A plank is hung from the ceiling by a rope attached 3 meters from one end. The plank is 8 meters long. A 25 kg can of paint is placed 25 meters from the long end of the plank. Wanting to not spill the paint, where should you place a 55 kg sandbag so as not to tip the can? Assume the plank is massless.
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- The figure shows a composite slab with dimensions d₁ = 11.9 cm, d₂ = 2.94 cm, and d3 = 12.8 cm. Half the slab consists of aluminum (density = 2.70 g/cm³) and half consists of iron (density = 7.85 g/cm³). What are (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the slab's center of mass? (a) Number (b) Number (c) Number dy Iron Units Units Units 2d₁ -Midpoint Aluminum dy 11A meter stick is supported by a knife-edge at the 50-cm mark. You hang masses of 0.40 kg and 0.60 kg from the 20-cm and 80-cm marks, respectively. Where should you hang a third mass of 0.30 kg to keep the stick balanced?A metal soda can of uniform composition has a mass of 0.134 kg and is 12.6 cm tall (see the figure). The can is filled with 1.42 kg of soda. Then small holes are drilled in the top and bottom (with negligible loss of metal) to drain the soda. What is the height h of the center of mass of the can and contents (a) initially and (b) after the can loses all the soda? (c) If x is the height of the remaining soda at any given instant, find x when the center of mass reaches its lowest point. (a) Number i Units (b) Number i Units (c) Number i Units Splash!
- A meter stick is hanging from the ceiling at the 50 cm marker, perfectly in balance.. A 10 kg mass is tied to the meter stick at the 70 cm marker. A 10 kg mass is tied to the meter stick at the 80 cm marker. Where should a 20 kg mass be placed to maintain equilibrium? 25 cm 10 cm 20 cm 35 cmConsider a method for measuring the mass of a person’s arm in anatomical studies. The subject lies on her back, extends her relaxed arm to the side and two scales are placed below the arm. One is placed under the elbow and the other under the back of her hand. Construct a problem in which you calculate the mass of the arm and find its center of mass based on the scale readings and the distances of the scales from the shoulder joint. You must include a free body diagram of the arm to direct the analysis. Consider changing the position of the scale under the hand to provide more information, if needed. You may wish to consult references to obtain reasonable mass values.A 2.0-m-long rod has a density in kilograms per meter A = a + bx ,where a = 1.0 kg/m, b = 1.0 k9/m², and x is the distance from the left end of the rod. The rod rests horizontally with each end supported by a scale. The force exerted by the left scales is 39.2 N 22.9 N 16.3 N 4.0 N 32.6 N
- You're rolling solid rubber balls on the kitchen floor. Ball 1 has a density of 1.16 × 103 kg/m3 and a radius of 28.0 mm. Ball 2 has an unknown density and a radius of 43.0 mm and is initially at rest. You roll ball 1 at an initial speed of 3.00 m/s, and the two balls collide head-on. Ball 1 reverses direction and comes back to you at 2.00 m/s, and after the collision, the speed of ball 2 is 1.00 m/s. The positive x axis is in the direction of ball 1's initial motion. A.What is the magnitude of the initial momentum of ball 1? Express your answer with the appropriate units. B. What is the magnitude of the final momentum of ball 1? Express your answer with the appropriate units. C. What is the magnitude of the initial momentum of ball 2? Express your answer with the appropriate units.ASAPA water molecule consists of an oxygen atomwith two hydrogen atoms bound to it. Theangle between the two bonds is 106◦. If each bond is 0.093 nm long, how far fromthe oxygen atom is the center of mass of themolecule? Take the mass of an oxygen atomto be 16 times the mass of a hydrogen atom.Answer in units of nm