EQUILIBRIUM/CENTER-OF-GRAVITY (honors) 1) Three boys are trying to balance on a seesaw, which consists of a rock, acting as a pivot at the center, and a very light board 3.60 m long. Two boys are already on either end. One has a mass of 50.0 kg, and the other a mass of 35.0 kg. Where should the third boy, whose mass is 25.0 kg, place himself so as to balance the seesaw? 2) A uniform, 12.0-m long girder has a mass of 500.0 kg. It rests unattached on a concrete slab with one end overhanging the edge by 5.50 m. How far can an 80.0-kg man walk out on the girder before it tips? 3) A short-wave antenna is attached to the top of a mast 20.0-m high, and exerts a tension force of 600. N on the mast. A guy wire running to the ground from a point 6.00 m below the top of the mast and inclined 60 to the horizontal supports the mast. The mast is pivoted on a hinge pin at its base. Determine the tension in the guy wire. 4) Approximately how much force must the muscle in the upper arm exert on the lower arm to hold a 7.30-kg shot? Assume the lower arm has a mass of 2.80 kg and its center-of-gravity is 12.0 cm from the elbow joint. 5) A uniform 100.-kg horizontal beam is supported at each end. A 300.-kg piano rests ¼ of the way from one end. What is the vertical force on each of the supports?
6) Calculate the forces exerted by the supports (A and B) of the 30.0-kg diving board pictured below when a 60.0-kg person stands at its tip. (the center-of-gravity of the board is at its center.) 7) Calculate the tension in the wire that supports the 30.0-kg beam shown below, and the horizontal and vertical components of the force exerted by the wall on the beam. (Beam is 2.50 meters long; CG is 1.00 meter from wall) 8) A 20.0-m uniform beam weighing 900. N is supported on walls A and B. a. Find the maximum weight a person can be to walk to the extreme right end without tipping the beam. b. Find the forces that the walls A and B exert on the beam when the person is standing at a point 2.00 m to the right of B. 9) A traffic light hangs from a structure (shown below). The uniform, diagonally oriented, aluminum pole is 7.50 m long and has a mass of 8.00 kg. The mass of the traffic light is 11.0 kg. Determine the tension in the horizontal cable and the vertical and horizontal components of the force exerted by the hinge pin on the diagonal aluminum pole.
10) A painter (mass = 60.0 kg) is standing ¾ of the way up a ladder (mass = 12.0 kg) which is leaning against a frictionless wall. Find the (horizontal) force the wall exerts on the ladder and the x-y components of the force the ground exerts on the ladder. (Center of gravity of the ladder is at its geometric center) 11) A 41.0-kg trapdoor, 1.20 m long, is supported by a hinge at A and a sloping rope at B. Find the tension in the rope and the vertical and horizontal reaction forces of the hinge when the door is just about to open. (Center of gravity of door is 0.900 meter from the hinge.) 12) Sawhorses A and B support a 40.0-kg plank that is 6.00 m long. A 60.0-kg crate is placed on the plank, 2.00 m from B. a. Find the reaction forces at A and B. b. If the box and sawhorse B are moved as shown below, find the reaction forces at A and B. 13) A 12.0-kg plank has three concrete blocks placed on it. If each block has a mass of 10.0 kg and a width of 24.0 cm, and the center-of-gravity of each block is at its geometric center, find the center-of-gravity of the entire system. (The plank is uniform in shape and density.)
14) A baton consists of a 4.00-cm diameter sphere weighing 2.00 N and an 8.00-cm diameter sphere weighing 6.00 N, joined by a uniform rod of weight 3.20 N and length 86.0 cm. Calculate the center-ofgravity of the baton. 15) A serving platter holds a 0.909-kg block of cheese, a 2.27-kg pitcher of water, and a 1.05-kg plate of bread. If the center-of-gravity of each object is denoted by the dots and the mass of the platter is 1.75 kg (CG of platter is at its geometric center), find the center-of-gravity of the system. 16) Two paramedics are carrying a man on a stretcher (stretcher is of negligible weight). The man is 1.83 m long. The paramedics are on either end; the one at his head exerting an upward force of 500. N, and the one at his feet exerting an upward force of 235 N. Locate the man's center-of-gravity. 17) An automobile weighing 3000. lb. (mass = 1364 kg) has a wheelbase -- length from front wheel to back wheel -- of 120. in. (305 cm). Its center-of-gravity is located 70.0 in. (178 cm) behind the front axle. Determine the amount of force exerted on (a) each of the front wheels (assumed equal) and (b) each of the back wheels (assumed equal) by the level ground. 18) A 70.0-kg adult sits at one end of a 10.0-m board (m = 10.0 kg), on the other end of which sits his 20.0-kg child. Where should the pivot be placed so the board is balanced? (board is uniform in composition)
19) A 170.-cm tall person lies in a horizontal position on a massless board that is supported by two scales, one under the feet and one beneath the top of the head. The two scales read 310. N and 344 N, respectively. Where is the center-of-gravity of this person? 20) A uniform horizontal beam of mass 20.0 kg is supported at its left end by a wall and at its right end by a cable. Find the tension in the cable. 21) Two window washers are on a 4.00-m long horizontal platform (m = 30.0 kg) suspended by two cables, one at each end. Harry (m = 80.0 kg) is 1.00 m from the left end, and Stan (m = 50.0 kg) is 1.50 m from the right end. If the center-of-gravity of the platform is at its geom. center, find the forces exerted by each cable. 22) A uniform stunt ramp (85.0 kg) is set as shown below. Calculate the magnitude of the force exerted by the right support and the vertical force exerted by the ground on the ramp. 90 15 23) A flag (10.0 kg) is suspended from a wall in the manner shown below. Calculate the tension in the wire and the x-y components of the force of the wall holder on the pole. (Pole is uniform in composition.) [length of pole = 3.00 m, mass of pole = 5.00 kg] (CG of flag is directly under the free end of the pole.)
24) If the uniform stick has a mass of 0.50 kg, the block on the left has a mass of 1.0 kg and the block on the right has a mass of 1.5 kg, find the center-of-gravity of the system. (centers-of-gravity of individual objects shown with dots) 25) Two birds, each of mass 0.15 kg, sit on a golf club (m = 0.55 kg) as shown below. Find the center-ofgravity of the system. (CG of objects shown w/ dots) ANSWERS: 1. 1.08 m to right of rock 2. 3.13 m from slab edge 3. 1710 N 4. 990. N 5. F L = 2.70 x 10 3 N up, F R = 1230 N up 6. F A = 1640 N down, F B = 2520 N up 7. T = 183 N, F y = 176 N up, F x = 140. N right 8. a. 600. N b. F A = 300. N up, F B = 1.20 x 10 3 N up, 9. T = 232 N, F y = 186 N up, F x = 232 N right 10. F w = 233 N, F x = 233 N right, F y = 706 N up 11. T = 333 N, F y = 100. N up, F x = 141 N left 12. 12. a. F A = 392 N up, F B = 588 N up b. F A = 327 N up, F B = 653 N up 13. 1.17 m from left end 14. 0.64 m from left end 15. 0.34 m from left end 16. 0.585 m from his head 17. a. 2780 N b. 3.90 x 10 3 N 18. 2.50 m from adult s end 19. 0.894 m from feet 20. 113 N 21. F 1 = 919 N up, F 2 = 649 N up 22. F sup = 402 N, F grd = 444 N up 23. T = 136 N, F x = 134 N right, F y = 123 N up 24. 24. 0.45 m from left end 25. 0.42 m from left end