7.2 kinetic and potential energy

7.2 Kinetic and potential energy

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21 Kinetic energy (KE)A force F acts on an object of mass m, increasing its velocity from u to v over a distance s…

Kinetic energy (KE) gained

F

s

= work done by force

Fu v


31 Kinetic energy (KE)

F

s

Fu v

KE gained =W = Fs

F = ma & KE gained = Fs

= ma2a

uv 22 )(

2 uv 22 )(1 m=

v2 u2 = 2as



KE gained = mv2

21 mu2

21

F

s

Fu v

When the object’s velocity is uKE mu2

21

=

When the object’s velocity is v KE mv2

21

=



Simulation


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(a) Find the KE of a passenger car of mass 1000 kg travelling at

(i) 70 km h–1, (ii) 100 km h–

1.(i) KEpassenger car at 70 km h–1

= 0.189 MJ= 189 000 J

Example 3KEpassenger car vs KEtruck

1000 21= (

3.670 2)


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(a) Find the KE of a passenger car of mass 1000 kg travelling at

(i) 70 km h–1, (ii) 100 km h–

1.(ii) KEpassenger car at 100 km h–1

= 0.386 MJ= 386 000 J


1000 21= (

3.6100 2)

KE of car at 70 km h1= 0.189 MJ



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(b) Find the KE of a 10-tonnes truck (10 000 kg) travelling at 70 km h–1.


KEtruck at 70 km h–1

= 1.89 MJ= 1 890 000 J

10 000 21= (

3.670 2)




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A car of mass 1500 kg is travelling at 20 m s–1 (72 km h –1).

= 300 000 J = 0.3 MJ

Example 4Braking distance (energy approach)

(a) What is the kinetic energy of the car?

KE = mv2

21

1500 20221=


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(b) Brakes are applied to stop the car. If the braking force is 7500 N (equal to half the weight of the car), what is the braking distance?

Example 4Braking distance (energy approach)

Data:

KE of car = 0.3 MJ

Data:

KE of car = 0.3 MJ


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To stop the car,

7500 s = 0 300 000

s = 40 m

Example 4Braking distance (energy approach) KE of car = 0.3 MJ

braking force = 7500 N

KE of car = 0.3 MJ

braking force = 7500 N

F = 7500 Nwork done by braking force = KE of the car

Fs = mv2 21

21

mu2force is ve because forward is taken as +ve


122 Gravitational potential energy (PE)

PE is the energy an object possesses due to its position above the ground.A box of mass m is lifted a height h above the ground.

Force needed to lift box = weight

Work done = force distance lifted= mgh (PE gained by box) (unit: J)

mg

mg

h

= mg


13• N.B: • 1. As the height is measured from the ground

up, we choose the ground to be the reference point and P.E of the load

at the ground level is taken to be zero.

• 2. However we could choose some other reference points. Then the potential energy of the load have a different value. But the change in potential energy remains the same with reference to the same reference point.

• 3. For the displacement of the load to the level below the reference point, the P.E. of the

load is negative.


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Points to note in calculating PE:Only the height lifted against gravity matters, NOT the actual distance moved.

h

PE = mgh

both have the same PE at the top!!

less force, but longer distance mass

m

mass m

g




Simulation


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A 2-kg box is lifted 1 m from the floor to a table top and then to a shelf 1 m above the table. What is the gravitational potential energy the box gains

Example 5Potential energy gain of the box

(a) at the table top,

(b) on the shelf?1 m

1 m


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(a) PE gain of box at the table top

(b) PE gain of box on the shelf

Example 5Potential energy gain of the box

= 2 10 1 = 20 J= mgh

= mgh

= 2 10 2 = 40 J

1 m

1 m


18A 0.2-kg stone is thrown with 5 m s1. Find the gain in KE of it.

Initial KE (KE1)

Q1 A 0.2-kg stone is...

5 m s1

mv12

21

=

____ ____ = ____ J21

= 0.2 52 2.5

Final KE (KE2) mv22

21

=

____ ____ = ____ J21

= 0.2 302 9030 m s1

KE gain = KE2 KE1 = ____ J87.5


19Pauline of mass 50 kg goes hiking. After walking for 5 km, she is 20 m vertically above her starting point.

Potential energy gained

= mgh = ____ 10 _____

= _________ J

50 20

10 000

Q2 Pauline of mass 50 kg...

(a) What is her potential energy gained?


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(b) If she takes a steeper route and keeps the start and end points the same, will her PE gain be different? Why?

Her PE gain will be _______________. It is because both her _________________ and ______________ displacement are the same.

the same weightvertic

al

Q2 Pauline of mass 50 kg...


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The End


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7.2 kinetic and potential energy

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