工程力學
Exam. # 4（01/06/2023）
1. (15pts) The 20-N block A and the 30-N block B are supported by an incline that is held in the position
as shown in Fig. 1. Knowing that the coefficient of static friction is 0.15 between all surfaces of
contact, determine the value of q for which motion is impending.
2. (15pts) Prove the following relation of the V-belt (Fig. 2):
T2/T1
where T1 and T1 are the tensions, µ s is the coefficient of static friction, b is the angle of belt contact,
and a is angle of the V-shape.
3. (10pts) Block A supports a pipe column and rests as shown in Fig. 3 on wedge B. Knowing that the
coefficient of static friction at all surfaces of contact is 0.25 and that q = 45°, determine the smallest
force P required to raise block A.
4. (20pts) The position of the automobile jack shown in Fig. 4 is controlled by a screw ABC that is
single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread has a pitch
of 2 mm and a mean diameter of 7.5 mm. If the coefficient of static friction is 0.15, determine the
magnitude of the couple M that must be applied to raise the automobile.
5. (10pts) Determine by direct integration the moment of inertia of the shaded area as shown in Fig. 5
with respect to the x axis.
6. (10pts) Two 20-mm steel plates are welded to a rolled S section as shown in Fig. 6. Determine the
moments of inertia of the combined section with respect to the centroidal x and y axes. For the S
section, A = 6010 mm2, Ix = 90.3 ´ 106 mm4, Iy = 3.88 ´ 106 mm4.
7. (20pts) The area shown in Fig. 7 is revolved about the x axis to form a homogeneous solid of
revolution of mass m. Determine by direct integration the mass moment of inertia of the solid with
respect to (a) the x axis, (b) the y axis. Express your answers in terms of m and the dimensions of the
solid.
Fig. 2
Fig. 3
Fig 1
Fig. 4
Fig. 5
Fig. 6
Fig. 7