Several cranes have been put to use in the construction of our new football stadium. The purpose of a crane is very similar to that of an elevator except that a crane can not only lifts things, but can also move them horizontally. Consider a crane consisting of a large base with a long boom extending from the base. The base is on the ground and the angle of the boom can be raised and lowered, but its length remains constant. To lift objects there is a strong cable running along the boom and over a pulley at the top of the boom. After going over the pulley the free end of the cable hangs straight down and can be attached to whatever needs to be lifted. For simplicity, assume that the cable has no mass in this problem. In order to move things with the crane the cable can be reeled in to lift them, the base can be rotated to move them horizontally, and the boom can be raised or lowered to move them nearer of farther from the crane.
1. The crane's boom is pointing upward at a 45 degree angle measured from the flat horizontal ground and a construction worker attaches the cable to a heavy I-beam that is sitting on the ground. The cable goes straight up, over the pulley, and along the boom to a cylinder where is can be wound up to lift the I-beam. A torque applied to the cylinder provides the force on the cable required to lift the object. How large must this force be to start lifting the I-beam? Please give a descriptive answer.
2. Once the I-beam starts moving upward at a constant velocity how much tension is in the cable?
3. The crane operator needs to move a very heavy object from a position near the crane to a position far from the crane. To do this he angles the boom near vertical and attaches the cable to the heavy object. He then lifts the object straight up by reeling in the cable. Next, he slowly lowers the boom to move the object farther from the crane's base. If the object is too heavy the crane may tip over. Why?
4. Another danger in lifting a heavy object is that the cable may break. One situation in which the cable is likely to break is when the operator is lowering the heavy object at a constant velocity and suddenly brings the object to a stop. The acceleration needed to stop the object requires a force larger than the object's weight, which may be sufficient to break the cable. For the same object is there another situation in which the cable is likely to break? If so, describe it.
A car engine makes use of a chemical reaction to produce mechanical motion. However, not all of the energy of the chemical reaction is turned into useful work, some of it produces heat. In order for the engine to operate properly the engine's cooling system must remove most of this heat.
5. The chemical reaction that produced the heat is the burning of fuel. Compare the strength of the bonds that hold together the fuel molecules before the reaction to the strength of the bonds that hold together the molecules of the reaction products.
6. The engines cooling system makes use of a liquid to transfer heat between the engine and radiator. If the engine is hotter than the radiator, which way will heat flow between the two?
7. The explosive chemical reaction that is generating most of the heat in the engine occurs inside of several hollow metal cylinders inside the engine. This heat must flow through the metal block, from where the hollow cylinders are located to where the liquid coolant is located. What mechanism of heat transfer causes the heat to flow through the metal block?
8. After flowing through the block the heat is then transferred to the coolant. This coolant circulates between the engine and the radiator. What mechanism of heat transfer is causing heat to flow between the two?