Example 12.1
The Seesaw Revisited
A seesaw consisting of a uniform board of mass M and length l, supports at rest
a father and daughter with masses mf and md, respectively. The support (called
the fulcrum) is under the center of gravity of the board, the father is a distance
d from the center, and the daughter is a distance l/2 from the center.
(A) Determine the magnitude of the upward force n exerted by the support on
the board.
(B) Determine where the father
should sit to balance the system at
rest.
Example 12.2
Standing on a Horizontal Beam
A uniform horizontal beam with a length of l = 8.00 m and a weight of
Wb = 200 N is attached to a wall by a pin connection. Its far end is supported by
a cable that makes an angle of φ = 53.0º with the beam. A person of weight
Wp = 600 N stands a distance d = 2.00 m from the wall. Find the tension in the
cable as well as the magnitude and direction of the force exerted by the wall on
the beam.
Example 12.3
The Leaning Ladder
A uniform ladder of length l rests against a smooth, vertical wall. The mass of
the ladder is m, and the coefficient of static friction between the ladder and the
ground is μs = 0.40. Find the minimum angle θmin at which the ladder does not
slip.
Example 12.4
Negotiating a Curb
(A) Estimate the magnitude of the force F a person must apply to a
wheelchair’s main wheel to roll up over a sidewalk curb. This main wheel that
comes in contact with the curb has a radius r, and the height of the curb is h.
(B) Determine the magnitude and direction of R.
Example 12.5
Stage Design
In Example 8.2, we analyzed a cable used to support an actor as he swings onto
the stage. Now suppose the tension in the cable is 940 N as the actor reaches the
lowest point. What diameter should a 10-m-long steel cable have if we do not
want it to stretch more than 0.50 cm under these conditions?
Example 12.6
Squeezing a Brass Sphere
A solid brass sphere is initially surrounded by air, and the air pressure exerted
on it is 1.0 x 105 N/m² (normal atmospheric pressure). The sphere is lowered
into the ocean to a depth where the pressure is 2.0 x 107 N/m². The volume of
the sphere in air is 0.50 m³. By how much does this volume change once the
sphere is submerged?