4. m – mass of the
body
s – displacement
y - vertical
components
w – weight (mg)
Fother - some forces
acting on the body
5. m – mass of the
body
s – displacement
y - vertical
components
w – weight (mg)
Fother - some forces
acting on the body
The quantity
(y1 –y2) is negative,
and Wgrav is
negative because
the weight and
displacement are in
opposite direction.
7. Conservation of MechanicalEnergy
(Gravitational Forces Only)
Work- Energy TheoremWtot = ΔK = K2 - K1
Wtot = Wgrav = -ΔUgrav = Ugrav,1 - Ugrav,2
ΔK = -ΔUgrav
K2 - K1 = Ugrav,1 - Ugrav,2
K1 +Ugrav,1 = K2 + Ugrav,2
If only gravity does
work
8. E = K + Ugrav
Potential
energy
kinetic
energy
E1 = K1 + Ugrav,1 E2 = K2 + Ugrav,2
9. When only the force of gravity does work,
the total mechanical energy is constant—
that is, it is conserved.
CONSERVATION OF
MECHANICAL
ENERGY
10.
11. Problem Sample
You throw a 0.145-kg baseball straight up, giving it an
initial velocity of magnitude 20.0 m/s. Find how high it
goes, ignoring air resistance.
12.
13. When ForcesOther Than Gravity Do Work
Wother + Wgrav = K2 - K1
Wgrav = Ugrav,1 - Ugrav,2
Wother + Ugrav,1 - Ugrav,2 = K2 - K1
K1 +Ugrav,1 = K2 + Ugrav,2
If forces other than gravity do work
14. Elasticpotential energy
• The process of storing energy in a deformable
body such as a spring or rubber band in terms
of elastic potential energy.
• A body is called elastic if it returns to its
original shape and size after being deformed.
15. F = kx
F – force on the spring
k - force constant of the spring
x - displacement
19. The work done by all forces other than the
gravitational force or elastic force equals
the change in the total mechanical energy E
= K + U of the system, where U = Ugrav +
Uel is the sum of the gravitational potential
energy and the elastic potential energy.