2. Oct. 19, 2001 Dr. Larry Dennis, FSU Department of Physics1 Physics 2053C – Fall 2001 Chapter 9 Equilibrium

3. 2 Equilibrium Conditions An object at rest in in equilibrium.  F = ma = 0 for an object at rest.   = I  = 0 for an object at rest.

4. 3 Example Problem  F = ma = 0   = I  = 0 W = Mg F1F1 F2F2 First Draw a Free Body Diagram M = 300 kg  = 53° 

5. 4 Example Problem W = Mg F1F1 F2F2 Use Newton’s Law in both the Horizontal direction: F 1 – F 2 cos  = 0 Vertical direction: F 2 sin  – W = 0 

6. 5 Using Torques Two boys, one with mass 47 kg, the other with a mass of 63 kg are trying to balance a 3 m long teeter-totter (mass = 40 kg). Where should the center be to balance the beam? Mg N M2gM2g M1gM1g L x

7. 6 Using Torques Two boys, one with mass 47 kg, the other with a mass of 63 kg are trying to balance a 3 meter long teeter-totter (mass = 40 kg). Where should the center be to balance the beam? Mg N M2gM2g M1gM1g Select this as our axis of rotation.   = I  = 0

8. 7 Using Torques Two boys, one with mass 47 kg, the other with a mass of 63 kg are trying to balance a 3 meter long teeter-totter (mass = 40 kg). Where should the center be to balance the beam? - M 1 g*x + M 2 g*(L-x) – (L/2 – x)*Mg= 0 Mg N M2gM2g M1gM1g   = I  = 0 -  1 +  2 -  cm = 0

9. 8 Using Torques Two boys, one with mass 47 kg, the other with a mass of 63 kg are trying to balance a 3 meter long teeter-totter (mass = 40 kg). Where should the center be to balance the beam? - M 1 g * x + M 2 g * (L-x) – (x-L/2) * Mg = 0 g * L (M 2 +M/ 2 ) - gx* (M 1 + M 2 + M) = 0 g * L (M 2 + M/2) = gx* (M 1 + M 2 + M) x = L (M 2 + M/2)/(M 1 + M 2 +M) x = 3 m * (63 + 40/2) /(47+63+40)) = 3 * 83/150 = 1.66 m Mg N M2gM2g M1gM1g

10. 9 Using Torques – CAPA 1 & 2 A 20 N weight is held in the out-stretched hand of a person whose elbow-to-shoulder length is 30 cm and whose elbow-to-wrist length is 25 cm. The center of the weight is 7.0 cm from the person’s wrist. Determine the magnitude of the torque about the elbow produced by the weight. pivot W = Mg  F = ma = 0   = I  = 0  = WL L

11. 10 Using Torques – CAPA 1 & 2 A 20 N weight is held in the out-stretched hand of a person whose elbow-to-shoulder length is 30 cm and whose elbow-to-wrist length is 25 cm. The center of the weight is 7.0 cm from the person’s wrist. Determine the magnitude of the torque about the elbow produced by the weight. pivot W = Mg  F = ma = 0   = I  = 0  = WL 2 = 0.62 * 20 N  = 12.4 N L2L2

12. 11 Problems 3-5 W = Mg = T 2 T3T3 T 3 cos  -T 2 = 0 T 3 sin  – T 1 = 0  T1T1

13. 12 Next Time Chapter 9 Prepare for Quiz Discussion of CAPA Please see me with any questions or comments. See you on Monday.