1. Chapter 7
Work and Energy

2. Alternative description of dynamics
Energy
Momentum
Integration over space
Integration over time
Scalar
Vector
Significance: They are conserved
Valuable when the forces are not detailed
Wide range including Relativity & Quantum M.
Energy is useful in all areas of physics and in other science as well

3. Work done by constant force
Accomplished by action of force over a distance
Work done by a constant force
When W = 0?
Example1: An object moves as ,
and there is a force acting on it, what is the work done by this force in 0~2s? 3

4. Work done by varying force
Divide the path into short intervals
During each interval, force ~ constant
Work
Total work
Sum → Integral
General definition of work

5. This is called a line integral.
Work in component form F a b
This is called a line integral.
Work can be written as
Or: 5

6. Work depends on the specific path from a to b
Work depends on path
Work depends on the specific path from a to b
Moves on horizontal ground,
3 different paths from a to b, work by friction is different! a b 1 2 3
Friction is called a nonconservative force 6

7. Work done by gravity is path independent. L a b mg o y x 
Gravity of object: ha C hb
Work done by gravity is path independent.
Determined only by the initial and final position.
Gravity is called a conservative force.
All constant forces are conservative. 7

8. Lose weight by climbing
Example2: Bob (80kg) wants to lose weight by climbing mountains. How many calories he loses at least when he goes from A to B? ( 1cal=4.184J )
Solution: The work done by gravity is
So Bob loses energy A B
h=1500m
That is about 31g fat. 8

9. Solution: force to stretch a spring: F = k x
Stretching a spring
Example3: Someone slowly pulls a spring from unstretched to make the object m leave the ground, calculate the work done by this person.
Solution: force to stretch a spring:
F = k x m F
How to make m leave the ground? k
Work : 9

10. Kinetic Energy
Energy: one of most important concepts in science.
There are many types of energy, it can be usually regarded as “the ability to do work”.
Moving objects can do work → have energy
The energy of motion is called kinetic energy
Object starts from rest under constant net force:
Translational kinetic energy

11. Work-energy principle
For varying force, 3 dimensional motion:
Work-energy principle
The net work done on an object is equal to the change in its kinetic energy. 11

12. Work in an elliptical motion
Example4: A particle m moves under the equation
, where a, b,  are positive constants. Determine the net work during t=0~/2.
Solution1: The net force is
Net work 12

13. Example4: A particle m moves under the equation
, where a, b,  are positive constants. Determine the net work during t=0~/2.
Solution2: Using work-energy principle
t=0: v0= b;
t=/2: v = a
Net work equals to the change of kinetic energy: 13

14. Work done by friction
Example5: An object moves along a semi-circular wall on smooth horizontal plane. Known: v0 and µ, determine the work done by friction from A to B.
Radial force
Solution: N fµ v o v0 . A
Tangential force  R B

15. Kinetic energy of spring
Example6: Considering the mass of spring ms (k, L), it is attached by a mass M, determine kinetic energy of the spring when M is moving with velocity v.
Solution: take dx of the spring, the mass is ms·dx/L
If the spring deforms uniformly, then vdx = v·x/L x dx M
Effective mass 15

16. There are 5 main forms of energy
Mechanical
Thermal / heat
Electromagnetic
Chemical
Nuclear
(Fission & Fusion)
Chain reaction

17. “Little boy” & “Fat man”
*Nuclear bomb
“If the radiance of a thousand suns were to burst into the sky, that would be like the splendor of the Mighty One.” 
“Little boy” & “Fat man”
The effects of nuclear bomb:
Heat, shock wave and radiation (γ ray and neutrons)