Answer to Question #217839 in Mechanical Engineering for john Smith

Question

A Tram used in San Francisco has a mass of 300 tons has a tractive resistance of 45000 N as shown in the figure below.

a) Calculate the total force required to accelerate the tram uniformly form 18km/h for one minute over a distance of 750 meters up an incline 1 in 150.

b) What is the maximum power developed by the locomotive under those conditions?

c) Calculate the angular velocity of the wheels under conditions of maximum power is found to be 191 rev/min. What toque is the locomotive developing and what is the diameter of the driving wheels?

Answer 1

a.

$F=f+mg sin \theta\\ F=45000+300000*9.8* \frac{1}{150.0033}\\ F=64600N\\ a= \frac{F}{m}\\ a= \frac{64600}{30000}\\ a= 0.213 m/s^2$

b.

$P= \frac{w}{t}\\ P= \frac{64600*750}{60}\\ P=807500W\\ P=807.5kW$

c.

$v=u+at\\ v=5+0.128*60\\ v=17.6 m/s\\ r= \frac{v}{w}\\ r=\frac{17.6*60}{2*3.14*191}\\ r=0.88 m\\ T= Fr\\ T=64600*0.88\\ T=56848 Nm\\ d= 2r\\ d=2*0.88\\ d=1.76 m$