### Potential Energy   in Joules [J]

Example: How much is the kinetic, potential, and total mechanical energy of a car (m=1200 kg) moving at 20 m/s at p. A?

Question: How much is the total energy at B in the absence of any dissipative forces?

Question: How much is the speed of the car at p.B in the absence of any dissipative forces?

Question: How much is the total energy at B if friction removed 10,000 J from the car as it moved from p. A to p.B?

📌 Check Point

### Work done by a Force on an object

📚 Review of Vector Dot Product

Constant Force applied to an object with displacement d

Example: A 1,470-N force pushes a  500-kg piano up a 10-m long ramp as shown on the diagram. What is the work done by (a) Gravity; (b) the pushing force; and (c) the normal force.

Question. What is the acceleration of the piano?

1-Dimensional Variable Force applied to an object with displacement x

Example: A 1-dimensional force acts on an object. Calculate its work as the object moves from 0 to 2.0 m

1-Dimensional Graphical Representation of the Work: F vs. x diagram

Example: What is the work of the force F from x=1 to x=3 m?

3-Dimensional Variable Force applied to an object with displacement

Example: A force N is applied on an object as it moves from position (1,0,0) m to position (1,-4, 8) m. Determine the work done by the force.

📌 Check Point

### Measured in Watts [W]

Average Power

Instantaneous Power

### Unit Conversions

1 horsepower  = 745.7 W  (Power)

1 KW.h = 3.6 MJ   (Energy)