Page 211 - Schaum's Outline of Theory and Problems of Applied Physics

196 FLUIDS AT REST [CHAP. 16

SOLVED PROBLEM 16.15
A hydraulic press has an input cylinder 2 cm in diameter and an output cylinder 12 cm in diameter.
(a) Assuming 100 percent efficiency, find the force exerted by the output piston when a force of 80 N is
applied to the input piston. (b) If the input piston is moved through 10 cm, how much is the output piston
moved?
(a) At 100 percent efficiency the actual mechanical advantage equals the IMA, and
F out A out
=
F in A in
2
2
Since A = πr = πd /4,
d out (12 cm)
2 2
F out = F in 2 = (80 N) = 2880 N
d in (2cm) 2
2 2
A in d in (2cm)
(b) L out = L in = L in 2 = (10 cm) 2 = 0.28 cm
A out d out (12 cm)
Multiple-Choice Questions

16.1. The pressure on the bottom of a vessel filled with liquid does not depend upon the
(a) height of the liquid
(b) area of the liquid surface
(c) liquid density
(d) acceleration of gravity

16.2. Buoyancy occurs because, as the depth in a fluid increases, the
(a) density increases (c) pressure increases
(b) density decreases (d) pressure decreases
16.3. The pressure of the atmosphere at sea level corresponds to which one or more of the following?

(a) 1.013 Pa (c) 1013 mbar
(b) 98 N/m 2 (d) 14.7 lb/in. 2

16.4. The output piston of a hydraulic press cannot exceed the input piston’s
(a) displacement (c) work
(b) velocity (d) force

16.5. A 2-N stone dropped into a lake sinks. The buoyant force on the stone is
(a) 0 (c) 2 N
(b) less than 2 N (d) more than 2 N

16.6. Seawater has a density 3 percent greater than that of freshwater. A boat will float
(a) higher in seawater than in freshwater
(b) at the same level in seawater and in freshwater
(c) lower in seawater than in freshwater
(d) any of the above, depending on the shape of the boat’s hull

3
3
16.7. The density of copper is 8.9 × 10 kg/m . The volume of a 15-g copper bracelet is
(a) 0.6 cm 3 (c)17 cm 3
(b) 1.7 cm 3 (d) 134 cm 3