An Introduction to Statics
Unit 3, Presentation 4
What is Statics?

Statics: The study of the forces
associated with objects at equilibrium
with each other.

No motion with objects in equilibrium

All accelerations are equal to 0

All net forces are equal to 0
Statics Example Problem
A traffic light of mass 50 kg hangs from a vertical cable tied
to two other cables that are fastened to a support (see
below). The upper cables make angles of 37.0° and 53.0°
with the horizontal. Find the tension in each of the three
cables.
37.0°
53.0°
T1
T2
T3
Statics Example Problem Cntd.
Consider drawing free body diagrams for two objects: the
stop light and the knot connecting the three cables.
FBD for the Stop Light
T3
mg
T3  m g  m a  0
T3  m g  50(9.8)  490N
FBD for the knot
T1
T2
T3
Must break down vectors T1
and T2 into x and y
components.
Statics Example Problem Cntd.
37.0°
T1
T1y
T1x
T1x  T1 cos37.0
T1y  T1 sin 37.0
53.0°
T2
T2y
T2x
T2 x  T2 cos53.0
T2 y  T2 sin 53.0
Statics Example Problem Cntd.
x-direction
y-direction
T2 cos53  T1 cos37  0 T2 sin 53  T1 sin 37  m g  0
Note: Two equations, two
unknowns…solve a system
of linear equations.
T2 sin 53  T1 sin 37  m g
T2 sin 53  T1 sin 37  50(9.8)  490N
1.33T1 (sin 53)  T1 sin 37  490
We’ll use substitution.
T1 cos 37
T2 
 1.33T1
cos 53
1.06T1  0.60T1  490
1.66T1  490
T1  295N
T2  1.33T1  1.33(295N )  392N
Another Statics Example Problem
A sled is tied to a tree on a frictionless, snow-covered hill, as
shown below. If the sled weighs 77.0 N, find the force
exerted by the rope on the sled and the magnitude of the
normal force exerted by the hill on the sled.
Fn
T
mg
30.0°
Another Statics Example Problem
x-direction
T  m gsin   0
T  m gsin 
T  77(sin 30)  38.5 N
T ?
FN  ?
m g  77.0 N
  30.0
y-direction
FN  m g cos  0
FN  m gsin 
FN  77(cos30)  66.7 N