12. A 40-kg crate is being lowered with a downward acceleration is 2.0 m/s by means of a rope. (a) What is the magnitude of the force exerted by the rope on the crate? (b) What would be the magnitude of the force exerted by the rope if the crate were being raised with an acceleration of 2.0 m/s? 14. In a certain particle accelerator, a proton reaches an acceleration of 9.0 1013 m/s. The mass of a proton is 1.67 10-27 kg. What is the force on the proton? 19. A very light wire is used to hang a series of 8.0-kg bricks. This wire will break if the tension in it exceeds 450 N. The bricks are hung one below the other from a hook in the ceiling using this wire, as shown in the figure. (a) How many whole bricks can be hung without breaking the wire? (b) If you add one more brick to the number found in part (a), which string will break? 24. Three blocks, light connecting ropes, and a light frictionless pulley comprise a system, as shown in the figure. An external force of magnitude P is applied downward on block A, causing block A to accelerate downward at a constant 2.5 m/s. The tension in the rope connecting block B and block C is equal to 60 N. (a) What is the magnitude of the force P? (b) What is the mass of block C? 18 kg B 60 N C a=2.5 m/s A 12 kg P 25. A locomotive is pulling three train cars along a level track with a force of 100,000 N. The car next to the locomotive has a mass of 80,000 kg, the next one, 50,000 kg, and the last one, 70,000 kg. You can neglect the friction on the cars being pulled. (a) What is the magnitude of the force between that the 80,000-kg car exerts on the 50,000-kg car? (b) What is the magnitude of the force that the 50,000-kg car exerts on the 70,000-kg car? 26. A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force must be applied to the box to cause it to start sliding along the surface? 27. A bulldozer attempts to drag a log weighing 500 N along the rough horizontal ground. The cable attached to the log makes an angle of 30 above the ground. The coefficient of static friction between the log and the ground is 0.50, and the coefficient of kinetic friction is 0.35. What minimum tension is required in the cable in order for the log to begin to slide? 28. The figure shows a system consisting of three blocks, a light frictionless pulley, and light connecting ropes that act horizontally on the upper two blocks. The 9.0-kg block is on a perfectly smooth horizontal table. The surfaces of the 12-kg block are rough, with k = 0.30 between the 12-kg and 9.0-kg blocks. The mass M of the hanging block is set so that it descends at a constant velocity of 3.25 m/s. (a) What is the mass M of the hanging block? (b) The mass M is now changed to 5.0 kg, causing it to accelerate downward after it is released. What is the acceleration of the hanging mass? 12 kg 9.0 kg M 29. As shown in the figure, block B on a horizontal tabletop is attached by very light horizontal strings to two hanging blocks, A and C. The pulleys are ideal, and the coefficient of kinetic friction between block B and the tabletop is 0.100. The masses of the three blocks are mA = 12.0 kg, mB = 7.00 kg, and mc = 10.0 kg. Find the magnitude and direction of the acceleration of block B after the system is gently released and has begun to move. A B C 30. A 7.5-kg stone moves up frictionless hill that slopes upward at 41 above the horizontal. If the stone has an initial velocity of 8.5 m/s at the bottom, how far (as measured along the surface of the hill) will it go before stopping?