1. Conservation of Mechanical Energy: Learning Goal
The student will investigate a simple energy transformation, explain the energy input and output, and calculate the efficiency.

2. Conservation of Mechanical Energy
SPH4C

3. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

4. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

5. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

6. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its gravitational potential energy.

7. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its kinetic energy.

8. Starting with Gravitational Potential
An object of mass 3.0 kg is suspended at a height of 12 m above the ground. Calculate its kinetic energy.
v = 0 so Ek = 0

9. The Object is Released
The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

10. The Object is Released
The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

11. The Object is Released
The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

12. The Object is Released
The object is released and hits the ground at a speed of 15.3 m/s. What is its kinetic energy when it hits the ground?

13. And Now We Have Kinetic Energy
Calculate the gravitational potential energy of the object when it hits the ground.

14. And Now We Have Kinetic Energy
Calculate the gravitational potential energy of the object when it hits the ground.
h = 0 so Eg = 0

15. And Now We Have Kinetic Energy
Our energy has been entirely transformed from gravitational potential energy to kinetic energy.

16. And Now We Have Kinetic Energy
Our energy has been entirely transformed from gravitational potential energy to kinetic energy.
But the total mechanical energy of the object (potential energy + kinetic energy) has not changed.

17. Conservational of Mechanical Energy
In general, if no work is being done on an object by an outside force, the total mechanical energy of the system will remain constant:

18. In Real Life
Note that in real life, energy is never transformed with 100% efficiency: a ball dropped from a given height will never bounce back up to that same height.
Some energy is always “lost” as heat energy or sound energy because of friction. However, just as we often neglect friction, we will often neglect these losses.

19. Efficiency
Efficiency is the ratio of useful energy or work output to the total energy or work input:

20. Efficiency
Efficiency is the ratio of useful energy or work output to the total energy or work input (written as a percent):

21. Efficiency Example 1
A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

22. Efficiency Example 1
A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

23. Efficiency Example 1
A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

24. Efficiency Example 1
A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

25. Efficiency Example 1
A model rocket engine contains explosives storing 3500 J of chemical potential energy. Calculate how efficiently the rocket transforms stored chemical energy into gravitational potential energy if the 0.50 kg rocket is propelled to a height of 1.0 x 102 m.

26. Efficiency, alternately
Efficiency is also the ratio of useful power output to the power input:

27. Efficiency Example 2
A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

28. Efficiency Example 2
A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

29. Efficiency Example 2
A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

30. Efficiency Example 2
A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.

31. Efficiency Example 2
A 120-W motor accelerates a 5.0-kg mass from rest to a speed of 4.0 m/s in 2.0 s. Calculate the motor’s efficiency.