Dr- Sonia Reda chapter 7 Kinetic energy and Work 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5 Workandkinetic Energy 7.5 Work and kinetic Energy

Dr- Sonia RedaDr- Sonia Reda


chapter 7chapter 7Kinetic energy and WorkKinetic energy and Work

7.2 What is energy7.2 What is energy

7.37.3 Kinetic energyKinetic energy

7.47.4 WorkWork

7.57.5 WorkWork andand kinetickinetic EnergyEnergy

7.67.6 Work done by the gravitational forceWork done by the gravitational force

7.77.7 Work done by a Spring forceWork done by a Spring force

7.8 Power7.8 Power

7.2 What is energy7.2 What is energy

7.37.3 Kinetic energyKinetic energy

7.47.4 WorkWork

7.57.5 WorkWork andand kinetickinetic EnergyEnergy

7.67.6 Work done by the gravitational forceWork done by the gravitational force

7.77.7 Work done by a Spring forceWork done by a Spring force

7.8 Power7.8 Power

Outline Chapter 7Outline Chapter 7Work and Kinetic energyWork and Kinetic energy

Work done by a net force results in kinetic energy

Some examples: gravity, spring, friction


What is Energy? What is Energy? The term energy is so broad that a clear definition is difficult to write.

Technically,

Energy is a scalar quantity associated with the state (or condition) of one or

more objects.

However, this definition is too vague to be of help to us now.


Kinetic EnergyKinetic Energy

Kinetic energyKinetic energy KK is energy associated is energy associated with the with the state of motionstate of motion of an object. of an object.

For an object of mass For an object of mass mm whose speed whose speed vv is well is well below the speed of light, below the speed of light, Kinetic energyKinetic energy KK is: is:

Unit for Unit for Kinetic energyKinetic energy is: is:

Kinetic energy is a scalar quantity.


WorkWork

Work Work WW is energy transferred to or from an object by is energy transferred to or from an object by means of a force acting on the object.means of a force acting on the object.

Energy transferred to the object is positive work,Energy transferred to the object is positive work, Energy transferred from the object is negative work.Energy transferred from the object is negative work.


Properties of WorkProperties of Work

Only the force component along the object’s Only the force component along the object’s displacement will contribute to work. displacement will contribute to work.

The force component perpendicular to the The force component perpendicular to the displacement does zero work. displacement does zero work.

A force does positive work when it has a vector A force does positive work when it has a vector component in the same direction displacement,component in the same direction displacement,

A force does negative work when it has a vector A force does negative work when it has a vector component in the opposite direction. component in the opposite direction.

Work is a scalar quantity.Work is a scalar quantity.


Finding an Expression for WorkFinding an Expression for Work

we can use Eq. 2-16 to write, for components along the x axis,v2

=vo2 + 2axd

By multiplying the above Eq with ½ m


Finding an Expression for WorkFinding an Expression for Work


Kinetic Energy

Work-Kinetic Energy Theorem

Change in KE work done by all forces

K w


xixf

f

i

f

i

vv

vv vmdvvm ]/[. 221

= 1/2mvf2 – 1/2mvi

2

= Kf - Ki

= KK

Work done by net force

= change in KE

f

i

xx dxFw .

f

i

xx dxma .

f

i

f

i

xx

xx dv

dtdx

mdxdtdv

m ..

Work-Kinetic Energy TheoremF

x

Vec

tor

sum

of

all f

orce

s ac

ting

on

the

body


Checkpoint 1 Checkpoint 1

A particle moves along an A particle moves along an xx axis. Does the axis. Does the kinetic energy of the particle increase, kinetic energy of the particle increase, decrease, or remain the same if the decrease, or remain the same if the particle’s velocity changesparticle’s velocity changes

(a) from −3 m/s to −2 m/s and (a) from −3 m/s to −2 m/s and

(b) from −2 m/s to 2 m/s? (b) from −2 m/s to 2 m/s?

(c) In each situation, is the work done on the (c) In each situation, is the work done on the particle positive, negative, or zero?particle positive, negative, or zero?


Example 7-3Example 7-3

During a storm, a crate of crepe is sliding across a During a storm, a crate of crepe is sliding across a slick, oily parking lot through a displacement slick, oily parking lot through a displacement

while a steady wind pushes against while a steady wind pushes against the crate with a force . The the crate with a force . The situation and coordinate axes are shown in Fig. situation and coordinate axes are shown in Fig. 7-57-5. .

(a) How much work does this force do on the crate (a) How much work does this force do on the crate during the displacement? during the displacement?

.


