FORCE as a VECTOR II
(Applications of Geometric Vectors)
A.
STATE of EQUILIBRIUM
Consider the resultant of three forces acting on an object as shown:
𝐹𝐹11
What is the resultant?
𝐹3
In what state is the object?
𝐹2
A closed path is formed.
For a system to be in equilibrium, it is necessary that a closed path be formed.
Therefore, the triangle inequality must hold true for the forces (ie) the largest
force must be less than or equal to the sum of the other 2 forces.
Recall the triangle inequality:
Ex 
𝑐 ≤ 𝑎 + 𝑏
Identify which of the following sets of forces acting on an object could
produce equilibrium:
a)
7N, 5N, 15N
b)
11N, 10N, 19N
B.
TENSION PROBLEMS
Ex 
A particle of mass 20kg is suspended by two strings each 10cm long.
The top ends are 15cm apart. Determine the tension in the strings.
Ex 
A disco ball is suspended from the ceiling by two wires that make angles of
20o and 30o with the ceiling. If the ball weighs 12kg, determine the tensions
in the wires.
C.
RAMP PROBLEMS
There are three forces to consider when an object rests on a (frictionless) ramp:
1.
2.
3.
the downward force of gravity
the normal force perpendicular to the surface of the ramp
the applied force parallel to the ramp
The above three forces form a closed path and keep the object stationary.
Ex 
A 20kg trunk rests on a ramp inclined at 15o to the ground. Determine the
force applied parallel to the ramp that would prevent the trunk from moving.
15o
Homework:
p.362–364
#3, 6, 10, 11, 16, 17