Page 156 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 11] EQUILIBRIUM 141

Let us consider the plywood piece to be made up of two sections, one a rectangle 3 m long and 1 m wide and
the other a square 1 m on each side. The centers of gravity of these sections are at their geometric centers, as in
Fig. 11-16(b). If the plywood has a mass of m 0 per square meter, section 1 has a mass of 3m 0 and section 2 has a
2
mass of m 0 , since their respective areas are 3 and 1 m . The x and y coordinates of the center of gravity of the entire
plywood piece are therefore

m 1 x 1 + m 2 x 2 (3m 0 )(0.5m) + (m 0 )(1.5m)
X = = = 0.75 m
m 1 + m 2 3m 0 + m 0
m 1 y 1 + m 2 y 2 (3m 0 )(1.5m) + (m 0 )(0.5m)
Y = = = 1.25 m
m 1 + m 2 3m 0 + m 0

m 1 = 3 m 0 m 2 = m 0
x 1 = 0.5m x 2 = 1.5m
y 1 = 1.5m y 2 = 0.5m

Multiple-Choice Questions

11.1. Which one or more of the following sets of horizontal forces could leave an object in equilibrium?
(a) 5, 10, and 20 N (c) 8,8,and8N
(b) 6, 12, and 18 N (d) 2, 4, 8, and 16 N

11.2. A box of weight w is supported by two ropes. The magnitude of
(a) the tension in each rope must be w/2
(b) the tension in each rope must be w
(c) the vector sum of the tensions in both ropes must be w
(d) the vector sum of the tensions in both ropes must be greater than w

11.3. The torques that act on an object in equilibrium have a vector sum of zero about
(a) one point only (c) all points
(b) one or more points (d) any of the above, depending on the situation
11.4. The point about which torques are calculated when studying the equilibrium of an object

(a) must pass through the center of gravity of the object
(b) must pass through one end of the object
(c) must be located inside of the object
(d) may be located anywhere
11.5. A 250-N box hangs from a rope. If the box is pushed with a horizontal force of 145 N, the angle between the rope
and the vertical is
(a) 30 ◦ (c) 60 ◦
(b) 45 ◦ (d) 75 ◦

11.6. A box is suspended by a rope. When a horizontal force of 100 N acts on the box, it moves to the side until the rope
◦
is at an angle of 20 with the vertical. The weight of the box is
(a) 36 N (c) 275 N
(b) 106 N (d) 292 N