1. Total Mechanical Energy

2. Total Mechanical Energy (ET):
Energy can be transferred or transformed, never lost  Law of Conservation of Energy
*If friction negligible
If friction is not negligible then….

3. Ex#1
A 56kg diver runs & dives from the edge of a cliff into the water which is located 4m below. If she is moving at 8m/s the instant she leaves the cliff, determine the speed at which she enters the water.
Before Jump
At Water Level Eg Ek Eg Ek
m = 56 kg
m = 56 kg
m = 56 kg
m = 56 kg
g = 9.8 N/kg
v = 8 m/s
g = 9.8 N/kg
v = ?
h = 4 m
h = 0 m =

4. Before Jump
At Water Level

5. Ex#2
A child throws a 0.2kg rock at a tree. When the rock leaves the child’s hand, it is moving at 20m/s & is located 1.5m above the ground. How high above the ground does the rock strike the tree if it is moving at 10m/s at that instant?
Throw
Tree Eg Ek Eg Ek
m = 0.2 kg
m = 0.2 kg
m = 0.2 kg
m = 0.2 kg
g = 9.8 N/kg
v = 20 m/s
g = 9.8 N/kg
v = 10 m/s
h = 1.5 m
h = ? =

6. Throw
Tree

7. Ex#3
A 2 kg ball rolls along a frictionless surface. It passes point C at a speed of 20m/s. What was the speed of the ball at point A? A C
25 m
20 m
Point A
Point C Eg Ek Eg Ek
m = 2 kg
m = 2 kg
m = 2 kg
m = 2 kg
g = 9.8 N/kg
v = ? m/s
g = 9.8 N/kg
v = 20m/s
h = 20 m
h = 25 m =

8. Point A
Point C

9. So work applied to move mass 5m
Ex#4
Law of
Conservation
of Energy
A force of 16N is applied to a 400g mass, starting at rest, over a distance of 5m. How long does it take the mass to move 5m?
Before
After 5m Eg Ek Eg Ek
Eg = 0
m = 0.4 kg
Eg = 0
m = 0.4 kg
v = 0 m/s
v = ?
Recall, work = energy
So work applied to move mass 5m

10. Work required to set block in motion

12. Ex#5 You are playing with a toy slider track.
The top of the “hump” is 1.2m above the level of the slider at the beginning of the track. The average force of friction between the 0.15kg slider & the track is 0.11N. The distance from point A to point B along the track is 2.3m.
You propel the slider by applying a constant force of 6.6N hoping to get it over the “hump”. How far must you push the slider to ensure that it makes it over the “hump”?

13. Recall, energy= work Recall, work = energy
Top:
Bottom:
Recall, energy= work
BUT….friction…
Recall, work = energy