Whenever we have two-dimensional vector problems in which no two vectors are parallel, the easiest method of solution is to pick a convenient coordinate system and project the vectors onto its axes. In this case the best coordinate system has one axis horizontal and the other vertical. We call the horizontal the
-axis
and the vertical the
-axis.
Solution
First, we need to resolve the tension vectors into their horizontal and vertical components. It helps to draw a new free-body diagram showing all of the horizontal and vertical components of each force acting on the system.
When the vectors are projected onto vertical and horizontal axes, their components along those axes must add to zero, since the tightrope walker is stationary. The small angle results in
being much greater than
.
Consider the horizontal components of the forces (denoted with a subscript
):
The net external horizontal force
, since the person is stationary. Thus,
Now, observe
[link] . You can use trigonometry to determine the magnitude of
and
. Notice that:
Equating
and
:
Thus,
as predicted. Now, considering the vertical components (denoted by a subscript
), we can solve for
. Again, since the person is stationary, Newton’s second law implies that net
. Thus, as illustrated in the free-body diagram in
[link] ,
Observing
[link] , we can use trigonometry to determine the relationship between
,
,
and
.
As we determined from the analysis in the horizontal direction,
:
Now, we can substitute the values for
and
, into the net force equation in the vertical direction:
and
so that
and the tension is
Discussion
Note that the vertical tension in the wire acts as a normal force that supports the weight of the tightrope walker.
The tension is almost six times the 686-N weight of the tightrope walker. Since the wire is nearly horizontal, the vertical component of its tension is only a small fraction of the tension in the wire. The large horizontal components are in opposite directions and cancel, and so most of the tension in the wire is not used to support the weight of the tightrope walker.
If we wish to
create a very large tension, all we have to do is exert a force perpendicular to a flexible connector, as illustrated in
[link] . As we saw in the last example, the weight of the tightrope walker acted as a force perpendicular to the rope. We saw that the tension in the roped related to the weight of the tightrope walker in the following way:
We can extend this expression to describe the tension
created when a perpendicular force (
) is exerted at the middle of a flexible connector:
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills