1. Conservation of Energy

2. Facts Conservation of energy
When gravity is the only force which does work on a body, mechanical energy is conserved.
PEstart + KEstart = PEend + KEend
This is also true when an external force is applied
PEstart + KEstart + Win = PEend + KEend+ Wout

3. Examples
A toolbox of mass 3 kg, is knocked off a table which is 0.3 m above the ground. Using conservation of energy, calculate the vertical speed with which the toolbox lands on the ground. 3g
0.3 m
Zero PE level
As the toolbox falls the initial PE at the start is converted into KE at the end
PEstart = KEend
mgh = ½mv²
3 x 9.8 x 0.3 = ½ x 3 x v²
v² = 5.88
v = 2.42 ms-1

4. There is an external force being applied so
A 10 kg mass is pulled along a rough horizontal surface by a horizontal force of magnitude 100N. The mass is initially at rest and it is pulled by the force for a distance of 10m. The coefficient of friction between the mass and the surface is Use the work – energy principle to find the final speed of the mass.
0 ms-1
v ms-1 R Fr
100 N
 = 0.6
10g
10 m
There is an external force being applied so
PEstart + KEstart + Win = PEend + KEend+ Wout
Fs = 0 + ½mv² + Frs
100 x 10 = ½ x 10gv² + Frs
1000 = 5gv² + 10 x 6g
1000 – 60g = 5gv²
v² = 412
v = 9.08 ms-1 (3 s.f.)
We need to find friction
Fr= R
= 0.6 x 10g
= 6g

5. PEstart + KEstart + Win = PEend + KEend+ Wout
A female athlete of mass 65kg runs up a slope inclined a 5º to the horizontal. Her speed at the bottom of the slope is 4 ms-1 and her speed decreases to 3 ms-1 at the top of the slope. The slope is 120 m long and the resistances to motion can be assumed constant at 40 N. Determine the constant force she must exert to get to the top of the slope.
3 ms-1 R F
120 m
40 N
4 ms-1
65g R
h = 120sin 5º F
40 N 5º
zero PE level
65g
The athlete starts with KE and work and ends with KE, PE and resistances
PEstart + KEstart + Win = PEend + KEend+ Wout
0 + (½ x 65gx 4²) + 120F = (65g x 120sin 5º) + (½ x 65gx 3²) + (40 x 120)
F =
120F =
F = 93.6 N (3 s.f.)

6. Your turn now
Blue book pg 261, 262
Mechanics 2 exercise 4B page 86 all the questions