Physics 151: Lecture 26 Today’s Agenda Today’s Topics Statics (Chapter 12)

Statics: See text: 12.1-3 Objects are at rest (Static) when : AND No translation No rotation When choosing axes about which to calculate torque, we can be clever and make the problem easy....

Example 2 The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W stands for the weight. In which diagram(s) is the wheel in equilibrium? a. A b. B c. C d. D e. A and C

Example 4 A bridge of length 50.0 m and mass 8.00 x 104 kg is supported on a smooth pier at each end as in Figure below. A truck of mass 3.00 x 104 kg is located 15.0 m from one end. What are the forces on the bridge at the points of support? Solution : nA = 5.98 x 105 N nB = 4.80 x 105 N :

Example 5 A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable? a. 610 lb b. 540 lb c. 640 lb d. 570 lb e. 2000 lb

Example 3 A square of side L/2 is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C’. The distance from C to C’ is :

Lecture 26, Act 1 Statics A box is placed on a ramp in the configurations shown below. Friction prevents it from sliding. The center of mass of the box is indicated by a white dot in each case. In which cases does the box tip over ? (a) all (b) 2 & 3 (c) 3 only 3 1 2

Lecture 26, Act 1 Addendum What are the torques ?? (where do the forces act ?) t goes to zero at critical point t switches sign at critical point t always zero rN N tN  rG mg tg  rf f tf = 0

Example 7 Two identical uniform bricks of length L are placed in a stack over the edge of a horizontal surface with the maximum overhang possible without falling, as in Figure below. Find the distance x. SOLUTION: If the CM of the two bricks does not lie over the edge, then the bricks balance. If the lower brick is placed L/4 over the edge, then the second brick may be placed so that its end protrudes 3L/4 over the edge.

Example 6 A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor? a. 43 lb b. 34 lb c. 38 lb d. 47 lb e. 24 lb

Recap of today’s lecture Today’s Topics Statics (Chapter 12)

Lecture 24, Act 1 Statics Suppose you have a gyroscope that is supported on a gymbals such that it is free to move in all angles, but the rotation axes all go through the center of mass. As pictured, looking down from the top, which way will the gyroscope precess? (a) clockwise (b) counterclockwise (c) it won’t precess 

Lecture 24, Act 1 Statics Remember that W = t/L. So what is t? t = r x F r in this case is zero. Why? Thus W is zero. It will not precess. At All. Even if you move the base. This is how you make a direction finder for an airplane.  Answer (c) it won’t precess