Total Mechanical EnergyTotal Mechanical Energy• The total mechanical energy of a system is

defined to be the sum of:• The total potential energy of the system• The total kinetic energy of the system

• The symbol used for total mechanical energy is E. The units of E are joules.

• The total mechanical energy of a system can be negative if and only if the total potential energy is negative and has a greater magnitude than the total kinetic energy.

• The total mechanical energy of a system is defined to be the sum of:• The total potential energy of the system• The total kinetic energy of the system

• The symbol used for total mechanical energy is E. The units of E are joules.

• The total mechanical energy of a system can be negative if and only if the total potential energy is negative and has a greater magnitude than the total kinetic energy.

Example

A 50.0 gram tennis ball is at rest on the ground.

The tennis ball is then thrown upward…

A 50.0 gram tennis ball is thrown upward – when it is at a height of 0.75 meters above the ground…

The change in gravitational potential energy of the tennis ball is:

if mghmghPEg if PEPEPE

m) 00.0)(s

m 80.9)(kg 0500.0(-m) 75.0)(

s

m 80.9)(kg 0500.0(

22PE

J 37.0PE

0.75 m

A 50.0 gram tennis ball is thrown upward – when it is at a height of 0.75 meters above the ground…

When the ball reaches the height of 0.75 m, it is traveling at 1.35 m/s. The kinetic energy of the ball is:

2

2

1mvKE

J 046.0KE

0.75 m

2)sm 35.1kg)( 050.0(2

1KE

1.35 m/s

A 50.0 gram tennis ball is lifted to a height of 0.75 meters above the ground.

When the ball reaches the height of 0.75 m, it is traveling at 1.35 m/s. What is the total mechanical energy of the system?

J 046.0KE

0.75 m

1.35 m/s

J 37.0PE

J 42.0

J 37.0J 046.0

ME

ME

PEKEME