(a) How much work does this force from the wind (a) How much work does this force from the wind do on the crate during the displacement?do on the crate during the displacement?

i)m0.3(j)N0.6(i)N0.2(dFW

J0.60)1()J0.6(

ij)m0.3()N0.6(ii)m0.3()N0.2(

Work done by the wind force on crate :

SOLUTION:

The wind force does negative work, i.e. kinetic energy is taken out of the crate.


(b) If the crate has a kinetic energy of 10 J at the (b) If the crate has a kinetic energy of 10 J at the beginning of displacement , what is its kinetic beginning of displacement , what is its kinetic

energy at the end of ?energy at the end of ?d

d

J0.4)J0.6(J10WKK if

SOLUTION:


mg

F

h

Lift mass m with constant velocity

Work done by me (take down as +ve)

= F.(-h) = -mg(-h) = mghWork done by gravity

= mg.(-h) = -mgh ________

Total work by ALL forces (W) = 0

What happens if I let go?

=K

Gravitation and work

Work done by ALL forces = change in KE

W = K


Work Done by a Spring ForceWork Done by a Spring Force

The spring forceThe spring force given by given by Hooke’s Law:Hooke’s Law:

springxF k x

The work done by spring The work done by spring forceforce::

2 22 1

1 1( )2 2

springW kx kx


Compressing a spring

Compress a spring by an amount x

Work done by me Fdx = kxdx = 1/2kx2

Work done by spring -kxdx =-1/2kx2

Total work done (W) =

0=K

What happens if I let go?

x

F -kx


Ff

dWork done by me = F.d

Work done by friction = -f.d = -F.d

Total work done = 0What happens if I let go? NOTHING!!

Gravity and spring forces are Conservative

Friction is NOT!!

Moving a block against friction at constant velocity


Sample Problem 7-8Sample Problem 7-8

In Fig. 7-11, a cumin canister of mass In Fig. 7-11, a cumin canister of mass mm = 0.40 kg = 0.40 kg slides across a horizontal frictionless counter with speed slides across a horizontal frictionless counter with speed vv = 0.50 m/s. It then runs into and compresses a spring = 0.50 m/s. It then runs into and compresses a spring of spring constant of spring constant kk = 750 N/m. When the canister is = 750 N/m. When the canister is momentarily stopped by the spring, by what distance momentarily stopped by the spring, by what distance dd is the spring compressed?is the spring compressed?


SOLUTION:

We assume the spring is massless. Work done by the spring on the canister is negative. This work is :

221

S kdW

Kinetic energy change of the canister is : 2

21

if mvkk Therefore, 2

212

21 mvkd

cm2.1m10x2.1

m/N750

kg40.0)s/m50.0(

k

mvd

2


PowerPower The rate at which work is done by a force The rate at which work is done by a force

is called the is called the power.power. The average power due to the work done by a force The average power due to the work done by a force

during that time interval as during that time interval as

We define the We define the instantaneous powerinstantaneous power PP as the as the instantaneous rate of doing work, so thatinstantaneous rate of doing work, so that

W = F . W = F . ΔΔxx


The units of power The units of power


Sample Problem 7-10Sample Problem 7-10

Figure 7-14 shows constant forces and Figure 7-14 shows constant forces and acting on a box as the box slides rightward acting on a box as the box slides rightward across a frictionless floor. Force is horizontal, across a frictionless floor. Force is horizontal, with magnitude 2.0 N; force is angled upward with magnitude 2.0 N; force is angled upward by 60° to the floor and has magnitude 4.0 N. by 60° to the floor and has magnitude 4.0 N. The speed The speed vv of the box at a certain instant is 3.0 of the box at a certain instant is 3.0 m/s.m/s.

1F

1F

2F

2F


(a) What is the power due to each force acting on the box (a) What is the power due to each force acting on the box at that instant, and what is the net power? Is the net power at that instant, and what is the net power? Is the net power

changing at that instant?changing at that instant?

SOLUTION:

0

0.6

60cos)/0.3()0.4(60cos

0.6

180cos)/0.3()0.2(180cos

21

22

11

PPP

W

smNvFP

W

smNvFP

net

The kinetic energy of the box is not changing. The speed of the box remains at 3 m/s. The net power does not change.


(b) If the magnitude of is, instead, 6.0 N, what (b) If the magnitude of is, instead, 6.0 N, what now is the net power, and is it changing?now is the net power, and is it changing?

2F

SOLUTION:

W0.3

W0.9W0.6PPP

W0.9

60cos)s/m0.3()N0.6(60cosvFP

21net

22

There is a net rate of transfer of energy to the box. The kinetic energy of the box increases. The net power also increases.


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Dr- Sonia Reda chapter 7 Kinetic energy and Work 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5 Workandkinetic Energy 7.5 Work and kinetic Energy