STATICS OF RIGID BODIES 2
FRICTIONAL FORCE
Friction or Frictional Force - The force which opposes the movement or the tendency of movement. It is due
to the resistance to motion offered by minutely projecting particles at the contact surfaces.
Limiting Friction - Limiting value of frictional force when the motion is impending.
Static Friction - Friction force when the body remains at rest and has a value between zero and the limiting
friction.
Dynamic friction - The frictional resistance experienced by the body while moving. Dynamic friction is less
than limiting friction.
Coefficient of friction - A constant ratio of the magnitude of limiting friction to the normal reaction between two
surfaces.
a. Coefficient Static of friction,
𝝁𝒔 =
𝑭
𝑵
𝝁𝒌 =
𝑭
𝑵
where:
F = limiting friction
N = normal reaction between the contact surfaces
b. Coefficient of Kinetic friction,
where:
F = dynamic friction
N = normal reaction between the contact surfaces
Angle of Friction
Let F be the frictional force developed and N the normal reaction. Thus, at contact surface the reactions are F
and N.
They can be graphically combined to get the reaction R which acts at angle θ to the normal reaction.
This angle θ called the angle of friction is given by:
As P increases, F increases and hence θ also increases. θ can reach the maximum value α when F reaches
limiting value. At this stage,
This value of α is called Angle of Limiting Friction.
Belt Friction
𝑻𝟐
= 𝒆𝝁𝒔 ∙𝜷
𝑻𝟏
Notes:
• In the equation, T2 will always be larger than T1.
• β must be in radians and may be larger than 2π.
• If a rope is wrapped around a post n times, β = 2πn
• If the belt is actually slipping, use μk.
Sample Problems
1.The coefficient of static and kinetic friction between the 90-kg crate and the slanting floor (ϴ= 10°) are μS =
0.45 and μK = 0.30. If the angle α=20°, what tension (N) must the person exert on the rope to move the crate at
constant speed.
A. 436.8
B. 569.9
C. 397.3
D. 352.4
2. Determine the minimum horizontal force P required to hold the 150-kg block shown. The coefficient of
friction between the block and the inclined plane is 0.45. Angleϴ= 30°.
A. 2041.7 N
B. 368.9 N
C. 148.7 N
D. 1254.5 N
3. Determine the horizontal force P required to start the 100-kg block up the plane as shown in the previous
problem. The coefficient of friction between the block and the inclined plane is 0.30. Angleϴ= 35°.
A. 1587.9
B. 1241.7 N
C. 324.3
D. 632.7
Situation 1: The 150-kg block shown is resting on a horizontal force. The block is pushed by a force P acting
at angleϴ= 40° with the horizontal. The coefficient of friction between the block and the floor is μ = 0.45.
4. If P = 1000 N, compute the magnitude (N) of the friction force at the contact surface between the block and
the floor.
A. 832
B. 1015
C. 951
D. 766
5. Determine the maximum force P (N) that can be applied without causing the block to move.
A. 1388.3
B. 1256.9
C. 1425.7
D. 1069.9
6. If the force P = 1500 N, determine the minimum coefficient of static friction that will not cause the block the
move.
A. 0.521
B. 0.472
C. 0.325
D. 0.426
Situation 2: The 6-m long ladder weighing 720 N is shown. The coefficient of static friction between the ladder
and the surface at A and B is 0.20.
7. Determine the minimum horizontal force P (N) that must be exerted at point C 0=30° to prevent the ladder
from sliding.
A. 418.4
B. 456.8
C. 397.4
D. 489.6
8. Compute the resultant reaction (N) at A.
A. 612
B. 624
C. 639
D. 664
9. Compute the resultant reaction (N) at B.
A. 532.4
B. 569.8
C. 551.5
D. 540.8
Situation 3: The uniform 50-kg plank shown is resting on friction surfaces at A and B. The plank is 4 m long,
the angleϴ= 42˚, and the coefficients of static friction at A and B are 0.20 0.40, respectively. A 90-kg man
starts walking from A toward B.
10. Neglecting the weight of the plank, determine the distance x (meters) when the plank will start to slide.
A. 1.24
B. 1.32
C. 1.56
D. 1.41
11. Considering the weight of the plank, determine the distance x (meters) when the plank will start to slide.
A. 1.08
B. 1.18
C. 1.21
D. 0.87
12. Considering the weight of the plank compute the resultant reaction (N) at B.
A. 515.2
B. 478.3
C. 889.4
D. 907.1
Situation 4 - For the region bounded as shown,
13. What is the area of the region (in mm^2)?
A. 10043
B. 10432
C. 11822
D. 12282
14. Determine the distance of the centroid of area from
the y-axis (in mm).
A. 35.25
B. 37.93
C. 36.02
D. 39.45
15. Determine the distance of the centroid of the region
from the x-axis (in mm).
A. 32.00
B. 34.98
C. 32.04
D. 36.02
Given the parabola 3x2 + 40y – 4800 = 0.
16. What is the area bounded by the parabola and the X-axis?
A. 6 200 unit2
B. 8 300 unit2
C. 5 600 unit2
D. 6 400 unit2
17. What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit4
B. 18 362 000 unit4
C. 11 100 000 unit4
D. 21 065 000 unit4
18. What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units