final_04_solutions

final_04_solutions - Problem 1 You are an assistant physics...

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Problem 1 You are an assistant physics consultant for Disneyworld. The management has come up with an idea for a new ride. This consists of a circular dish with flat sides that slope at 30 o which rotates about its vertical axis as in the figure, and which has a radius of 5m at its top. The riders will enter at the bottom while the ride is rotating at a constant angular velocity and be given special easy-slip mats which have a coefficient of static friction of 0.05. They sit on the mat and will slide up the slope until they are in equilibrium half way up the slope. You need to calculate the angular velocity to run the ride so that they can circle in this position. To exit the ride the angular velocity would be slowly reduced until the rider reaches the outer rim of the dish at which point they fly off onto a soft mat 1m below the level of the dish rim. You need to calculate the horizontal distance from the ejection point that they fly to determine the size of the soft mat. In which direction will they fly? For the purposes of your calculation you can assume that just before they fly off they are in equilibrium at the outer rim of the dish. Resultant force towards center for circular motion =mr ω 2 Resolving horizontally mr ω 2 = Nsin K + fcos K Resolving vertically Ncos K = mg + fsin K By friction law f = µ N Collecting terms in N N(sin K + µ cos K )=mr ω 2 N(cos K - µ sin K )=mg Eliminating N r ω 2 = g(sin K + µ cos K )/(cos K - µ sin K ) For µ =0.05 and K =30 r ω 2 =6.33 To be in equilibrium half way up the slope, r=2.5m ω = 2.53=1.59 rads/sec The radius will be 5m when ω = 6.33/5 = 1.12 rads/sec The linear velocity at the point of ejection is v=r ω =5.6 m/s Time to fall 1m; -1.0=-1/2 gt 2 t= 1.0x2/9.8 =0.45sec Horizontal distance traveled = vt = 2.5m They will fly off in a direction tangential to the outer rim. 5m K =30 1m N f mg mr ω 2
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Problem 2 You have a vacation job as an airport baggage handler. One day the ramp that carries the bags up to the plane broke down and your supervisor told you to pull up two suitcases by a rope that ran over a pulley at the top of the ramp, the suitcases being attached to each other by a rope. The suitcases weighed 15kg and 20kg. The ramp angle was 40 o and coefficients of sliding and static friction between the suitcases and the ramp are 0.2 and 0.25 for the 15kg bag and 0.3 and 0.35 for the 20kg bag. You can exert a force of 350 Newtons on the rope. Will the bags move? If they do how long will it take to pull them 3m up the ramp from rest. You can assume that the pulley is frictionless and massless. Assume they are moving with acceleration a
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This note was uploaded on 10/07/2009 for the course PHYS 1301W taught by Professor Marshak during the Fall '08 term at Minnesota.

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final_04_solutions - Problem 1 You are an assistant physics...

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