity are acting


Roller coaster

• The zero point of PE can be located anywhere convenient

• The change is PE is the same


Example Hecht Example 6.11

• A 60 kg skier starts from rest at the top of a 60 m high slope. She descends without using her poles.

• What is her initial gravitational PE?• Assuming friction is negligible, what is her speed at the

bottom of the slope?• If her speed at the bottom of the run is 25 m/s, what is the

net energy transferred via friction (i.e. “lost” to warming her, the skis, the slope and the air)?

• Energy is conserved – in what other forms?


Summary

• Energy and Work and very closely related concepts in Mechanics• Work is a change in energy resulting from the application of a

force • Kinetic Energy (KE)

• Gravitational Potential Energy (PE)

• If no additional forces are applied to a system, no energy is transferred into or out of the system, and mechanical energy (KE + PE) is conserved.

• NEXT: Jumping

PE = mgh KE =

12mv2

lecture 11 - university of sydney school of physicshelenj/spm/lecture11.pdf · lecture 11 energy...

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