1. King Fahd University of Petroleum & Minerals
Mechanical Engineering
Dynamics ME 201 BY
Dr. Meyassar N. Al-Haddad
Lecture # 15

2. Rectangular Coordinates

3. Normal and Tangential Coordinates

4. Free-Body Diagram n = tan-1(dy/dx) an Between vertical and normal
Select the object
Establish n, t, b coordinate system
Set an always acts in the positive n direction
Assume at acts in the positive t
Set W = mg always acts in a vertical direction–downward
Set normal force FN along normal line
Set frictional force Ff opposite to t direction n
= tan-1(dy/dx)
Between vertical and normal
positive negative an Ff at FN t mg

5. Problem 13-67 W=600 Ib Stat from rest at A Fn=? At point B V= 15 ft/s
Neglect friction

6. Cylindrical Coordinates

7. Free-Body Diagram r q Select the object
Establish r, q coordinate system
Set ar always acts in the positive r direction
Assume aq acts in the positive q
Set W = mg always acts in a vertical direction–downward in vertical problem neglect weight in horizontal problem
Set the tangent line
Set normal force FN perpendicular to tangent line
Set frictional force Ff opposite to tangent
Set acting force F along q direction
Calculate the y angle using
Calculate other angles
Apply
tangent F ar r y FN aq Ff mg q

8. Problem 13-93
m=2 kg
Smooth horizontal
r = 0.4 q
Ptangent = ?
N=?
At q= 45o P N

9. Work and Energy relation
Initial K.E Work Done = Final K.E

10. Problem 14-11
W=6 Ib
From rest
Smooth
S=?

11. Power and Efficiency
Power is defined as the amount of work performed per unit of time. “rate of downing work”
Mechanical Efficiency :

12. Problem 14-56 M=50 kg From rest Constant acc. V=4m/s after 8 m P=?
Neglect friction
e=0.74

13. Conservation of Mechanical Energy
For a system of Particles

14. Problem 14-84
KA=300 N/m
kB=200 N/m
m=2 kg
s=?

15. Thank you