Forces in Two Dimensions

1
Chapter 5

• Forces in Two Dimensions

Equilibrium
2
Equilibrium Occurs when the sum of the net
force on an object is zero.
If ABC0 Then ABC are at equilibrium
C
B
B
A
C
A
3
Finding the Equilibrant Force
The force causing equilibrium for vectors AB
would be the resultant of vectors AB in the
opposite direction.
B
A
B
Resultant
A
Resultant in the opposite direction
4
Equilibrium Problem Solving

• The sum of the net forces must equal zero
• Draw all forces on the object
• Break forces into (x,y) components
• Combine forces that are in the same direction

5
Example A 168N sign is hanging by two ropes that
make 22.5 degree angles with the horizontal.
What is the tension in the ropes?
22.5
22.5
Fizics is phun!!!
First identify all the forces involved.
6
22.5
22.5
Fizics is phun!!!
Fa
Fb
Fw
7
Fa
Fb
Break forces into horizontal and vertical
components.
Fw
Fa
Fb
Fay
Fby
Fbx
Fax
Fw
8
Fa
Fb
Fay
Fby
Fbx
Fax
Fw
Fa
FayFasin22.5 FaxFacos22.5
Fay
Fax
Fb
FbyFbsin22.5 FbxFbcos22.5
Fby
Fbx
9
Resolve Forces By Direction
Fa
Fb
Fay
Fby
Fbx
Fax
Fnety0 FnetyFasin22.5Fbsin22.5-Fw 02Fasin22.5-
Fw 2Fasin22.5Fw Fa168N/2sin22.5 Fa220NFb
Fnetx0 Fnetx-FaxFbx 0-Facos22.5Fbcos22.5 Faco
s22.5Fbcos22.5 FaFb
Fw
10
Forces on an Object on an Incline
Remember mFf/FN So FfmFN
FN
Ff
Fwmg
If FpFf the
object will accelerate down the incline
because FnetFp-Ffma
q
Fp
FNFwcosq
q
Fw
FpFwsinq
11
Homework

• Pages 140-144
• Numbers 49,51,57,62,73,80,81,83,85,88,89,
  90,92,94,95,97,98,100,105