LMU PSY 101 - Dynamics (5 pages)

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Dynamics



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Dynamics

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Pages:
5
School:
Loyola Marymount University
Course:
Psy 101 - Intro to Psychology

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Physics 101 Spring 2007 Dynamics Problems Solutions You are helping with set design of the latest play on campus In the script there is a scene which calls for the male lead to rise into the air as if ascending into the clouds Your plan involves attaching a rope to a harness that the actor will wear The rope is then put over a pulley and a counterweight is attached to the other end When the weight is released the actor will be pulled upward The director has told you that he wants the actor to ascend the 20 feet in 3 seconds As part of your planning you weigh the actor and find that he has mass of 70kg You first make some calculations to determine how much concrete to buy for the counterweight and which rope to buy Your production is on a tight budget and the stronger rope costs more than the thinner weaker rope You need to optimize your budget by buying the cheapest rope that will not result in the actor plummeting to the stage Essentially this is a Newtonian problem with constant forces and acceleration We will use N2 and N3 to relate the forces to the motion of the actor Assume that the actor doesn t jump off of the stage no initial velocity While a real rope isn t massless it will likely have a much smaller mass than the person or block so assuming an ideal rope isn t too crazy of an idea Also an ideal rope is rigid does not stretch The pulley should also be treated as having no mass and being free of friction This may not be obvious now since we haven t covered rotation in depth but it is a necessary assumption Otherwise we would need to know the pulley s mass and the friction within its bearings I would expect the block s mass to be just a bit more than the actor s If it is hundreds of kg s the actor would feel a very large jerk upwards If the block s mass is actually less than the actor s then it simply wouldn t pull the actor up Let s assign some variables to the various quantities in the problem This will keep the mat neat tidy m 70kg actor s mass y 20 6 1 m



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