1. Physics 121

2. 9. Equilibrium and Elasticity
9.1 Statics: Forces in Equilibrium
9.2 Conditions for Equilibrium
9.3 Solving Statics Problems
9.4 Measurement and Uncertainty
9.5 Stability and Balance
9.6 Elasticity: Stress and Strain

3. What is the tension in the string?
Example The String
What is the tension in the string?
300
2 kg
W = 1 kg

4. The Conditions for Equilibrium
 Fx = 0
 Fy = 0
  = 0
300
2 kg
W = 1 kg

5. (2)(10)(L) + (1)(10)(L/2) = (T sin 30)(L)
Solution The String
  = 0
(2)(10)(L) + (1)(10)(L/2) = (T sin 30)(L)
T = 50 N

6. Are there any (reaction) forces at the hinge?
Example The Hinge
Are there any (reaction) forces at the hinge?
300
2 kg
W = 1 kg

7. All the forces on the beam are shown
Solution The Hinge
All the forces on the beam are shown
Solution continues on the next slide
20 N
10 N H V
T sin 30
T cos 30

8.  Fx = 0 So H = T cos 300 or H = 50 * 0.87 or H = 44 N
Solution The Hinge
 Fx = 0 So H = T cos 300 or H = 50 * 0.87 or H = 44 N
 Fy = 0 So V + 50 sin 300 = or V = 5 N
20 N
10 N H V
T sin 30
T cos 30

9. Young’s Modulus = Stress / Strain
Elasticity
Stress = Force / Area
Strain =  L / L
Young’s Modulus = Stress / Strain

10. Example The Piano
A 1.6 m long steel piano wire has a diameter of 0.20 cm. How great is the tension in the wire if it stretches 0.30 cm when tightened.
[ Young’s Modulus for steel is E = 2.0 x N / m2 ]

11. Solution The Piano
strain =  L / L = 0.003/1.6 = x m
stress = F / A = F/  r2 = F /3 .1 x m2
E = stress / strain
2.0 x = F /(3 .1 x )(1.875 x )
F = 1200 N

12. That’s all folks!