3. An electric fan rotates at 800 revolutions per minute. Consider a point on th

Question

3. An electric fan rotates at 800 revolutions per minute. Consider a point on the blade a distance of 0.16 m from the axis. Calculate the speed of this point and its centripetal acceleration. The fastest train in the US is the Amtrak X2000, with a top speed of about 70 m/s (about 157 mi/h). Train passengers find the ride slightly uncomfortable if their acceleration exceeds 0.05 g. 4. What is the smallest radius of curvature for a bend in the track that can be tolerated within this limit? a) If the train had to go around a curve of radius 1.20 km, to what speed would the train have to be slowed in order not to exceed an acceleration of 0.05 g? b)

Explanation / Answer

3. 800 rev/minutes so 800 rev/60s= 13.33 rev/s = 13.33*2pi rad/s = 83.73 rad/s

so the angular freq is 83.73 rad/s

so speed at 0.16 m, v= 0.16*83.73= 13.397 m/s

centripetal acceleration a= v2/r = 13.397*13.397/0.16 = 1211.775 m/s2

4. a. a=v2/r

0.05*9.8= 70*70/r

0.49=4900/r

r=10000 m

b. a=v2/r

0.05*9.8= v2/(1.2*1000)

v= sqrt 588 = 24.25 m/s

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