Torque and Static Equilibrium
Example 1
A child of
mass m is supported on a light plank by his parents, who exert the forces 
and 
as
indicated. Find the forces required to keep the plank in static equilibrium.
Use the right end of the plank as the axis of rotation.
Example 2
A 5.00 m long diving board of negligible mass is supported by two pillars. One pillar is at the left end of the diving board, as shown below; the other is 1.50 m away. Find the forces exerted by the pillars when a 90.0 kg diver stands at the far end of the board.
Example 3
A cat walks along a uniform plank that is 4.00 m long and has a mass of 7.00 kg. The plank is supported by two sawhorses, one 0.440 m from the left end of the board and the other 1.50 m from its right end. When the cat reaches the right end, the plank just begins to tip. What is the mass of the cat?
Example 4
A hiker who has
broken his forearm rigs a temporary sling using a cord stretching from
his shoulder to his hand. The cord holds the forearm level and makes
an angle of 40.0° with the horizontal where it attaches to the hand.
Consider the forearm and hand to be uniform, with a total mass of 1.31
kg and a length of 0.300 m, find (a) the tension in
the cord and (b) the horizontal and vertical components
of the force, 
,
exerted by the humorous (the bone of the upper arm) on the radius and
ulna (the bones of the forearm).
Example 5
An 85 kg person
stands on a lightweight ladder, as shown. The floor is rough; hence it
exerts both a normal force, 
,
and a frictional force, 
,
on the ladder. The wall, on the other hand, is frictionless; it exerts
only a normal force, 
.
Using the dimensions given in the figure, find the magnitudes of , ,
and .
Example 6
The little bridge in the figure has a weight of 20.0 kN, which acts at its center. Calculate the reaction forces at points A and B.
Example 7
Find the force 
in
the figure by taking torques about both point A and the point where the
lines-of-action of the two tensile forces on the ropes intersect.
Springs
The force of the spring is proportional to the displacement of the end of the spring.
Example 8
A hand exerciser utilizes a coiled spring. A force of 89.0 N is required to compress the spring by 0.0191 m. Determine the force needed to compress the spring by 0.0508 m.