1. Physics 7C lecture 15 Quilibrium
Thursday November 19, 8:00 AM – 9:20 AM
Engineering Hall 1200

2. Introduction
Many bodies, such as bridges, aqueducts, and ladders, are designed so they do not accelerate.
Real materials are not truly rigid. They are elastic and do deform to some extent.
We shall introduce concepts such as stress and strain to understand the deformation of real bodies.

3. Conditions for equilibrium
First condition: The sum of all the forces is equal to zero:
Fx = Fy = Fz = 0
Second condition: The sum of all torques about any given point is equal to zero.

4. Conditions for equilibrium
First condition: The sum of all the forces is equal to zero:
Fx = Fy = Fz = 0
Second condition: The sum of all torques about any given point is equal to zero.

5. Conditions for equilibrium
First condition: The sum of all the forces is equal to zero:
Fx = Fy = Fz = 0
Second condition: The sum of all torques about any given point is equal to zero.

6. Conditions for equilibrium
First condition: The sum of all the forces is equal to zero:
Fx = Fy = Fz = 0
Second condition: The sum of all torques about any given point is equal to zero.

7. C. a thrown baseball that does not rotate as it sails through the air
Q11.1
Which of the following situations satisfies both the first condition for equilibrium (net force = 0) and the second condition for equilibrium (net torque = 0)?
A. an automobile crankshaft turning at an increasing angular speed in the engine of a parked car
B. a seagull gliding at a constant angle below the horizontal and at a constant speed
C. a thrown baseball that does not rotate as it sails through the air
D. more than one of the above
E. none of the above
Answer: B

8. A11.1
Which of the following situations satisfies both the first condition for equilibrium (net force = 0) and the second condition for equilibrium (net torque = 0)?
A. an automobile crankshaft turning at an increasing angular speed in the engine of a parked car
B. a seagull gliding at a constant angle below the horizontal and at a constant speed
C. a thrown baseball that does not rotate as it sails through the air
D. more than one of the above
E. none of the above

9. Center of gravity
We can treat a body’s weight as though it all acts at a single point— the center of gravity.
If we can ignore the variation of gravity with altitude, the center of gravity is the same as the center of mass.

10. Walking the plank
find the stable positions

11. Walking the plank
find the stable positions

12. Q11.2
A rock is attached to the left end of a uniform meter stick that has the same mass as the rock. How far from the left end of the stick should the triangular object be placed so that the combination of meter stick and rock is in balance?
less than 0.25 m
0.25 m
C. between 0.25 m and 0.50 m
D m
E. more than 0.50 m
Answer: B

13. A11.2
A rock is attached to the left end of a uniform meter stick that has the same mass as the rock. How far from the left end of the stick should the triangular object be placed so that the combination of meter stick and rock is in balance?
less than 0.25 m
0.25 m
C. between 0.25 m and 0.50 m
D m
E. more than 0.50 m

14. Will the ladder slip?
find the tilt angles for stable conditions

15. Will the ladder slip?
find the tilt angles for stable conditions

16. What is the tension in the cable?
Q11.3
A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle q from the horizontal.
What is the tension in the cable?
T = w sin q
T = w cos q
C. T = w/(sin q)
D. T = w/(cos q)
E. none of the above
Answer: C

17. A11.3
A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle q from the horizontal.
What is the tension in the cable?
T = w sin q
T = w cos q
C. T = w/(sin q)
D. T = w/(cos q)
E. none of the above

18. Which of these forces is least?
A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle q from the horizontal.
Which of these forces is least?
the weight of the sign
the tension in the cable
C. the vertical force component exerted on the rod by hinge P
D. two or more of these are tied for least
Answer: C

19. A11.4
A metal advertising sign (weight w) is suspended from the end of a massless rod of length L. The rod is supported at one end by a hinge at point P and at the other end by a cable at an angle q from the horizontal.
Which of these forces is least?
the weight of the sign
the tension in the cable
C. the vertical force component exerted on the rod by hinge P
D. two or more of these are tied for least

20. Equilibrium and pumping iron
Follow Example 11.4 using Figure below.