1J40.70 Crane Boom
Abstract
When an object hangs at equalibrium there is no net force acting on it. Although there may be many different
forces acting on the object, the direction and magnitude of the forces are such that they all sum to zero. The
crane boom demonstrates this concept by hanging a mass in such a way that three forces are acting on it, each
in a different direction. By separating each force vector into horizontal and vertical components it can be seen
that they do in fact sum to zero.
Picture
Equipment
• Ringstand
• Hooked weight
• Nylon string
• Two spring scales
• Protractor
• Measuring stick with hooks
Procedure
Clamp the measuring stick midway up the ringstand. Using the nylon string, attach the spring scale to the
hook at the top of the measuring stick and tie the other end to the top of the ringstand. Note that tape can
be used in order to prevent the string from slipping down the ringstand. Next tie a piece of nylon string to the
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hooked weight and fix it to the other hook on the top of the measuring stick. Finally adjust all of the components
so that the measuring stick, the ringstand and the spring scale resemble a right angle triangle or as close to one
as possible.
Theory
F~scale
F~ruler
F~g
There are three relevant forces in this set up: the force of gravity F~g , the tension force of the spring scale
F~scale , and the reaction force (thrust) of the ruler F~ruler . These vectors form a right angle triangle, so the
magnitude of the force that the ruler exerts can be easily calculated if the magnitudes of the other two forces are
known.
F~ruler
F~g
F~scale
By using the Pythagorean theorem it can be seen that
q
Fruler = Fg 2 + Fscale 2
. The magnitude of the force exerted by the scale can simply by read off of the spring scale and the force of
gravity can be calculated as
Fg = mg
where m is the mass of the weight and g is the acceleration due to gravity. Therefore the force exurted by the
ruler can be rewritten as
q
2
Fruler = (mg) + Fscale 2
.
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