Problem 1.14
If the weight of a certain object on the surface of the Earth is 0.254 lb, determine its mass in kilograms.
Problem 1.15
If the mass of a certain object is 69.1 kg, determine its weight on the surface of the Earth in pounds.
Solution
Problem 1.16
Use Eq. (1.11) on p. 16 to compute a theoretical value of acceleration due to gravity
g
, and compare this
value with the actual acceleration due to gravity at the Earth’s poles, which is about 0.3% higher than the
value reported in Eq. (1.12). Comment on the agreement.
Problem 1.17
Two identical asteroids travel side by side while touching one another. If the asteroids are composed
of homogeneous pure iron and are spherical, what diameter in feet must they have for their mutual
gravitational attraction to be 1 lb?
Solution
Problem 1.18
The mass of the Moon is approximately
7:35 1022
kg, and its mean distance from the Earth is about
3:80 108
km. Determine the force of mutual gravitational attraction in newtons between the Earth and
Moon. In view of your answer, discuss why the Moon does not crash into the Earth.
Solution
Problem 1.19
Consider a spacecraft that is positioned directly between the Earth and Moon. The mass of the Moon is
approximately
7:35 1022
kg, and at the instant under consideration, the Moon is
3:80 108
km from
Earth. Determine the distances the spacecraft must be from the Earth and Moon for the gravitational force
of the Earth on the spacecraft to be the same as the gravitational force of the Moon on the spacecraft.
Solution
Statics 2e 25
Problem 1.20
The gravity tractor, as shown in the artist’s rendition, is a proposed spacecraft
that will fly close to an asteroid whose trajectory threatens to impact the Earth.
Due to the gravitational attraction between the two objects and a prolonged
period of time over which it acts (several years), the asteroid’s trajectory is
changed slightly, thus hopefully diverting it from impacting the Earth. If the
gravity tractor’s weight on earth is
20;000 lb
and it flies with its center of
gravity
160 ft
from the surface of the asteroid, and the asteroid is homogeneous
pure iron with
1290 ft
diameter spherical shape, determine the force of mutual
attraction. Idealize the gravity tractor to be a particle.
Problem 1.21
If a person standing at the first-floor entrance to the Sears Tower (recently renamed Willis Tower) in
Chicago weighs exactly 150 lb, determine the weight while he or she is standing on top of the building,
which is 1450 ft above the first-floor entrance. How high would the top of the building need to be for the
person’s weight to be 99% of its value at the first-floor entrance?
Solution
Problem 1.22
The specific weights of several materials are given in U.S. Customary units. Convert these to specific
weights in SI units (kN/m3), and also compute the densities of these materials in SI units (kg/m3).
(a) Zinc die casting alloy, D0:242 lb/in.3.
(b) Oil shale (30 gal/ton rock), D133 lb/ft3.
(c) Styrofoam (medium density), D2:0 lb/ft3.
(d) Silica glass, D0:079 lb/in.3.
Solution
Problem 1.23
The cross-sectional dimensions for a steel
W10 22
wide-flange I beam are
shown (the top and bottom flanges have the same thickness). The beam is
18 ft
long (into the plane of the figure), and the steel has
490 lb=ft3
specific
weight. Determine the cross-sectional dimensions in millimeters (show these
on a sketch), the length in meters, and the mass of the beam in kilograms.
Solution
Statics 2e 31
Problem 1.24
The cross-sectional dimensions of a concrete traffic barrier are shown. The barrier
is
2
m long (into the plane of the figure), and the concrete has
2400 kg=m3
density.
Determine the cross-sectional dimensions in inches (show these on a sketch), the
length in feet, and the weight of the barrier in pounds.
Solution
Problem 1.25
The densities of several materials are given in SI units. Convert these to densities in U.S. Customary units
(slug/ft3), and also compute the specific weights of these materials in U.S. Customary units (lb/ft3).
(a) Lead (pure), D11:34 g/cm3.
(b) Ceramic (alumina Al2O3), D3:90 Mg/m3.
(c) Polyethylene (high density), D960 kg/m3.
(d) Balsa wood, D0:2 Mg/m3.
Solution
Problem 1.26
A Super Ball is a toy ball made of hard synthetic rubber called Zectron. This material has a high coefficient
of restitution so that if it is dropped from a certain height onto a hard fixed surface, it rebounds to a
substantial portion of its original height. If the Super Ball has 5 cm diameter and the density of Zectron is
about 1.5 Mg/m
3
, determine the weight of the Super Ball on the surface of the Earth in U.S. Customary
units.
Problem 1.27
An ice hockey puck is a short circular cylinder, or disk, of vulcanized rubber with 3.00 in. diameter and
1.00 in. thickness, with weight between 5.5 and 6.0 oz (
16 oz D1lb
). Compute the range of densities for
the rubber, in conventional SI units, that will provide for a puck that meets these specifications.
Problem 1.28
Convert the angles given to the units indicated.
(a) Convert D35:6ıto rad.
(b) Convert D.1:08 103/ıto mrad.
(c) Convert D4:65 rad to degrees.
(d) Convert D0:254 mrad to degrees.
Problem 1.29
Many of the examples of failure discussed in Section 1.7 have common causes, such as loads that were not
anticipated, overestimation of the strength of materials, unanticipated use, etc. Using several paragraphs,
identify those examples that have common causes of failure and discuss what these causes were.
Solution