# Quiz Number 4 PHYSICS April 17, 2009

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3 Last name : First name : Student id : TA : Problem 1 (25 points) Because of your physics background, you have been asked to help evaluate the safety preparations for new ethanol factory. Safety requirements stipulate that all fire doors must be able to be closed within 15 seconds of an alarm even without power to the building. The factory has a large loading area which can be closed by a large door 2.5 m high and 4 m wide weighing 2500 kg. You estimate that three loading dock staff could reach the door within 10 seconds, leaving 5 seconds to close the door. You estimate that each staff member can push with a force of 300 N and that they will need 1 m between each of them as they push on the door. The door, which has a moment of inertia of 1/3Mr 2 around its hinges, needs to rotate 120 degrees for it to close completely. Does this arrangement meet the safety requirement if the stafff members position themselves optimally? The torque on the door will be: τ = τ 1 + τ 2 + τ 3 = 4 m 300 N + 3 m 300 N + 2 m 300 N = 2.7 kn m This will generate an angular acceleration by τ = Iα. This torque will allow the door to rotate and we must determine the time for the door to rotate by 120 o. Yes. This design meets the requirement. φ = 1 2 αt2 2φ t = α 2φI = τ 2φMr 2 = 3τ = 4.5 s Page 3

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5 Last name : First name : Student id : TA : Problem 2 (25 points) You have been hired to help set up a trade-show introduction for a new steamroller. The tradeshow is being held in a hall where the engine cannot be operated, so the artistic designer would like to have the steamroller roll down an incline and then across the stage at a stately 0.5 m/s and finally be stopped by large spring while having the rollers make a last quarter-rotation for dramatic effect. The steamroller consists of two thin steel cylinders rollers of radius 80 cm and mass 5000 kg (each) which function as the front and rear tires and a body containing the engine and cab which has a mass of 3000 kg. Your role is to determine the necessary height of the incline and the spring constant of the necessary stopping spring. You decide to neglect any effects of rolling friction in solving the problem the axles on this new steamroller are very well made and the rollers will turn easily. This is an energy problem. As the steamroller crosses the stage, it will have a kinetic energy : K = 1 2 mv Iω2 = 1 2 mv I v2 R 2 I = 2m c R 2 K = 1 2 (m b + 2m c )v 2 + m c v 2 This energy must be provided by the incline: = 1 2 (m b + 4m c )v 2 = 2875 J K = mgh = (m b + 2m c )gh h = 2.25 cm At the end of the process, the full energy will be absorbed by the spring while the wheels make a quarter turn. U s = 1 2 kx2 x = 1 2πR = 1.26 m 4 k = 2K = 3640 N/m x2 Page 5

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