Linear Acceleration, Force Components (7) Weight, Normal, Friction: While working in a mechanical structures laboratory, your boss assigns you to test the strength of ropes under different conditions. Your test set-up consists of two ropes attached to a 30 kg block which slides on a 5.0 m long horizontal table top. Two low friction, light weight pulleys are mounted at opposite ends of the table. One rope is attached to each end of the 30 kg block. Each of these ropes runs horizontally over a different pulley. The other end of one of the ropes is attached to a 12 kg block which hangs straight down. The other end of the second rope is attached to a 20 kg block also hanging straight down. The coefficient of kinetic friction between the block on the table and the table’s surface is 0.08. The 30 kg block is initially held in place by a mechanism that is released when the test begins so, that the block is accelerating during the test. During this test, what is the force exerted on the rope supporting the 12 kg block? (8) Human, Weight, Normal: You are taking care of two small children, Sarah and Rachel, who are twins. On a nice cold, clear day you decide to take them ice skating on Lake of the Isles. To travel across the frozen lake you have Sarah hold your hand and Rachel’s hand. The three of you form a straight line as you skate, and the two children just glide. Sarah must reach up at an angle of 60 degrees to grasp your hand, but she grabs Rachel’s hand horizontally. Since the children are twins, they are the same height and the same weight, 50 lbs. To get started you accelerate at 2.0 m/s2. You are concerned about the force on the children’s arms which might cause shoulder damage. So you calculate the force Sarah exerts on Rachel’s arm, and the force you exert on Sarah’s other arm. You assume that the frictional forces of the ice surface on the skates are negligible. (9). Tension, Weight, Normal, and Friction: You are planning to build a log cabin in northern Minnesota. You will pull the logs up a long, smooth hill to the building site by means of a rope attached to a winch. You need to buy a rope for this purpose, so you need to know how strong the rope must be. Stronger ropes cost more. You know that the logs weigh a maximum of 200 kg. You measure that the hill is at an angle of 30o with respect to the horizontal, and the coefficient of kinetic friction between a log and the hill is 0.90. When pulling a log up the hill, you will make sure that the rope stays parallel to the surface of the hill and the acceleration of the log is never more than 0.80 m/s2. How strong a rope should you buy? (10). Tension, Weight, Normal, Friction: You have taken a summer job at a warehouse and have designed a method to help get heavy packages up a 15° ramp. In your system a package is attached to a rope which runs parallel to the ramp and over a pulley at the top of the ramp. After passing over the pulley the other end of the rope is attached to a counterweight which hangs straight down. In your design the mass of the counterweight is always adjusted to be twice the mass of the package. Your boss is worried about this pulley system. In particular, she is concerned that the package will be too difficult to handle at the top of the ramp and tells you to calculate its acceleration. To determine the influence of friction between the ramp and the package you run some tests. You find that you can push a 50 kg package with a horizontal force of 250 Newtons at a constant speed along a level floor made of the same material as the ramp.
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