Mechanical Technology 1
Tutorial Questions 1A
1. State the laws of
 Static friction
 Kinetic or Dynamic friction
 Solid friction
 Fluid friction
2. Explain the two types of friction between lubricated surfaces
3. Explain and derive the equation for the angle of repose
4. A body of mass (m), is placed on an inclined plane with an angle α to the horizontal. If
the body just begin to slip due to the action of its own weight, using a well-drawn
diagram indicating all the forces acting, derive the equation for the coefficient of
friction µ.
5. Two boxes, one on top of the other are being lowered down a ramp by a rope as shown
in figure 1 below. The boxes move together at a constant speed of 15cm/s. The
coefficient of kinetic friction between the ramp and the lower box is 0.44 and the
coefficient of static friction between the two boxes is 0.8. (a) What force is required to
accomplish this task? (b) What is magnitude and direction of the friction force on the
upper box
[Ans: 57.1 N; 146 N up the ramp]
Figure 1
6. A block of mass m1 = 7.4 kg, on a plane
T
Figure 2
inclined at angle  = 30 to horizontal, is
connected by a cord over a massless,
m1
frictionless pulley to a sphere of mass m2
a
hanging vertically as shown in figure 2. The
block is moving down the slope and has
m2
acceleration of magnitude a = 2.1 m s–2
directed down the slope. A kinetic friction force of magnitude Fk is exerted by the
plane on the block, and the tension in the cord is T = 14.3 N.
(a) Draw a free-body diagram of the block, showing all forces acting on it as labelled
arrows.
(b) Find the value of N, the magnitude of the normal force of the plane on the block.
(c) Calculate the value of the kinetic friction coefficient μk between the plane and the block.
(d) Find the mass m2 of the sphere.
7. A 20.0 kg block rests on a horizontal surface, were the coefficients of static and kinetic
friction between the block and surface are 0.8 and 0.6 respectively. A horizontal string
is attached to the block and a constant tension T is maintained in the string. Determine
the force of friction acting on the block if
(a) T = 17.0 N (b) T = 17.0 N, but the string is now at an angle of 400 with the horizontal.
[ Ans; 156.96N; The friction is the same]
8. A 5-kg block sits on a 30 degree incline. It is attached to string that is thread over a
pulley mounted at the top of the incline. A 7.5-kg block hangs from the string.
a) Calculate the tension in the string if the acceleration of the system is 1.2 m/s/s
b) Calculate the coefficient of kinetic friction.
[Ans: 64.5 N µk = 0.8]
9. Two objects are connected by a massless string, as shown in figure 3. The incline has
coefficients of static and kinetic friction of 0.42 and 0.35 and pulley is frictionless. Find
the acceleration of the objects and the tension in the string for Ө = 300, m1 = m2 = 5 kg.
[ Ans: 0.975 m/s2; 44.188N]
Figure 3
10. In the diagram shown in figure 2, has a weight of 1.5KN and the incline has
coefficients of static and kinetic friction of 0.25 and 0.20 respectively. Determine
whether the block is equilibrium, and find the friction force.
[Ans: The object
slides down; 200 N]
Figure 4
11. In the system shown in Figure 2, the pulley is smooth and the coefficient of friction
between the other contact surfaces is 0.2. Determine the magnitude of force P to impend
the motion.
Figure 5
12. A body weighing 200 kN is to be raised by means of the wedges A and B as shown in Figure 6.
Find the value of force P for impending motion of block C upwards, if coefficient of friction is
0.20 for all contacts surfaces. Weights of the wedges may be neglected.
Figure 6
13. Determine the force P, required to start the movement of wedge as shown in figure 7.
The angle of friction for all surfaces of contact is 18o.
Figure 7
14 Figure 7 shows bock A with weight of 4 kN and block B with weight of 2.5 kN
respectively, are connected by a wire passing over a smooth frictionless pulley. The
value of P in the system is 4.5 kN. The coefficient of friction between the all contact
surfaces is 0.25. (a) Draw the free body diagrams for both blocks (b) Determine the
angle ϴ, if the system just experience an impending motion to the right of the system.
[Hint: cos2   1  sin 2  ]
Figure 7
ϴ
15 The three flat blocks are positioned on the 30o incline as shown in figure 8, and a force,
P parallel to the incline is applied to the middle block. The upper and bottom blocks are
prevented from moving by wires which that are attached to the fixed support as shown
in figure 8. The coefficients of static friction for each of the three pairs of mating
surfaces are indicated in the figure. Determine the tensions (T1 and T2) in each wire and
the maximum value of force P, which is required before any slipping takes place.
T1
T2
Figure 8