Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration, but it is important to remember that these conditions are relative. For example, an object may be at rest when viewed from our frame of reference, but the same object would appear to be in motion when viewed by someone moving at a constant velocity. We now make use of the knowledge attained in
Newton’s Laws of Motion , regarding the different types of forces and the use of free-body diagrams, to solve additional problems in
particle equilibrium .
Different tensions at different angles
Consider the traffic light (mass of 15.0 kg) suspended from two wires as shown in
[link] . Find the tension in each wire, neglecting the masses of the wires.
A traffic light is suspended from two wires. (b) Some of the forces involved. (c) Only forces acting on the system are shown here. The free-body diagram for the traffic light is also shown. (d) The forces projected onto vertical (
y ) and horizontal (
x ) axes. The horizontal components of the tensions must cancel, and the sum of the vertical components of the tensions must equal the weight of the traffic light. (e) The free-body diagram shows the vertical and horizontal forces acting on the traffic light.
Strategy
The system of interest is the traffic light, and its free-body diagram is shown in
[link] (c). The three forces involved are not parallel, and so they must be projected onto a coordinate system. The most convenient coordinate system has one axis vertical and one horizontal, and the vector projections on it are shown in
[link] (d). There are two unknowns in this problem (
and
), so two equations are needed to find them. These two equations come from applying Newton’s second law along the vertical and horizontal axes, noting that the net external force is zero along each axis because acceleration is zero.
Solution
First consider the horizontal or
x -axis:
Thus, as you might expect,
This gives us the following relationship:
Thus,
Note that
and
are not equal in this case because the angles on either side are not equal. It is reasonable that
ends up being greater than
because it is exerted more vertically than
Now consider the force components along the vertical or
y -axis:
This implies
Substituting the expressions for the vertical components gives
There are two unknowns in this equation, but substituting the expression for
in terms of
reduces this to one equation with one unknown:
which yields
Solving this last equation gives the magnitude of
to be
Finally, we find the magnitude of
by using the relationship between them,
, found above. Thus we obtain
Significance
Both tensions would be larger if both wires were more horizontal, and they will be equal if and only if the angles on either side are the same (as they were in the earlier example of a tightrope walker in
Newton’s Laws of Motion .
Questions & Answers
Biology is a branch of Natural science which deals/About living Organism.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
