1. Chapter IV Work and Energy
Work Done by a Constant Force
The Work-Energy Theorem
Work Done by a Varying Force or on Curved Path
Power
Gravitational Potential Energy and Elastic Potential Energy
When Total Mechanical Energy is Conserved

2. A. Work Done by a Constant Force
Fx = F cos   x
The work W done on an object by an agent exerting a constant force on the object is the product of the component of the force in the direction of the displacement and the magnitude of the displacement:
W = F  X
W = F Cos  X F W x

3. B. The Work-Energy Theorem
W = F x
= m a x
v 2 = vo2 + 2 a x
Kinetic energy  K = ½ m v2
W = K – Ko
Wt =  K  work-kinetic energy theorem
The net work done on a particle by a constant net force F acting on it equals the change in kinetic energy of the particle

4. C. Work Done by a Varying Force or on Curved Path
W = F  x
W =  W = Limit  F  x
 x  0
W =  F dx =  m a dx
a = dv/dt = (dv/dx)(dx/dt) = (dv/dx) v
W =  m a dx =  m (dv/dx) v dx
W =  m dv v
W = ½ m v 2 - ½ m vo2 = K – Ko
Wt =  K W W x
 x
The net work done on a particle by the net force acting on it is equal to the change in the kinetic energy of the particle.
By spring
F = - k x
By hand
F = k x
W =  F dx =  k x dx = ½ k x2 Elastic Potential Energy

5. D. Power P = Power (watt  W) W = work (joule  J)
The time rate of doing work is called power.
P = Power (watt  W)
W = work (joule  J)
t = time (second  s)
x = displacement (meter  m)
v = velocity (m/s)

6. E. Gravitational Potential Energy and Elastic Potential Energy
W = F y = mg (h2 – h1) = m g h2 - m g h1
Gravitational potential energy = V = mgh
W = V2 – V1
W =  V  work done by palm force
W = -  V  work done by gravitation force
WK = -  V h2 v h1
WK = work done by concervative force (J)
g = acceleration of gravity (m/s2)
m = mass(kg)
V = Potential energy (J)
WK = - (½ k x22 - ½ k x12 )  work done by spring force
k = force constant of the spring(J/m2  N/m)

7. Conservative Force
Conservative forces have two important properties: 1. A force is conservative if the work it does on a particle moving between any two points is independent of the path taken by the particle. 2. The work done by a conservative force on a particle moving through any closed path is zero. (A closed path is one in which the beginning and end points are identical.)

8. E. When Total Mechanical Energy is Conserved
Wt = WNK + WK
WNK = Wt – WK
WNK =  K – (-  V)
WNK = (K2 – K1) + (V2 – V1)
WNK = work done by nonconcervative force (J)
If WNK = 0, than
K1 + V1 = K2 + V2
Mechanical energy  M = K + V
M1 = M2  M = constant
½ m v 2 + mgh = constant  Conservation of Mechanical
Energy

9. Increase (or decrease) in potential energy is accompanied by an equal decrease (or increase) in kinetic energy.
The total mechanical energy of a system remains constant in any isolated system of objects that interact only through conservative forces.