4. What is Friction?
• Force that acts oppose the relative motion of
two surfaces
• High for dry and rough surface
• Low for smooth and wet surface
5. Law of Friction
Experiments have shown that the force solid
friction force is
• directly dependent to the normal reaction
• opposes the motion between the surface
• dependents upon the material of the surface
• is independent of the area of contact
• is independent of velocity of sliding
6. Normal Force, FN
Friction Force, F’
Applied Force F
Force Gravity, W
W = mg
FN = W
F = F’
Free Body Diagram
7. Body is in motion
Free Body Diagram
W = R cos
F = R sin
Normal Force, FN
Friction Force, F’ Applied Force F
Force Gravity, W
Resultant Force, R
'
N NF F F
'
tan N
N N
FF
F F
Where is known as limiting angle of friction or angle of friction
9. Problem 1.
A body, resting on a rough horizontal plane required a pull of 180 N
inclined at 30º to the plane just to move it. It was found that a push of 220
N inclined at 30º to the plane just moved the body. Determine the weight of
the body and the coefficient of friction.
Resolving the forces horizontally,
F = 220 cos 30º = 220 × 0.866 = 190.5 N
Resolving the forces horizontally,
F = 180 cos 30º = 180 × 0.866 = 156 N
Now resolving the forces vertically,
RN = W – 180 sin 30º = W – 180 × 0.5 =(W– 90) N
We know that F = μ. RN or 156 = μ (W – 90)
Now resolving the forces vertically,
RN =W+220 sin 30º = W + 220 × 0.5 = (W + 110) N
We know that F = μ. RN or 190.5 = μ (W + 110)
W = 1000 N, and μ = 0.1714 Ans.
10. Friction of a Body Lying on a
Rough Inclined Plane
(a) Angle of inclination less
than angle of friction
(b) Angle of inclination more
than angle of friction.
13. Efficiency of Inclined Plane
The motion of the body up the plane
The ratio of the effort required neglecting friction (i.e. P0) to the effort required considering friction
(i.e. P) is known as efficiency of the inclined plane. Mathematically, efficiency of the inclined plane,
Multiplying the numerator and denominator by sin ( + ) sin , we get
14. Inclined Plane
The motion of the body down the plane (With and Without Friction)
(With Friction)
(With Friction) (Without Friction) Efficiency of Inclined Plane
15. Problem 2: An effort of 1500 N is required to just move a certain body up an inclined
plane of angle 12º, force acting parallel to the plane. If the angle of inclination is
increased to 15º, then the effort required is 1720 N. Find the weight of the body and the
coefficient of friction.
When the effort applied is parallel to the plane, then θ = 90º + α.
